WO2023230679A1 - Modulation method for operating an mmc to maximise common mode voltage, reducing circulating currents, and machine-readable medium - Google Patents

Modulation method for operating an mmc to maximise common mode voltage, reducing circulating currents, and machine-readable medium Download PDF

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Publication number
WO2023230679A1
WO2023230679A1 PCT/BR2022/050190 BR2022050190W WO2023230679A1 WO 2023230679 A1 WO2023230679 A1 WO 2023230679A1 BR 2022050190 W BR2022050190 W BR 2022050190W WO 2023230679 A1 WO2023230679 A1 WO 2023230679A1
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Prior art keywords
mmc
voltage
operating
common mode
arms
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PCT/BR2022/050190
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French (fr)
Portuguese (pt)
Inventor
Gean JACQUES MAIA DE SOUSA
Juliano RAFAEL SCHOENHALZ
Joable ANDRADE ALVES
Marcelo LOBO HELDWEIN
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Weg Drives & Controls - Automação Ltda
Universidade Federal De Santa Catarina
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Priority to PCT/BR2022/050190 priority Critical patent/WO2023230679A1/en
Publication of WO2023230679A1 publication Critical patent/WO2023230679A1/en

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Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/505—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a thyratron or thyristor type requiring extinguishing means
    • H02M7/515—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a thyratron or thyristor type requiring extinguishing means using semiconductor devices only
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters

Definitions

  • the present invention falls within the fields of generation, distribution and transmission of electrical energy, as well as drive of electrical machines. Specifically, the present invention refers to technologies used in the processing of electrical energy at high powers, supplied at medium voltage (above 1 kV and below 69 kV) or high voltage (above 69 kV and below 230 kV) and, more specifically, those involving modular multilevel converters or MMC (Modular Multilevel Converter).
  • Static electronic converters are mainly composed of semiconductor devices that function as current switches, with diodes, IGBTs (Insulated Gate Bipolar Transistor), MOSFETs and thyristors being the most used. These devices currently have the ability to block voltages lower than those necessary to drive high-power electrical machines.
  • IGBTs Insulated Gate Bipolar Transistor
  • MOSFETs Metal Organic Semi-oxide-semiconductor
  • thyristors being the most used. These devices currently have the ability to block voltages lower than those necessary to drive high-power electrical machines.
  • multilevel converters which have the property of maintaining a reduced voltage on semiconductor devices.
  • MMCs stand out for their ability to operate ideally at any voltage level, ensuring a balanced division of current and voltage efforts between the semiconductor devices and capacitors that make them up.
  • FIG. 1 presents a representation of a typical structure of a conventional DC-AC MMC (1) of the prior art, containing a first port (4) configured to receive a direct current supply and a second port (5) configured to supply a current voltage three-phase alternating.
  • a port symbolizes a set of terminals through which the MMC is connected to an external circuit.
  • the first port (4) has two input terminals, one positive (p) and one negative (n), connected to a direct current voltage source represented by voltages v 1.2 and v 2.1 in relation to the reference.
  • Each terminal of the first port (4) is connected to each of the terminals of the second port (5) through a series circuit composed of an arm (2) and an inductor (3).
  • Each arm (2) is composed of the series association of submodules (SMs) (8), forming a chain of SMs, and arms connected to the positive terminal (p) are called positive arms (6) while arms connected to the negative terminal ( n) are called negative arms (7).
  • SMs submodules
  • the load (14) connected to the second port (5) is represented by resistive elements for simplification purposes, and the load (14) can be of any configuration of passive elements, another alternating current network, an electrical generator of alternating current or other electronic system.
  • the currents i c ⁇ and i c ⁇ flow only internally to the conventional DC-AC MMC (1) and are called circulation currents. These currents can be used to optimize the operation of the conventional DC-AC MMC (1) and also to reduce the ripple of energy stored in the arms (2), allowing low frequency operation with a relatively reduced number of energy storage elements.
  • the voltages v B1,1 , v B1,2 and v B1,3 represent the voltages generated by the positive arms (6), while v B2,1 , v B2,2 and v B2,3 represent the voltages generated by the negative arms (7), v CM is the common mode voltage generated by the MMC (1), i a and i b represent two of the three currents of the second port (5), while the current i cc represents the current on the first door (4). Knowing these currents and the currents i c ⁇ and i c ⁇ , all the currents of the conventional DC-AC MMC (1) can be determined.
  • Each SM (8) is composed of two connection terminals, a capacitor (10) and an arrangement of switches (9).
  • the switch arrangement (9) may, for example, be one or more electronic switches.
  • the number of SMs (8) employed must be such that it results in an arm voltage range v B that can be generated greater than the voltage range necessary for the proper functioning of MMC (1, 15, 16).
  • Figure 4 shows the two main types of SMs used in prior art MMCs (1, 15, 16): the half-bridge SM (11) and the full-bridge SM (12).
  • the half-bridge SM (11) is the most used, consisting of two bidirectional voltage switches (13), normally composed of an IGBT transistor and a diode, and a capacitor (10).
  • the half-bridge SM (11) is capable of instantly generating only zero and V c values, therefore, an arm (2) consisting of these SMs can generate only unipolar voltages, including zero voltage.
  • the half-bridge SM (11) is mainly applied in conventional DC-AC MMC (1).
  • the full bridge SM (12) has a capacitor (10) and four bidirectional voltage switches (13), also usually composed of an IGBT and a diode. It is also capable of instantly generating zero values, +V c and ⁇ V c , therefore, an arm (2) consisting of these SMs can generate positive and negative voltages, including zero voltage.
  • SM full bridge (12) is mainly applied in AC-AC MMC matrices (15) and Hexverters (15, 16), but can also be used in conventional CC-CA CMMs (1).
  • Another possible SM configuration uses two or more capacitors. In this case, the arrangement of switches (9), in addition to allowing the generation of a zero c SM voltage, must also allow generating voltages relating to combinations of capacitor voltages (10), such as the sum or difference of these. Other SM configurations are found in the literature, but fundamentally they present the functionalities listed here.
  • FIG. 5 Referring now to Figure 5, the structure of a generalized MMC (17) is shown, in which each port has a number of terminals greater than two.
  • a terminal of one port is connected to all terminals of the other port through the series connection of an arm (2) and an inductor (3), with the number of terminals of the first port (4) represented by F and the number of terminals of the second port (5) represented by H.
  • the function of the inductors (3) is limit the amplitude of the high frequency currents that circulate between the arms (2) due to the instantaneous voltage differences generated by each arm (2).
  • the load (14) connected to the H terminals of the second port (5) is represented by H resistive elements for simplification purposes, and the load (14) can be of any configuration of passive elements, another alternating current network or another electronic system .
  • the voltages present at the F terminals of the first port (4), with respect to the reference, are represented by v j,1 , with j ⁇ ⁇ 1, ... , F ⁇ , while the currents at the same terminals are represented by i j,1 .
  • the potential differences over the H elements of the load (14) connected to the second port (5) are represented by v k,2 with k E ⁇ 1, H ⁇ , while the currents in these elements are represented by i k2 .
  • the tensions on the arms (2) are represented by Vj. k , while the currents that cross them are represented by ij k .
  • the objective of the MMC (1, 15, 16, 17) is to inject or drain currents into its ports (4,5) in order to transfer power from one to the other.
  • the currents must have a suitable waveform for the application in question, thus, when a port (4,5) is connected to the electrical network or to an alternating current electrical machine, for example, it is desired that the currents be sinusoidal with minimal distortion.
  • Control of the MMC currents is achieved by switching the bidirectional voltage switches (13) that form the SMs, which, depending on their states, on or off, can apply a greater or lesser voltage to the inductors (3), increasing or decreasing the derivative of the current that flows through them and, consequently, increasing or decreasing the derivative of the currents that flow through the ports (4,5) and circulation currents.
  • the scheme used to define how the bidirectional voltage switches (13) are turned on or off is known as modulation.
  • a commonly employed strategy consists of pulse width modulation, in which the relationship between the duration of the time interval in which a bidirectional voltage switch (13) remains on and the total duration of a cycle composed of an on and an off period is defined such that the time-averaged tension generated by an arm approaches a desired arm tension reference value .
  • the control system of an MMC (1, 15, 16, 17), responsible for regulating the voltages of the capacitors (10) and the port and circulation currents is mainly composed of sensors capable of measuring these variables and signal processing systems that are based on control algorithms. The control algorithms maintain, through feedback loops, the measured currents and voltages as close as possible to the desired values.
  • the outputs of these algorithms are the arm voltage references , which will be used by the modulator to define the pulse patterns that the arms (2) must generate through the switching of the bidirectional voltage switches (13).
  • the voltages of all capacitors (10) of the MMC must be controlled so that the voltages on the bidirectional voltage switches (13) remain within acceptable limits. Normally, this is carried out on two different and independently operating levels.
  • the first level is responsible for equalizing the voltages of the capacitors (10) of the SMs within the same arm (2).
  • the maximum instantaneous voltage value that an arm (2) can generate, as well as the minimum value, can only be reached for a single combination of states of the bidirectional voltage switches (13).
  • the second level is responsible for keeping the sum of the voltages of the capacitors (10) of the arms (2) as close as possible to a reference and with minimal differences between them.
  • the voltage on the arm terminals (2) is valid, disregarding the voltage drops across the inductors (3): [041]
  • the voltage on one of its arms (2) is a composition of a portion coming from the first port (4), and an AC portion coming from the second port (5), and the common mode voltage which, according to the circuit equations, is imposed through the average of the arm voltages, i.e.
  • the common mode voltage is also defined by the average of the arm voltages multiplied by -1, this is where [043]
  • the common mode voltage within certain limits, it can be adjusted without interfering with the port currents (4,5) of the MMC (1, 15, 16, 17) or the circulation currents. It is, therefore, an additional degree of freedom that can be used to optimize the functioning of the MMC (1, 15, 16, 17).
  • the current flowing through an arm (2) of the MMC (1, 15, 16, 17) is a composition of the port currents (4,5).
  • the current that passes through it is [044]
  • the arm currents are composed of an alternating sinusoidal portion at frequency ⁇ of the second port (5), and a DC component.
  • the product between the terms that make up the voltage and current referring to an arm (2) results in the power absorbed by it.
  • this power Considering steady-state operation, ideally this power has zero mean. However, it also has sinusoidal components if considered a common mode voltage. null.
  • FIG. 6 shows the main waveforms referring to the conventional DC-AC MMC (1) when operating without circulation currents or common mode voltage injection.
  • Figure 6(a) shows the voltages at the terminals of the first port (4) and at the terminals of the second port (5).
  • Figure 6(b) shows the currents that the MMC injects into the port terminals (4,5).
  • Figure 6(c) shows the currents flowing in the arms, while Figure 6(d) shows the tensions on these.
  • Figure 6(e) shows the ripples of energy stored in the arms These have a frequency component in and another in [047] It can be seen, from the analysis of the equation (1.5), that the amplitudes of energy ripples are inversely proportional to their frequencies. Therefore, low-frequency operation on the first port (4) of the conventional DC-CA MMC (1), or on at least one of the ports (4,5) of the generalized MMC (17), or even with frequencies close to the case of generalized MMC (17), results in larger energy ripples when compared to those resulting from operation at higher and distinct frequencies, in the case of generalized MMC (17).
  • the maximum absolute voltage value that an arm (2) can generate is always limited by the sum of the voltages of its capacitors (10).
  • both the minimum negative voltage and the maximum positive voltage are limited by the sum capacitor voltages (10).
  • the minimum voltage, in absolute value is always zero, and the maximum absolute value is always the sum of the voltages of the capacitors (10).
  • the polarity of the voltage that arm (2) generates can be positive or negative, depending on how it is connected to the rest of the circuit. According to the convention adopted in Figure 1, the positive arms (6) always generate positive voltage, while the negative arms (7) always generate negative voltage.
  • the amplitude of the common mode voltage in the prior art is usually limited to a higher value lower than the maximum possible to try to guarantee the correct functioning of the MMC, that is, to avoid possible operation with overmodulation and the consequent generation of harmonic distortion in the MMC voltages.
  • the invention described here can be applied to MMCs that perform any type of conversion involving alternating current (AC) and/or direct current (DC), that is, MMC DC-DC, MMC CC-AC , MMC AC-DC or MMC AC-AC with any number of phases.
  • AC alternating current
  • DC direct current
  • the MMC capacitor voltage ripples tend to increase in amplitude when the input frequency approaches the output frequency. It is not possible, for example, for the DC-CA MMC to operate with zero frequency at the AC output.
  • This invention proposes an optimized operating mode that results in a maximized common mode voltage.
  • FIG. 1 shows a three-phase DC-CA MMC in the state of technique.
  • Figure 2 shows a matrix CA-CA MMC and a Hexverter CA-CA MMC according to the state of the art.
  • Figure 3 shows the general internal structure of an arm of a MMC.
  • Figure 4 shows a half-bridge SM and a full-bridge SM according to the state of the art.
  • Figure 5 shows the structure of a generalized MMC.
  • Figure 6 shows the main waveforms relating to the operation of the MMC CC-CA.
  • Figure 7 shows a simplified diagram of the control system of a generalized MMC according to the present invention.
  • Figure 8 presents a method of generating the common mode voltage reference for the DC-AC MMC with smoothed transitions in accordance with the present invention.
  • Figure 9 presents a comparison between simulation results obtained for the conventional method and for the method according to the present invention.
  • Figure 10 presents a comparison between the losses obtained by simulation for the conventional method and for the method according to the present invention.
  • Figure 11 shows experimental results of a MMC operating in accordance with the present invention.
  • Figure 12 presents a comparison between the losses measured when the MMC operates with the conventional method and with the method according to the present invention. DETAILED DESCRIPTION OF THE PRESENT INVENTION [072] Specific embodiments of the present disclosure are described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the report descriptive.
  • the present invention proposes a method of operating the MMC (1, 15, 16, 17) that minimizes the energy ripple in the capacitors (10), allowing operation at low frequencies, in the case of the conventional DC-AC MMC ( 1), or operation with equal or close frequencies on ports (4,5) in the case of AC-CA MMCs (15,16,17).
  • the possibility of operating in an extended frequency range allows the application of the conventional DC-AC MMC (1) in machine drive systems, whose port connected to the machine operates with frequencies that vary from zero, at start-up, to nominal.
  • the method of operation disclosed here is applicable to any MMC whose structure can be defined from the generalized MMC (17), resulting in a common mode voltage v CM maximized at any instant of time and simultaneously ensuring that none of the arms will operate in overmodulation due to the addition of the common mode voltage v CM .
  • the circulation currents necessary to reduce the voltage ripple of the capacitors (10) are reduced, minimizing losses due to currents. circulation and simultaneously ensuring the proper functioning of the MMC (1, 15, 16, 17) even in severe transients.
  • the present method provides greater efficiency in the operation of the MMC.
  • Another advantage of the present method is the possibility of reducing the size of the MMC due to lower Joule losses.
  • Yet another advantage of the present method is the reduction of interference introduced into the system by MMC reactive losses.
  • the operation of the method of the present invention is analyzed when applied to the conventional CC-CA MMC (1), illustrated in Figure 1.
  • the positive arms (6) are composed of half-bridge SMs (11), so that the positive arms are capable of generating only voltages positive or null.
  • the negative arms (7) are also composed of half-bridge SMs (11), and are connected in such a way that they are capable of generating only negative or zero voltages.
  • Overmodulation is understood as the condition in which it is not possible for an arm (2) to generate the reference voltage calculated by the control system (21) due to being outside the voltage range possible to be synthesized by the arm (2).
  • Positive (6) and negative (7) arms can generate any average voltage, within their operating limits, through the use of a pulse width modulator, which generates command signals for the switches (13 ) so that the average value of the arm tension calculated during a switching cycle approaches the reference value
  • a conventional CC-CA MMC control system (1) is briefly shown employing an exemplary, that is, non-limiting, implementation of the method of the present invention.
  • the reference signals for the arm voltages without adding the common mode voltage are calculated by the voltage and current controllers (18) from the measured arm current values of the sums of the voltages of the measured capacitors (10) and the reference signals for the sums of capacitor voltages and the reference signals for the currents in one of the ports. In the example in Figure 7, these will be taken as the currents of the second port (5) however, the currents from the first port (4) could be taken without departing from the scope of the present invention. [082] Control algorithms are used to calculate what voltages the arms (2) must generate so that the MMC currents and voltages follow their references with low error and reject disturbances.
  • the common mode voltage v CM does not interfere with the MMC arm currents, but is used by the method of the present invention to reduce the voltage ripple in the capacitors (10).
  • the common mode voltage reference is added to the references calculated by the controllers (18) through (19), resulting in arm voltage references.
  • the most likely consequence is failure to follow reference of door currents (4,5) and/or circulation currents.
  • the present invention proposes a mode of operation in which the conventional CC-CA MMC (1) alternately operates in two distinct operating states: a first operating state and a second operating state.
  • the arms (2) corresponding to the other half generate the maximum voltage that does not result in overmodulation of any arm (2) of the conventional DC-AC MMC (1) and, therefore, that does not result in harm to the control of any current of conventional MMC CC-CA (1).
  • the voltage and current controllers (18), during each of these operating states force circulation currents that cause the aforementioned imbalances in the arm currents (2).
  • the arms (2) that generate lower voltage and conduct greater current the other group conducts smaller currents that act to balance the energy stored in their capacitors (10). As these arms generate the highest possible voltage, the circulation currents required to control their energies are minimized.
  • the references used to control the circulation currents are calculated by capacitor voltage controllers (10) based on the measured voltage values and reference values suitable for the operation of the conventional DC-AC MMC (1).
  • the common mode voltage v CM must be increased. By increasing v CM , a positive arm (6) can reach the lower limit of its linear operating range (0 V), or a negative arm (7) can reach the upper limit, in absolute value, of its operating range. operation, generating a negative voltage whose absolute value corresponds to the sum of the voltages of all its capacitors (10).
  • a negative arm (7) By decreasing the common mode voltage v CM , or a negative arm (7) can reach the lower limit, in absolute voltage value, of its linear operating range (0 V) with all bidirectional voltage switches (13 ) of all its half-bridge SMs (11) closed, or a positive arm (6) may reach the upper limit, in absolute values, of its operating range, with all of the upper bidirectional voltage switches (13) of the SM half-bridge (11) closed.
  • an operating mode in which the common mode voltage v CM is calculated for the first and second operating states so that only one arm (2) of the MMC CC-CA is always conventional (1) reaches the lower or upper limit of the voltage range that it can synthesize, defined by zero or the sum of the voltages of all its capacitors (10) always minimizing, in absolute values, the tensions generated by half of the arms (2) and maximizing the tensions generated by half of the other arms (2).
  • This ensures that smaller circulation currents, calculated by the control system (18), are necessary to regulate the voltages of the capacitors (10) of the arms (2) that are generating higher voltage at values close to their references.
  • v CM The maximum value of v CM that would take a single negative arm (7) to the limit is [092]
  • the maximum common mode voltage that leads to only one arm (2) of the conventional DC-AC MMC (1) to synthesize the maximum or minimum possible voltage is [093]
  • the minimum common mode voltage v CM that takes a positive arm (6) of the conventional DC-AC MMC (1) to the maximum limit of the voltage that can be generated or a negative arm (7) the minimum value, in absolute value, of the voltage that can be generated is worth [094]
  • the controllers (18) will force a circulating current in phase k of the conventional DC-AC MMC (1) in order to increase the current in the positive arm k (6) and decrease the current in the negative arm what in this state it synthesizes maximum tension.
  • the current in the negative arm can have a positive or negative direction, depending on the relationship between the current in the second port (5) ⁇ ⁇ and the circulation current forced by the controllers (18).
  • the negative arm (7) of the phase ⁇ absorbs or supplies energy, and it is possible to control the voltage of its capacitors (10).
  • the positive arm current ⁇ (6) for the condition analyzed it is always positive, resulting in energy absorption and a consequent increase in the voltages of the capacitors (10) that compose it, although in a minimized way, since the voltages that the arms (2) generate are the minimum possible that guarantee prevent overmodulation from occurring.
  • the adders (22) and (23) together with the blocks that calculate minimum (24) and maximum (25) values implement equations (1.8) and (1.9).
  • the key (20) selects according to the signal .
  • the frequency with where s c alternates between 0 and 1 defines the frequency of the common mode voltage v CM .
  • the shape of v CM is approximately rectangular, but with an envelope defined by It is In some applications, such as machine drive systems, the high-frequency content of the common mode voltage v CM must be reduced in order to limit the amplitude of the common mode current flowing through the machine, which can cause damage to the bearings. of the machine.
  • the high frequency content of the common mode voltage v CM can be reduced if the transitions between the values are carried out less abruptly.
  • the reference signal in the transition from the second operating state to the first operating state, the reference signal can have its value gradually increased until the value of In the transition from the second operating state to the first operating state, the reference signal may have its value decreased until the value of The value of the increment and decrement can be determined in order to limit the absolute value of the maximum derivative, with respect to time, of the common mode voltage v CM .
  • Figure 9 presents an exemplary implementation of the generation with reduced derivatives.
  • the signal v tr has the form triangular and frequency equal to that specified for the common mode voltage v CM .
  • the comparator (26) is responsible for generating the signal s c , which becomes 1 as soon as the triangular sign v tr becomes positive, and 0 as soon as ⁇ ⁇ becomes negative.
  • the derivative with respect to time during transitions is defined by the derivative of The amplitude of can be chosen so that the derivative of Have a predetermined value during state transitions.
  • the variations in the voltages of the capacitors (10) are also smaller, so that it is possible to increase the durations of the first and second operating states even keeping the voltages of the capacitors (10) within acceptable limits.
  • the s c signal switches its value, changing the operating state of the conventional CC-CA MMC (1).
  • the frequency of v CM is variable according to the operating point of the conventional DC-AC MMC (1).
  • All propositions previously presented for the conventional CC-CA MMC (1) can be extended to the CA-CA MMCs (15,16), or, more generally, to the generalized MMC (17).
  • These MMCs can use SMs with the ability to generate positive and negative voltages, such as the full bridge SM (12).
  • both the maximum and minimum limits of the voltage that can be generated by an arm (2) are defined by the sum of the voltages of the capacitors (10).
  • the maximum common mode voltage v CM that leads to just one arm (2) of the MMC (15, 16, 17) to reach its lower limit of its voltage generating capacity is given by [104]
  • the minimum common mode voltage v CM that leads to only one arm (2) of the MMC (15,16,17) to reach its upper limit of its voltage generation capacity is given by [105] It is also possible, in the case of MMC AC-AC converters (15, 16, 17), to employ common mode voltage v CM and currents DC circulation system to transfer power between the arms (2) of the MMC (15, 16, 17). In this case, the proposed technique can still be used, as long as the common mode voltage v CM is maintained at its maximum value v CM max or minimum value v CM min .
  • the signal s c switches its value”, are applicable to the MMC (15, 16, 17), as long as are calculated according to (1.10) and (1.11), respectively.
  • An inherent advantage of the present invention when applied to any of the MMC (1, 15, 16), or more generally, to the generalized MMC (17), is the greater ability to maintain controlled currents during abrupt voltage transients of the doors (4,5) or the references of the door chains.
  • the amplitude of the common mode voltage reference is calculated so that there is a certain pre-set margin. defined between the maximum and minimum values of the arm tension references and the voltage limits that the arms (2) can generate.
  • the common mode voltage reference is calculated so as to the maximum voltage range that the arms (2) can generate is used, but without ever exceeding the voltage limits that the arms (2) can synthesize, as long as the references do not already exceed them. This results in the technical effect lower circulation currents, resulting in lower losses, and at the same time an operation that is more resilient to fast transients in the port voltages (4.5) and current references.
  • the present invention can also be used in conversion systems that employ more than one MMC (1, 15, 16, 17), such as, for example, in a configuration in which a first port (4, 5) of a first MMC (1, 15, 16, 17) is connected to a first port (4, 5) of a second MMC (1, 15, 16, 17), the second port of the first MMC (4, 5) is connected to the network and the second port (4, 5) of the second MMC (1, 15, 16, 17) is connected to a load (14), for example, an AC machine.
  • a load for example, an AC machine.
  • the proposed method can be used only in the second MMC (1, 15, 16, 17), which feeds the load (14), allowing its operation at low frequency, or also in the first MMC (1, 15, 16, 17), which is connected to the network, allowing the use of capacitors (10) with lower capacitance and smaller volume.
  • EXAMPLES OF EMBODIMENT OF THE INVENTION [115] Two examples of embodiment of the invention are presented. These examples aim to illustrate the functioning and application of the method presented here. Therefore, the following examples should not be taken as limiting.
  • the first example refers to the simulation of a medium voltage DC-AC conversion system.
  • the second example refers to the experimentation of a low voltage machine drive system. Both employ the conventional DC-CA MMC (1) with half-bridge SM (11).
  • a voltage of 11.5 kV is applied to the first port (4) of the DC-CA MMC conventional (1) and the second port (5) feeds a load with an effective line voltage of 1.725 kV and a frequency of 15 Hz.
  • the common mode voltage v CM resulting from the method of the present invention, shown in (d) has an amplitude that varies over time, but on average it has a higher amplitude than that of the conventional method, presented in (a).
  • the amplitudes and effective values of the circulation currents necessary to control the voltages of the capacitors (10) are smaller, reducing losses.
  • the arm modulation index reference is a design parameter that allows you to vary the use of the arm. the voltage range that a arm (2) can synthesize. The closer to 1, the greater the amplitude of the common mode voltage applied, resulting in less backlash and a greater propensity for overmodulation during transients. On the other hand, the greater the amplitude of the common mode voltage , the lower the circulation currents and, consequently, the lower the losses.
  • the real value, obtained by simulation, of the highest modulation index M B obtained among the six arms (2) of the conventional CC-CA MMC (1) is shown on the horizontal axis of the graph presented in Figure 11 for each point of operation tested.
  • the method guarantees that the conventional DC-AC MMC (1) will not enter the overmodulation region.
  • Comparing the losses obtained with the method of the present invention and the losses obtained with the conventional method for it is found that there is a reduction in these by 21.4%, 27.5% and 24.3% for the 1 Hz, 8 Hz and 15 Hz scenarios, respectively.
  • the waveforms represented were obtained with a scale prototype of a conventional DC-AC MMC (1) configured to drive a machine with a nominal voltage of 380 V and a nominal frequency of 60 Hz.
  • Each arm (2) is composed of five half-bridge SMs (11) and the first port (4) of the conventional DC-AC MMC (1) is connected to a 640 V DC voltage source.
  • FIG. 12 The waveforms in Figure 12 were obtained when the conventional DC-AC MMC (1) drove the machine with an electrical frequency of 15 Hz and effective currents of 17 A using the method of the present invention.
  • Graph (b) in Figure 12 shows the currents of the second port (5), to which the machine is connected. The currents have low distortion and are not influenced by the use of the method of the present invention.
  • the method of the present invention presents loss reductions of 27.3%, 25%, and 12.5% for frequencies of 5 Hz, 10 Hz and 15 Hz, respectively. .
  • the operating method according to the present invention is Suitable for, but not limited to, operation at low frequencies.
  • the converter under these conditions, would operate using the method of the present invention up to a transition frequency f t and, from there, the normal method, without using common mode voltage injection.
  • the transition frequency f t is chosen so that the voltage ripple in the capacitors (10) resulting from normal operation is already low enough, not requiring compensation.
  • Figure 14 shows, in a generic way, how the losses in a conventional MMC DC-AC converter (1) must vary with frequency for the nominal current in the second port (5).
  • the method of the present invention allows losses in the converter to be reduced throughout the low frequency operating range.
  • the need for ripple compensation occurs mainly when the frequencies of ports (4,5) are close.
  • the transition frequency ⁇ ⁇ defines the point from which the converter operates with the method of the present invention. For frequencies below f t , the converter operates in normal mode, without voltage ripple mitigation.
  • a non-transient medium is also provided machine readable.
  • the medium may be, for example, a memory, a flash memory, a hard disk, a compact disk, or any other device capable of storing computer instructions.
  • the machine is enabled to perform the method of controlling and operating a MMC (1, 15, 16, 17) as described in the present disclosure.

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Abstract

The present invention proposes a mode of operation in which a conventional DC-AC MMC (1) operates alternatingly in two distinct states: a first state of operation and a second state of operation. During each of these states, half of the MMC arms (2) carries a greater portion of the current in the positive port (4) which, in normal operation without circulating currents, would be equally split between the two arms that compose a phase. The arms (2) carrying the greater current are controlled so as to generate the lowest possible voltage that does not produce overmodulation in any arm (2), causing no negative interference with the control of the current in the ports (4, 5) or with the circulating current control. Energy absorption by these arms (2) is minimised in that minimum voltages are synthetised, thereby reducing energy variation in the capacitors (10). At the same time, the arms (2) corresponding to the other half generate the highest possible voltage that does not produce overmodulation in any arm (2) of the MMC (1), and that therefore does not hinder the control of any current of the MMC (1). Voltage and current controllers (18) in which of these states impose circulating currents that cause the mentioned imbalances in the currents in the arms (2). Thus, while the arms (2) that generate less voltage carry a greater current, the other group carries smaller currents that act towards balancing the energy stored in the capacitors (10). Since these arms generate the highest possible voltage, the circulating currents required to control the energies therein are minimised.

Description

MÉTODO DE MODULAÇÃO PARA OPERAR UM MMC PARA MAXIMIZAR A TENSÃO DE MODO COMUM REDUZINDO CORRENTES CIRCULANTES, E MEIO LEGÍVEL POR MÁQUINA CAMPO DA INVENÇÃO [001] A presente invenção se insere nos campos da geração, distribuição e transmissão de energia elétrica, bem como do acionamento de máquinas elétricas. Especificamente, a presente invenção se refere a tecnologias utilizadas no processamento de energia elétrica em altas potências, alimentados em média tensão (acima de 1 kV e inferior a 69 kV) ou alta tensão (acima de 69 kV e inferior a 230 kV) e, mais especificamente, as que envolvem conversores modulares multiníveis ou MMC (Modular Multilevel Converter). FUNDAMENTOS DA INVENÇÃO [002] O uso de dispositivos eletrônicos para medição, manipulação e tratamento da energia elétrica é cada vez mais empregado em todas as áreas da Engenharia Elétrica. Em sistemas que utilizam máquinas elétricas, por exemplo, a possibilidade de regular a frequência de saída e o torque mecânico, através de conversores eletrônicos estáticos, permite um controle de processo com maior precisão, menor consumo de energia elétrica e menor desgaste mecânico dos componentes envolvidos quando comparados a sistemas de acionamento puramente elétricos e/ou mecânicos. [003] Sistemas elétricos de alta potência, incluindo as máquinas elétricas, empregam tensões elevadas com o objetivo de diminuir a magnitude da corrente elétrica necessária para um mesmo valor de potência desejada. Uma corrente menor resulta em menores perdas ôhmicas e em máquinas e componentes de tamanhos menores. [004] Conversores eletrônicos estáticos são compostos principalmente por dispositivos semicondutores que funcionam como interruptores de corrente, sendo os diodos, os IGBTs (Insulated Gate Bipolar Transistor), os MOSFETs e os tiristores os mais utilizados. Estes dispositivos possuem, atualmente, uma capacidade de bloquear tensões menores do que as necessárias para o acionamento de máquinas elétricas de elevada potência. [005] Uma possibilidade é o emprego de conversores multiníveis, que possuem a propriedade de manter uma tensão reduzida sobre os dispositivos semicondutores. Há várias topologias diferentes de conversores multiníveis, cada uma com suas vantagens e desvantagens, nichos de aplicação e faixas de tensão de operação mais adequadas. [006] MMCs se destacam pela sua capacidade de operar idealmente com qualquer nível de tensão, garantindo uma divisão equilibrada dos esforços de corrente e de tensão entre os dispositivos semicondutores e capacitores que o compõem. Esta característica torna soluções de acionamento baseadas no MMC escalonáveis em termos de tensão de operação. Além disso, os MMCs, assim como outros conversores multiníveis, geram tensões com baixa distorção harmônica, eliminando a necessidade de filtros passivos conectados em seus terminais. ESTADO DA TÉCNICA [007] A Figura 1 apresenta é uma representação de uma estrutura típica de um MMC CC-CA convencional (1) do estado da técnica, contendo uma primeira porta (4) configurada para receber uma alimentação em corrente contínua e uma segunda porta (5) configurada para fornecer uma tensão em corrente alternada trifásica. Uma porta simboliza um conjunto de terminais através dos quais o MMC é conectado a um circuito externo. A primeira porta (4) apresenta dois terminais de entrada, um positivo (p) e um negativo (n), ligados a uma fonte de tensão em corrente contínua representada pelas tensões v1,2 e v2,1 em relação à referência. [008] Cada terminal da primeira porta (4) é conectado a cada um dos terminais da segunda porta (5) através de um circuito série composto por um braço (2) e um indutor (3). Cada braço (2) é composto pela associação em série de submódulos (SMs) (8), formando uma cadeia de SMs, e braços conectados ao terminal positivo (p) são chamados de braços positivos (6) enquanto braços conectados ao terminal negativo (n) são chamados de braços negativos (7). [009] A carga (14) conectada à segunda porta (5) é representada por elementos resistivos para fins de simplificação, podendo a carga (14) ser de qualquer configuração de elementos passivos, uma outra rede em corrente alternada, um gerador elétrico de corrente alternada ou outro sistema eletrônico. [010] As correntes icα e icβ fluem apenas internamente ao MMC CC-CA convencional (1) e são denominadas correntes de circulação. Estas correntes podem ser empregadas para otimizar o funcionamento do MMC CC-CA convencional (1) e também para diminuir a ondulação das energias armazenadas nos braços (2), permitindo a operação em baixa frequência com uma quantidade relativamente reduzida de elementos armazenadores de energia. [011] As tensões vB1,1, vB1,2 e vB1,3 representam as tensões geradas pelos braços positivos (6), enquanto vB2,1, vB2,2 e vB2,3 representam as tensões geradas pelos braços negativos (7),vCM é a tensão de modo comum gerada pelo MMC (1), ia e ib representam duas das três correntes da segunda porta (5), enquanto a corrente icc representa a corrente na primeira porta (4). Conhecendo-se estas correntes e as correntes icα e icβ, todas as correntes do MMC CC-CA convencional (1) podem ser determinadas. [012] Além do MMC CC-CA convencional (1), outras configurações de MMCs foram propostas para conversão CA-CA trifásica, como os apresentados na Figura 2, mais conhecidos como MMC CA-CA matricial (15) e MMC CA-CA Hexverter (16). Este último, proposto no documento DE102010013862 A1, é uma versão reduzida do primeiro, no qual menos braços são utilizados. [013] Assim, como no MMC CC-CA convencional (1), no MMC CA-CA Hexverter (16) cada terminal da primeira porta (4) é conectado a cada um dos terminais da segunda porta (5) através de um circuito composto pela conexão série de um braço (2) e um indutor (3). [014] No caso do MMC CA-CA matricial (15) trifásico, existem oito correntes independentes, sendo duas correntes na primeira porta (4) e duas correntes na segunda porta (5) e quatro correntes de circulação. [015] Em MMCs com número de braços reduzido, como o MMC CA-CA Hexverter (16), o número de correntes independentes é menor. O MMC CA-CA Hexverter (16) possui cinco correntes independentes, sendo duas correntes na primeira porta (4) e duas correntes na segunda porta (5) e uma corrente de circulação. [016] Fazendo agora referência à Figura 3, é representada a estrutura interna de um braço (2) do MMC (1,15,16) como a associação em série de um número n de SMs (8). Cada SM (8) é composto por dois terminais de ligação, um capacitor (10) e um arranjo de interruptores (9). O arranjo de interruptores (9) pode, por exemplo, ser um ou mais interruptores eletrônicos. O número de SMs (8) empregados deve ser tal que resulte numa faixa de tensão de braço vB possível de ser gerada maior que a faixa de tensão necessária para o funcionamento adequado de MMC (1, 15, 16). [017] A figura 4 apresenta os dois tipos principais de SMs empregados em MMCs do estado da técnica (1, 15, 16): o SM meia ponte (11) e o SM ponte completa (12). [018] O SM meia ponte (11) é o mais utilizado, sendo constituído de dois interruptores bidirecionais em tensão (13), normalmente compostos por um transistor IGBT e um diodo, e um capacitor (10). [019] O SM meia ponte (11) é capaz de gerar instantaneamente apenas os valores zero e Vc, portanto, um braço (2) constituído por estes SMs pode gerar apenas tensões unipolares, incluindo a tensão zero. O SM meia ponte (11) é aplicado principalmente em MMC CC-CA convencional (1). [020] O SM ponte completa (12) possui um capacitor (10) e quatro interruptores bidirecionais em tensão (13), também usualmente compostos de um IGBT e um diodo. Também é capaz de gerar instantaneamente os valores zero, +Vc e −Vc, portanto, um braço (2) constituído por estes SMs pode gerar tensões positivas e negativas, incluindo a tensão zero. O SM ponte completa (12) é aplicado principalmente em MMC CA-CA matriciais (15) e Hexverters (15, 16), mas também pode ser utilizado em MMC CC-CA convencionais (1). [021] Outra configuração possível de SM utiliza dois capacitores ou mais. Neste caso, o arranjo de interruptores (9), além de permitir gerar uma tensão cSM nula, deve permitir também gerar tensões referentes às combinações das tensões dos capacitores (10), como a soma ou a diferença destas. Outras configurações de SM são encontradas na literatura, mas fundamentalmente apresentam as funcionalidades aqui listadas. [022] Fazendo agora referência à Figura 5, é mostrada a estrutura de um MMC generalizado (17), no qual cada porta possui um número de terminais maior que dois. Em sua forma normal, não reduzida, como no MMC CC-CA convencional (1) e no MMC CA-CA matricial (15), um terminal de uma porta é conectado a todos os terminais da outra porta através da conexão série de um braço (2) e um indutor (3), com o número de terminais da primeira porta (4) representado por F e o número de terminais da segunda porta (5) representado por H. [023] A função dos indutores (3) é limitar a amplitude das correntes de alta frequência que circulam entre os braços (2) devido às diferenças instantâneas de tensão geradas por cada braço (2). A carga (14) conectada aos H terminais da segunda porta (5) é representada por H elementos resistivos para fins de simplificação, podendo a carga (14) ser de qualquer configuração de elementos passivos, uma outra rede em corrente alternada ou outro sistema eletrônico. As tensões presentes nos F terminais da primeira porta (4), com relação à referência, são representadas por vj,1, com j ∈ {1, … , F}, enquanto as correntes nos mesmos terminais são representadas por ij,1. Por sua vez, as diferenças de potencial sobre os H elementos da carga (14) conectada à segunda porta (5) são representadas por vk,2 com k E {1, H}, enquanto as correntes nestes elementos são representadas por ik2. As tensões sobre os braços (2) são representadas por Vj.k, enquanto as correntes que os atravessam são representadas por ijk. MODULATION METHOD FOR OPERATING A MMC TO MAXIMIZE COMMON MODE VOLTAGE BY REDUCING CIRCULATING CURRENTS, AND A MACHINE-READABLE MEDIUM FIELD OF THE INVENTION [001] The present invention falls within the fields of generation, distribution and transmission of electrical energy, as well as drive of electrical machines. Specifically, the present invention refers to technologies used in the processing of electrical energy at high powers, supplied at medium voltage (above 1 kV and below 69 kV) or high voltage (above 69 kV and below 230 kV) and, more specifically, those involving modular multilevel converters or MMC (Modular Multilevel Converter). BACKGROUND OF THE INVENTION [002] The use of electronic devices for measuring, manipulating and treating electrical energy is increasingly used in all areas of Electrical Engineering. In systems that use electrical machines, for example, the possibility of regulating the output frequency and mechanical torque, through static electronic converters, allows process control with greater precision, lower electrical energy consumption and less mechanical wear on the components involved. when compared to purely electrical and/or mechanical drive systems. [003] High-power electrical systems, including electrical machines, employ high voltages with the aim of reducing the magnitude of the electrical current required for the same desired power value. A smaller current results in lower ohmic losses and smaller sized machines and components. [004] Static electronic converters are mainly composed of semiconductor devices that function as current switches, with diodes, IGBTs (Insulated Gate Bipolar Transistor), MOSFETs and thyristors being the most used. These devices currently have the ability to block voltages lower than those necessary to drive high-power electrical machines. [005] One possibility is the use of multilevel converters, which have the property of maintaining a reduced voltage on semiconductor devices. There are several different topologies of multilevel converters, each with its advantages and disadvantages, application niches and most suitable operating voltage ranges. [006] MMCs stand out for their ability to operate ideally at any voltage level, ensuring a balanced division of current and voltage efforts between the semiconductor devices and capacitors that make them up. This feature makes MMC-based drive solutions scalable in terms of operating voltage. Furthermore, MMCs, like other multilevel converters, generate voltages with low harmonic distortion, eliminating the need for passive filters connected to their terminals. STATE OF THE ART [007] Figure 1 presents a representation of a typical structure of a conventional DC-AC MMC (1) of the prior art, containing a first port (4) configured to receive a direct current supply and a second port (5) configured to supply a current voltage three-phase alternating. A port symbolizes a set of terminals through which the MMC is connected to an external circuit. The first port (4) has two input terminals, one positive (p) and one negative (n), connected to a direct current voltage source represented by voltages v 1.2 and v 2.1 in relation to the reference. [008] Each terminal of the first port (4) is connected to each of the terminals of the second port (5) through a series circuit composed of an arm (2) and an inductor (3). Each arm (2) is composed of the series association of submodules (SMs) (8), forming a chain of SMs, and arms connected to the positive terminal (p) are called positive arms (6) while arms connected to the negative terminal ( n) are called negative arms (7). [009] The load (14) connected to the second port (5) is represented by resistive elements for simplification purposes, and the load (14) can be of any configuration of passive elements, another alternating current network, an electrical generator of alternating current or other electronic system. [010] The currents i cα and i cβ flow only internally to the conventional DC-AC MMC (1) and are called circulation currents. These currents can be used to optimize the operation of the conventional DC-AC MMC (1) and also to reduce the ripple of energy stored in the arms (2), allowing low frequency operation with a relatively reduced number of energy storage elements. [011] The voltages v B1,1 , v B1,2 and v B1,3 represent the voltages generated by the positive arms (6), while v B2,1 , v B2,2 and v B2,3 represent the voltages generated by the negative arms (7), v CM is the common mode voltage generated by the MMC (1), i a and i b represent two of the three currents of the second port (5), while the current i cc represents the current on the first door (4). Knowing these currents and the currents i cα and i cβ , all the currents of the conventional DC-AC MMC (1) can be determined. [012] In addition to the conventional MMC DC-AC (1), other configurations of MMCs have been proposed for three-phase AC-AC conversion, such as those presented in Figure 2, better known as matrix MMC AC-AC (15) and MMC AC-CA Hexverter (16). The latter, proposed in document DE102010013862 A1, is a reduced version of the first, in which fewer arms are used. [013] Thus, as in the conventional DC-CA MMC (1), in the AC-AC Hexverter MMC (16) each terminal of the first port (4) is connected to each of the terminals of the second port (5) through a circuit composed of the series connection of an arm (2) and an inductor (3). [014] In the case of the three-phase matrix AC-AC MMC (15), there are eight independent currents, two currents in the first port (4) and two currents in the second port (5) and four circulation currents. [015] In MMCs with a reduced number of arms, such as the MMC CA-CA Hexverter (16), the number of independent currents is smaller. The MMC AC-AC Hexverter (16) has five independent currents, two currents in the first port (4) and two currents in the second port (5) and a circulation current. [016] Referring now to Figure 3, the internal structure of an arm (2) of the MMC (1,15,16) is represented as the series association of a number n of SMs (8). Each SM (8) is composed of two connection terminals, a capacitor (10) and an arrangement of switches (9). The switch arrangement (9) may, for example, be one or more electronic switches. The number of SMs (8) employed must be such that it results in an arm voltage range v B that can be generated greater than the voltage range necessary for the proper functioning of MMC (1, 15, 16). [017] Figure 4 shows the two main types of SMs used in prior art MMCs (1, 15, 16): the half-bridge SM (11) and the full-bridge SM (12). [018] The half-bridge SM (11) is the most used, consisting of two bidirectional voltage switches (13), normally composed of an IGBT transistor and a diode, and a capacitor (10). [019] The half-bridge SM (11) is capable of instantly generating only zero and V c values, therefore, an arm (2) consisting of these SMs can generate only unipolar voltages, including zero voltage. The half-bridge SM (11) is mainly applied in conventional DC-AC MMC (1). [020] The full bridge SM (12) has a capacitor (10) and four bidirectional voltage switches (13), also usually composed of an IGBT and a diode. It is also capable of instantly generating zero values, +V c and −V c , therefore, an arm (2) consisting of these SMs can generate positive and negative voltages, including zero voltage. SM full bridge (12) is mainly applied in AC-AC MMC matrices (15) and Hexverters (15, 16), but can also be used in conventional CC-CA CMMs (1). [021] Another possible SM configuration uses two or more capacitors. In this case, the arrangement of switches (9), in addition to allowing the generation of a zero c SM voltage, must also allow generating voltages relating to combinations of capacitor voltages (10), such as the sum or difference of these. Other SM configurations are found in the literature, but fundamentally they present the functionalities listed here. [022] Referring now to Figure 5, the structure of a generalized MMC (17) is shown, in which each port has a number of terminals greater than two. In its normal, unreduced form, as in the conventional DC-AC MMC (1) and matrix AC-AC MMC (15), a terminal of one port is connected to all terminals of the other port through the series connection of an arm (2) and an inductor (3), with the number of terminals of the first port (4) represented by F and the number of terminals of the second port (5) represented by H. [023] The function of the inductors (3) is limit the amplitude of the high frequency currents that circulate between the arms (2) due to the instantaneous voltage differences generated by each arm (2). The load (14) connected to the H terminals of the second port (5) is represented by H resistive elements for simplification purposes, and the load (14) can be of any configuration of passive elements, another alternating current network or another electronic system . The voltages present at the F terminals of the first port (4), with respect to the reference, are represented by v j,1 , with j ∈ {1, … , F}, while the currents at the same terminals are represented by i j,1 . In turn, the potential differences over the H elements of the load (14) connected to the second port (5) are represented by v k,2 with k E {1, H}, while the currents in these elements are represented by i k2 . The tensions on the arms (2) are represented by Vj. k , while the currents that cross them are represented by ij k .
[024] Considerando que a primeira porta (4) do MMC generalizado (17) possui F terminais e a segunda porta (5) possui H terminais, o número total de braços (2) do MMC generalizado (17) é F multiplicado por H. Assim, é possível obter as estruturas do MMC CC-CA convencional (1) e do MMC CA-CA matricial (15) fazendo-se F = 2 e H = 3 no primeiro caso, e F = 3 e H = 3 no segundo caso. [024] Considering that the first port (4) of the generalized MMC (17) has F terminals and the second port (5) has H terminals, the total number of arms (2) of the generalized MMC (17) is F multiplied by H Thus, it is possible to obtain the structures of the conventional MMC CC-CA (1) and the matrix MMC CA-CA (15) by setting F = 2 and H = 3 in the first case, and F = 3 and H = 3 in the second case.
[025] A análise do circuito revela que o MMC generalizado (17) apresenta FH — 1 correntes controláveis. Destas, F + H — 2 são as correntes que o MMC generalizado (17) injeta ou drena nos terminais das portas (4,5) . As FH — F — H + 1 correntes independentes restantes são chamadas correntes de circulação e fluem internamente ao MMC generalizado (17) . [025] Circuit analysis reveals that the generalized MMC (17) presents FH — 1 controllable currents. Of these, F + H — 2 are the currents that the generalized MMC (17) injects or drains into the gate terminals (4,5). The remaining independent FH — F — H + 1 currents are called circulation currents and flow internally to the generalized MMC (17) .
[026] No caso do MMC CC-CA convencional (1) , que possui dois terminais na primeira porta (4) , e três terminais na segunda porta (5) , o número de correntes independentes que fluem nas portas são três: uma referente à primeira porta (4) , e duas referentes à segunda porta (5) . O número de correntes de circulação é dois. [026] In the case of the conventional DC-AC MMC (1), which has two terminals on the first port (4), and three terminals on the second port (5), the number of independent currents flowing in the ports are three: one referring to the first door (4), and two referring to the second door (5). The number of circulation chains is two.
[027] No caso do MMC CA-CA matricial (15) , existem duas correntes independentes em cada das portas (4,5) , totalizando quatro correntes independentes, e quatro correntes de circulação. [028] Estruturas com número de braços reduzido, como o MMC CA-CA Hexverter (16), também podem ser obtidas. Para tal, pode-se retirar braços (2) do MMC generalizado (17) de forma que ainda resultem pelo menos dois braços, em série com indutores (3), conectando cada terminal de uma porta (4,5) a pelo menos dois terminais da outra porta (4,5). [029] O documento “Loss optimization of MMC by second- order harmonic circulating current injection” (IEEE Transactions on Power Electronics, 2017) ensina que as correntes de circulação são graus de liberdade que podem ser explorados para otimizar a operação do MMC (1, 15, 16, 17), no qual correntes de circulação com formato específico são utilizadas para diminuir as perdas nos semicondutores do MMC CC-CA convencional (1). [030] Como descrito no documento “Generalized control approach for a class of modular multilevel converter topologies” (IEEE Transactions on Power Electronics, 2017), as correntes de circulação são usadas para transferir energia entre os braços (2), com o objetivo de balanceamento das tensões dos capacitores (10). [031] O objetivo do MMC (1, 15, 16, 17) é injetar ou drenar correntes em suas portas (4,5) de modo a transferir potência de uma à outra. As correntes devem possuir uma forma de onda adequada para a aplicação em questão, desta forma, quando uma porta (4,5) é conectada à rede elétrica ou a uma máquina elétrica de corrente alternada, por exemplo, deseja- se que as correntes sejam senoidais com distorção mínima. [032] O controle das correntes do MMC é conseguido através da comutação dos interruptores bidirecionais em tensão (13) que formam os SMs, que, dependendo de seus estados, ligados ou desligados, podem aplicar uma tensão maior ou menor sobre os indutores (3), aumentando ou diminuindo a derivada da corrente que flui através destes e, consequentemente aumentando ou diminuindo a derivada das correntes que fluem nas portas (4,5) e das correntes de circulação. [033] O esquema utilizado para definir como os interruptores bidirecionais em tensão (13) são ligados ou desligados é conhecida como modulação. Uma estratégia usualmente empregada consiste na modulação por largura de pulso, na qual a relação entre a duração do intervalo de tempo em que um interruptor bidirecional em tensão (13) permanece ligado e a duração total de um ciclo composto por um período ligado e um desligado é definida de tal forma que a tensão média no tempo gerada por um braço se aproxima de um valor de referência de tensão de braço desejada
Figure imgf000011_0001
. [034] O sistema de controle de um MMC (1, 15, 16, 17), responsável por regular as tensões dos capacitores (10) e as correntes das portas e de circulação é composto, principalmente, por sensores capazes de medir essas variáveis e sistemas de processamento de sinais que se baseiam em algoritmos de controle. Os algoritmos de controle mantêm, através de malhas de realimentação, as correntes e tensões medidas o mais próximo possível dos valores desejados. As saídas destes algoritmos são as referências das tensões de braço
Figure imgf000011_0002
, que serão utilizadas pelo modulador para definir os padrões de pulsos que os braços (2) devem gerar através da comutação dos interruptores bidirecionais em tensão (13). [035] As tensões de todos os capacitores (10) do MMC devem ser controladas de forma que as tensões sobre os interruptores bidirecionais em tensão (13) permaneçam dentro de limites aceitáveis. Normalmente, isto é realizado em dois níveis diferentes e de funcionamentos independentes. [036] O primeiro nível é responsável pela equalização das tensões dos capacitores (10) dos SMs dentro de um mesmo braço (2). O valor máximo de tensão instantânea que um braço (2) pode gerar, assim como o valor mínimo, só pode ser atingido para uma única combinação de estados dos interruptores bidirecionais em tensão (13). Para todos os outros possíveis valores intermediários de tensão instantânea de braço que podem ser gerados, há mais de uma combinação para os estados dos interruptores bidirecionais em tensão (13) que resultam na mesma tensão. Cada combinação diferente de estados dos interruptores bidirecionais em tensão (13) resulta num conjunto diferente de capacitores (10) que são atravessados pela corrente de braço. Os capacitores (10) deste conjunto podem ser carregados ou descarregados, dependendo do sentido da corrente de braço e do estado específico dos interruptores bidirecionais em tensão (13) de seu SM (8). Para cada valor instantâneo de tensão que deve ser gerado pelo braço (2), pode-se escolher os estados dos interruptores bidirecionais em tensão (13) que levam as tensões dos capacitores (10) a se aproximarem, como proposto em “Reduced Switching-Frequency Modulation and Circulating Current Suppression for Modular Multilevel Converters” (IEEE Transactions on Power Delivery, 2011). Assim, as tensões dos capacitores (10) de um mesmo braço (2) tendem a se manterem balanceadas. [037] O segundo nível é responsável por manter a soma das tensões dos capacitores (10) dos braços (2) a mais próxima possível de uma referência e com diferenças mínimas entre si. [038] As trocas de potência necessárias para balancear as energias armazenadas nos braços (2) e, consequentemente, a soma das tensões dos capacitores (10), pode ser conseguida através das correntes de circulação do MMC como na estratégia proposta no documento US 8,144,489 B2. [039] A tensão sintetizada por um braço (2) do MMC (1, 15, 16, 17), desconsideradas as quedas de tensão sobre os indutores (3) é uma composição das tensões presentes nas portas (4,5) e da tensão de modo comum A tensão de modo
Figure imgf000013_0004
comum
Figure imgf000013_0006
é definida como sendo a diferença entre a média das tensões aplicadas à primeira porta (4) e a média das tensões presentes na segunda porta (5). Para dois sistemas equilibrados em estrela conectados às portas (4,5) do MMC (1, 15, 16, 17), como apresentado na Figura 5, a tensão de modo comum
Figure imgf000013_0005
corresponde à diferença de potencial entre os centros das duas estrelas. [040] Portanto, a tensão sobre os terminais do braço (2)
Figure imgf000013_0003
vale, desconsiderando-se as quedas de tensão sobre os indutores (3):
Figure imgf000013_0001
[041] No caso do MMC CC-CA convencional (1), a tensão sobre um de seus braços (2) é uma composição de uma parcela
Figure imgf000013_0007
vinda da primeira porta (4), e uma parcela CA vinda da segunda porta (5), e da tensão de modo comum
Figure imgf000013_0002
que, de acordo com as equações do circuito, é imposta através da média das tensões de braço , isto é
Figure imgf000014_0002
Figure imgf000014_0001
[042] Para o MMC generalizado (17), a tensão de modo comum também é definida pela média das tensões de braço
Figure imgf000014_0003
multiplicada por -1, isto é onde
Figure imgf000014_0005
[043] A tensão de modo comum
Figure imgf000014_0007
dentro de certos limites, pode ser ajustada sem que haja interferência nas correntes das portas (4,5) do MMC (1, 15, 16, 17) ou nas correntes de circulação. É, portanto, um grau de liberdade adicional que pode ser utilizado para otimizar o funcionamento do MMC (1, 15, 16, 17). Idealmente, se não há correntes de circulação, a corrente que flui através de um braço (2) do MMC (1, 15, 16, 17) é uma composição das correntes das portas (4,5). Para o braço
Figure imgf000014_0004
do MMC CC-CA convencional (1), por exemplo, a corrente que o atravessa vale
Figure imgf000014_0006
[044] Ou seja, as correntes de braço são compostas por uma parcela alternada senoidal na frequência ω da segunda porta (5), e uma componente CC. O produto entre os termos que compõem a tensão e a corrente referentes a um braço (2) resulta na potência absorvida por este. Considerando-se operação em regime permanente, idealmente esta potência possui média nula. Contudo, também possui componentes senoidais em se considerada uma tensão de modo comum
Figure imgf000015_0003
nula. [045] É possível concluir, através de análise similar, que quando as portas (4,5) do MMC generalizado (17) operam com correntes alternadas de frequências diferentes,
Figure imgf000015_0002
aparecerem componentes senoidais de potência pm de frequências
Figure imgf000015_0001
Em ambos os casos, cada uma destas componentes senoidais de potência resulta em uma componente de energia armazenada no braço de mesma frequência, já que:
Figure imgf000015_0008
[046] A Figura 6 apresenta as principais formas de onda referentes ao MMC CC-CA convencional (1) quando operando sem correntes de circulação nem injeção de tensão de modo comum. A Figura 6(a) apresenta as tensões nos terminais da primeira porta (4) e nos terminais da segunda porta (5). A Figura 6(b) apresenta as correntes que o MMC injeta nos terminais das portas (4,5). A Figura 6(c) apresenta as correntes que fluem nos braços , enquanto a Figura 6(d) apresenta
Figure imgf000015_0004
as tensões sobre estes. A Figura 6(e) apresenta as ondulações das energias armazenadas nos braços
Figure imgf000015_0005
Estas possuem uma componente de frequência em
Figure imgf000015_0006
e outra em [047] Percebe-se, da análise da equação
Figure imgf000015_0007
(1.5), que as amplitudes das ondulações de energia são inversamente proporcionais às suas frequências. Portanto, a operação em baixa frequência na primeira porta (4) do MMC CC-CA convencional (1), ou em pelo menos uma das portas (4,5) do MMC generalizado (17), ou ainda com frequências próximas no caso do MMC generalizado (17), resulta em ondulações de energia maiores quando comparadas às resultantes da operação em frequências mais altas e distintas, no caso do MMC generalizado (17). Para que as tensões dos capacitores (10) se mantenham dentro de valores adequados para a operação do MMC (1, 15, 16, 17), seria necessário dimensionar as capacitâncias para a mínima frequência de operação do MMC (1, 15, 16, 17), ou para a mínima diferença entre as frequências, no caso de MMCs CA-CA (15,16,17). A operação com frequência nula, no caso do MMC CC-CA convencional (1), ou ainda frequências iguais, no caso de MMCs CA-CA (15,16,17), não seria possível com o método normal de funcionamento, sem correntes de circulação ou injeção de tensão de modo comum. Estas situações podem ser encontradas quando o MMC (1, 15, 16, 17) é aplicado em sistemas de acionamento de máquinas elétricas. No caso do MMC CC-CA convencional (1), o momento da partida seria o mais crítico com relação à ondulação de energia, mas qualquer ponto de operação em baixa velocidade também implica em um aumento das ondulações de energia. No caso dos MMCs CA-CA (15,16), ou mais genericamente em (17), a operação com frequência nominal da máquina, se esta é igual ou próxima à frequência da rede, seria também uma operação crítica. Do ponto de vista econômico, não é interessante dimensionar os capacitores (10) para operação em baixa frequência, uma vez que estes teriam que as capacitâncias e o tamanho seriam muito grandes. [048] Para tentar solucionar este problema, o documento WO2009115141 A1 revela a utilização da tensão de modo comum de frequência mais alta que as presentes na segunda porta
Figure imgf000016_0001
(5) do MMC CC-CA convencional (1) para diminuição da ondulação de energia nos capacitores (10). [049] Em “Low output frequency operation of the Modular Multi-Level Converter” (IEEE Energy Conversion Congress and Exposition, 2010), é proposta a utilização da tensão de modo comum vCM em conjunto com correntes de circulação de mesma frequência no MMC CC-CA convencional (1) para gerar uma componente de potência adicional que, quando modulada na frequência de operação da segunda porta (5), elimina as componentes de baixa frequência de energia presente nos capacitores (10). [050] Estratégia semelhante é encontrada em “A Broad Range of Speed Control of a Permanent Magnet Synchronous Motor Driven by a Modular Multilevel TSBC Converter” (IEEE Transactions on industry applications, vol. 53, no. 4). [051] No entanto, as soluções convencionais possuem limitações importantes. Uma das dificuldades é o cálculo da amplitude apropriada para a referência da tensão de modo comum vCM. Como descrito na equação (1.1), a tensão que um braço gera é função das tensões das portas (4,5) e da tensão de modo comum vCM. Idealmente, vCM deve possuir a maior amplitude possível, de modo que a amplitude das correntes de circulação necessária para transferir a quantidade de potência desejada seja minimizada, assim minimizando as perdas nos interruptores bidirecionais em tensão (13). [052] Contudo, o valor de tensão absoluto máximo que um braço (2) consegue gerar é sempre limitado pela soma das tensões de seus capacitores (10). No caso de um braço (2) composto por SMs ponte completa (12), tanto a mínima tensão negativa quanto a máxima positiva são limitadas pela soma das tensões dos capacitores (10). No caso de um braço (2) composto por SMs meia ponte (11), a tensão mínima, em valor absoluto, é sempre zero, e o valor absoluto máximo é sempre a soma das tensões dos capacitores (10). A polaridade da tensão que o braço (2) gera pode ser positiva ou negativa, dependendo de como este é conectado ao resto do circuito. De acordo com a convenção adotada na Figura 1, os braços positivos (6) sempre geram tensão positiva, enquanto os braços negativos (7) sempre geram tensão negativa. [053] A tentativa de gerar uma tensão maior ou menor que a disponível pelo braço (2) resulta em sobremodulação. Ao operar neste modo, as tensões sintetizadas pelo MMC (1, 15, 16, 17) são limitadas à máxima tensão disponível, causando distorções nos padrões das tensões sintetizadas e consequentemente nas correntes das portas (4,5), além de ocasionar possíveis sobrecorrentes nos braços (2) do MMC (1, 15, 16, 17) devido à impossibilidade de controlar com precisão as correntes de circulação e/ou das portas. [054] Em regime permanente, a amplitude máxima da tensão de modo comum vCM que o MMC pode produzir sem causar sobremodulação pode ser estimada a partir das amplitudes das tensões das portas (4,5). Contudo, uma certa margem de segurança deve ser usada, de modo a garantir que os braços (2) não causarão sobremodulação mesmo na ocorrência de transientes nas tensões das portas e/ou nas referências que definem o ponto de operação do MMC CC-CA convencional (1), ou mesmo devido à ondulação de tensão existente nos capacitores (10). [055] Assim, a amplitude da tensão de modo comum no estado da técnica é usualmente limitada em um valor mais baixo do que a máxima possível para tentar garantir o correto funcionamento do MMC, ou seja, evitar uma possível operação com sobremodulação e a consequente geração de distorção harmônica nas tensões do MMC. BREVE DESCRIÇÃO DA PRESENTE INVENÇÃO [056] A invenção aqui descrita pode ser aplicada em MMCs que realizam qualquer tipo de conversão envolvendo corrente alternada (CA) e/ou corrente contínua (CC), ou seja, MMC CC- CC, MMC CC-CA, MMC CA-CC ou MMC CA-CA com qualquer número de fases. [057] As ondulações das tensões dos capacitores do MMC tendem a aumentar de amplitude quando a frequência de entrada se aproxima da frequência de saída. Não é possível, por exemplo, que o MMC CC-CA opere com frequência zero na saída CA. [058] Esta invenção propõe um modo de funcionamento otimizado que resulta numa tensão de modo comum maximizada. Isto reduz as amplitudes das correntes de circulação necessárias para compensar as ondulações de tensão, permitindo o MMC operar numa ampla faixa de frequências com a redução das perdas Joule internas ao conversor. BREVE DESCRIÇÃO DAS FIGURAS [059] O presente invento passará a ser descrito a seguir com referência às concretizações típicas do mesmo e também com referência aos desenhos apensos, nos quais: [060] A Figura 1 apresenta um MMC CC-CA trifásico do estado da técnica. [061] A Figura 2 apresenta um MMC CA-CA matricial e um MMC CA-CA Hexverter de acordo com o estado da técnica. [062] A Figura 3 apresenta a estrutura geral interna de um braço de um MMC. [063] A Figura 4 apresenta um SM meia ponte e um SM ponte completa de acordo com o estado da técnica. [064] A Figura 5 apresenta a estrutura de um MMC generalizado. [065] A Figura 6 apresenta as principais formas de onda referentes ao funcionamento do MMC CC-CA. [066] A Figura 7 apresenta um diagrama simplificado do sistema de controle de um MMC generalizado de acordo com a presente invenção. [067] A Figura 8 apresenta um método de gerar a referência da tensão de modo comum para o MMC CC-CA com transições suavizadas de acordo com a presente invenção. [068] A Figura 9 apresenta uma comparação entre resultados de simulação obtidos para o método convencional e para o método de acordo com a presente invenção. [069] A Figura 10 apresenta uma comparação entre as perdas obtidas por simulação para o método convencional e para o método de acordo com a presente invenção. [070] A Figura 11 apresenta resultados experimentais de um MMC operando de acordo com a presente invenção. [071] A Figura 12 apresenta uma comparação entre as perdas medidas quando o MMC opera com o método convencional e com o método de acordo com a presente invenção. DESCRIÇÃO DETALHADA DA PRESENTE INVENÇÃO [072] Modalidades específicas da presente divulgação são descritas abaixo. Em um esforço para fornecer uma descrição concisa dessas modalidades, todos os recursos de uma implementação real podem não ser descritos no relatório descritivo. Deve ser apreciado que no desenvolvimento de qualquer implementação real, como em qualquer projeto de engenharia ou design, inúmeras decisões específicas de implementação devem ser feitas para atingir os objetivos específicos dos desenvolvedores, como conformidade com restrições relacionadas ao sistema e negócios, que pode variar de uma implementação para outra. Além disso, deve ser apreciado que tal esforço de desenvolvimento pode ser complexo e demorado, mas seria, no entanto, um empreendimento de rotina de design, e fabricação para aqueles de habilidade comum tendo o benefício desta divulgação. [073] A presente invenção propõe um método de operação do MMC (1, 15, 16, 17) que minimiza a ondulação de energia nos capacitores (10), permitindo a operação em baixas frequências, no caso do MMC CC-CA convencional (1), ou a operação com frequências iguais ou próximas nas portas (4,5) no caso dos MMCs CA-CA (15,16,17). A possibilidade de operar numa faixa estendida de frequência permite a aplicação do MMC CC-CA convencional (1) em sistemas de acionamento de máquinas, cuja porta conectada à máquina opera com frequências que variam desde zero, na partida, até a nominal. [074] O método de operação aqui revelado é aplicável a qualquer MMC cuja estrutura possa ser definida a partir do MMC generalizado (17), resultando em uma tensão de modo comum vCM maximizada em qualquer instante de tempo e simultaneamente garantindo que nenhum dos braços operará em sobremodulação devido à adição da tensão de modo comum vCM. Desta forma, as correntes de circulação necessárias para a redução da ondulação das tensões dos capacitores (10) são reduzidas, minimizando as perdas devido às correntes de circulação e simultaneamente garantindo o funcionamento adequado do MMC (1, 15, 16, 17) mesmo em transientes severos. [075] Vantajosamente, o presente método proporciona maior eficiência na operação do MMC. [076] Outra vantagem do presente método é a possibilidade de reduzir o tamanho dos MMC em decorrência das menores perdas Joule. [077] Ainda outra vantagem do presente método é a redução da interferência introduzida no sistema pelas perdas reativas do MMC. [078] Primeiramente, o funcionamento do método da presente invenção é analisado quando aplicado ao MMC CC-CA convencional (1), ilustrado na Figura 1. Os braços positivos (6) são compostos por SMs meia-ponte (11), de forma que os braços positivos são capazes de gerar apenas tensões
Figure imgf000022_0002
positivas ou nulas. Os braços negativos (7), são também compostos por SMs meia ponte (11), e são conectados de forma que são capazes de gerar apenas tensões negativas ou nulas.
Figure imgf000022_0001
[079] Entende-se como sobremodulação a condição na qual não é possível um braço (2) gerar a tensão de referência
Figure imgf000022_0003
calculada pelo sistema de controle (21) devido a estar fora da faixa de tensão possível de ser sintetizada pelo braço (2). [080] Braços positivos (6) e negativos (7) podem gerar uma tensão média qualquer, dentro de seus limites de operação, por meio da utilização de um modulador por largura de pulso, o qual gera sinais de comando para os interruptores (13) de forma que o valor médio da tensão de braço calculada durante um ciclo de comutação se aproxime do valor de referência
Figure imgf000023_0002
[081] Fazendo referência à Figura 7, é mostrado resumidamente um sistema de controle do MMC CC-CA convencional (1) empregando uma implementação exemplificativa, isto é, não limitativa, do método da presente invenção. Os sinais de referências das tensões de braço sem adição da tensão de modo comum, são
Figure imgf000023_0001
calculados pelos controladores de tensões e correntes (18) a partir dos valores de corrente de braço medidas
Figure imgf000023_0010
das somas das tensões dos capacitores (10) medidas e dos
Figure imgf000023_0009
sinais de referência para as somas das tensões dos capacitores
Figure imgf000023_0004
e dos sinais de referência para as correntes em uma das portas. No exemplo da Figura 7, essas serão tomadas como as correntes da segunda porta (5)
Figure imgf000023_0008
porém as correntes da primeira porta (4) poderiam ser tomadas sem se afastar do escopo da presente invenção. [082] Algoritmos de controle são usados para calcular quais devem ser as tensões que os braços (2) devem gerar para que as correntes e tensões do MMC sigam suas referências com baixo erro e rejeitar perturbações. A tensão de modo comum vCM não interfere nas correntes de braço do MMC,
Figure imgf000023_0003
mas é utilizada pelo método da presente invenção para diminuir a ondulação de tensão nos capacitores (10). A referência da tensão de modo comum é adicionada às
Figure imgf000023_0007
referências
Figure imgf000023_0005
calculadas pelos controladores (18) por meio de (19), resultando nas referências das tensões de braço Na ocorrência de sobremodulação de algum braço (2) do
Figure imgf000023_0006
MMC (1), a consequência mais provável é o não seguimento de referência das correntes das portas (4,5) e/ou das correntes de circulação. [083] Para uma dada corrente de braço (2), quanto maior o valor absoluto da tensão que o braço (2) gera, maior a taxa com que a energia é absorvida ou entregue. A presente invenção propõe um modo de funcionar no qual o MMC CC-CA convencional (1) opera alternadamente em dois estados de operação distintos: um primeiro estado de operação e um segundo estado de operação. Durante cada um destes estados de operação, metade dos braços (2) conduz uma parcela maior da corrente da porta (4), que, em operação normal sem correntes de circulação, seria dividida igualmente entre os dois braços que compõem uma fase. [084] Os braços (2) que conduzem maior corrente são comandados a gerar a mínima tensão possível que não resulte em sobremodulação em qualquer braço (2), não resultando em nenhuma interferência negativa no controle das correntes das portas (4,5), nem no controle das correntes de circulação. Ao sintetizar tensões mínimas, a absorção de energia por estes braços (2) é minimizada, reduzindo a variação de energias em seus capacitores (10). Enquanto isso, os braços (2) correspondentes à outra metade geram a máxima tensão que não resulte em sobremodulação de qualquer braço (2) do MMC CC-CA convencional (1) e, portanto, que não resulte em prejuízo ao controle de qualquer corrente do MMC CC-CA convencional (1). [085] Os controladores de tensão e corrente (18), durante cada um destes estados de operação, força correntes de circulação que causam os desequilíbrios mencionados nas correntes dos braços (2). Assim, enquanto os braços (2) que geram menor tensão conduzem uma maior corrente, o outro grupo conduz correntes menores que agem no sentido de equilibrar as energias armazenadas em seus capacitores (10). Como estes braços geram a maior tensão possível, as correntes de circulação necessárias para controlar suas energias são minimizadas. [086] As referências usadas no controle das correntes de circulação são calculadas por controladores de tensão dos capacitores (10) a partir dos valores medidos de tensão e de valores de referência propícios para o funcionamento do MMC CC-CA convencional (1). [087] No primeiro estado de operação, deseja-se minimizar o valor absoluto das tensões geradas pelos braços positivos (6), e maximizar o valor absoluto das tensões geradas pelos braços negativos (7). Para isto, a tensão de modo comum vCM deve ser aumentada. Ao aumentar-se o vCM, um braço positivo (6) pode atingir o limite inferior da sua faixa linear de operação (0 V), ou um braço negativo (7) pode atingir o limite superior, em valor absoluto, da sua faixa de operação, gerando uma tensão negativa cujo valor absoluto corresponde à soma das tensões de todos os seus capacitores (10). A ocorrência de um tipo de limitação ou outra depende dos valores das referências
Figure imgf000025_0001
que não incluem ainda a tensão de modo comum calculadas pelos
Figure imgf000025_0002
controladores de tensões e correntes (18), e das somas das tensões dos capacitores (10) de cada braço (2), representadas por que determinam a máxima tensão, em valor absoluto,
Figure imgf000025_0003
que cada braço (2) pode gerar. [088] No segundo estado de operação, deseja-se minimizar o valor absoluto das tensões geradas pelos braços negativos (7), e maximizar o valor absoluto das tensões geradas pelos braços positivos (6). Disto resulta que a tensão de modo comum vCM deve ser diminuída. Ao se diminuir a tensão de modo comum vCM, ou um braço negativo (7) pode atingir o limite o inferior, em valor absoluto de tensão, da sua faixa linear de operação (0 V) com todos os interruptores bidirecionais de tensão (13) inferiores de todos os seus SMs meia-ponte (11) fechados, ou um braço positivo (6) pode atingir o limite superior, em valores absolutos, da sua faixa de operação, com todos os interruptores bidirecionais de tensão (13) superiores do SM meia-ponte (11) fechados. [089] De acordo com o presente método, é fornecido um modo de operação no qual a tensão de modo comum vCM é calculada para o primeiro e segundo estados de operação de forma que sempre apenas um braço (2) do MMC CC-CA convencional (1) atinja o limite inferior ou superior da faixa de tensão que este pode sintetizar, definido por zero ou a soma das tensões de todos os seus capacitores (10)
Figure imgf000026_0004
sempre minimizando, em valores absolutos, as tensões geradas por metade dos braços (2) e maximizando as tensões geradas por metade dos outros braços (2). Isto garante que correntes de circulação menores, calculadas pelo sistema de controle (18), são necessárias para regular as tensões dos capacitores (10) dos braços (2) que estão gerando maior tensão em valores próximos de suas referências A tensão de modo comum otimizada vCM calculada de a
Figure imgf000026_0003
cordo com o presente método é somada através do somador (19), com sinal oposto, às referências calculadas pelo sistema de controle (18),
Figure imgf000026_0002
de forma que as referências finais das tensões de braço são dadas por
Figure imgf000026_0001
[090] No primeiro estado de operação, a máxima tensão vCM que levaria a apenas um braço positivo (6) a gerar a mínima tensão possível (0 V) é
Figure imgf000027_0001
[091] Por outro lado, ao se aumentar vCM, há a possibilidade de um braço negativo (7) atingir o limite inferior de tensão que pode ser sintetizada, igual a
Figure imgf000027_0005
cujo valor absoluto corresponde a soma de todas as tensões dos capacitores (10). O valor máximo de vCM que levaria um único braço negativo (7) ao limite é
Figure imgf000027_0002
[092] Ao se combinar as duas restrições, encontra-se que a tensão máxima de modo comum que leva a apenas um braço (2) do MMC CC-CA convencional (1) a sintetizar a máxima ou a mínima tensão possível é
Figure imgf000027_0003
[093] Similarmente, encontra-se que a mínima tensão de modo comum vCM que leva um braço positivo (6) do MMC CC-CA convencional (1) ao limite máximo da tensão que pode ser gerada ou um braço negativo (7) ao valor mínimo, em valor absoluto, da tensão que pode ser gerada vale
Figure imgf000027_0004
[094] Durante o primeiro estado de operação, supondo-se uma corrente positiva na fase k da segunda porta (5) do MMC CC-CA convencional (1), os controladores (18) forçarão uma corrente de circulação na fase k do MMC CC-CA convencional (1) de modo a aumentar a corrente no braço positivo k
Figure imgf000028_0009
(6) e diminuir a corrente no braço negativo
Figure imgf000028_0004
que
Figure imgf000028_0001
neste estado sintetiza tensão máxima. A corrente no braço negativo pode ter um sentido positivo ou negativo,
Figure imgf000028_0002
dependendo da relação entre a corrente na segunda porta (5) ^^^ e a corrente de circulação forçada pelos controladores (18). Assim, é possível controlar se o braço negativo (7) da fase ^^ absorve ou fornece energia, sendo possível controlar a tensão de seus capacitores (10). Por outro lado, a corrente do braço positivo ^^ (6)
Figure imgf000028_0003
para a condição analisada, é sempre positiva, resultando em absorção de energia e consequente aumento das tensões dos capacitores (10) que o compõem, embora de forma minimizada, já que as tensões que os braços (2) geram são as mínimas possíveis que garantem que não ocorra a sobremodulação. [095] Assim, é necessário alternar entre o primeiro e segundo estados de operação para que seja possível controlar as tensões dos capacitores (10) de ambos os grupos de braços positivos (6) e negativos (7). Isto é simbolizado, na Figura 7, pela chave (20), que comuta a referência da tensão de modo comum
Figure imgf000028_0008
entre os sinais
Figure imgf000028_0005
através do sinal sc Por exemplo, pode-se definir que a chave (20) deixa passar o sinal
Figure imgf000028_0007
quando sc vale 1, e
Figure imgf000028_0006
quando ^^^ vale 0. Evidentemente, esta definição é apenas exemplificativa e não limitativa. Outras definições são possíveis dentro do escopo da presente invenção. [096] Com referência à Figura 8, é apresentado um diagrama de blocos de uma forma de implementação exemplificativa do esquema de geração da tensão de modo comum otimizada descrito. Os somadores (22) e (23) em conjunto com os blocos que calculam valores mínimo (24) e máximo (25) implementam as equações (1.8) e (1.9). A chave (20) seleciona de acordo com o sinal
Figure imgf000029_0004
. A frequência com
Figure imgf000029_0001
que sc alterna entre 0 e 1 define a frequência da tensão de modo comum vCM. O formato de vCM é aproximadamente retangular, mas com uma envoltória definida por
Figure imgf000029_0003
e
Figure imgf000029_0002
Em algumas aplicações, como sistemas de acionamento de máquinas, o conteúdo de alta frequência da tensão de modo comum vCM deve ser reduzido, de forma a limitar a amplitude da corrente de modo comum que circula através da máquina, que pode ocasionar danos aos rolamentos da máquina. [097] De acordo com o método da presente invenção, o conteúdo de alta frequência da tensão de modo comum vCM pode ser reduzido se as transições entre os valores
Figure imgf000029_0005
forem realizadas de forma menos abrupta. Assim, na transição do segundo estado de operação para o primeiro estado de operação, o sinal de referência
Figure imgf000029_0006
pode ter seu valor gradualmente incrementado até que se atinja o valor de Na transição do segundo estado de operação para o
Figure imgf000029_0007
primeiro estado de operação, o sinal de referência
Figure imgf000029_0009
pode ter seu valor decrementado até que se atinja o valor de
Figure imgf000029_0008
O valor do incremento e do decremento pode ser determinado de forma a limitar o valor absoluto da derivada máxima, com relação ao tempo, da tensão de modo comum vCM. [098] A Figura 9 apresenta uma implementação exemplificativa da geração de com derivadas reduzidas. O cálculo do valor máximo da tensão de modo comum
Figure imgf000029_0010
agora leva em consideração também, além dos sinais já utilizados em (1.8), sinal O sinal vtr tem formato
Figure imgf000030_0001
Figure imgf000030_0002
triangular e frequência igual à especificada para a tensão de modo comum vCM. O comparador (26) é responsável por gerar o sinal sc, que se torna 1 assim que o sinal triangular vtr se torna positivo, e 0 assim que ^^௧^ se torna negativo. [100] Tanto no início quanto no final do período em que o MMC CC-CA convencional (1) se encontra no primeiro estado de operação, definido por
Figure imgf000030_0014
, o valor de
Figure imgf000030_0015
é menor que os valores de para todo cabível,
Figure imgf000030_0003
Figure imgf000030_0016
portanto, o valor mínimo calculado por (24) corresponderá ao valor de
Figure imgf000030_0009
Tanto no início quanto no final do período em que o MMC CC-CA convencional (1) se encontra no segundo estado de operação, definido por
Figure imgf000030_0012
, o valor de
Figure imgf000030_0013
é maior que os valores de
Figure imgf000030_0004
para todo k cabível, portanto, o valor máximo calculado por (25) corresponderá ao valor de vtr. O valor de
Figure imgf000030_0005
é definido por
Figure imgf000030_0011
nas transições entre o primeiro e segundo estados de operação e vice-versa. Portanto, a derivada com relação ao tempo de durante as
Figure imgf000030_0006
transições é definida pela derivada de
Figure imgf000030_0010
A amplitude de pode ser escolhida de modo que a derivada de
Figure imgf000030_0007
tenha um
Figure imgf000030_0008
valor pré-determinado durante as transições de estado. [101] Em outro exemplo não limitativo, é possível reduzir o conteúdo de alta frequência da tensão de modo comum vCM pela a diminuição da frequência com que se alterna entre o primeiro e segundo estados de operação. Quando o MMC CC- CA convencional (1) opera com correntes na segunda porta (5) menores, as variações nas tensões dos capacitores (10) também são menores, de forma que é possível aumentar as durações do primeiro e segundo estados de operação ainda mantendo-se as tensões dos capacitores (10) dentro de limites aceitáveis. [102] É possível ainda definir quando o estado deve mudar de 1 para 2 e de 2 para 1 a partir das próprias tensões dos capacitores (10). Sempre que uma tensão
Figure imgf000031_0003
atingir um valor máximo ou mínimo pré-determinado, o sinal sc comuta seu valor, mudando o estado de operação do MMC CC-CA convencional (1). Neste exemplo, a frequência de vCM é variável de acordo com o ponto de operação do MMC CC-CA convencional (1). [103] Todas as proposições apresentadas anteriormente para o MMC CC-CA convencional (1) podem ser estendidas para os MMCs CA-CA (15,16), ou, mais genericamente, para o MMC generalizado (17). Estes MMCs podem utilizar SMs com capacidade de gerar tensões positivas e negativas, como o SM ponte completa (12). Assim, ambos os limites máximo e mínimo da tensão que pode ser gerada por um braço (2) é definida pela soma das tensões dos capacitores (10). A máxima tensão de modo comum vCM que leva a apenas um braço (2) do MMC (15, 16, 17) a atingir o seu limite inferior de sua capacidade de geração de tensão é dada por
Figure imgf000031_0001
[104] A mínima tensão de modo comum vCM que leva a apenas um braço (2) do MMC (15,16,17) a atingir o seu limite superior de sua capacidade de geração de tensão é dada por
Figure imgf000031_0002
[105] É possível, ainda, no caso de conversores MMC CA- CA (15, 16, 17), empregar tensão de modo comum vCM e correntes de circulação CC para transferir potências entre os braços (2) do MMC (15, 16, 17). Neste caso, pode-se ainda empregar a técnica proposta, bastando que a tensão de modo comum vCM seja mantida em seu valor máximo vCM max ou mínimo vCM min. [106] Uma diferença importante na operação do MMC (15, 16, 17), de acordo com a presente invenção, com relação ao MMC CC-CA convencional (1), é a forma com que os sinais vCM max e vCM min são calculados. A suavização das transições, por qualquer método que limite a derivada da referência da tensão de modo comum, ou, mais especificamente, através
Figure imgf000032_0005
do método exemplificado na Figura 8, e a operação com frequência variável descrita anteriormente, ou seja, que “definir quando o estado deve mudar de 1 para 2 e de 2 para 1 a partir das próprias tensões dos capacitores (10) (...) sempre que uma tensão atingir um valor máximo ou mínimo
Figure imgf000032_0004
pré-determinado, o sinal sc comuta seu valor”, são aplicáveis ao MMC (15, 16, 17), bastando que
Figure imgf000032_0003
sejam calculadas de acordo com (1.10) e (1.11), respectivamente. [107] Uma vantagem inerente da presente invenção, quando aplicada a qualquer um dos MMC (1, 15, 16), ou mais genericamente, ao MMC generalizado (17), é a maior capacidade de manter as correntes controladas durante transitórios abruptos nas tensões das portas (4,5) ou nas referências das correntes das portas. [108] Em métodos convencionais, a amplitude da referência da tensão de modo comum é calculada de modo que exista uma certa margem pré-de
Figure imgf000032_0002
finida entre os valores máximo e mínimo das referências das tensões de braço
Figure imgf000032_0001
e os limites de tensão que os braços (2) podem gerar. Assim, ainda há alguma folga para atuação dos controladores (18) das correntes em caso de transitórios abruptos. No caso de variações muito rápidas e de grandes amplitudes nas tensões das portas (4, 5) ou nas referências de corrente, as referências de tensão de braço que os controladores (18) calculam, quando combinadas
Figure imgf000033_0002
com a referência da tensão de modo comum
Figure imgf000033_0001
podem ultrapassar os limites de tensão que os braços (2) podem sintetizar, resultando em distorções nas correntes das portas (4, 5) e de circulação. [109] Quanto menor a amplitude da referência da tensão de modo comum mais distantes de seus limites de tensão
Figure imgf000033_0003
os braços (2) operarão, tornando a operação do MMC (1, 15, 16, 17) mais resiliente. Por outro lado, maiores serão as amplitudes das correntes de circulação necessárias para controlar as somas das tensões dos capacitores resultando em maiores perdas.
Figure imgf000033_0004
[110] Na presente invenção, vantajosamente, a referência da tensão de modo comum é calculada de modo a
Figure imgf000033_0006
se utilizar o máximo da faixa tensão que os braços (2) podem gerar, mas sem nunca ultrapassar os limites de tensão que os braços (2) podem sintetizar, desde que as referências não já os excedam. Isto resulta no efeito técnic
Figure imgf000033_0005
o de correntes de circulação menores, implicando em menores perdas, e ao mesmo tempo uma operação mais resiliente a transitórios rápidos nas tensões das portas (4,5) e nas referências de corrente. [111] As perdas no MMC (1, 15, 16, 17) são ainda menores quando o presente método é empregado devido à menor frequência de comutação dos interruptores bidirecionais em tensão (13), já que sempre (ou na maior parte do tempo, se a suavização da tensão de modo comum vCM é empregada) um dos braços (2) do MMC (1, 15, 16, 17) gera tensão máxima ou mínima, condição na qual nenhum interruptor bidirecional em tensão (13) comuta, reduzindo as perdas por comutação. [112] O método de maximização da tensão de modo comum vCM proposto nesta descrição pode ser empregado apenas quando se faz necessária a redução das ondulações de energia dos capacitores (10). Quando a ondulação é naturalmente pequena, por exemplo, devido a operação com baixa corrente ou elevada frequência, pode-se operar o MMC (1, 15, 16, 17) sem injeção da tensão de modo comum vCM maximizada proposta. [113] Por outro lado, pode-se dimensionar os capacitores (10) do MMC (1, 15, 16, 17) de forma que sempre, ou a partir de um valor mínimo de corrente e/ou máximo de frequência em uma porta (4, 5), seja necessário compensar as ondulações de energia dos capacitores (10) de acordo com a invenção. Neste caso, seria possível empregar capacitores (10) de menor capacitância e menor volume em aplicações nas quais o MMC (1, 15, 16, 17) opera sempre com alta frequência, como em retificadores conectados à rede. [114] A presente invenção pode ser empregada também em sistemas de conversão que empregam mais de um MMC (1, 15, 16, 17), como, por exemplo, numa configuração na qual uma primeira porta (4, 5) de um primeiro MMC (1, 15, 16, 17) está conectada a uma primeira porta (4, 5) de um segundo MMC (1, 15, 16, 17), a segunda porta do primeiro MMC (4, 5) é conectada à rede e a segunda porta (4, 5) do segundo MMC (1, 15, 16, 17) é conectada a uma carga (14), por exemplo, uma máquina CA. Neste caso, o método proposto pode ser empregado apenas no segundo MMC (1, 15, 16, 17), que alimenta a carga (14), permitindo sua operação em baixa frequência, ou também no primeiro MMC (1, 15, 16, 17), que é conectado à rede, permitindo o emprego de capacitores (10) de menor capacitância e menor volume. EXEMPLOS DE CONCRETIZAÇÃO DA INVENÇÃO [115] Dois exemplos de concretização da invenção são apresentados. Estes exemplos têm como objetivo ilustrar o funcionamento e aplicação do método aqui apresentado. Sendo assim, os exemplos que se seguem não devem ser tomados como limitativos. [116] O primeiro exemplo refere-se à simulação de um sistema de conversão CC-CA em média tensão. O segundo exemplo refere-se à experimentação de um sistema de acionamento de máquina em baixa tensão. Ambos empregam o MMC CC-CA convencional (1) com SM meia ponte (11). [117] Voltando-se para a Figura 10, é apresentada uma comparação entre as formas de onda obtidas com um método de funcionamento convencional que emprega uma tensão de modo comum vCM com amplitude constante e as formas de ondas resultantes do método de funcionamento da presente invenção descrito anteriormente. Ambos os métodos foram testados em um MMC CC-CA convencional (1) por meio de simulação. Um cenário equivalente ao de um sistema de acionamento de máquina de média tensão de 6,9 kV foi escolhido. [118] As formas de onda (a), (b) e (c) são as formas de onda do método convencional, enquanto as formas de onda (d), (e) e (f) são formas de onda referentes ao método aqui revelado do sistema operando em regime permanente. [119] O sistema simulado possui 10 SMs por braço, um indutor (3) de 1 mH e capacitores (10) de 2,7 mF. Uma tensão de 11,5 kV é aplicada à primeira porta (4) do MMC CC-CA convencional (1) e a segunda porta (5) alimenta uma carga com tensão de 1,725 kV eficaz de linha e frequência de 15 Hz. [120] A tensão de modo comum vCM resultante do método da presente invenção, apresentada em (d), possui uma amplitude que varia ao longo do tempo, mas na média tem uma amplitude superior àquela do método convencional, apresentada em (a). Como consequência, as amplitudes e os valores eficazes das correntes de circulação necessárias para controlar as tensões dos capacitores (10) são menores, reduzindo as perdas. Isto pode ser percebido ao se comparar a corrente de braço ^^^^,^ obtida com o método convencional, apresentada em (b), e com o método da presente invenção, apresentada em (e). [121] As referências tem formato senoidal e suas
Figure imgf000036_0001
amplitudes e fases são calculadas, para ambos os métodos, de forma a minimizar as amplitudes das correntes de circulação resultantes. Os gráficos (c) e (f) apresentam as somas das tensões dos capacitores (10) referentes ao braço
Figure imgf000036_0002
positivo (1,1), bem como as tensões sobre estes,
Figure imgf000036_0003
Verifica-se que o limite da capacidade de sintetização de tensão do braço (1,1) é quase alcançado no intervalo de tempo em torno de 7,04 s no método convencional (c). [122] Uma perturbação ocorrida nos intervalos em que os limites de tensão dos braços (2) são aproximados podem levar facilmente à região de sobremodulação, resultando na distorção das correntes das portas (4, 5) e de circulação. No método da presente invenção, o limite é alcançado durante vários intervalos de tempo, mas a referência da tensão de modo comum é calculada de forma que o limite não é
Figure imgf000037_0006
ultrapassado. [123] A Figura 11 apresenta uma comparação entre as perdas obtidas com o método convencional e com o método da presente invenção para três pontos de operação distintos, correspondentes às frequências e tensões da segunda porta (5) de 1 Hz e 115 V, 8 Hz e 920 V, e 15 Hz e 1,725 kV, respectivamente, configurando uma estratégia de controle escalar V/F com uma razão de 115 V/Hz. O mesmo modelo de simulação descrito no parágrafo anterior foi utilizado. Um módulo de potência composto por IGBTs e diodos de especificações apropriadas foi escolhido para compor os interruptores bidirecionais em tensão (13) dos SMs do tipo meia-ponte (11) que compõem os braços (2) do MMC CC-CA convencional (1). Modelos das perdas de condução e comutação do IGBT e do diodo que constituem o módulo em conjunto com as formas de onda obtidas por simulação foram utilizados para calcular as perdas apresentadas na Figura 11. [124] Para cada ponto de operação, o método convencional foi testado para três amplitudes diferentes para a referência da tensão de modo comum
Figure imgf000037_0002
calculadas a partir da referência do índice de modulação de braço de acordo com
Figure imgf000037_0003
Figure imgf000037_0001
[125] onde é a amplitude da tensão de modo comum, VC é o valor médio
Figure imgf000037_0005
das tensões nos capacitores (10), e ^^ é o valor de pico da tensão da segunda porta (5). A referência do índice de modulação de braço é um parâmetro de projeto que permite variar a utilizaçã
Figure imgf000037_0004
o da faixa de tensão que um braço (2) pode sintetizar. Quanto mais próximo de 1, maior a amplitude da tensão de modo comum
Figure imgf000038_0001
aplicada, resultando numa menor folga, e numa maior propensão à sobremodulação durante transitórios. Por outro lado, quanto maior a amplitude da tensão de modo comum
Figure imgf000038_0002
, menores as correntes de circulação e, consequentemente, menores também serão as perdas. [126] O valor real, obtido por simulação, do maior índice de modulação MB obtido entre os seis braços (2) do MMC CC-CA convencional (1) é mostrado no eixo horizontal do gráfico apresentado na Figura 11 para cada ponto de operação testado. As ondulações de tensão dos capacitores (10) e as quedas de tensão sobre os indutores (3) aumentam significativamente os valores medidos dos índices de modulação de braço MB quando comparados aos valores de referência
Figure imgf000038_0003
Isto exemplifica uma das dificuldades do método convencional, que é encontrar uma amplitude para a tensão de modo comum
Figure imgf000038_0004
levando-se em consideração o compromisso entre perdas e capacidade de reação a transitórios. [127] O valor de referência
Figure imgf000038_0005
resulta em valores aceitáveis de índice de modulação de MB = 0,94 para o cenário de 1 Hz, MB = 0,96 para o cenário de 8 Hz e MB = 0,95 para o cenário de 15 Hz. Vantajosamente, o método de acordo com a presente invenção sempre resulta no máximo aproveitamento da capacidade de sintetização de tensão do braço, confirmado pelo índice de modulação MB = 1 encontrado em todos os casos em que foi aplicado. Contudo, o método garante que o MMC CC- CA convencional (1) não entrará na região de sobremodulação. [128] Comparando-se as perdas obtidas com o método da presente invenção e as perdas obtidas com o método convencional para
Figure imgf000039_0003
encontra-se que há redução destas em 21,4%, 27,5% e 24,3% para os cenários de 1 Hz, 8 Hz e 15 Hz, respectivamente. [129] Com referência à Figura 12, as formas de onda representadas foram obtidas com um protótipo em escala de um MMC CC-CA convencional (1) configurado para acionar uma máquina de tensão nominal de 380 V e frequência nominal de 60 Hz. Cada braço (2) é composto por cinco SMs do tipo meia- ponte (11) e a primeira porta (4) do MMC CC-CA convencional (1) é conectada a uma fonte de tensão CC de 640 V. Os indutores (3) e os capacitores (10) possuem valores nominais de 1 mH e 2,35 mF, respectivamente. [130] As formas de onda da Figura 12 foram obtidas quando o MMC CC-CA convencional (1) acionava a máquina com uma frequência elétrica de 15 Hz e correntes eficazes de 17 A utilizando o método da presente invenção. As somas das tensões dos capacitores (10), exemplificadas por
Figure imgf000039_0002
no gráfico (a) da Figura 12, são controladas de forma que seus valores médios foram regulados em 640 V e o valor pico a pico de suas ondulações em 25% deste valor. [131] O gráfico (b) da Figura 12 apresenta as correntes da segunda porta (5), à qual a máquina está conectada. As correntes possuem baixa distorção e não são influenciadas pela utilização do método da presente invenção. [132] Os intervalos nos quais não há comutação dos interruptores bidirecionais em tensão (13) resultantes do método da presente invenção podem ser identificados na tensão sintetizada pelo braço mostrada em no gráfico (c) da
Figure imgf000039_0001
Figura 12. Nestes instantes, a tensão é a máxima ou a mínima que o braço (2) consegue gerar.
Figure imgf000040_0002
[133] O gráfico (d) da Figura 12 apresenta a corrente de braço
Figure imgf000040_0001
na qual pode-se verificar a presença das componentes de média frequência utilizadas para o balanço das tensões dos capacitores (10). [134] O gráfico (e) da Figura 12 apresenta a referência da tensão de modo comum
Figure imgf000040_0003
resultante do método de operação proposto. Neste caso, foi utilizada uma frequência fixa de 150 Hz e a derivada de
Figure imgf000040_0004
foi limitada em aproximadamente 10 V/µs através da estratégia apresentada na Figura 9. [135] As perdas obtidas para os pontos de operação referentes às frequências de 5 Hz, 10 Hz e 15 Hz e corrente eficaz de 17 A são apresentadas na Figura 13. Para cada ponto de operação foram testados três valores de referência para o índice de modulação de braço para o método convencional,
Figure imgf000040_0006
e o método da presente invenção. [136] Devido às ondulações de tensão nos capacitores (10) e as quedas de tensão sobre os indutores (3), os valores medidos de índice de modulação apresentados no eixo
Figure imgf000040_0005
horizontal, são maiores que as referências. A maioria dos casos testados nos quais empregou-se o método convencional resultou em sobremodulação. O único valor de referência que não resultou em sobremodulação nos três pontos de operação foi
Figure imgf000040_0007
Quando comparados aos resultados obtidos com o método convencional para este valor, o método da presente invenção apresenta reduções de perdas de 27,3%, 25%, e 12,5% para as frequências de 5 Hz, 10 Hz e 15 Hz, respectivamente. [137] No caso do MMC CC-CA convencional (1), o método de funcionamento de acordo com a presente invenção é indicado, mas não limitado, à operação em baixas frequências. O conversor, nestas condições, operaria empregando o método da presente invenção até uma frequência de transição ft e, a partir desta, o método normal, sem emprego de injeção de tensão de modo comum. A frequência de transição ft é escolhida de forma que a ondulação de tensão nos capacitores (10) resultante da operação normal já seja suficientemente baixa, não requerendo compensação. [138] A Figura 14 apresenta, de forma genérica, como as perdas em um conversor MMC CC-CA convencional (1) devem variar com a frequência para a corrente nominal na segunda porta (5). O método da presente invenção permite que as perdas no conversor sejam reduzidas em toda a faixa de operação em baixa frequência. [139] No caso de MMCs CA-CA, especificamente as topologias matricial (15) ou Hexverter (16), ou ainda o MMC generalizado (17) operando como conversor CA-CA, a necessidade de compensação de ondulação ocorre principalmente quando as frequências das portas (4,5) são próximas. Assim, a frequência de transição ^^௧ define o ponto a partir do qual o conversor opera com o método da presente invenção. Para frequências abaixo de ft, o conversor opera no modo normal, sem mitigação da ondulação de tensão. [140] Considerando que a frequência nominal da segunda porta é a própria frequência da primeira porta, a redução das perdas no conversor devido à utilização do método da presente invenção seria como mostrado na Figura 15. [141] É fornecido também um meio não transitório legível por máquina. O meio pode ser, por exemplo uma memória, uma memória flash, um disco rígido, um disco compacto, ou qualquer outro dispositivo capaz de armazenar instruções por computador. Quando o meio legível da presente modalidade é lido por uma máquina, a máquina é habilitada a realizar o método de controle e operação de um MMC (1, 15, 16, 17) como descrito na presente revelação. [142] Embora a invenção tenha sido amplamente descrita, é óbvio para aqueles versados na técnica que várias alterações e modificações podem ser feitas sem que as referidas alterações não estejam cobertas pelo escopo da invenção. [027] In the case of the matrix AC-AC MMC (15), there are two independent currents in each of the ports (4,5), totaling four independent currents, and four circulation currents. [028] Structures with a reduced number of arms, such as the MMC CA-CA Hexverter (16), can also be obtained. To this end, arms (2) can be removed from the generalized MMC (17) so that at least two arms still result, in series with inductors (3), connecting each terminal of a port (4,5) to at least two terminals of the other port (4,5). [029] The document “Loss optimization of MMC by second-order harmonic circulating current injection” (IEEE Transactions on Power Electronics, 2017) teaches that circulation currents are degrees of freedom that can be exploited to optimize the operation of the MMC (1 , 15, 16, 17), in which circulation currents with a specific shape are used to reduce semiconductor losses in conventional DC-AC MMC (1). [030] As described in the document “Generalized control approach for a class of modular multilevel converter topologies” (IEEE Transactions on Power Electronics, 2017), circulation currents are used to transfer energy between the arms (2), with the aim of balancing the voltages of the capacitors (10). [031] The objective of the MMC (1, 15, 16, 17) is to inject or drain currents into its ports (4,5) in order to transfer power from one to the other. The currents must have a suitable waveform for the application in question, thus, when a port (4,5) is connected to the electrical network or to an alternating current electrical machine, for example, it is desired that the currents be sinusoidal with minimal distortion. [032] Control of the MMC currents is achieved by switching the bidirectional voltage switches (13) that form the SMs, which, depending on their states, on or off, can apply a greater or lesser voltage to the inductors (3), increasing or decreasing the derivative of the current that flows through them and, consequently, increasing or decreasing the derivative of the currents that flow through the ports (4,5) and circulation currents. [033] The scheme used to define how the bidirectional voltage switches (13) are turned on or off is known as modulation. A commonly employed strategy consists of pulse width modulation, in which the relationship between the duration of the time interval in which a bidirectional voltage switch (13) remains on and the total duration of a cycle composed of an on and an off period is defined such that the time-averaged tension generated by an arm approaches a desired arm tension reference value
Figure imgf000011_0001
. [034] The control system of an MMC (1, 15, 16, 17), responsible for regulating the voltages of the capacitors (10) and the port and circulation currents, is mainly composed of sensors capable of measuring these variables and signal processing systems that are based on control algorithms. The control algorithms maintain, through feedback loops, the measured currents and voltages as close as possible to the desired values. The outputs of these algorithms are the arm voltage references
Figure imgf000011_0002
, which will be used by the modulator to define the pulse patterns that the arms (2) must generate through the switching of the bidirectional voltage switches (13). [035] The voltages of all capacitors (10) of the MMC must be controlled so that the voltages on the bidirectional voltage switches (13) remain within acceptable limits. Normally, this is carried out on two different and independently operating levels. [036] The first level is responsible for equalizing the voltages of the capacitors (10) of the SMs within the same arm (2). The maximum instantaneous voltage value that an arm (2) can generate, as well as the minimum value, can only be reached for a single combination of states of the bidirectional voltage switches (13). For all other possible intermediate values of instantaneous arm voltage that can be generated, there is more than one combination for the states of the bidirectional switches in voltage (13) that result in the same voltage. Each different combination of states of the bidirectional voltage switches (13) results in a different set of capacitors (10) that are crossed by the arm current. The capacitors (10) of this set can be charged or discharged, depending on the direction of the arm current and the specific state of the bidirectional voltage switches (13) of your SM (8). For each instantaneous voltage value that must be generated by the arm (2), one can choose the states of the bidirectional voltage switches (13) that bring the voltages of the capacitors (10) closer together, as proposed in “Reduced Switching- Frequency Modulation and Circulating Current Suppression for Modular Multilevel Converters” (IEEE Transactions on Power Delivery, 2011). Thus, the voltages of the capacitors (10) on the same arm (2) tend to remain balanced. [037] The second level is responsible for keeping the sum of the voltages of the capacitors (10) of the arms (2) as close as possible to a reference and with minimal differences between them. [038] The power exchanges necessary to balance the energies stored in the arms (2) and, consequently, the sum of the capacitor voltages (10), can be achieved through the MMC circulation currents as in the strategy proposed in document US 8,144,489 B2. [039] The voltage synthesized by an arm (2) of the MMC (1, 15, 16, 17), disregarding the voltage drops on the inductors (3) is a composition of the voltages present at the ports (4,5) and the common mode voltage
Figure imgf000013_0004
common
Figure imgf000013_0006
is defined as the difference between the average voltage applied to the first port (4) and the average voltage present in the second port (5). For two balanced star systems connected to ports (4,5) of the MMC (1, 15, 16, 17), as shown in Figure 5, the common mode voltage
Figure imgf000013_0005
corresponds to the potential difference between the centers of the two stars. [040] Therefore, the voltage on the arm terminals (2)
Figure imgf000013_0003
is valid, disregarding the voltage drops across the inductors (3):
Figure imgf000013_0001
[041] In the case of the conventional DC-AC MMC (1), the voltage on one of its arms (2) is a composition of a portion
Figure imgf000013_0007
coming from the first port (4), and an AC portion coming from the second port (5), and the common mode voltage
Figure imgf000013_0002
which, according to the circuit equations, is imposed through the average of the arm voltages, i.e.
Figure imgf000014_0002
Figure imgf000014_0001
[042] For the generalized MMC (17), the common mode voltage is also defined by the average of the arm voltages
Figure imgf000014_0003
multiplied by -1, this is where
Figure imgf000014_0005
[043] The common mode voltage
Figure imgf000014_0007
within certain limits, it can be adjusted without interfering with the port currents (4,5) of the MMC (1, 15, 16, 17) or the circulation currents. It is, therefore, an additional degree of freedom that can be used to optimize the functioning of the MMC (1, 15, 16, 17). Ideally, if there are no circulating currents, the current flowing through an arm (2) of the MMC (1, 15, 16, 17) is a composition of the port currents (4,5). For the arm
Figure imgf000014_0004
of the conventional DC-AC MMC (1), for example, the current that passes through it is
Figure imgf000014_0006
[044] In other words, the arm currents are composed of an alternating sinusoidal portion at frequency ω of the second port (5), and a DC component. The product between the terms that make up the voltage and current referring to an arm (2) results in the power absorbed by it. Considering steady-state operation, ideally this power has zero mean. However, it also has sinusoidal components if considered a common mode voltage.
Figure imgf000015_0003
null. [045] It is possible to conclude, through similar analysis, that when the ports (4,5) of the generalized MMC (17) operate with alternating currents of different frequencies,
Figure imgf000015_0002
appear sinusoidal components of power p m of frequencies
Figure imgf000015_0001
In both cases, each of these sinusoidal power components results in an energy component stored in the arm with the same frequency, since:
Figure imgf000015_0008
[046] Figure 6 shows the main waveforms referring to the conventional DC-AC MMC (1) when operating without circulation currents or common mode voltage injection. Figure 6(a) shows the voltages at the terminals of the first port (4) and at the terminals of the second port (5). Figure 6(b) shows the currents that the MMC injects into the port terminals (4,5). Figure 6(c) shows the currents flowing in the arms, while Figure 6(d) shows
Figure imgf000015_0004
the tensions on these. Figure 6(e) shows the ripples of energy stored in the arms
Figure imgf000015_0005
These have a frequency component in
Figure imgf000015_0006
and another in [047] It can be seen, from the analysis of the equation
Figure imgf000015_0007
(1.5), that the amplitudes of energy ripples are inversely proportional to their frequencies. Therefore, low-frequency operation on the first port (4) of the conventional DC-CA MMC (1), or on at least one of the ports (4,5) of the generalized MMC (17), or even with frequencies close to the case of generalized MMC (17), results in larger energy ripples when compared to those resulting from operation at higher and distinct frequencies, in the case of generalized MMC (17). In order for the voltages of the capacitors (10) to remain within values suitable for the operation of the MMC (1, 15, 16, 17), it would be necessary to size the capacitances for the minimum operating frequency of the MMC (1, 15, 16, 17), or for the minimum difference between frequencies, in the case of AC-CA MMCs (15,16,17). Operation with zero frequency, in the case of conventional DC-AC MMC (1), or even equal frequencies, in the case of AC-AC MMCs (15,16,17), would not be possible with the normal method of operation, without currents circulation or common mode voltage injection. These situations can be encountered when MMC (1, 15, 16, 17) is applied to electrical machine drive systems. In the case of the conventional DC-AC MMC (1), the moment of starting would be the most critical in relation to the energy ripple, but any operating point at low speed also implies an increase in the energy ripples. In the case of AC-AC MMCs (15,16), or more generally in (17), operation at the machine's nominal frequency, if this is equal to or close to the network frequency, would also be a critical operation. From an economic point of view, it is not interesting to size the capacitors (10) for low frequency operation, since their capacitances and size would be very large. [048] To try to solve this problem, document WO2009115141 A1 reveals the use of a common mode voltage with a higher frequency than those present in the second port
Figure imgf000016_0001
(5) of the conventional DC-AC MMC (1) to reduce the energy ripple in the capacitors (10). [049] In “Low output frequency operation of the Modular Multi-Level Converter” (IEEE Energy Conversion Congress and Exposition, 2010), it is proposed to use the common mode voltage v CM in conjunction with circulation currents of the same frequency in the MMC Conventional DC-AC (1) to generate an additional power component that, when modulated at the operating frequency of the second port (5), eliminates the low frequency energy components present in the capacitors (10). [050] A similar strategy is found in “A Broad Range of Speed Control of a Permanent Magnet Synchronous Motor Driven by a Modular Multilevel TSBC Converter” (IEEE Transactions on industry applications, vol. 53, no. 4). [051] However, conventional solutions have important limitations. One of the difficulties is calculating the appropriate amplitude for the reference common mode voltage v CM . As described in equation (1.1), the voltage that an arm generates is a function of the gate voltages (4.5) and the common mode voltage v CM . Ideally, v CM should have the largest possible amplitude, so that the amplitude of the circulation currents necessary to transfer the desired amount of power is minimized, thus minimizing voltage losses in bidirectional switches (13). [052] However, the maximum absolute voltage value that an arm (2) can generate is always limited by the sum of the voltages of its capacitors (10). In the case of an arm (2) composed of full bridge SMs (12), both the minimum negative voltage and the maximum positive voltage are limited by the sum capacitor voltages (10). In the case of an arm (2) composed of half-bridge SMs (11), the minimum voltage, in absolute value, is always zero, and the maximum absolute value is always the sum of the voltages of the capacitors (10). The polarity of the voltage that arm (2) generates can be positive or negative, depending on how it is connected to the rest of the circuit. According to the convention adopted in Figure 1, the positive arms (6) always generate positive voltage, while the negative arms (7) always generate negative voltage. [053] Attempting to generate a voltage greater or less than that available through the arm (2) results in overmodulation. When operating in this mode, the voltages synthesized by the MMC (1, 15, 16, 17) are limited to the maximum available voltage, causing distortions in the synthesized voltage patterns and consequently in the port currents (4,5), in addition to causing possible overcurrents. in the arms (2) of the MMC (1, 15, 16, 17) due to the impossibility of precisely controlling the circulation and/or door currents. [054] In steady state, the maximum amplitude of the common mode voltage v CM that the MMC can produce without causing overmodulation can be estimated from the amplitudes of the gate voltages (4,5). However, a certain safety margin must be used to ensure that the arms (2) will not cause overmodulation even in the event of transients in the port voltages and/or in the references that define the operating point of the conventional DC-AC MMC. (1), or even due to the voltage ripple existing in the capacitors (10). [055] Thus, the amplitude of the common mode voltage in the prior art is usually limited to a higher value lower than the maximum possible to try to guarantee the correct functioning of the MMC, that is, to avoid possible operation with overmodulation and the consequent generation of harmonic distortion in the MMC voltages. BRIEF DESCRIPTION OF THE PRESENT INVENTION [056] The invention described here can be applied to MMCs that perform any type of conversion involving alternating current (AC) and/or direct current (DC), that is, MMC DC-DC, MMC CC-AC , MMC AC-DC or MMC AC-AC with any number of phases. [057] The MMC capacitor voltage ripples tend to increase in amplitude when the input frequency approaches the output frequency. It is not possible, for example, for the DC-CA MMC to operate with zero frequency at the AC output. [058] This invention proposes an optimized operating mode that results in a maximized common mode voltage. This reduces the amplitudes of the circulation currents needed to compensate voltage ripples, allowing the MMC to operate over a wide range of frequencies with reduced Joule losses internal to the converter. BRIEF DESCRIPTION OF THE FIGURES [059] The present invention will now be described below with reference to typical embodiments thereof and also with reference to the attached drawings, in which: [060] Figure 1 shows a three-phase DC-CA MMC in the state of technique. [061] Figure 2 shows a matrix CA-CA MMC and a Hexverter CA-CA MMC according to the state of the art. [062] Figure 3 shows the general internal structure of an arm of a MMC. [063] Figure 4 shows a half-bridge SM and a full-bridge SM according to the state of the art. [064] Figure 5 shows the structure of a generalized MMC. [065] Figure 6 shows the main waveforms relating to the operation of the MMC CC-CA. [066] Figure 7 shows a simplified diagram of the control system of a generalized MMC according to the present invention. [067] Figure 8 presents a method of generating the common mode voltage reference for the DC-AC MMC with smoothed transitions in accordance with the present invention. [068] Figure 9 presents a comparison between simulation results obtained for the conventional method and for the method according to the present invention. [069] Figure 10 presents a comparison between the losses obtained by simulation for the conventional method and for the method according to the present invention. [070] Figure 11 shows experimental results of a MMC operating in accordance with the present invention. [071] Figure 12 presents a comparison between the losses measured when the MMC operates with the conventional method and with the method according to the present invention. DETAILED DESCRIPTION OF THE PRESENT INVENTION [072] Specific embodiments of the present disclosure are described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the report descriptive. It should be appreciated that in the development of any actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the specific objectives of the developers, such as compliance with system- and business-related constraints, which may vary from one implementation to another. Furthermore, it should be appreciated that such a development effort may be complex and time-consuming, but would nevertheless be a routine design and manufacturing undertaking for those of ordinary skill having the benefit of this disclosure. [073] The present invention proposes a method of operating the MMC (1, 15, 16, 17) that minimizes the energy ripple in the capacitors (10), allowing operation at low frequencies, in the case of the conventional DC-AC MMC ( 1), or operation with equal or close frequencies on ports (4,5) in the case of AC-CA MMCs (15,16,17). The possibility of operating in an extended frequency range allows the application of the conventional DC-AC MMC (1) in machine drive systems, whose port connected to the machine operates with frequencies that vary from zero, at start-up, to nominal. [074] The method of operation disclosed here is applicable to any MMC whose structure can be defined from the generalized MMC (17), resulting in a common mode voltage v CM maximized at any instant of time and simultaneously ensuring that none of the arms will operate in overmodulation due to the addition of the common mode voltage v CM . In this way, the circulation currents necessary to reduce the voltage ripple of the capacitors (10) are reduced, minimizing losses due to currents. circulation and simultaneously ensuring the proper functioning of the MMC (1, 15, 16, 17) even in severe transients. [075] Advantageously, the present method provides greater efficiency in the operation of the MMC. [076] Another advantage of the present method is the possibility of reducing the size of the MMC due to lower Joule losses. [077] Yet another advantage of the present method is the reduction of interference introduced into the system by MMC reactive losses. [078] Firstly, the operation of the method of the present invention is analyzed when applied to the conventional CC-CA MMC (1), illustrated in Figure 1. The positive arms (6) are composed of half-bridge SMs (11), so that the positive arms are capable of generating only voltages
Figure imgf000022_0002
positive or null. The negative arms (7) are also composed of half-bridge SMs (11), and are connected in such a way that they are capable of generating only negative or zero voltages.
Figure imgf000022_0001
[079] Overmodulation is understood as the condition in which it is not possible for an arm (2) to generate the reference voltage
Figure imgf000022_0003
calculated by the control system (21) due to being outside the voltage range possible to be synthesized by the arm (2). [080] Positive (6) and negative (7) arms can generate any average voltage, within their operating limits, through the use of a pulse width modulator, which generates command signals for the switches (13 ) so that the average value of the arm tension calculated during a switching cycle approaches the reference value
Figure imgf000023_0002
[081] Referring to Figure 7, a conventional CC-CA MMC control system (1) is briefly shown employing an exemplary, that is, non-limiting, implementation of the method of the present invention. The reference signals for the arm voltages without adding the common mode voltage are
Figure imgf000023_0001
calculated by the voltage and current controllers (18) from the measured arm current values
Figure imgf000023_0010
of the sums of the voltages of the measured capacitors (10) and the
Figure imgf000023_0009
reference signals for the sums of capacitor voltages
Figure imgf000023_0004
and the reference signals for the currents in one of the ports. In the example in Figure 7, these will be taken as the currents of the second port (5)
Figure imgf000023_0008
however, the currents from the first port (4) could be taken without departing from the scope of the present invention. [082] Control algorithms are used to calculate what voltages the arms (2) must generate so that the MMC currents and voltages follow their references with low error and reject disturbances. The common mode voltage v CM does not interfere with the MMC arm currents,
Figure imgf000023_0003
but is used by the method of the present invention to reduce the voltage ripple in the capacitors (10). The common mode voltage reference is added to the
Figure imgf000023_0007
references
Figure imgf000023_0005
calculated by the controllers (18) through (19), resulting in arm voltage references. In the event of overmodulation of any arm (2) of the
Figure imgf000023_0006
MMC (1), the most likely consequence is failure to follow reference of door currents (4,5) and/or circulation currents. [083] For a given arm current (2), the greater the absolute value of the voltage that arm (2) generates, the greater the rate at which energy is absorbed or delivered. The present invention proposes a mode of operation in which the conventional CC-CA MMC (1) alternately operates in two distinct operating states: a first operating state and a second operating state. During each of these operating states, half of the arms (2) conduct a larger portion of the port current (4), which, in normal operation without circulating currents, would be divided equally between the two arms that make up a phase. [084] The arms (2) that carry the highest current are commanded to generate the minimum possible voltage that does not result in overmodulation in any arm (2), resulting in no negative interference in the control of port currents (4,5), nor in the control of circulation currents. By synthesizing minimum voltages, energy absorption by these arms (2) is minimized, reducing the energy variation in their capacitors (10). Meanwhile, the arms (2) corresponding to the other half generate the maximum voltage that does not result in overmodulation of any arm (2) of the conventional DC-AC MMC (1) and, therefore, that does not result in harm to the control of any current of conventional MMC CC-CA (1). [085] The voltage and current controllers (18), during each of these operating states, force circulation currents that cause the aforementioned imbalances in the arm currents (2). Thus, while the arms (2) that generate lower voltage and conduct greater current, the other group conducts smaller currents that act to balance the energy stored in their capacitors (10). As these arms generate the highest possible voltage, the circulation currents required to control their energies are minimized. [086] The references used to control the circulation currents are calculated by capacitor voltage controllers (10) based on the measured voltage values and reference values suitable for the operation of the conventional DC-AC MMC (1). [087] In the first operating state, it is desired to minimize the absolute value of the voltages generated by the positive arms (6), and maximize the absolute value of the voltages generated by the negative arms (7). To do this, the common mode voltage v CM must be increased. By increasing v CM , a positive arm (6) can reach the lower limit of its linear operating range (0 V), or a negative arm (7) can reach the upper limit, in absolute value, of its operating range. operation, generating a negative voltage whose absolute value corresponds to the sum of the voltages of all its capacitors (10). The occurrence of one type of limitation or another depends on the values of the references
Figure imgf000025_0001
which do not yet include the common mode voltage calculated by
Figure imgf000025_0002
voltage and current controllers (18), and the sums of voltages of the capacitors (10) of each arm (2), represented by which determine the maximum voltage, in absolute value,
Figure imgf000025_0003
that each arm (2) can generate. [088] In the second operating state, it is desired to minimize the absolute value of the voltages generated by the negative arms (7), and maximize the absolute value of the voltages generated by the positive arms (6). It follows that the common mode voltage v CM must be decreased. By decreasing the common mode voltage v CM , or a negative arm (7) can reach the lower limit, in absolute voltage value, of its linear operating range (0 V) with all bidirectional voltage switches (13 ) of all its half-bridge SMs (11) closed, or a positive arm (6) may reach the upper limit, in absolute values, of its operating range, with all of the upper bidirectional voltage switches (13) of the SM half-bridge (11) closed. [089] According to the present method, an operating mode is provided in which the common mode voltage v CM is calculated for the first and second operating states so that only one arm (2) of the MMC CC-CA is always conventional (1) reaches the lower or upper limit of the voltage range that it can synthesize, defined by zero or the sum of the voltages of all its capacitors (10)
Figure imgf000026_0004
always minimizing, in absolute values, the tensions generated by half of the arms (2) and maximizing the tensions generated by half of the other arms (2). This ensures that smaller circulation currents, calculated by the control system (18), are necessary to regulate the voltages of the capacitors (10) of the arms (2) that are generating higher voltage at values close to their references. v CM calculated from to
Figure imgf000026_0003
according to the present method is added through the adder (19), with opposite sign, to the references calculated by the control system (18),
Figure imgf000026_0002
so that the final references of the arm tensions are given by
Figure imgf000026_0001
[090] In the first operating state, the maximum voltage v CM that would lead to just one positive arm (6) generating the minimum possible voltage (0 V) is
Figure imgf000027_0001
[091] On the other hand, when increasing v CM , there is the possibility of a negative arm (7) reaching the lower limit of voltage that can be synthesized, equal to
Figure imgf000027_0005
whose absolute value corresponds to the sum of all capacitor voltages (10). The maximum value of v CM that would take a single negative arm (7) to the limit is
Figure imgf000027_0002
[092] When combining the two restrictions, it is found that the maximum common mode voltage that leads to only one arm (2) of the conventional DC-AC MMC (1) to synthesize the maximum or minimum possible voltage is
Figure imgf000027_0003
[093] Similarly, it is found that the minimum common mode voltage v CM that takes a positive arm (6) of the conventional DC-AC MMC (1) to the maximum limit of the voltage that can be generated or a negative arm (7) the minimum value, in absolute value, of the voltage that can be generated is worth
Figure imgf000027_0004
[094] During the first operating state, assuming a positive current in phase k of the second port (5) of the MMC conventional DC-AC (1), the controllers (18) will force a circulating current in phase k of the conventional DC-AC MMC (1) in order to increase the current in the positive arm k
Figure imgf000028_0009
(6) and decrease the current in the negative arm
Figure imgf000028_0004
what
Figure imgf000028_0001
in this state it synthesizes maximum tension. The current in the negative arm can have a positive or negative direction,
Figure imgf000028_0002
depending on the relationship between the current in the second port (5) ^^ ^ and the circulation current forced by the controllers (18). Thus, it is possible to control whether the negative arm (7) of the phase ^^ absorbs or supplies energy, and it is possible to control the voltage of its capacitors (10). On the other hand, the positive arm current ^^ (6)
Figure imgf000028_0003
for the condition analyzed, it is always positive, resulting in energy absorption and a consequent increase in the voltages of the capacitors (10) that compose it, although in a minimized way, since the voltages that the arms (2) generate are the minimum possible that guarantee prevent overmodulation from occurring. [095] Therefore, it is necessary to alternate between the first and second operating states so that it is possible to control the voltages of the capacitors (10) of both groups of positive (6) and negative (7) arms. This is symbolized, in Figure 7, by the switch (20), which switches the common mode voltage reference
Figure imgf000028_0008
between the signs
Figure imgf000028_0005
through the signal s c For example, it can be defined that the switch (20) allows the signal to pass
Figure imgf000028_0007
when s c is 1, and
Figure imgf000028_0006
when ^^ ^ is 0. Obviously, this definition is only exemplary and not limiting. Other definitions are possible within the scope of the present invention. [096] With reference to Figure 8, a block diagram of a form of implementation is presented exemplary of the described optimized common mode voltage generation scheme. The adders (22) and (23) together with the blocks that calculate minimum (24) and maximum (25) values implement equations (1.8) and (1.9). The key (20) selects according to the signal
Figure imgf000029_0004
. The frequency with
Figure imgf000029_0001
where s c alternates between 0 and 1 defines the frequency of the common mode voltage v CM . The shape of v CM is approximately rectangular, but with an envelope defined by
Figure imgf000029_0003
It is
Figure imgf000029_0002
In some applications, such as machine drive systems, the high-frequency content of the common mode voltage v CM must be reduced in order to limit the amplitude of the common mode current flowing through the machine, which can cause damage to the bearings. of the machine. [097] According to the method of the present invention, the high frequency content of the common mode voltage v CM can be reduced if the transitions between the values
Figure imgf000029_0005
are carried out less abruptly. Thus, in the transition from the second operating state to the first operating state, the reference signal
Figure imgf000029_0006
can have its value gradually increased until the value of In the transition from the second operating state to the
Figure imgf000029_0007
first operating state, the reference signal
Figure imgf000029_0009
may have its value decreased until the value of
Figure imgf000029_0008
The value of the increment and decrement can be determined in order to limit the absolute value of the maximum derivative, with respect to time, of the common mode voltage v CM . [098] Figure 9 presents an exemplary implementation of the generation with reduced derivatives. Calculation of the maximum common mode voltage value
Figure imgf000029_0010
now also takes into account, in addition to the signs already used in (1.8), signal The signal v tr has the form
Figure imgf000030_0001
Figure imgf000030_0002
triangular and frequency equal to that specified for the common mode voltage v CM . The comparator (26) is responsible for generating the signal s c , which becomes 1 as soon as the triangular sign v tr becomes positive, and 0 as soon as ^^ ௧^ becomes negative. [100] Both at the beginning and at the end of the period in which the conventional CC-AC MMC (1) is in the first operating state, defined by
Figure imgf000030_0014
, the value of
Figure imgf000030_0015
is less than the values of for all applicable,
Figure imgf000030_0003
Figure imgf000030_0016
therefore, the minimum value calculated by (24) will correspond to the value of
Figure imgf000030_0009
Both at the beginning and at the end of the period in which the conventional CC-CA MMC (1) is in the second operating state, defined by
Figure imgf000030_0012
, the value of
Figure imgf000030_0013
is greater than the values of
Figure imgf000030_0004
for all applicable k, therefore, the maximum value calculated by (25) will correspond to the value of v tr . The value of
Figure imgf000030_0005
is defined by
Figure imgf000030_0011
in transitions between the first and second operating states and vice versa. Therefore, the derivative with respect to time during
Figure imgf000030_0006
transitions is defined by the derivative of
Figure imgf000030_0010
The amplitude of can be chosen so that the derivative of
Figure imgf000030_0007
Have a
Figure imgf000030_0008
predetermined value during state transitions. [101] In another non-limiting example, it is possible to reduce the high-frequency content of the common mode voltage v CM by decreasing the frequency with which it switches between the first and second operating states. When the conventional DC-AC MMC (1) operates with smaller currents in the second port (5), the variations in the voltages of the capacitors (10) are also smaller, so that it is possible to increase the durations of the first and second operating states even keeping the voltages of the capacitors (10) within acceptable limits. [102] It is also possible to define when the state should change from 1 to 2 and from 2 to 1 based on the voltages of the capacitors (10). Whenever a tension
Figure imgf000031_0003
reaches a pre-determined maximum or minimum value, the s c signal switches its value, changing the operating state of the conventional CC-CA MMC (1). In this example, the frequency of v CM is variable according to the operating point of the conventional DC-AC MMC (1). [103] All propositions previously presented for the conventional CC-CA MMC (1) can be extended to the CA-CA MMCs (15,16), or, more generally, to the generalized MMC (17). These MMCs can use SMs with the ability to generate positive and negative voltages, such as the full bridge SM (12). Thus, both the maximum and minimum limits of the voltage that can be generated by an arm (2) are defined by the sum of the voltages of the capacitors (10). The maximum common mode voltage v CM that leads to just one arm (2) of the MMC (15, 16, 17) to reach its lower limit of its voltage generating capacity is given by
Figure imgf000031_0001
[104] The minimum common mode voltage v CM that leads to only one arm (2) of the MMC (15,16,17) to reach its upper limit of its voltage generation capacity is given by
Figure imgf000031_0002
[105] It is also possible, in the case of MMC AC-AC converters (15, 16, 17), to employ common mode voltage v CM and currents DC circulation system to transfer power between the arms (2) of the MMC (15, 16, 17). In this case, the proposed technique can still be used, as long as the common mode voltage v CM is maintained at its maximum value v CM max or minimum value v CM min . [106] An important difference in the operation of the MMC (15, 16, 17), according to the present invention, with respect to the conventional CC-CA MMC (1), is the way in which the signals v CM max and v CM min are calculated. The smoothing of transitions, by any method that limits the derivative of the reference common mode voltage, or, more specifically, through
Figure imgf000032_0005
of the method exemplified in Figure 8, and the variable frequency operation described previously, that is, that “define when the state should change from 1 to 2 and from 2 to 1 based on the voltages of the capacitors (10) (... ) whenever a voltage reaches a maximum or minimum value
Figure imgf000032_0004
predetermined, the signal s c switches its value”, are applicable to the MMC (15, 16, 17), as long as
Figure imgf000032_0003
are calculated according to (1.10) and (1.11), respectively. [107] An inherent advantage of the present invention, when applied to any of the MMC (1, 15, 16), or more generally, to the generalized MMC (17), is the greater ability to maintain controlled currents during abrupt voltage transients of the doors (4,5) or the references of the door chains. [108] In conventional methods, the amplitude of the common mode voltage reference is calculated so that there is a certain pre-set margin.
Figure imgf000032_0002
defined between the maximum and minimum values of the arm tension references
Figure imgf000032_0001
and the voltage limits that the arms (2) can generate. Therefore, there is still some slack for controllers to act (18) of currents in case of abrupt transients. In the case of very rapid variations and large amplitudes in port voltages (4, 5) or current references, the arm voltage references that the controllers (18) calculate, when combined
Figure imgf000033_0002
with common mode voltage reference
Figure imgf000033_0001
they can exceed the voltage limits that the arms (2) can synthesize, resulting in distortions in the port (4, 5) and circulation currents. [109] The smaller the amplitude of the common mode voltage reference, the further away from its voltage limits
Figure imgf000033_0003
the arms (2) will operate, making the operation of the MMC (1, 15, 16, 17) more resilient. On the other hand, the greater the amplitudes of the circulation currents necessary to control the sums of capacitor voltages, resulting in greater losses.
Figure imgf000033_0004
[110] In the present invention, advantageously, the common mode voltage reference is calculated so as to
Figure imgf000033_0006
the maximum voltage range that the arms (2) can generate is used, but without ever exceeding the voltage limits that the arms (2) can synthesize, as long as the references do not already exceed them. This results in the technical effect
Figure imgf000033_0005
lower circulation currents, resulting in lower losses, and at the same time an operation that is more resilient to fast transients in the port voltages (4.5) and current references. [111] The losses in the MMC (1, 15, 16, 17) are even smaller when the present method is used due to the lower switching frequency of the bidirectional voltage switches (13), since always (or most of the time , if smoothing of the common mode voltage v CM is employed) one of arms (2) of the MMC (1, 15, 16, 17) generate maximum or minimum voltage, a condition in which no bidirectional voltage switch (13) switches, reducing switching losses. [112] The method of maximizing the common mode voltage v CM proposed in this description can only be used when it is necessary to reduce the energy ripples of the capacitors (10). When the ripple is naturally small, for example, due to low current or high frequency operation, the MMC (1, 15, 16, 17) can be operated without injection of the proposed maximized common mode voltage v CM . [113] On the other hand, you can size the capacitors (10) of the MMC (1, 15, 16, 17) so that always, or from a minimum value of current and/or maximum frequency on a port (4, 5), it is necessary to compensate for the energy ripples of the capacitors (10) according to the invention. In this case, it would be possible to use capacitors (10) with smaller capacitance and smaller volume in applications in which the MMC (1, 15, 16, 17) always operates at high frequency, such as in rectifiers connected to the network. [114] The present invention can also be used in conversion systems that employ more than one MMC (1, 15, 16, 17), such as, for example, in a configuration in which a first port (4, 5) of a first MMC (1, 15, 16, 17) is connected to a first port (4, 5) of a second MMC (1, 15, 16, 17), the second port of the first MMC (4, 5) is connected to the network and the second port (4, 5) of the second MMC (1, 15, 16, 17) is connected to a load (14), for example, an AC machine. In this case, the proposed method can be used only in the second MMC (1, 15, 16, 17), which feeds the load (14), allowing its operation at low frequency, or also in the first MMC (1, 15, 16, 17), which is connected to the network, allowing the use of capacitors (10) with lower capacitance and smaller volume. EXAMPLES OF EMBODIMENT OF THE INVENTION [115] Two examples of embodiment of the invention are presented. These examples aim to illustrate the functioning and application of the method presented here. Therefore, the following examples should not be taken as limiting. [116] The first example refers to the simulation of a medium voltage DC-AC conversion system. The second example refers to the experimentation of a low voltage machine drive system. Both employ the conventional DC-CA MMC (1) with half-bridge SM (11). [117] Turning to Figure 10, a comparison is presented between the waveforms obtained with a conventional operating method employing a common mode voltage v CM with constant amplitude and the waveforms resulting from the present invention described above. Both methods were tested on a conventional CC-CA MMC (1) through simulation. A scenario equivalent to a 6.9 kV medium voltage machine drive system was chosen. [118] Waveforms (a), (b) and (c) are the conventional method waveforms, while waveforms (d), (e) and (f) are waveforms referring to the conventional method. revealed here of the system operating in steady state. [119] The simulated system has 10 SMs per arm, an inductor (3) of 1 mH and capacitors (10) of 2.7 mF. A voltage of 11.5 kV is applied to the first port (4) of the DC-CA MMC conventional (1) and the second port (5) feeds a load with an effective line voltage of 1.725 kV and a frequency of 15 Hz. [120] The common mode voltage v CM resulting from the method of the present invention, shown in (d) , has an amplitude that varies over time, but on average it has a higher amplitude than that of the conventional method, presented in (a). As a consequence, the amplitudes and effective values of the circulation currents necessary to control the voltages of the capacitors (10) are smaller, reducing losses. This can be seen when comparing the arm current ^^ ^^,^ obtained with the conventional method, presented in (b), and with the method of the present invention, presented in (e). [121] References have a sinusoidal shape and their
Figure imgf000036_0001
amplitudes and phases are calculated, for both methods, in order to minimize the amplitudes of the resulting circulation currents. Graphs (c) and (f) show the sums of voltages of the capacitors (10) referring to the arm
Figure imgf000036_0002
positive (1,1), as well as the tensions on these,
Figure imgf000036_0003
It is found that the limit of the voltage synthesis capacity of the arm (1,1) is almost reached in the time interval around 7.04 s in the conventional method (c). [122] A disturbance occurring in the intervals in which the voltage limits of the arms (2) are approached can easily lead to the overmodulation region, resulting in distortion of the port (4, 5) and circulation currents. In the method of the present invention, the limit is reached during various time intervals, but the voltage reference is common mode is calculated so that the limit is not
Figure imgf000037_0006
exceeded. [123] Figure 11 presents a comparison between the losses obtained with the conventional method and the method of the present invention for three different operating points, corresponding to the frequencies and voltages of the second port (5) of 1 Hz and 115 V, 8 Hz and 920 V, and 15 Hz and 1.725 kV, respectively, configuring a V/F scalar control strategy with a ratio of 115 V/Hz. The same simulation model described in the previous paragraph was used. A power module composed of IGBTs and diodes of appropriate specifications was chosen to compose the bidirectional voltage switches (13) of the half-bridge type SMs (11) that make up the arms (2) of the conventional DC-AC MMC (1) . Models of the conduction and switching losses of the IGBT and the diode that constitute the module together with the waveforms obtained by simulation were used to calculate the losses presented in Figure 11. [124] For each operating point, the conventional method was tested for three different amplitudes for common mode voltage reference
Figure imgf000037_0002
calculated from the arm modulation index reference according to
Figure imgf000037_0003
Figure imgf000037_0001
[125] where is the amplitude of the common mode voltage, VC is the average value
Figure imgf000037_0005
of the voltages in the capacitors (10), and ^^ is the peak value of the voltage of the second port (5). The arm modulation index reference is a design parameter that allows you to vary the use of the arm.
Figure imgf000037_0004
the voltage range that a arm (2) can synthesize. The closer to 1, the greater the amplitude of the common mode voltage
Figure imgf000038_0001
applied, resulting in less backlash and a greater propensity for overmodulation during transients. On the other hand, the greater the amplitude of the common mode voltage
Figure imgf000038_0002
, the lower the circulation currents and, consequently, the lower the losses. [126] The real value, obtained by simulation, of the highest modulation index M B obtained among the six arms (2) of the conventional CC-CA MMC (1) is shown on the horizontal axis of the graph presented in Figure 11 for each point of operation tested. The voltage ripples of the capacitors (10) and the voltage drops across the inductors (3) significantly increase the measured values of the MB arm modulation indices when compared to the reference values
Figure imgf000038_0003
This exemplifies one of the difficulties of the conventional method, which is finding an amplitude for the common mode voltage
Figure imgf000038_0004
taking into account the compromise between losses and capacity to react to transients. [127] The reference value
Figure imgf000038_0005
results in acceptable modulation index values of M B = 0.94 for the 1 Hz scenario, M B = 0.96 for the 8 Hz scenario and M B = 0.95 for the 15 Hz scenario. Advantageously, The method according to the present invention always results in maximum use of the arm's voltage synthesis capacity, confirmed by the modulation index M B = 1 found in all cases in which it was applied. However, the method guarantees that the conventional DC-AC MMC (1) will not enter the overmodulation region. [128] Comparing the losses obtained with the method of the present invention and the losses obtained with the conventional method for
Figure imgf000039_0003
it is found that there is a reduction in these by 21.4%, 27.5% and 24.3% for the 1 Hz, 8 Hz and 15 Hz scenarios, respectively. [129] With reference to Figure 12, the waveforms represented were obtained with a scale prototype of a conventional DC-AC MMC (1) configured to drive a machine with a nominal voltage of 380 V and a nominal frequency of 60 Hz. Each arm (2) is composed of five half-bridge SMs (11) and the first port (4) of the conventional DC-AC MMC (1) is connected to a 640 V DC voltage source. and the capacitors (10) have nominal values of 1 mH and 2.35 mF, respectively. [130] The waveforms in Figure 12 were obtained when the conventional DC-AC MMC (1) drove the machine with an electrical frequency of 15 Hz and effective currents of 17 A using the method of the present invention. The sums of capacitor voltages (10), exemplified by
Figure imgf000039_0002
in graph (a) of Figure 12, they are controlled so that their average values were regulated at 640 V and the peak-to-peak value of their ripples at 25% of this value. [131] Graph (b) in Figure 12 shows the currents of the second port (5), to which the machine is connected. The currents have low distortion and are not influenced by the use of the method of the present invention. [132] The intervals in which there is no switching of the voltage bidirectional switches (13) resulting from the method of the present invention can be identified in the voltage synthesized by the arm shown in graph (c) of
Figure imgf000039_0001
Figure 12. At these moments, the tension is the maximum or minimum that the arm (2) can generate.
Figure imgf000040_0002
[133] Graph (d) of Figure 12 shows the arm current
Figure imgf000040_0001
in which the presence of the medium frequency components used to balance the voltages of the capacitors (10) can be verified. [134] Graph (e) of Figure 12 presents the common mode voltage reference
Figure imgf000040_0003
resulting from the proposed operating method. In this case, a fixed frequency of 150 Hz was used and the derivative of
Figure imgf000040_0004
was limited to approximately 10 V/µs through the strategy presented in Figure 9. [135] The losses obtained for the operating points referring to frequencies of 5 Hz, 10 Hz and 15 Hz and effective current of 17 A are presented in Figure 13 For each operating point, three reference values for the arm modulation index for the conventional method were tested,
Figure imgf000040_0006
and the method of the present invention. [136] Due to the voltage ripples in the capacitors (10) and the voltage drops over the inductors (3), the measured modulation index values presented on the axis
Figure imgf000040_0005
horizontal, are larger than the references. Most of the cases tested in which the conventional method was used resulted in overmodulation. The only reference value that did not result in overmodulation at all three operating points was
Figure imgf000040_0007
When compared to the results obtained with the conventional method for this value, the method of the present invention presents loss reductions of 27.3%, 25%, and 12.5% for frequencies of 5 Hz, 10 Hz and 15 Hz, respectively. . [137] In the case of the conventional CC-CA MMC (1), the operating method according to the present invention is Suitable for, but not limited to, operation at low frequencies. The converter, under these conditions, would operate using the method of the present invention up to a transition frequency f t and, from there, the normal method, without using common mode voltage injection. The transition frequency f t is chosen so that the voltage ripple in the capacitors (10) resulting from normal operation is already low enough, not requiring compensation. [138] Figure 14 shows, in a generic way, how the losses in a conventional MMC DC-AC converter (1) must vary with frequency for the nominal current in the second port (5). The method of the present invention allows losses in the converter to be reduced throughout the low frequency operating range. [139] In the case of AC-AC MMCs, specifically the matrix (15) or Hexverter (16) topologies, or even the generalized MMC (17) operating as an AC-AC converter, the need for ripple compensation occurs mainly when the frequencies of ports (4,5) are close. Thus, the transition frequency ^^ ௧ defines the point from which the converter operates with the method of the present invention. For frequencies below f t , the converter operates in normal mode, without voltage ripple mitigation. [140] Considering that the nominal frequency of the second port is the frequency of the first port itself, the reduction in losses in the converter due to the use of the method of the present invention would be as shown in Figure 15. [141] A non-transient medium is also provided machine readable. The medium may be, for example, a memory, a flash memory, a hard disk, a compact disk, or any other device capable of storing computer instructions. When the readable medium of the present embodiment is read by a machine, the machine is enabled to perform the method of controlling and operating a MMC (1, 15, 16, 17) as described in the present disclosure. [142] Although the invention has been extensively described, it is obvious to those skilled in the art that various changes and modifications can be made without said changes falling within the scope of the invention.

Claims

Reivindicações 1. Método para operar um MMC, o MMC compreendendo: uma primeira porta (4) e uma segunda porta (5), cada porta compreendendo um conjunto de pelo menos dois terminais do MMC para conexão externa, pelo menos quatro cadeias de submódulos, SMs, (2) cada uma contendo pelo menos um SM (8), cada SM contendo dois terminais do SM, um indutor (3) em série com cada cadeia de SMs, em que cada terminal do MMC de uma dentre a primeira porta (4) e a segunda porta (5) é conectado a pelo menos outros dois terminais do MMC da outra dentre a primeira porta (4) e a segunda porta (5) através de uma conexão série entre uma referida cadeia de SMs (2) e seu referido respectivo indutor (3), em que cada SM possui um circuito de potência sendo composto por: um ou mais capacitores (10), e um arranjo de interruptores (9) conectando seletivamente: a) um terminal do SM ao outro terminal do SM; ou b) um capacitor dos referidos um ou mais capacitores aos terminais do SM em apenas um sentido, ou nos dois sentidos possíveis; ou c) um ou mais capacitores dos referidos um ou mais capacitores aos terminais do SM em série, paralelo ou em uma combinação série e paralelo; um sistema de controle compreendendo: um sistema de aquisição de correntes e tensões, e um sistema digital capaz de calcular algoritmos de controle para manter reguladas correntes e tensões do MMC através do chaveamento de cada arranjo de interruptores (9) de cada SM, o método caracterizado pelo fato de que compreende as etapas de: durante um primeiro estado de operação, controlar, pelo sistema de controle, o arranjo de interruptores (9) de cada SM de forma a sintetizar a máxima tensão de modo comum, vCM max, possível que resulta em apenas uma cadeia de SMs atingindo o limite máximo ou mínimo da sua capacidade de sintetizar tensão, e durante um segundo estado de operação, controlar, pelo sistema de controle, o arranjo de interruptores (9) de cada SM de forma a sintetizar a mínima tensão de modo comum, vCM min, possível que resulta em apenas uma cadeia de SMs atingindo o limite máximo ou mínimo de sua capacidade de sintetizar tensão, e alternar, pelo sistema de controle, entre o primeiro e o segundo estado de operação, em que durante o primeiro e o segundo estados de operação há exatamente uma cadeia de SMs (2) sintetizando a máxima tensão capaz de ser sintetizada ou há exatamente uma cadeia de SMs (2) sintetizando a mínima tensão capaz de ser sintetizada. Claims 1. Method for operating an MMC, the MMC comprising: a first port (4) and a second port (5), each port comprising a set of at least two terminals of the MMC for external connection, at least four chains of submodules, SMs, (2) each containing at least one SM (8), each SM containing two terminals of the SM, an inductor (3) in series with each chain of SMs, wherein each terminal of the MMC is one of the first port ( 4) and the second port (5) is connected to at least two other MMC terminals of the other of the first port (4) and the second port (5) through a series connection between a said chain of SMs (2) and its respective inductor (3), in which each SM has a power circuit consisting of: one or more capacitors (10), and an arrangement of switches (9) selectively connecting: a) one terminal of the SM to the other terminal of the SM; or b) a capacitor of said one or more capacitors to the terminals of the SM in only one direction, or in both possible directions; or c) one or more capacitors of said one or more capacitors to the terminals of the SM in series, parallel or in a series and parallel combination; a control system comprising: a current and voltage acquisition system, and a digital system capable of calculating control algorithms to maintain MMC currents and voltages regulated through the switching of each switch arrangement (9) of each SM, the method characterized by the fact that it comprises the steps of: during a first state of operation, controlling, by the control system, the arrangement of switches (9) of each SM in order to synthesize the maximum common mode voltage, v CM max , possibly resulting in only one chain of SMs reaching the maximum or minimum limit of its capacity to synthesize voltage, and during a second state of operation, controlling, by the control system, the arrangement of switches (9) of each SM in a way to synthesize the minimum common mode voltage, v CM min , possible that results in just one chain of SMs reaching the maximum or minimum limit of their ability to synthesize voltage, and switching, by the control system, between the first and second states of operation, in which during the first and second operating states there is exactly one chain of SMs (2) synthesizing the maximum voltage capable of being synthesized or there is exactly one chain of SMs (2) synthesizing the minimum voltage capable of being synthesized.
2. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por a transição entre o valor de tensão de modo comum máxima gerada no primeiro estado de operação e o valor mínimo de tensão de modo comum gerada no segundo estado de operação, e vice-versa, ser feita de maneira suavizada, durante a qual os arranjos de interruptores (9) comutam de modo que a tensão de modo comum, vCM, do MMC tem uma derivada com relação ao tempo menor que um valor pré-determinado. 2. Method for operating an MMC, according to claim 1, characterized by the transition between the maximum common mode voltage value generated in the first operating state and the minimum common mode voltage value generated in the second operating state, and vice versa, be done in a smoothed manner, during which the switch arrays (9) switch so that the common mode voltage, v CM , of the MMC has a derivative with respect to time less than a predetermined value .
3. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por alternar entre o primeiro e o segundo estados de operação mediante uma frequência fixa. 3. Method for operating an MMC, according to claim 1, characterized by alternating between the first and second operating states at a fixed frequency.
4. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por alternar entre o primeiro e o segundo estados de operação mediante uma frequência variável. 4. Method for operating an MMC, according to claim 1, characterized by alternating between the first and second operating states at a variable frequency.
5. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por o MMC ser configurado para alternar entre o primeiro e o segundo estados de operação somente quando a tensão de qualquer um dos capacitores (10) dos SMs (8) ou a combinação de tensões dos capacitores (10) dos SMs (8) atingir um valor máximo ou mínimo, em que o valor máximo e o valor mínimo são definidos pelos algoritmos do sistema de controle. 5. Method for operating an MMC, according to claim 1, characterized in that the MMC is configured to switch between the first and second operating states only when the voltage of any of the capacitors (10) of the SMs (8) or the combination of voltages of the capacitors (10) of the SMs (8) reaches a maximum or minimum value, where the maximum value and minimum value are defined by the control system algorithms.
6. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por o MMC ser configurado para forçar correntes de circulação, que fluem internamente ao MMC, para minimizar a ondulação de tensão sobre os capacitores (10) dos SMs (8). 6. Method for operating an MMC, according to claim 1, characterized in that the MMC is configured to force circulating currents, which flow internally to the MMC, to minimize voltage ripple over the capacitors (10) of the SMs (8) .
7. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por ser empregado apenas quando se fizer necessária a redução das ondulações de energia dos capacitores (10), e quando a ondulação é naturalmente reduzida, o MMC opera sem geração de tensão de modo comum, vCM, maximizada. 7. Method for operating an MMC, according to claim 1, characterized in that it is used only when it is necessary to reduce the energy ripples of the capacitors (10), and when the ripple is naturally reduced, the MMC operates without generating common mode voltage, v CM , maximized.
8. Método para operar um conversor MMC, de acordo com a reivindicação 1, caracterizado por uma das portas (4, 5) do MMC estar conectada a uma porta de um segundo MMC, em que o segundo MMC é opcionalmente capacitado para executar o método como definido na reivindicação 1. 8. Method for operating an MMC converter, according to claim 1, characterized in that one of the ports (4, 5) of the MMC is connected to a port of a second MMC, wherein the second MMC is optionally enabled to perform the method as defined in claim 1.
9. Método para operar um MMC, de acordo com a reivindicação 1, caracterizado por um dos estados de operação ter duração de tempo nula, de modo que sempre seja obtida a máxima tensão de modo comum, vCM max, ou a mínima tensão de modo comum, vCM min, que resulte em apenas uma cadeia de SMs Ĩ2) atingindo o limite máximo ou mínimo de sua capacidade de sintetizar tensão. 9. Method for operating an MMC, according to claim 1, characterized in that one of the operating states has a zero time duration, so that the maximum common mode voltage, v CM max , or the minimum common mode voltage is always obtained. common mode, v CM min , which results in just one chain of SMs Ĩ2) reaching the maximum or minimum limit of its ability to synthesize tension.
10. Meio não transitório legível por máquina compreendendo instruções, caracterizado por as instruções, quando lidas por uma máquina, fazem com que a máquina execute o método como definido em qualquer uma das reivindicações 1 a 9. 10. Non-transitory machine-readable medium comprising instructions, characterized in that the instructions, when read by a machine, cause the machine to perform the method as defined in any one of claims 1 to 9.
PCT/BR2022/050190 2022-06-01 2022-06-01 Modulation method for operating an mmc to maximise common mode voltage, reducing circulating currents, and machine-readable medium WO2023230679A1 (en)

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Publication number Priority date Publication date Assignee Title
US20130279211A1 (en) * 2010-10-27 2013-10-24 Alstom Technology Ltd Modular Multilevel Converter
EP2677653A1 (en) * 2012-06-19 2013-12-25 Siemens Aktiengesellschaft Modular multilevel converter
US20140092661A1 (en) * 2012-09-28 2014-04-03 General Electric Company Multilevel converter system

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Publication number Priority date Publication date Assignee Title
US20130279211A1 (en) * 2010-10-27 2013-10-24 Alstom Technology Ltd Modular Multilevel Converter
EP2677653A1 (en) * 2012-06-19 2013-12-25 Siemens Aktiengesellschaft Modular multilevel converter
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