CN113113920B - Dynamic oscillation suppression method based on modular multilevel direct-current transformer topology - Google Patents
Dynamic oscillation suppression method based on modular multilevel direct-current transformer topology Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
- H02J3/241—The oscillation concerning frequency
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- 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
- H02M7/487—Neutral point clamped inverters
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- 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
- H02M7/5387—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 in a bridge configuration
- H02M7/53871—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 in a bridge configuration with automatic control of output voltage or current
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- 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
- H02M7/539—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 with automatic control of output wave form or frequency
- H02M7/5395—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 with automatic control of output wave form or frequency by pulse-width modulation
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]
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Abstract
The application discloses a dynamic oscillation suppression method based on a modularized multi-level direct current transformer topology. The method introduces oscillation suppression angles, the switching-on time of two continuous modules of an upper bridge arm or a lower bridge arm in each half sub-module switching period is correspondingly adjusted under the action of the oscillation suppression angles (the switching signals are switched on in advance or switched off in a delayed manner when the oscillation suppression angles are larger than zero, and the switching signals are switched off in advance or switched on in a delayed manner when the oscillation suppression angles are smaller than zero), and pulse voltages generated in bridge arm inductors are generated by the simultaneous switching-on or simultaneous switching-off of sub-modules at corresponding positions of the upper and lower sub-bridge arms, so that the circulation change trend is controlled. The application can lead the loop current to track the instruction value rapidly by adjusting the oscillation suppression angle through the loop current closed loop, eliminates oscillation generated by insufficient damping of the modularized multi-level direct current transformer topology in the load abrupt change process, and improves the system stability.
Description
Technical Field
The application belongs to the technical field of high-voltage high-power electronics, and mainly relates to a dynamic oscillation suppression method based on a modular multilevel direct-current transformer topology.
Background
The series structure of the submodule capacitor C, the bridge arm inductance L and the parasitic resistor R in the modularized multi-level direct current transformer can cause RLC series resonance, and the specific process is as follows: the sub-module capacitor charges the bridge arm inductor and generates magnetic energy stored in the inductance core; after a period of time, the bridge arm inductance charges the capacitor in turn, converting the magnetic energy into electric energy, and so on. If parasitic resistance in the bridge arm inductance is ignored, energy loss is not generated in the magnetic energy-electric energy repeated conversion process, and continuous constant-amplitude damping oscillation phenomenon is generated in capacitor voltage and circulation. However, the parasitic resistance in the actual inductance cannot be ignored, and the process of magnetic energy-electric energy alternation generates energy loss in the parasitic resistance, so that under-damped oscillation with amplitude decaying with time is generated in capacitor voltage and circulation. In this case, if the direct current side voltage or the transmission power command is changed, the dynamic process may exacerbate the under-damped oscillations in the circulating current and the capacitor voltage, severely threatening the stable operation of the system.
Disclosure of Invention
The application aims to: aiming at the problems that RLC series resonance exists in a modularized multi-level direct current transformer, under-damped oscillation is generated under the load/power abrupt change working condition, the running stability of a system is affected and the like, the application provides a dynamic oscillation suppression method based on the modularized multi-level direct current transformer topology.
The technical scheme is as follows: the application discloses a dynamic oscillation suppression method based on a modularized multi-level direct current transformer topology, wherein the topology comprises two groups of MMC bridge arms, each group of MMC bridge arms respectively comprises an upper sub-bridge arm and a lower sub-bridge arm, each upper sub-bridge arm and each lower sub-bridge arm respectively comprises N sub-modules which are connected in series, and N is a positive integer. The dynamic oscillation suppression method comprises the following steps:
(1) A closed-loop control system is constructed by taking the circulation between the upper and lower sub-bridge arms of each group of MMC bridge arms as a controlled quantity and taking an oscillation suppression angle as a control quantity, wherein the oscillation suppression angle is determined by the difference between the actual value and the given value of the circulation;
(2) Constructing a modularized multi-level direct current transformer state space average model by taking submodule capacitance and circulation as state quantities, carrying out small signal analysis, simultaneously considering the dynamic state of an oscillation suppression angle, deriving a control-output transfer function of the closed loop control system under the small signal model through Laplacian transformation, solving a characteristic root of the closed loop control system according to the control-output transfer function, and showing a damping ratio; the damping ratio is made to be critical damping 1, and the gain of the closed-loop controller under the condition of optimal damping compensation is obtained;
(3) Calculating a corresponding oscillation suppression angle according to the obtained closed-loop controller gain to be used as the optimal oscillation suppression angle;
(4) And controlling the switch of each sub-module of the two groups of MMC bridge arms by taking the optimal oscillation suppression angle as a control quantity, thereby controlling the change of the circulation.
Further, in step (1), the given value i of the circulating current c * ma The input power for the modular multi-level direct current transformer topology is equal to the output workCirculation at rate; wherein the input power is equal to the product of the circulating current and the topological direct current side voltage, and the output power is equal to the square of the topological output voltage divided by the output resistance.
Further, in the step (2), the control-output transfer function is a polynomial obtained by taking the oscillation suppression angle as a denominator and the circulation as a numerator; the characteristic root of the closed-loop control system is a pair of conjugate complex roots and is related to the damping ratio xi; the damping ratio xi, the number N of submodules and the bridge arm self-coupling inductance L s Inductance L coupled with bridge arm m Sum, submodule capacitance C, controller gain k pi All related.
Further, the control-output transfer function is expressed as:
wherein ,
wherein ,represents the estimated value of circulation>Represents an oscillation suppression angle estimation value, s represents the Laplacian, U ca_sum Representing the sum of all sub-module capacitor voltages in a group of MMC bridge arms, I cma Represents circulation, R s Parasitic resistance, delta, representing bridge arm inductance d Representing the static operating point of the oscillation suppression angle.
The damping ratio is expressed as:
further, the step (4) specifically includes: in the upper and lower sub-bridge arms of the two groups of MMC bridge arms, the sub-modules are ordered, one sub-module is sequentially selected from the upper and lower sub-bridge arms of the two groups of MMC bridge arms according to the ordering in each half sub-module switching period, two groups of sub-module pairs are formed, and the optimal oscillation suppression angle delta is formed d ' control selected pairs of sub-modules as control variables such that the pulse edges of selected sub-modules are applied with the optimal oscillation suppression angle delta d ' the pulse edges of the remaining sub-modules remain unchanged.
Further, in the step (4), the optimal oscillation suppression angle δ d ' control selected pairs of sub-modules as control variables such that the pulse edges of selected sub-modules are applied with the optimal oscillation suppression angle delta d ' specifically, it includes: when delta d When' is negative, the selected sub-module is turned off and delta based on 50% square wave signal at falling edge delay d ' same angle, leading on and delta in advance at rising edge d ' same angle, thereby generating a magnitude U in the bridge arm inductance voltage sub ＝U ca_sum 16, duty cycle of 2δ d A positive pulse voltage of'/pi, and a circulation rises; wherein U is ca_sum Representing the sum of all sub-module capacitor voltages in a group of MMC bridge arms; when delta d ' positive, so that the selected submodule is turned on and delta at rising edge delay based on 50% square wave signal d ' same angle, early turn-off and delta at falling edge d ' same angle, thereby generating a magnitude U in the bridge arm inductance voltage sub And a duty cycle of 2δ d The negative pulse voltage of'/pi, the circulating current drops.
Working principle: the circulation is subjected to closed loop control to obtain an optimal oscillation suppression angle of control quantity, the optimal oscillation suppression angle acts on the pulse edges of the switch signals of the sub-modules of the upper and lower sub-bridge arms to form an area where the upper and lower bridge arms are simultaneously turned on or simultaneously turned off, and pulse voltage with positive or negative amplitude is generated in the bridge arm voltage, so that the circulation change trend is controlled, the command value is tracked rapidly in a dynamic state, and the purpose of suppressing oscillation is achieved.
The beneficial effects are that: compared with the prior art, the control quantity oscillation suppression angle in the circulation closed loop system acts on the rising edge or the falling edge of a group of 50% duty ratio switch pairs in the upper and lower sub-bridge arms respectively, the on and off moments of the switch pulse are adjusted, and the problems that the inductance voltage stress is too high, the primary side voltage utilization rate of the transformer is reduced, the switching loss is too high caused by the fact that the oscillation suppression angle acts on all sub-modules of the upper and lower sub-bridge arms simultaneously are avoided.
Drawings
FIG. 1 is a modular multilevel DC transformer topology;
FIG. 2 is a block diagram of a closed loop control loop;
FIG. 3 shows the damping ratio ζ, the proportional controller gain k under loop closed-loop control pi And oscillation suppression angle static operating point delta d Is a relationship diagram of (1);
FIGS. 4 (a) and 4 (b) are respectively the values of positive (2δ) for the optimal oscillation suppression angle under square-wave like modulation d '<θ) and bridge arm module conduction state diagram;
FIGS. 5 (a) and 5 (b) are respectively the values of positive (delta) for the optimal oscillation suppression angle under square-wave like modulation d A switching timing diagram and a bridge arm module conduction state diagram when' > (N-1) theta);
fig. 6 (a), 6 (b), 6 (c) and 6 (d) are respectively dynamic response characteristics of the capacitance voltage, the loop current, the bridge arm inductance voltage and the output voltage of the submodule of the MMDCT system without the dynamic oscillation suppression method of the present application;
FIG. 7 is a waveform of a dynamic simulation of the variable of an MMDCT system using the dynamic oscillation suppression method of the present application during a load bump;
FIG. 8 is a waveform of a dynamic simulation of the variable of an MMDCT system using the dynamic oscillation suppression method of the present application during load shedding;
FIG. 9 is a waveform of a dynamic simulation of oscillation suppression angle and circulating current for five switching cycles after load shedding using the dynamic oscillation suppression method of the present application;
FIG. 10 is a waveform of a dynamic simulation of oscillation suppression angle and circulating current for five switching cycles after a sudden load increase using the dynamic oscillation suppression method of the present application;
fig. 11 shows switching signals S of arm 1 and arm 2 when the oscillation suppression angle is negative p1j and Sp2j Bridge arm voltage u 1 and u2 Bridge arm inductance voltage u La Circulation i cma Bridge arm midpoint voltage u aN Is a timing chart of (a).
Detailed Description
The modular multilevel direct current transformer topology used in the application is shown in figure 1. The primary side of the topology comprises two groups of MMC bridge arms, namely a bridge arm group a and a bridge arm group b. Both ends of the bridge arm group a and the bridge arm group b are connected with the high-voltage direct-current side voltage U dc The secondary side full bridge structure is used for providing a low-voltage direct current port, and the primary side and the secondary side are coupled through an intermediate frequency transformer. Bridge arm group a and bridge arm group b each include two upper and lower bridge arms (i.e., bridge arm 1 and bridge arm 2 in bridge arm a, and bridge arm 3 and bridge arm 4 in bridge arm b) in series. Each of the sub-bridge arms 1 to 4 comprises N cascaded half-bridge sub-modules, and the upper sub-bridge arm and the lower sub-bridge arm are self-coupled with each other through respective bridge arm self-coupling inductance L s And the two groups of bridge arms are respectively led out of ports a and b from the middle point of the self-coupling inductor and serve as primary side high-frequency alternating current input ports of the medium-voltage transformer. Wherein the port a is connected with the leakage inductance L of the transformer lk Is connected to an intermediate frequency transformer. Leakage inductance L of transformer lk The method is used for exchanging primary and secondary side power. In addition, the upper and lower sub-bridge arms of each group of MMC bridge arms are equivalently provided with mutual coupling inductance L m 。
Based on the above-mentioned modular multilevel direct current transformer topology, the dynamic oscillation suppression method based on the modular multilevel direct current transformer topology of the present embodiment is described below.
First, as shown in fig. 2, taking bridge arm group a as an example, the loop current i between upper and lower sub-arms 1,2 cma Closed loop control is built for a controlled variable defined as oscillation suppression angle delta d And the switching-on and switching-off time of the switching signals of the submodules is dynamically adjusted.
Then, a modular multilevel direct current transformer state space average model is constructed by taking submodule capacitance and circulation as state quantity, small signal analysis is carried out, meanwhile, the dynamic of oscillation suppression angle is considered, and a control-output transfer function G under the small signal model is deduced through Laplace transformation iδ (s)：
wherein ,
and wherein the first and second heat exchangers are configured to,represents the estimated value of circulation>Represents the oscillation suppression angle estimation value, s represents the Laplacian, U ca_sum Representing the sum of all sub-module capacitor voltages in a group of MMC bridge arms, I cma Represents circulation, R s Parasitic resistance, delta, representing bridge arm inductance within a set of MMC bridge arms d Representing the static operating point of the oscillation suppression angle. Wherein, the bridge arm inductance in a group of MMC bridge arms refers to the self-coupling inductance L of the upper and lower sub-bridge arms in a group of MMC bridge arms s Mutual coupling inductance L of bridge arm m The sum of 2 (L) s +L m )。
Solving a system characteristic root according to a characteristic equation of the closed loop system and showing a damping ratio xi:
let damping ratio xi be 1, obtain closed loop controller gain k under the optimal damping compensation condition pi Is calculated by the formula:
FIG. 3 shows the damping ratio ζ, the proportional controller gain k under loop closed-loop control pi And oscillation suppression angle static operating point delta d Is a graph of the relationship of (1).
According to the principle of conservation of power, the circulating current and the topological direct current side voltage U dc The product of (a) represents the input power, the topology output voltage U o Divided by the square of output resistance R o Representing the output power, thus obtaining the circulation given value
Then detecting the actual value i of the circulation cma Will give the valueAnd the actual value i cma Subtracting to obtain a circulation error value delta i cma The oscillation suppression angle delta is obtained through adjustment of a current inner loop proportional controller d 。
As described previously, the control-output transfer function G iδ And(s) is a polynomial obtained by taking the oscillation suppression angle as a denominator and the circular flow as a numerator. The system characteristic root is a pair of conjugate complex roots:
wherein ζ represents damping ratio, ω n Representing the frequency of the natural oscillation,
damping ratio xi and number of submodules N, bridge arm self-inductance and mutual inductance L s +L m Submodule capacitance C, controller gain k pi All related. With other parameters fixed, the larger the controller gain, the larger the system damping ratio, and critical damping, ζ=1, is the ideal damping state.
The loop closed loop is designed according to the gain of the closed loop controller obtained by critical damping calculation, so that the optimal oscillation suppression angle delta corresponding to the critical damping is obtained d ' and will optimize the oscillation suppression angle delta d The 'control quantity' acts on the pulse edges of the switching signals of the upper sub-bridge arm submodules and the lower sub-bridge arm submodules of the two groups of MMC bridge arms, so that the switching signals of the upper sub-bridge arm and the lower sub-bridge arm form a region which is simultaneously turned on or simultaneously turned off, pulse voltage is generated in bridge arm inductance voltage, thereby controlling the change of circulation and inhibiting dynamic damping oscillation. Wherein the bridge arm inductance voltage refers to the voltage applied to all self-coupling inductances and mutual coupling inductances of the upper and lower sub-bridge arms in a group of MMC bridge arms, namely 2 (L) s +L m ) And a voltage on the same.
Specifically, the pulse edge of each corresponding sub-module in the upper bridge arm and the lower bridge arm of each group of MMC bridge arms is applied with an optimal oscillation suppression angle delta in each half sub-module switching period d ' the remaining submodule pulses remain unchanged. When the optimal oscillation suppression angle acts on the switch signal to enable the switch signal to be turned off in a falling edge time delay way and the rising edge is turned on in advance, defining the optimal oscillation suppression angle delta at the moment d ' is negative; when the optimal oscillation suppression angle delta d ' when the applied switching signal is turned on in a rising edge delay manner and is turned off in a falling edge advance manner, an optimal oscillation suppression angle delta is defined at the moment d ' is positive.
To reduce dv/dt, it is necessary to introduce a shifting angle θ between the submodules in order to verify that the shifting angle does not affect optimal oscillation suppressionAngle delta d The' effect on the circulation takes N=8 as an example, and the optimal oscillation suppression angle is positive 2 delta is respectively shown in fig. 4 and 5 d'<θ and δd The module is conducted in the condition of 'N-1' theta. Under square wave modulation, the variation of the optimal oscillation suppression angle in one switching period to the circulation current is as follows:in fig. 4 (a), the gray solid line indicates the upper arm switch signal, the black solid line indicates the lower arm switch signal, and in fig. 4 (b), the black square indicates the module input, the white square indicates the module cut-off, and 18 switch modes are generated in total in one switch period, and are marked as 1,2, … and 18 in sequence. Each module output voltage is U under the assumption of balanced capacitance voltage and no ripple dc /8. Wherein the number of sub-modules in the mode 2 and the mode 12 is 7, and 2 delta is respectively conducted d ' corresponds to the inductance voltage u L ＝U dc 8; the conduction number of the remaining 16 modal neutron modules is 8, and the inductance voltage u is equal to L =0. The amount of circulation change can thus be expressed as: />When the oscillation suppression angle is large, the upper and lower bridge arm switch timing diagrams and the bridge arm module conduction state schematic diagrams are shown in fig. 5, and in the first half of the sub-module switch period, the number of conduction modules in mode 1 is 8, and the inductance voltage u is equal to L =0; while 7 modules in modes 2-9 are conducted, at this time, the inductance voltage u L ＝U dc /8, wherein mode 2 is conducting delta d ' mode 3 to mode 8 are respectively conducted with theta and mode 9 is conducted with delta d ' -6 theta. In the second half of the sub-module switching period, the number of conducting modules in mode 10 is 8, and the inductance voltage u L =0; while 7 modules in modes 11 to 18 are conducted, at this time, the inductance voltage u L ＝U dc /8, wherein mode 11 turns on delta d ' mode 12 to mode 17 are respectively conducted with theta and mode 18 is conducted with delta d ' -6 theta. The amount of circulation change in this case can thus be expressed as:
at an optimal oscillation suppression angle delta d When' is negative, the same conclusion can be drawn, so that the internal shift angle does not affect the optimal oscillation suppression angle delta d ' the amount of variation generated for the loop current at each switching cycle.
Optimal oscillation suppression angle delta d ' positive, the amplitude of the voltage U generated in the bridge arm inductance voltage is a single submodule sub ＝U ca_sum 16, duty cycle of 2δ d The positive pulse voltage of'/pi is generated each time by a group of switch pairs (switch signals S in the bridge arm 1) in the upper and lower sub-bridge arms of each group of MMC bridge arms p1j And switching signal S in bridge arm 2 p2j Or switching signal S in leg 3 p3j And switching signal S in bridge arm 4 p4j Where j=1 … 8) is formed in a region that is turned off more on the basis of a 50% square wave signal, and thus the circulation rises; similarly, the optimal oscillation suppression angle delta d When' is negative, the bridge arm inductance voltage generation amplitude is-U sub And a duty cycle of 2δ d The negative pulse voltage of'/pi is formed by the switch pairs in the upper and lower sub-bridge arms respectively in the multi-conduction area based on 50% square wave signal, so the loop current is reduced.
FIG. 11 depicts switch signals S for leg 1 and leg 2 when the optimal oscillation suppression angle is negative p1j ,S p2j Bridge arm voltage u 1 ,u 2 Bridge arm inductance voltage u La Circulation i cma Bridge arm midpoint voltage u aN Is a timing chart of (a). The duty ratio of two continuous modules of the upper bridge arm or two continuous modules of the lower bridge arm in each half sub-module switching period (recorded as an action period) is correspondingly changed under the action of the optimal oscillation suppression angle. Specifically: in the first action cycle, S p11 Advance delta d ' turn on and S p18 Delay delta d ' off, S p12 ～S p17 and Sp21 ～S p28 The switching signal remains unchanged; in the second action cycle, S p21 Delay timeδ d ' turn off and S p22 Advance delta d ' turn on, S p11 ～S p18 and Sp23 ～S p28 The switching signal remains unchanged; in the third action cycle, S p12 Delay delta d ' turn off and S p13 Advance delta d ' turn on, S p11 、S p14 ～S p18 and Sp21 ～S p28 The switching signal remains unchanged; in the fourth action cycle, S p23 Delay delta d ' turn off and S p24 Advance delta d ' turn on, S p11 ～S p18 and Sp21 、S p22 、S p25 ～S p28 The switching signal remains unchanged. Similarly, in the eighth action cycle, S p27 Delay delta d ' turn off and S p28 Advance delta d ' turn on, S p11 ～S p18 and Sp21 ～S p26 The switching signal remains unchanged.
The optimal oscillation suppression angle completes one round of action in 16 modules in eight action cycles, namely four switch cycles. Upper and lower bridge arm switch pair (S) p1j and Sp2j ) The circulation is continuously changed in two adjacent action periods. In the transverse direction, each sub-module is only involved in the regulation of the circulation current during one action cycle, while the 50% duty cycle is kept unchanged during the remaining seven action cycles. Under the action of the negative-direction optimal oscillation suppression angle, the upper bridge arm switch adjusts the pulse edge time only in the odd-number action period, so that the voltage of the bridge arm 1 can generate the amplitude value U at the rising edge and the falling edge in the odd-number action period ca_sum /16 and on time delta d ' level; the lower bridge arm switch only adjusts the pulse edge time in even number of operation period, so that the voltage of the bridge arm 2 generates a voltage with amplitude of U at rising edge and falling edge in even number of operation period ca_sum /16 and on time delta d ' level. The amplitude generated in the bridge arm inductance voltage is U ca_sum 16, duty cycle of 2δ d 'pi' pulse waveform, so that the inductance voltage is-U at the bridge arm ca_sum 2 delta of/16 d In the' region, the circulation assumes a descending situation, in which the number of experiencesAfter a certain action period, a new steady state value can be reached, and a new circulation command value is tracked in time when the load is suddenly changed, so that damped oscillation in a dynamic process is inhibited. Since the optimal oscillation suppression angle acts on a group of switch pairs simultaneously in opposite directions along the pulse edge at a time, generating + -U in each sub-bridge arm voltage ca_sum Gap of/16, thus output voltage u at bridge arm midpoint aN In additionally produce 7U ca_sum /32 and-7U ca_sum Two levels/32.
Similarly, the mechanism of action with the optimal oscillation suppression angle being positive is still analyzed with half the sub-module switching period as one action period, as shown in fig. 2. In the first action cycle, S p21 Advance delta d ' turn off and S p28 Delay delta d ' turn on, S p22 ～S p27 and Sp11 ～S p18 The switching signal remains unchanged; in the second action cycle, S p11 Delay delta d ' turn on and S p12 Advance delta d ' off, S p21 ～S p28 and Sp13 ～S p18 The switching signal remains unchanged; in the third action cycle, S p22 Delay delta d ' turn on and S p23 Advance delta d ' off, S p21 、S p24 ～S p28 and Sp11 ～S p18 The switching signal remains unchanged; in the fourth action cycle, S p13 Delay delta d ' turn on and S p14 Advance delta d ' off, S p21 ～S p28 and Sp11 、S p12 、S p15 ～S p18 The switch signal remains unchanged … … and so on, S in the eighth action period p17 Delay delta d ' turn on and S p18 Advance delta d ' off, S p21 ～S p28 and Sp11 ～S p16 The switching signal remains unchanged.
Under the effect of the forward optimal oscillation suppression angle, the upper bridge arm switch adjusts the pulse edge time only in the even number of operation periods, so that the voltage of the bridge arm 1 can generate amplitude at the rising edge and the falling edge respectively in the even number of operation periodsWith a value of 7U ca_sum /16 and on time delta d ' level; the lower bridge arm switch only adjusts the pulse edge time in the odd-numbered operation period, so that the voltage of the bridge arm 2 generates an amplitude of 7U at the rising edge and the falling edge in the odd-numbered operation period ca_sum /16 and on time delta d ' level. The amplitude generated in the bridge arm inductance voltage is U ca_sum 16, duty cycle of 2δ d The pulse waveform of'/pi, thus circulating at 2 delta d The 'region' assumes an ascending situation and after a few action cycles a new steady state value can be reached for damping the dynamically damped oscillations. Output voltage u at midpoint of bridge arm aN In a large number of (7U) ca_sum /32 and-7U ca_sum Two levels/32.
Fig. 6 is a simulation waveform of dynamic response of the submodule capacitor voltage, the loop current, the bridge arm inductance voltage and the output voltage without the oscillation suppression method. The waveform has obvious under-damped oscillation phenomenon, the oscillation frequency is 739rad/s, and the oscillation is more obvious after the load is suddenly changed.
Output voltage u of MMDCT system under the synergistic effect of circulation closed-loop control and output voltage closed-loop control o Primary and secondary side voltage u ab ,u s Circulation i cma Phase angle phi of the outer shift, and improved optimal oscillation suppression angle delta d ' in sudden load increase (R o ＝5Ω→R o =2.5Ω) and load burst (R o ＝2.5Ω→R o The simulated waveforms for the =5Ω) regime are shown in fig. 7 and 8, respectively.
Under the closed-loop control of the external phase-shifting angle, the output voltage can track the command value in real time, is not influenced by the load change of the secondary side of the transformer, and has good tracking performance and is stable at about 750V. Primary and secondary side voltage u of transformer ab ,u s The amplitudes of (a) are 4kV and 750V, respectively, the voltage ratio is equal to the transformer transformation ratio n=16:3, no reactive power is present.
In fig. 7, the output load R is at t=0.2 s o =5Ω burst as R o =2.5Ω. Because the direct current side voltage reaches 4kV, the transmission power between the primary side and the secondary side can be adjusted by only needing a small value for the outward phase shifting angle. According to power conservationConstant computable circulation i cma The dynamic process is only 0.15s, which increases from 14A to 28A at 0.2s load surge, and it can be seen from this figure that the dynamic damped oscillations are better suppressed after closed loop control, where the gain of the damping controller in the loop inner loop is set to 0.0044. Further, during the increase of the circulation, the optimal oscillation suppression angle is kept positive, and the optimal oscillation suppression angle is restored to 0 when the circulation reaches a steady state. In fig. 8, the output terminal carries R when t=0.2 s o =2.5 Ω burst to R o The phase angle of the outward shift is increased from 1 degree to 1.5 degrees, and the circulation i is realized under the condition of meeting the conservation of power cma The dynamic process continues for 0.1s with a decrease from 28A to 14A at a sudden load decrease of 0.2s, during which the optimal oscillation suppression angle remains negative, while the optimal oscillation suppression angle remains constant at 0 when the loop is in steady state.
To further verify the effect of the optimal oscillation suppression angle on the circulation, fig. 9 and 10 show the circulation i during load dump and load dump dynamics cma And an optimal oscillation suppression angle delta d ' simulation waveforms within five switching cycles after dynamic start. When the load suddenly decreases, the new circulation command value is smaller than the actual circulation value, the closed-loop controller detects the difference value, and an oscillation suppression angle smaller than zero is generated through closed-loop adjustment (fig. 9 (b)), and the oscillation suppression angle acts on 8 groups of switch pairs of the upper bridge arm and the lower bridge arm in turn in each half of the sub-module switching period. When the load suddenly increases (fig. 10), the loop current needs to track the newly increased command value rapidly under the regulation of the closed-loop controller, so that a forward oscillation suppression angle (fig. 10 (b)) is needed to act on each group of switch pairs to generate a region of simultaneous turn-off, and a magnitude U is constructed in the bridge arm inductance dc Forward pulse voltage of/8. The optimal oscillation suppression angle acts on eight groups of switch pairs in turn under the regulation action of the closed-loop controller, so that the new instruction value is tracked on the circulation.
Claims (3)
1. A dynamic oscillation suppression method based on a modularized multi-level direct current transformer topology comprises two groups of MMC bridge arms, wherein each group of MMC bridge arms respectively comprises an upper sub-bridge arm and a lower sub-bridge arm, each upper sub-bridge arm and each lower sub-bridge arm respectively comprises N sub-modules which are connected in series, and N is a positive integer; the dynamic oscillation suppression method is characterized by comprising the following steps of:
(1) A closed-loop control system is constructed by taking the circulation between the upper and lower sub-bridge arms of each group of MMC bridge arms as a controlled quantity and taking an oscillation suppression angle as a control quantity, wherein the oscillation suppression angle is determined by the difference between the actual value and the given value of the circulation;
(2) Constructing a modularized multi-level direct current transformer state space average model by taking submodule capacitance and circulation as state quantities, carrying out small signal analysis, simultaneously considering the dynamic state of an oscillation suppression angle, deriving a control-output transfer function of the closed loop control system under the small signal model through Laplacian transformation, solving a characteristic root of the closed loop control system according to the control-output transfer function, and showing a damping ratio; the damping ratio is made to be critical damping 1, and the gain of the closed-loop controller under the condition of optimal damping compensation is obtained;
the control-output transfer function is expressed as:
wherein ,
wherein ,represents the estimated value of circulation>Represents the oscillation suppression angle estimation value, s represents the Laplacian, U ca_sum Representing all sub-module capacitance electricity in a group of MMC bridge armsSum of pressures, I cma Represents circulation, R s Parasitic resistance, delta, representing bridge arm inductance d A static operating point representing an oscillation suppression angle;
the damping ratio is expressed as:
(3) Calculating a corresponding oscillation suppression angle according to the obtained closed-loop controller gain to be used as an optimal oscillation suppression angle;
(4) The optimal oscillation suppression angle is used as a control quantity to control the switch of each sub-module of the two groups of MMC bridge arms, so that the change of the circulation is controlled; the method specifically comprises the following steps:
in the upper and lower sub-bridge arms of the two groups of MMC bridge arms, the sub-modules are ordered, one sub-module is sequentially selected from the upper and lower sub-bridge arms of the two groups of MMC bridge arms according to the ordering in each half sub-module switching period, two groups of sub-module pairs are formed, and the optimal oscillation suppression angle delta is formed d ' control selected pairs of sub-modules as control variables such that the pulse edges of selected sub-modules are applied with the optimal oscillation suppression angle delta d ' the pulse edges of the rest submodules remain unchanged;
the optimal oscillation suppression angle delta d ' control selected pairs of sub-modules as control variables such that the pulse edges of selected sub-modules are applied with the optimal oscillation suppression angle delta d ' specifically, it includes:
when delta d When' is negative, the selected sub-module is turned off and delta based on 50% square wave signal at falling edge delay d ' same angle, leading on and delta at rising edge d ' same angle, thereby generating a magnitude U in the bridge arm inductance voltage ca_sum 16, duty cycle of 2δ d A positive pulse voltage of'/pi, and a circulation rises; wherein U is ca_sum Representing the sum of all sub-module capacitor voltages in a group of MMC bridge arms;
when delta d ' positive, so that the selected sub-module is extended on the rising edge based on 50% square wave signalTime conduction delta d ' same angle, early turn-off and delta at falling edge d ' same angle, thereby generating a magnitude U in the bridge arm inductance voltage ca_sum 16, duty cycle of 2δ d The negative pulse voltage of'/pi, the circulating current drops.
2. The method for dynamic oscillation suppression based on modular multilevel direct current transformer topology according to claim 1, wherein the method comprises the following steps: in step (1), the given value of the circulating currentCirculating current when the input power of the modular multilevel direct current transformer topology is equal to the output power; wherein the input power is equal to the product of the circulating current and the topological direct current side voltage, and the output power is equal to the square of the topological output voltage divided by the output resistance.
3. The method for dynamic oscillation suppression based on modular multilevel direct current transformer topology according to claim 1, wherein the method comprises the following steps: in the step (2), the control-output transfer function is a polynomial obtained by taking an oscillation suppression angle as a denominator and a circulation as a numerator; the characteristic root of the closed-loop control system is a pair of conjugate complex roots and is related to the damping ratio xi; the damping ratio xi, the number N of submodules and the bridge arm self-coupling inductance L s Inductance L coupled with bridge arm m Sum, submodule capacitance C, controller gain k pi All related.
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