CN110855169A - Single-phase inverter model prediction control method without voltage sensor - Google Patents

Single-phase inverter model prediction control method without voltage sensor Download PDF

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CN110855169A
CN110855169A CN201911243035.7A CN201911243035A CN110855169A CN 110855169 A CN110855169 A CN 110855169A CN 201911243035 A CN201911243035 A CN 201911243035A CN 110855169 A CN110855169 A CN 110855169A
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phase inverter
voltage
observer
grid voltage
power grid
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CN110855169B (en
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范宜标
蔡小伟
郑亮
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Fujian Guangjun Power Technology Co Ltd
Longyan University
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Fujian Guangjun Power Technology Co Ltd
Longyan University
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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
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • 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
    • H02M1/0003—Details of control, feedback or regulation circuits
    • H02M1/0009—Devices or circuits for detecting current in a converter

Abstract

The invention provides a single-phase inverter model prediction control method without a voltage sensor, which comprises the following steps: s1, establishing a single-phase inverter system model, creating a linear time-varying observer, initializing a digital controller, and presetting the maximum sampling times; s2, measuring output current variable i of the systemo(k) (ii) a S3, calculating the state variable of the observerS4, calculating the observed value of the grid voltage
Figure DDA0002306789480000012
S5, calculating the predicted output current of the next sampling period of the output current of the single-phase inverter system in different switching states

Description

Single-phase inverter model prediction control method without voltage sensor
Technical Field
The invention relates to the field of power electronic converter control, in particular to a single-phase inverter model prediction control method without a voltage sensor.
Background
The function of the inverter is to effect the conversion of direct current to alternating current. The inverter is widely used as an interface for new energy networking and is an important component of clean energy systems such as photovoltaic systems. Normally, when the power grid is in a stable operation state, the waveform is a standard sine. The aim of controlling the inverter is to generate sinusoidal alternating current with the same frequency and phase as the power grid, so as to realize high-power factor injection of electric energy. However, sometimes the grid is operating in a distorted state, which is especially common for micro grid systems. In the distorted state, the goal of controlling the inverter is to produce a sinusoidal alternating current that is in frequency and phase with the grid voltage fundamental signal. In a traditional inverter control method, a voltage sensor is used for collecting the voltage of a power grid so as to extract fundamental waves; on the basis of this, a current reference signal is regenerated.
Disclosure of Invention
The invention aims to provide a single-phase inverter model prediction control method without a voltage sensor, and accurate tracking control of current is realized.
The invention is realized by the following steps: a single-phase inverter model prediction control method without a voltage sensor comprises the following steps:
s1, establishing a single-phase inverter system model, creating a linear time-varying observer, initializing a digital controller, and presetting the maximum sampling times;
s2, measuring the output current variable i of the system by a current sensoro(k)；
S3, calculating the state variable of the observer
Figure BDA0002306789460000011
S4, according to the stateVariables ofCalculating the observed value of the grid voltage
Figure BDA0002306789460000013
S5, according to the current observation value
Figure BDA0002306789460000014
Variable of output current io(k) And the discrete model of the single-phase inverter system is used for calculating the predicted output current of the next sampling period of the output current of the single-phase inverter system in different switching states
Figure BDA0002306789460000021
S6, calculating a cost function of each switch state; selecting an optimal switching state that minimizes the cost function;
and S7, outputting the optimal switching state to the single-phase inverter, entering the next sampling period when the maximum sampling frequency is not exceeded, and turning to the step S2.
Further, the establishing of the single-phase inverter system model specifically includes: firstly, establishing a continuous model of a single-phase inverter system:
Figure BDA0002306789460000022
wherein R is resistance value, L is inductance value, ioOutput current value, U, for the circuitinIs an input voltage value ugFor grid voltage values, S ∈ { -1,0,1} denotes the switching unit S1-S4The circuit working states under different switch state combinations;
according to the first-order forward Euler approximation method, based on equation (1), the discrete model of the system can be represented as:
wherein, TsIs the sampling period.
Further, the observer creating the linear time variation specifically includes: according to the periodic characteristics of the power grid voltage, expressing the power grid voltage as a linear combination form of a sine function and a cosine function:
Figure BDA0002306789460000024
substituting equation (3) into equation (1), the continuous model of the single-phase inverter system is represented as:
Figure BDA0002306789460000025
under the condition that the voltage output of the power grid is stable, each coefficient of the formula (3) is constant, namely
Figure BDA0002306789460000026
With x ═ x1x2x3x4… x2n+1x2n+2]T＝[ioα0α1β1… αnβn]TRepresents a state variable of said system, u ═ sUinRepresenting the input to the system, y ═ x1＝ioRepresenting the output of the system, the form of augmentation of the system can be represented as
Figure BDA0002306789460000031
Wherein
Figure BDA0002306789460000032
Figure BDA0002306789460000033
C＝[1 01×(2n+1)]
The linear time-varying observer is designed according to equation (5) in combination with the Lorberg observer structure, in the form of
Figure BDA0002306789460000034
Wherein
Figure BDA0002306789460000035
Further, a Lyapunov function is designed, and the convergence of the observer is explained according to the Lasalel invariant set principle, specifically:
an error system can be obtained from equations (5) to (6), and is expressed as follows:
wherein
Figure BDA0002306789460000037
And
Figure BDA0002306789460000038
defining functions
Figure BDA0002306789460000039
Wherein
Figure BDA00023067894600000310
When g is reached2,g3,g4,…g2n+1,g2n+2When < 0, function
Figure BDA00023067894600000311
Is positively determined in relation to
Figure BDA00023067894600000312
The derivative of (c) is:
Figure BDA0002306789460000041
from the above formula, g is1At the time of the > -R,
Figure BDA0002306789460000042
i.e. functionIs Lyapunov function, and only if it is known according to Lasalel invariant set principle
Figure BDA0002306789460000044
When the temperature of the water is higher than the set temperature,
Figure BDA0002306789460000045
thus, the observer is convergent.
Further, the step S4 is specifically: the discrete form of the observer is obtained according to equation (6):
Figure BDA0002306789460000046
where I is the identity matrix, θ (k) ═ θ (k-1) + ω TsThe phase angle of the power grid voltage at the current moment is omega, and the angular frequency of the power grid voltage is the phase angle of the power grid voltage;
the observation value of the power grid voltage can be known as
Figure BDA0002306789460000047
Further, the step S5 is specifically: according to the FCS-MPC principle, combining the discrete model of the system represented by the formula (2) and the observed value of the grid voltage in the formula (10), the predicted value of the current of the system at the next moment can be calculated, which is expressed as follows
Figure BDA0002306789460000048
Further, the step S6 is specifically: the cost function is expressed as
Figure BDA0002306789460000049
Wherein iref(k +1) is the reference current at time k + 1;
selecting an optimal switching state s (k) by selecting a method that minimizes the cost function, following the equation:
Figure BDA00023067894600000410
the invention has the following advantages: 1. the invention expresses the voltage of the power grid into a linear combination of trigonometric functions, designs a linear time-varying observer according to the structure of the Longbeige observer on the basis, and ensures the convergence of the observer by the Lyapunov function and the Lasalel invariant set principle, thereby realizing the observation of the amplitude of each component and finally realizing the observation of the voltage of the power grid.
2. Compared with the traditional model prediction control method, the method provided by the invention has the advantages that the observation of the power grid voltage is realized by utilizing the designed observer, the power grid voltage sensor is eliminated, the online reconstruction of the power grid voltage is realized through a software algorithm, the complexity and the cost of the system hardware design are reduced, the reliability of the system is improved, and meanwhile, the accurate current tracking control can be realized.
Drawings
The invention will be further described with reference to the following examples with reference to the accompanying drawings.
Fig. 1 is a schematic circuit diagram of a conventional single-phase bridge inverter.
Fig. 2 is a block diagram of the control method of the present invention.
Fig. 3 is a flowchart of a program used in the control method of the present invention.
Fig. 4 is a simulation result of the output of the present invention when the grid voltage changes, where fig. 4(a) shows the actual voltage and the reference voltage and the error therebetween, fig. 4(b) shows the reference current and the tracking current and the error therebetween, and fig. 4(c) shows the Total Harmonic Distortion (THD) of the tracking current.
Fig. 5 is a simulation result of the output of the present invention when the reference current is changed, wherein fig. 5(a) shows the actual voltage and the reference voltage and the error therebetween, fig. 5(b) shows the reference current and the tracking current and the error therebetween, and fig. 5(c) shows the THD of the tracking current.
Detailed Description
Referring to fig. 1 to 5, a preferred embodiment of the voltage sensor-less single-phase inverter model predictive control method of the present invention; the method comprises the following steps:
s1, establishing a single-phase inverter system model, creating a linear time-varying observer, initializing a digital controller, and presetting the maximum sampling times;
the establishment of the single-phase inverter system model specifically comprises the following steps: according to the circuit schematic diagram of the single-phase bridge inverter shown in fig. 1, a continuous model of the single-phase inverter system is established:
Figure BDA0002306789460000061
wherein R is resistance value, L is inductance value, i0For outputting current values of the circuit, UinFor input voltage values of DC signals, ugFor the voltage value of the power grid as an alternating current signal, S belongs to { -1,0,1} to represent a switch unit S1-S4And the working state of the circuit under different switch state combinations. S1-S4The switch unit is a combination of an MOS (metal oxide semiconductor) tube and a freewheeling diode, wherein the conduction of the MOS tube indicates that the switch unit is in an open state, and the cut-off of the MOS tube indicates that the switch unit is in a closed state; when S is1And S4Opening, S2And S3Closing, wherein s takes a value of 1; when S is1And S4Closing, S2And S3Starting, wherein s takes the value of-1; otherwise, s takes the value 0.
According to the first-order forward Euler approximation method, based on equation (1), the discrete model of the system can be represented as:
Figure BDA0002306789460000062
wherein, TsIs a sampling period; i.e. io(k +1) represents a circuit output current value i at the time of sampling at the (k +1) th timeo(k) Represents the output current value of the circuit during the k-th sampling, s (k) represents the value of the switch state adopted during the k-th sampling, ug(k) And the grid voltage value at the k sampling is shown.
The observer for creating the linear time variation specifically includes: according to the periodic characteristics of the power grid voltage, expressing the power grid voltage as a linear combination form of a sine function and a cosine function:
Figure BDA0002306789460000063
substituting equation (3) into equation (1), the continuous model of the single-phase inverter system is represented as:
Figure BDA0002306789460000064
under the condition that the voltage output of the power grid is stable, each coefficient of the formula (3) is constant, namely
Figure BDA0002306789460000065
With x ═ x1x2x3x4… x2n+1x2n+2]T＝[ioα0α1β1… αnβn]TRepresents a state variable of said system, u ═ sUinRepresenting the input to the system, y ═ x1＝ioRepresenting the output of the system, the form of augmentation of the system can be represented as
Figure BDA0002306789460000071
Wherein
Figure BDA0002306789460000072
Figure BDA0002306789460000073
C＝[1 01×(2n+1)]
A linear time-varying observer is designed according to equation (5) in combination with the Lorberg observer structure, which is in the form of
Figure BDA0002306789460000074
Wherein
Figure BDA0002306789460000075
Designing a Lyapunov function, and explaining the convergence of the observer according to the Lasalel invariant set principle, wherein the method specifically comprises the following steps: an error system can be obtained from equations (5) to (6), and is expressed as follows:
wherein
Figure BDA0002306789460000077
And
Figure BDA0002306789460000078
defining functions
Figure BDA0002306789460000079
Wherein
Figure BDA00023067894600000710
When g is reached2,g3,g4,…g2n+1,g2n+2When < 0, functionIs positively determined in relation to
Figure BDA00023067894600000712
The derivative of (c) is:
Figure BDA00023067894600000713
from the above formula, g is1At the time of the > -R,i.e. function
Figure BDA0002306789460000082
Is Lyapunov function, and only if it is known according to Lasalel invariant set principle
Figure BDA0002306789460000083
When the temperature of the water is higher than the set temperature,
Figure BDA0002306789460000084
thus, the observer is convergent.
S2, measuring the output current variable i of the system by a current sensoro(k)；
S3, calculating the state variable of the observer
Figure BDA0002306789460000085
I.e. the system state variable (i) at the kth sampleoα0α1β1… αnβn)；
S4, according to the state variableCalculating the observed value of the grid voltageThe method specifically comprises the following steps: the discrete form of the observer is obtained according to equation (6):
Figure BDA0002306789460000088
where I is the identity matrix, θ (k) ═ θ (k-1) + ω TsThe phase angle of the power grid voltage at the current moment is omega, and the angular frequency of the power grid voltage is the phase angle of the power grid voltage;
the observation value of the power grid voltage can be known as
Figure BDA0002306789460000089
S5, according to the current observation value
Figure BDA00023067894600000810
Variable of output current io(k) And the discrete model of the single-phase inverter system is used for calculating the predicted output current of the next sampling period of the output current of the single-phase inverter system in different switching states
Figure BDA00023067894600000811
The method specifically comprises the following steps: according to the FCS-MPC principle, in combination with the discrete model of the system represented by the formula (2) and the observed value of the grid voltage in the formula (10), the predicted value of the current of the system at the next moment can be calculated, and is expressed as follows
Figure BDA00023067894600000812
S6, calculating a cost function of each switch state; selecting an optimal switching state that minimizes the cost function; the method specifically comprises the following steps: the cost function is expressed as
Wherein iref(k +1) is the reference current at time k + 1;
selecting an optimal switching state s (k) by selecting a method that minimizes the cost function, following the equation:
Figure BDA0002306789460000091
since s ∈ { -1,0,1 }; namely, s (k) has three value conditions in the k sampling, and the k sampling can be known according to the formula (11)There are three kinds of value-taking conditions, and the value-taking conditions are calculated in sequence
Figure BDA0002306789460000093
Obtaining a corresponding value function result value; and finally, finding out the optimal switching state which minimizes the cost function.
And S7, outputting the optimal switching state to the single-phase inverter, entering the next sampling period when the maximum sampling frequency is not exceeded, and turning to the step S2. And when the maximum sampling times are reached, stopping sampling and exiting the calculation program.
In order to demonstrate the performance of the control method provided by the present invention, the control method provided will be briefly described below with reference to some embodiments of the present invention in the accompanying drawings, which mainly simulate the algorithm by simulation software MATLAB/SIMULINK, and with reference to the above formula, the simulation parameters are shown in Table 1, wherein u is the circuit parameters shown in FIG. 1, in addition to the circuit parameters shown in FIG. 1gmRepresenting the amplitude of the grid voltage, iref,mRepresenting the amplitude of the reference current, f0Representing the fundamental frequency, f, of the circuit AC voltage currentsRepresenting the sampling frequency.
TABLE 1
Figure BDA0002306789460000094
FIG. 4 is a waveform diagram of the control variables and observed values of the single-phase inverter when the grid voltage changes, wherein the grid voltage amplitude is set to 0.2s
Figure BDA0002306789460000095
Down to
Figure BDA0002306789460000096
Change back again at 0.3sIn addition to the fundamental wave, the grid voltage contains 5, 7, 11, and 13 th harmonics, which are 5%, 3%, and 3% of the fundamental wave, respectively, and the same result is obtained in fig. 5. As can be seen from the observed value of the grid voltage and the error between the observed value and the actual value in fig. 4(a), the observer according to the present invention can observe the value of the grid voltage well, and the observation error is small. Meanwhile, when the grid voltage changes, the observer can quickly converge to the changed value within one ac cycle. As can be seen from the tracking currents and THD values in fig. 4(b) and (c), the control method of the present invention can obtain a better tracking effect.
Fig. 5 is a waveform diagram of the control variables and observed values of the single-phase inverter when the reference current changes, wherein the reference current amplitude rises from 18A to 24A at 0.2s, and changes back to 18A at 0.3 s. As can be seen from the observed values of the grid voltage in fig. 5(a), the effect of the observer is substantially unaffected by the tracking current. As can be seen from the tracking current in fig. 5(b) and the error between the tracking current and the reference value, the control method of the present invention has a better dynamic response effect, and as can be seen from the THD value in fig. 5(c), the tracking effect of the output current is better.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.

Claims (7)

1. A single-phase inverter model prediction control method without a voltage sensor is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a single-phase inverter system model, creating a linear time-varying observer, initializing a digital controller, and presetting the maximum sampling times;
s2, measuring the output current variable i of the system by a current sensoro(k)；
S3, calculating the state variable of the observer
Figure FDA0002306789450000011
S4, according to the state variable
Figure FDA0002306789450000012
Calculating the observed value of the grid voltage
Figure FDA0002306789450000013
S5, according to the current observation value
Figure FDA0002306789450000014
Variable of output current io(k) And the discrete model of the single-phase inverter system is used for calculating the predicted output current of the next sampling period of the output current of the single-phase inverter system in different switching states
Figure FDA0002306789450000015
S6, calculating a cost function of each switch state; selecting an optimal switching state that minimizes the cost function;
and S7, outputting the optimal switching state to the single-phase inverter, entering the next sampling period when the maximum sampling frequency is not exceeded, and turning to the step S2.
2. The voltage-sensorless single-phase inverter model predictive control method of claim 1, characterized in that: the establishment of the single-phase inverter system model specifically comprises the following steps: firstly, establishing a continuous model of a single-phase inverter system:
Figure FDA0002306789450000016
wherein R is resistance value, L is inductance value, ioOutput current value, U, for the circuitinIs an input voltage value ugFor grid voltage values, S ∈ { -1,0,1} denotes the switching unit S1-S4The circuit working states under different switch state combinations;
according to the first-order forward Euler approximation method, based on equation (1), the discrete model of the system can be represented as:
wherein, TsIs the sampling period.
3. The voltage-sensorless single-phase inverter model predictive control method of claim 2, characterized in that: the observer for creating the linear time variation specifically includes: according to the periodic characteristics of the power grid voltage, expressing the power grid voltage as a linear combination form of a sine function and a cosine function:
substituting equation (3) into equation (1), the continuous model of the single-phase inverter system is represented as:
Figure FDA0002306789450000022
under the condition that the voltage output of the power grid is stable, each coefficient of the formula (3) is constant, namely
Figure FDA0002306789450000023
With x ═ x1x2x3x4… x2n+1x2n+2]T＝[ioα0α1β1… αnβn]TRepresents a state variable of said system, u ═ sUinRepresenting the input to the system, y ═ x1＝ioRepresenting the output of the system, the form of augmentation of the system can be represented as
Figure FDA0002306789450000024
Wherein
Figure FDA0002306789450000025
Figure FDA0002306789450000026
C＝[1 01×(2n+1)]
The linear time-varying observer is designed according to equation (5) in combination with the Lorberg observer structure, in the form of
Wherein
Figure FDA0002306789450000028
4. The voltage-sensorless single-phase inverter model predictive control method of claim 3, characterized in that: designing a Lyapunov function, and explaining the convergence of the observer according to the Lasalel invariant set principle, wherein the method specifically comprises the following steps:
an error system can be obtained from equations (5) to (6), and is expressed as follows:
Figure FDA0002306789450000031
wherein
Figure FDA0002306789450000032
And
Figure FDA0002306789450000033
defining functions
Figure FDA0002306789450000034
Wherein
When g is reached2,g3,g4,…g2n+1,g2n+2When < 0, function
Figure FDA0002306789450000036
Is positively determined in relation to
Figure FDA0002306789450000037
The derivative of (c) is:
Figure FDA0002306789450000038
from the above formula, g is1At the time of the > -R,
Figure FDA0002306789450000039
i.e. function
Figure FDA00023067894500000310
Is Lyapunov function, and only if it is known according to Lasalel invariant set principle
Figure FDA00023067894500000311
When the temperature of the water is higher than the set temperature,
Figure FDA00023067894500000312
thus, the observer is convergent.
5. The voltage-sensorless single-phase inverter model predictive control method of claim 3, characterized in that: the step S4 specifically includes: the discrete form of the observer is obtained according to equation (6):
Figure FDA00023067894500000313
where I is the identity matrix, θ (k) ═ θ (k-1) + ω TsThe phase angle of the power grid voltage at the current moment is omega, and the angular frequency of the power grid voltage is the phase angle of the power grid voltage;
the observation value of the power grid voltage can be known as
Figure FDA0002306789450000041
6. The voltage-sensorless single-phase inverter model predictive control method of claim 5, characterized in that: the step S5 specifically includes: according to the FCS-MPC principle, combining the discrete model of the system represented by the formula (2) and the observed value of the grid voltage in the formula (10), the predicted value of the current of the system at the next moment can be calculated, which is expressed as follows
7. The voltage-sensorless single-phase inverter model predictive control method of claim 6, characterized in that: the step S6 specifically includes: the cost function is expressed as
Figure FDA0002306789450000043
Wherein iref(k +1) is the reference current at time k + 1;
selecting an optimal switching state s (k) by selecting a method that minimizes the cost function, following the equation:
Figure FDA0002306789450000044
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