Four-vector model predictive voltage control method based on grid simulator inverter link

Abstract

The application discloses a four-vector model predictive voltage control method based on an inverter link of a power grid simulator, which comprises the following steps: firstly, collecting three-phase load voltages, three-phase filter inductance currents and three-phase load currents at the current time, and performing Clarke transformation; then, calculating a virtual output voltage vector of the inverter at the next time, judging a tetrahedron where the virtual output voltage vector is located, and finding three active output voltage vectors and one zero voltage vector which constitute the tetrahedron; calculating corresponding target functions of the three active output voltage vectors and the one zero voltage vector, and calculating duty ratios of the four vectors, so as to determine on and off time of each switch of the inverter link of the power grid simulator, thereby realizing accurate control of the load voltage. Compared with a traditional model predictive control algorithm, the application has higher control precision, and can more accurately simulate power grid voltage waveform distortion caused by specific harmonic waves.

Description

Technical Field

[0001] This invention relates to control algorithms for power grid simulators, and more particularly to a model predictive voltage control method based on the inverter stage of a power grid simulator. Background Technology

[0002] Voltage anomalies such as three-phase voltage imbalance, frequency deviation, harmonic distortion, and voltage surges sometimes occur in power grids. With the large-scale integration of various large power electronic devices (grid-connected converters, active filters, dynamic voltage restorers, etc.) into the grid, power grid companies have placed higher demands on these devices. The requirement is no longer simply that they disconnect from the grid when voltage anomalies occur, but rather that they maintain grid-connected operation for a certain period. Therefore, before integrating various power electronic devices into the grid, it is usually necessary to simulate various abnormal grid voltage conditions to test the devices and analyze their operating characteristics under abnormal voltage conditions. However, within laboratory conditions, it is difficult to reproduce various abnormal grid voltage conditions using only the power grid. Therefore, a grid simulator capable of simulating both normal grid operation and various abnormal grid voltage conditions has attracted close attention from researchers.

[0003] Currently, power grid simulators typically consist of a rectifier stage and an inverter stage. To realistically simulate voltage asymmetry, the inverter stage in a power grid simulator usually employs a three-phase, four-arm structure. While the three-phase, four-arm inverter structure is simple, low-cost, and compact, and can handle various types of loads, the addition of the fourth arm increases the complexity of control and modulation compared to a three-phase, three-arm inverter structure. Therefore, it is necessary to study its control algorithm.

[0004] Finite Set Model Predictive Control (FCS-MPC) algorithms, based on the mathematical model of the converter, can directly utilize the discrete characteristics and finite switching states of the converter to control the controlled object. Traditional finite set model predictive algorithms have advantages such as no need for modulation units, no need for adjustment of related control parameters, and fast dynamic response. However, because this algorithm can only act on a single output voltage vector within a sampling period, it suffers from drawbacks such as large computational load and variable switching frequency. If directly applied to a power grid simulator, it can easily cause the load voltage harmonic spectrum to disperse, affecting the accuracy of the power grid simulator in simulating normal power grid operation and waveform distortion conditions. Summary of the Invention

[0005] For a power grid simulator with a three-phase four-arm inverter structure, this invention proposes a four-vector model predictive voltage control method based on the inverter stage of the power grid simulator, in order to solve the shortcomings of the traditional finite set model prediction algorithm in simulating normal operation of the power grid and waveform distortion conditions.

[0006] The objective of this invention can be achieved through the following technical solution: a four-switch vector model predictive voltage control method based on the inverter stage of a power grid simulator, comprising the following steps:

[0007] Step 1: Real-time acquisition of three-phase load voltage, three-phase load current, and three-phase filter inductor current, and performance of Clarke coordinate transformation;

[0008] Step 2: Based on the results obtained in Step 1, calculate the inverter virtual voltage reference vector v at the next moment. ref (k+1);

[0009] Step 3: Based on the principle of three-dimensional spatial vector modulation, determine v ref Given the tetrahedral interval where (k+1) is located, find the output voltage vectors of the four inverters that constitute this tetrahedral interval, including the three active output voltage vectors v. m1 v m2 v m3 And a zero voltage vector v0, where m1, m2, m3 are natural numbers that are not equal between 1 and 14;

[0010] Step 4: Calculate the three active output voltage vectors v m1 v m2 v m3 The objective functions corresponding to g1, g2, g3 and the objective function corresponding to the zero voltage vector v0, respectively;

[0011] Step 5: Based on the results obtained in Step 4, calculate the three active output voltage vectors v. m1 v m2 v m3 The duty cycles d1, d2, d3 and the duty cycle d4 of the zero voltage vector v0 are given, and the duration d1T of each voltage vector within one sampling period is also given. s d2T s d3T s d4T s Feedback is sent to the modulator, which then provides a switching signal, where T... s Indicates the size of one sampling period;

[0012] Step 6: Once the current sampling period is over, return to Step 1.

[0013] Furthermore, step two involves calculating the inverter's virtual voltage reference vector v at the next moment.ref (k+1), v ref The specific calculation formulas for each component of (k+1) in the αβγ coordinate system are as follows:

[0014]

[0015]

[0016]

[0017] Where L represents the size of the three-phase filter inductor, and C represents the size of the three-phase filter capacitor. n Indicates the magnitude of the neutral line inductance, v oαref (k+1), v oβref (k+1), v oγref (k+1) represent the reference values ​​of the three-phase load voltage at the next sampling time, v oα (k), v oβ (k), v oγ (k) represent the magnitudes of the three-phase load voltages, i oα (k), i oβ (k), i oγ (k) represent the magnitudes of the three-phase load currents, i Lα (k), i Lβ (k), i Lγ (k) represents the magnitude of the three-phase inductor current.

[0018] Furthermore, the formula for calculating the objective function described in step four is as follows:

[0019] g = [v αn (k+1)-v αnref (k+1)] 2 +[v βn (k+1)-v βnref (k+1)] 2 +[v γn (k+1)-v γnref (k+1)] 2

[0020] Where v αn (k+1), v βn (k+1), v γn (k+1) represents the magnitude of the possible output voltage vector on the inverter side at the next moment.

[0021] Furthermore, the calculation basis for the duty cycles d1, d2, d3, and d4 of each voltage vector mentioned in step five is as follows:

[0022] v selected in step four m1 v m2v m3 The four inverter voltage vectors, v0, and v1, are combined into a virtual voltage vector v. p The duration of each switching vector is no longer the entire control cycle, as shown in the following formula:

[0023] v p =v m1 d1+v m2 d2+v m3 d3+v0d4

[0024] Where d1, d2, d3, and d4 represent vector v respectively. m1 v m2 v m3 The duty cycles of v0 satisfy d1+d2+d3+d4=1 and d1, d2, d3, and d4 are all greater than 0;

[0025] Define duty cycle weighted error d i e i , where e i Let i represent the inverter output voltage error caused by a single switching vector, i = 1, 2, 3, 4; the root mean square (RMS) value of the weighted error of the four switching vectors within one control cycle can be expressed as:

[0026]

[0027] Where g i (i = 1, 2, 3, 4) represent vector v respectively. m1 v m2 v m3 The objective function corresponding to v0;

[0028] According to the Lagrange multiplier method, construct the function. make After solving, the duty cycles of the four voltage vectors d1, d2, d3, and d4 can be obtained:

[0029]

[0030] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described four-vector model predictive voltage control method based on the inverter stage of a power grid simulator.

[0031] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described four-vector model predictive voltage control method based on the inverter stage of a power grid simulator.

[0032] Traditional finite set model prediction algorithms select only a single voltage vector in a sampling period, resulting in an unstable switching frequency and a dispersed output voltage spectrum. This leads to insufficient control accuracy when simulating normal grid operation and waveform distortion conditions.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) Based on the traditional finite set model predictive control, four output voltage vectors are selected within one control cycle, which solves the defect of low steady-state accuracy of the traditional finite set model predictive control algorithm and can more accurately simulate multiple harmonics.

[0035] (2) It reduces the computational load of traditional finite set model predictive control algorithms, and the method is simple, reliable, and easy to implement digitally. Attached Figure Description

[0036] Figure 1 This is a flowchart of the four-vector model predictive voltage control algorithm based on the inverter stage of a power grid simulator proposed in this invention.

[0037] Figure 2 This is the topology diagram of a three-phase four-bridge-arm inverter circuit.

[0038] Figure 3 This is a schematic diagram of the four-vector model predictive voltage control algorithm based on the inverter stage of a power grid simulator proposed in this invention.

[0039] Figure 4 This is a spatial distribution diagram of the output voltage vectors of a three-phase four-arm inverter.

[0040] Figures 5(a) to 5(b) The simulation results for the grid voltage waveform distortion when using the traditional model predictive voltage control algorithm are as follows: Figure 5(a) shows the three-phase load voltage waveform when the grid is stable, and Figure 5(b) shows the load voltage spectrum when the grid is stable.

[0041] Figures 6(a) to 6(b) The simulation results of the grid voltage waveform distortion when using the control algorithm of the present invention are as follows: Figure 6(a) shows the three-phase load voltage waveform when it is stable, and Figure 6(b) shows the load voltage spectrum when it is stable. Detailed Implementation

[0042] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention:

[0043] like Figure 2 As shown, the inverter stage of the power grid simulator adopts a three-phase four-bridge-arm inverter structure. This inverter structure consists of a DC power supply V dc 8 power switching transistors, a three-phase LC filter, and a neutral line inductor L nComposition. The grid-connected equipment under test is connected to the AC output side of a three-phase LC filter, with its neutral point connected to the neutral inductor L. n It is directly connected to the inverter.

[0044] The entire process of the four-vector model predictive voltage control algorithm based on the inverter stage of the power grid simulator proposed in this invention is as follows: Figure 1 and Figure 3 As shown. In one sampling period, after acquiring the three-phase load voltage, three-phase load current, and three-phase filter inductor current, the acquired values ​​are transformed into the αβγ coordinate system using Clarke transformation. Based on the system's discrete mathematical model, the inverter's virtual voltage vector reference value v for the next moment is calculated. ref (k+1)=(v αnref (k+1),v βnref (k+1),v γnref (k+1)), where v αnref (k+1), v βnref (k+1), v γnref (k+1) represent v respectively ref (k+1) components on the αβγ coordinate axes.

[0045] 1. The next moment's virtual voltage vector reference value v of the inverter ref Calculation of (k+1)

[0046] The switching functions of each phase arm of the inverter are defined as follows:

[0047]

[0048] If x can take the values ​​a, b, and c, then the output voltage of each phase of the three-phase four-arm inverter can be expressed as:

[0049] v xn =(s x -s n V dc (2)

[0050] According to Kirchhoff's voltage and current laws, the state equations of the three-phase four-arm inverter structure in the abc coordinate system can be obtained as follows:

[0051]

[0052]

[0053] i n +i La +i Lb +i Lc =0 (5)

[0054] In the formula iLx i ox v ox These represent the inductor current, load current, and load voltage of each phase, respectively. n L represents the current flowing through the neutral line, C represents the size of the filter inductor, and L represents the size of the filter capacitor. n The value represents the magnitude of the line inductance, and t represents time.

[0055] Using the Clarke transformation, the state equations of the system in the αβγ coordinate system can be written in the following form:

[0056]

[0057]

[0058] Among them, i Lα i Lβ i Lγ Let i represent the inductor currents of each phase α, β, and γ, respectively. oα i oβ i oγ V represents the load current of each phase α, β, and γ, respectively. oα v oβ v oγ These represent the load voltages of each phase, α, β, and γ, respectively.

[0059] Taking phase α as an example, let the system sampling period be T. s When T s Enough hours, i Lα and v oα They can be written in the following forms:

[0060]

[0061]

[0062] In the formula i Lα (k) and v oα (k) represent the inductor current and load voltage at time k, respectively, i Lα (k+1) represents the inductor current at time k+1, v oα (k-1) represents the load voltage at time k-1.

[0063] Substituting equation (8) into equation (6), we can obtain the estimated value of the inductor current i at time k+1. Lαp (k+1):

[0064]

[0065] Substituting equation (9) into equation (7), we can obtain the estimated value of the load voltage v at time k. oαp(k):

[0066]

[0067] Equation (11) can be rewritten as:

[0068]

[0069] In the formula i oαp (k+1) represents the estimated value of the load current at time k+1.

[0070] If T s The value of is small enough that the load current will not change within a sampling period. Substituting equation (10) into equation (12), we get:

[0071]

[0072] Similarly, the predicted values ​​of the load voltages v for phase β and phase γ at time k+1 can be obtained. oβp (k+1), v oγp (k+1):

[0073]

[0074]

[0075] According to the principle of no-difference beats, equations (13), (14), and (15) can be rewritten as follows:

[0076]

[0077]

[0078]

[0079] Thus, the inverter virtual voltage vector reference value v at the next moment ref (k+1) can be obtained by equations (16)-(18).

[0080] 2. Four-vector selection process

[0081] Based on the principle of three-dimensional spatial vector modulation, a three-phase four-arm inverter has 16 switching states, resulting in 14 active output voltage vectors and 1 zero output voltage vector v0. The spatial distribution of the 14 active output voltage vectors is as follows: Figure 4 As shown, its values ​​and corresponding switch states are shown in Table 1.

[0082] Table 1. Values ​​of the 14 active output voltage vectors and their corresponding switching states.

[0083]

[0084] from Figure 4 It can be seen that the 14 active output voltage vectors and the zero vector v0 form a hexagonal prism in space. This hexagonal prism is composed of 6 triangular prisms, and each triangular prism is composed of 4 tetrahedrons, so there are a total of 24 tetrahedral intervals in space. Each tetrahedral interval consists of three active voltage vectors and one zero voltage vector.

[0085] Based on the calculated v ref The magnitude and direction of (k+1) make it easy to determine v. ref (k+1) is located within the tetrahedral interval. According to the principle of three-dimensional spatial vector modulation, the four inverter output voltage vectors constituting this tetrahedron (three active voltage vectors and one zero voltage vector) are related to v. ref The four output voltage vectors that are closest to (k+1) are selected as candidate vectors.

[0086] 3. Calculation of objective functions for each vector

[0087] The formulas for calculating the objective function corresponding to the voltage vector of each inverter are as follows:

[0088] g = [v αn (k+1)-v αnref (k+1)] 2 +[v βn (k+1)-v βnref (k+1)] 2 +[v γn (k+1)-v γnref (k+1)] 2

[0089] Where v αn (k+1), v βn (k+1), v γn (k+1) represents the coordinate components of each voltage vector of the inverter at the next moment, v αnref (k+1), v βnref (k+1), v γnref (k+1) represents the inverter virtual voltage reference vector v at the next moment. ref The coordinate components of (k+1).

[0090] 4. Calculation of the action time of the four vectors

[0091] Assuming that within one control cycle, four output voltage vectors v that constitute a single tetrahedron are selected. m1 v m2 v m3The four vectors v0 (m1, m2, and m3 are unequal natural numbers between 1 and 14) are combined to form a single virtual voltage vector v. p , as shown in equation (19).

[0092] v p =v m1 d1+v m2 d2+v m3 d3+v0d4 (19)

[0093] In the formula 0≤d i ≤1,d i This represents the duty cycle of a single output voltage vector, i = 1, 2, 3, 4.

[0094] To ensure control accuracy, v p The size and direction must be as close as possible to v. ref (k+1), based on which, the duty cycle weighted error d can be defined. i e i , where i = 1, 2, 3, 4. Where e i This represents the inverter output voltage error caused by a single voltage vector. The root mean square (RMS) value of the weighted error of the four switching vectors over one sampling period can be expressed as:

[0095]

[0096] Where g i (i = 1, 2, 3, 4) represent vector v respectively. m1 v m2 v m3 The objective function corresponding to v0.

[0097] In order to achieve the highest possible control precision, It must be as small as possible. In order to find... Minimum value, constructor make After solving, the duty cycles of the four voltage vectors d1, d2, d3, and d4 can be obtained:

[0098]

[0099] Therefore, within each control cycle, according to the voltage vector v m1 v m2 v m3 The objective functions corresponding to v0 are g1, g2, g3, and g4, from which the duty cycles d1, d2, d3, and d4 of each output voltage vector can be solved.

[0100] The formulas for calculating each objective function are as follows:

[0101] g i =[v αn,i (k+1)-v αnref (k+1)] 2 +[v βn,i (k+1)-v βnref (k+1)] 2 +[v γn,i (k+1)-v γnref (k+1)] 2 (twenty one)

[0102] v αn,i (k+1), v βn,i (k+1), v γn,i (k+1) represents vector v mi The coordinate components are given by i = 1, 2, 3, 4.

[0103] The simulation model was built and performed using MATLAB / Simulink as described above. The main simulation parameters are as follows: DC power supply V dc =700V, load voltage fundamental RMS value is 220V, rated frequency is 50Hz; three-phase filter inductor L = 2mH, filter capacitor C = 40μF, neutral line inductance L n =1mH; Sampling period T s =50μs.

[0104] When the analog voltage waveform is distorted, if the given voltage contains 10% of the 3rd harmonic, 5% of the 5th harmonic, and 5% of the 7th harmonic, Figures 5(a) to 5(b) The image shows the three-phase load voltage waveform and load voltage spectrum using a traditional finite set model for predictive control. Figures 6(a) to 6(b) The figures show the three-phase load voltage waveform and load voltage spectrum controlled by this invention. A comparison reveals that, compared to traditional finite set model predictive control, this invention, when simulating grid voltage waveform distortion, produces load voltage harmonic content closer to the given voltage, and can more accurately simulate grid voltage waveform distortion caused by specific harmonics.

[0105] The above embodiments are merely illustrative and do not constitute a limitation on the scope of the present invention. These embodiments can also be implemented in various other ways, and various omissions, substitutions, and modifications can be made without departing from the technical spirit of the present invention.

Claims

1. A method of four-vector model predictive voltage control based on grid simulator inverse link, characterized in that, The method comprises the following steps: Step one: collecting three-phase load voltage, three-phase load current and three-phase filter inductance current in real time, and performing Clarke coordinate transformation; Step two: According to the result of step one, calculate the next time inverter virtual voltage reference vector ; In coordinate system, each coordinate component 、 、 The specific calculation formula is as follows: ； ； ； where L represents the size of the three-phase filter inductance, C represents the size of the three-phase filter capacitance, L n represents the size of the neutral line inductance, , , respectively represent the three-phase load voltage reference values at the next sampling time, respectively represent the sizes of the three-phase load voltages, respectively represent the sizes of the three-phase load currents, respectively represent the sizes of the three-phase inductance currents; Step three: according to the principle of three-dimensional space vector modulation, judging The tetrahedron interval, find out with the four inverter output voltage vector, including three active output voltage vector v m1 , v m2 , v m3 And a zero voltage vector v0, wherein m1, m2, m3 are natural numbers between 1-14 not equal; The judgment The tetrahedron interval is specifically: 14 non-zero voltage vectors and 1 zero voltage vector of the three-phase four-bridge arm inverter constitute 24 tetrahedron intervals in space, each tetrahedron interval is composed of 3 active output voltage vectors and 1 zero output voltage vector v0; when When falling into the mth tetrahedron interval, m=1, 2, 3, 4…24, three active output voltage vectors v m1 , v m2 , v m3 and a zero voltage vector v0 that constitute the tetrahedron are selected, wherein m1, m2, m3 are natural numbers between 1-14 and not equal; Step four: calculate three active output voltage vectors v m1 , v m2 , v m3 corresponding to the objective functions g1, g2, g3 and the objective function g4 corresponding to the zero voltage vector v0; the calculation formula is as follows: ； wherein , , represent the coordinate components of the voltage vector v mi at the next instant, respectively, with i = 1,2,3,4, , , represent the coordinate components of the inverter virtual voltage reference vector at the next instant, respectively. Step five: according to the result of step four, calculate the duty cycles d1, d2, d3 of the three active voltage vectors v m1 , v m2 , v m3 and the duty cycle d4 of the zero voltage vector v0, and feed back the time d1T s , d2T s , d3T s , d4T s of each voltage vector in a sampling period to the modulator, and the modulator gives the switching signal, wherein T s represents the size of a sampling period; the duty cycles of the voltage vectors are calculated as follows: (5.1) The selected v m1 , v m2 , v m3 , v0 of step four are combined into a virtual voltage vector v p , and the action time of each voltage vector is no longer the entire control period, as shown below: ； wherein d1, d2, d3, d4 represent the duty ratio of voltage vector v m1 m2 m3 v0, respectively, and satisfy and d1, d2, d3, d4 are all greater than 0.​​ (5.2) define the duty cycle weighted error d i e i where e i represents the inverter output voltage error value caused by a single voltage vector, i = 1, 2, 3, 4; the root mean square value of the four voltage vector weighted errors in a control cycle is represented as : ； where g i represent the target functions corresponding to the voltage vectors v m1 , v m2 , v m3 , v0, respectively, i = 1, 2, 3, 4. (5.3) Constructor , let , , , four voltage vector duty cycles d1, d2, d3, d4 are obtained after solving ； Step six: returning to step one when the current sampling period ends.

2. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the four-vector model predictive voltage control method based on the grid simulator inverse link when executing the program.

3. A computer-readable storage medium having stored thereon a computer program, characterized in that, The processor implements the four-vector model predictive voltage control method based on the grid simulator inverse link when executing the program.

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