Static synchronous reactive power compensation method and system based on model predictive control

Abstract

The present application relates to the field of power electronic control, more particularly to a kind of static synchronous reactive power compensation method and system based on model predictive control, the present application is based on the discrete mathematical model of chain STATCOM, the predictive mathematical model considering the delay compensation of calculation and optimization target value function are established, according to the constraint condition considering the control set and the model predictive control algorithm of adaptive adjustment control set search step length, the output control quantity of current time control system is obtained, while the present application considers the unbalanced problem of the DC side voltage of chain structure, adopts three-layer DC side voltage equalization control strategy the present application overall analysis power factor after reactive power compensation, grid current harmonic content, compared with the chain STATCOM under traditional limited control set model predictive control strategy (FCS-MPC), solve the problem of voltage imbalance and H bridge unit control system is relatively complex and traditional control mode is difficult to realize fast control problem.

Description

Technical Field

[0001] This invention relates to the field of power electronic control, and more specifically to a static synchronous reactive power compensation method and system based on model predictive control. Background Technology

[0002] The power system permeates all sectors of a country. It is indispensable in important areas such as industrial and agricultural production and residential life. The rapid development of the national economy will inevitably lead to a sharp increase in the demand for power supply. The development of the power system fully reflects the country's comprehensive development level. On June 2, 2023, the National Energy Administration released the "Blue Book on the Development of New Power Systems", which proposed that new power systems should have four important characteristics: safety and efficiency, clean and low carbon, flexibility and intelligence integration. Among them, safety and efficiency are the most important basic prerequisites for the development of new power systems.

[0003] Although current power grids use reactive power compensation equipment, thyristor-controlled reactors (TCRs) and thyristor-switched capacitors (TSCs) are still widely used in compensation schemes. These are traditional static var compensators (SVCs). However, SVCs have poor compensation performance when the grid voltage fluctuates significantly and are themselves harmonic sources, generating high-order harmonics. Therefore, it is necessary to adopt a chain-structured static synchronous compensator (STATCOM). Compared to SVCs, STATCOMs have faster response times and better dynamic compensation performance. Moreover, the chain-structured main circuit can be applied to high-voltage, high-capacity reactive power compensation scenarios. The chain structure consists of multiple cascaded H-bridges, resulting in high integration and ease of maintenance and repair. For example, Chinese patent CN117691620A discloses a reactive power compensation circuit, compensation method, computer equipment, and storage. The medium includes a smart meter and a reactive power compensation module; the smart meter and the reactive power compensation module are connected to the equipment and the load respectively, and the reactive power compensation module is connected to the smart meter; the smart meter is used to detect reactive power; the reactive power compensation module includes four sets of relays, three sets of mechanical adjustable capacitors and a smart management module; the smart management module is used to calculate the current required capacitor capacity based on the information detected by the smart meter, thereby controlling the corresponding relays to close or open, so as to connect or disconnect the corresponding mechanical adjustable capacitors to compensate for reactive power. However, due to the large number of DC-side capacitors in the chain-structured STATCOM and the independence of each module, the problem of DC-side capacitor voltage imbalance is inevitable. In addition, the large number of H-bridge units also makes the control system more complex and traditional control methods difficult to achieve fast and effective control. Summary of the Invention

[0004] To better address the above problems, this invention provides a static synchronous reactive power compensation method based on model predictive control, the method comprising the following steps: Step S1: Based on the equivalent circuit of the three-phase star-chain STATCOM, the mathematical model of the chain STATCOM is obtained, and then discretized by the forward Euler algorithm. After considering the calculation of delay compensation, the optimization objective value function of the model predictive controller is finally obtained. Step S2: Calculate the search step size of the model predictive controller using the output current and reference current of the chained STATCOM and the voltage deadbeat model of the chained STATCOM. Under the control set constraints, traverse the search space to find the control set that minimizes the value function and use it as the output of the model predictive controller. Step S3: To address the issue of unbalanced DC-side capacitor voltage in the chained STATCOM, a three-layer control strategy for DC-side capacitor voltage is adopted, namely global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system's H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM).

[0005] As a preferred embodiment of the present invention, in step S1, based on the equivalent circuit of a three-phase star-connected chain STATCOM, the mathematical model of the chain STATCOM is obtained, and then discretized using the forward Euler algorithm. After considering the calculation of delay compensation, the optimization objective value function of the model predictive controller is finally obtained. The specific steps are as follows: Based on the equivalent circuit of a three-phase star-connected STATCOM and Kirnov's voltage law, the mathematical model of the chained STATCOM system in the abc coordinate system can be written. Using the Clark transformation matrix, the mathematical model of the system in the abc coordinate system can be transformed to the αβ two-phase stationary coordinate system. The specific mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is as follows: Sampling control period in and Let be the instantaneous voltage in the αβ two-phase stationary coordinate system, and and Let α and β be the instantaneous currents in the α and β two-phase stationary coordinate system, L be the filter inductance, and R be the system equivalent resistance.

[0006] As a preferred embodiment of the present invention, in step S2, the search step size of the model predictive controller is calculated using the output current and reference current of the chained STATCOM and the voltage deadbeat model of the chained STATCOM. Under the control set constraints, the search space is traversed to find the control set that minimizes the value function and this set is used as the output of the model predictive controller. The specific steps are as follows: Based on the aforementioned formula and assuming that the predicted current perfectly tracks the reference current, the deadbeat voltage prediction output of the chained STATCOM system can be obtained. The specific mathematical model for deadbeat voltage prediction of the chained STATCOM system is as follows: The system output current at time k obtained from sampling , Output voltage , The search step size required for the model predictive controller optimization at time k can be calculated using the system voltage prediction value at time k+1 and the reference current at time k, as calculated above. The specific formula for calculating the search step size is as follows: Where: e is the adaptive adjustment parameter. The magnitude of the system output current. Let be the rated voltage of the DC-side capacitor of the H-bridge in the system, l1 and l2 be weighting coefficients, e be 1, and l1 and l2 be 0.5. The constraints on the search step size are as follows: Where: z represents the z mentioned earlier. ab (k), z max With z min Based on engineering experience, take respectively and .

[0007] As a preferred embodiment of the present invention, step S3 employs a three-layer control strategy for the DC-side capacitor voltage, namely global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system's H-bridge switching devices are obtained via carrier phase-shift pulse width modulation (CPS-PWM). The specific steps are as follows: The active power reference current of the system is obtained by proportional-integral (PI) regulation control based on the difference between the three-phase total voltage and the rated value of the DC-side capacitor voltage of the system H-bridge. This is to achieve the balance of the overall active power of the system, and thus realize the balanced control of the global DC voltage.

[0008] As a preferred embodiment of the present invention, step S3 employs an intra-phase voltage equalization control method by superimposing an additional control signal after generating the modulation wave. The specific method for generating the modulation wave signal is as follows: Where: x = a, b, c, j = 1, 2, 3, ..., N, mx is the modulation wave of phase x. The final modulated wave signal mxj is obtained by superimposing the additional control signal on the x-phase voltage output by the control system in the previous steps.

[0009] Where: mxj is the modulation signal of the j-th H-bridge unit in phase x. The control signal is obtained by passing the difference between the DC side capacitor voltage and the rated capacitor voltage of each H-bridge through the PI regulator. KCHG-x is the charging and discharging coefficient of phase x, and its value is equal to the positive or negative sign of the output current of the x-phase chained STATCOM system, taking only -1, 0, and 1. The modulated wave signal and its inverted signal are compared with a series of triangular carrier signals with phase angles of π / N, generating two sets of PWM waves to drive the left and right arms of the N H-bridges of the system respectively.

[0010] As a preferred embodiment of the present invention, the search step size and the control set S at time k-1 calculated in step S2 are described above. MPC (k-1)=[u cα (k-1),u cβ From (k-1)], we can obtain the control set at time k. The specific control set at time k is as follows: in, m is the optimization range, which can generally be any integer.

[0011] The control set constraints considered during the optimization process are as follows: ; Calculate the predicted current based on the current control set. and Then, the value function J is calculated using the reference current obtained from the multi-step prediction and the aforementioned value function calculation formula. The above steps are repeated until all possible control sets SMPC(k) at time k are traversed. At this time, the model predicts the controller output of the control set SMPC-opt that minimizes the value function J.

[0012] As a preferred embodiment of the present invention, in step S1, considering the calculation delay of the control system, multi-step prediction is required to compensate for the calculation delay. The specific method is as follows: In the k-th sampling control cycle, the optimal switching state calculated in the (k-1)-th sampling control cycle is applied, and the predicted current value at time k+1 is calculated using the prediction model. Furthermore, the predicted current value at time k+2 is calculated using the predicted current value at time k+1. At this point, the optimization search finds the objective value function. The minimum switching state, which acts on the converter at time k+1, is specifically considered in the prediction model for calculating delay compensation as follows: in, and It can be predicted by the following formula: Where ω is the angular frequency of the grid voltage; Based on the prediction model for calculating delay compensation and the prediction reference values ​​for multi-step prediction, the optimization objective value function of the model prediction controller can be obtained: ,in The reference value for the control system after multi-step prediction is as follows: The specific multi-step prediction method is as follows: .

[0013] As a preferred technical solution of the present invention, step S3 employs a zero-sequence voltage injection method to achieve the balance of active power among the three phases, thereby realizing the phase-to-phase DC voltage equalization control. First, the difference between the sampled real-time DC-side voltage of each phase and the rated value of the DC-side capacitor voltage of the system H-bridge is used for PI regulation control to obtain the changes in active power DPa, DPb, and DPc of each phase. Then, these changes are transformed to the αβ two-phase stationary coordinate system, where DPa and DPb are obtained. A low-pass filter is used before the PI regulator to filter out the second harmonic component of the DC-side voltage. The characteristic angular frequency of the low-pass filter is 100π. Finally, the cosine and sinine components of the zero-sequence voltage are calculated using the following formula: Where U0 is the magnitude of the zero-sequence voltage, j0 is the initial phase angle of the zero-sequence voltage, and the specific form of the matrix CZSV is as follows: in, and These are the system's active reference current and reactive reference current, respectively. Finally, the zero-sequence voltage u0 is calculated: ; The calculated zero-sequence voltage is directly superimposed on the output of the model predictive controller.

[0014] As a preferred embodiment of the present invention, in step S1, the forward Euler algorithm is used to approximate the differential using the difference, and the discrete mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is obtained through the mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system, that is, the prediction model is as follows: in: and It predicts the current output of the chained STATCOM at time k+1. and It is the current value of the chained STATCOM output sampled from the circuit at time k. and This is the measured voltage value of the three-phase power grid at time k. and It is a control variable, and its value is calculated by the controller at time k. s The sampling period.

[0015] The present invention also provides a static synchronous reactive power compensation system based on model predictive control. The system includes: a computing unit for the equivalent circuit of a three-phase star-chain STATCOM, obtaining the mathematical model of the chain STATCOM, discretizing it through the forward Euler algorithm, considering the calculation of delay compensation, and finally obtaining the optimization objective value function of the model predictive controller. The output unit is used to calculate the search step size of the model predictive controller by calculating the output current and reference current of the chained STATCOM and the voltage deadbeat model of the chained STATCOM. Under the control set constraints, the search space is traversed to find the control set that minimizes the value function and it is used as the output of the model predictive controller. The control unit employs a three-layer control strategy for the DC-side capacitor voltage imbalance problem of the chained STATCOM: global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system's H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM).

[0016] Compared with the prior art, the beneficial effects of the present invention are at least as follows: This invention proposes a chained STATCOM system based on model predictive control. This system integrates a multi-cascaded H-bridge chained STATCOM system, a model predictive control strategy, and a DC-side capacitor voltage hierarchical control strategy. It achieves effective control of the output current and DC-side voltage of the chained STATCOM, thereby improving the reactive power compensation effect and power quality of the power system. Specifically, it uses a deadbeat model of system voltage and current reference values ​​to establish a mathematical model of the control set search step size, thereby optimizing the search time of the predictive control set. Compared with traditional control methods in the prior art, this strategy can control the output of the STATCOM more accurately, effectively, and quickly, thereby improving the power factor of the system and improving the power quality of the power grid. Attached Figure Description

[0017] Figure 1 This is a flowchart of a static synchronous reactive power compensation method based on model predictive control according to the present invention. Figure 2 This is a structural diagram of a static synchronous reactive power compensation system based on model predictive control according to the present invention. Figure 3 This is the control flowchart of the chained STATCOM model predictive controller in this invention; Figure 4 The diagram shows the three-phase current waveforms of the power grid before and after compensation for the chained STATCOM system and the chained STATCOM system based on the traditional FCS-MPC in this invention. Figure 5 The above are FFT analysis diagrams of the grid current after compensation for the chained STATCOM system in this invention and the chained STATCOM system based on the traditional FCS-MPC. Figure 6 The diagram shows the power factor of the chain-type STATCOM system in this invention before and after compensation under high voltage conditions. Figure 7 The diagram shows the grid current waveforms before and after compensation for the chain-type STATCOM system in this invention under high voltage conditions. Figure 8 This is an FFT analysis diagram of the grid current after compensation under high voltage conditions for the chained STATCOM system in this invention; Figure 9 The diagram shows the three-phase current waveforms of the power grid before and after compensation for the chained STATCOM system in this invention under nonlinear load access. Figure 10 This is an FFT analysis diagram of the grid current before and after compensation for the chained STATCOM system in this invention under nonlinear load access; Figure 11 This is a topology diagram of the main circuit of the chain-type STATCOM system in this invention; Figure 12 This is a control block diagram of the chained STATCOM system for model predictive control in this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] This invention provides a static synchronous reactive power compensation method based on model predictive control, such as... Figure 1 As shown, the system includes: Step S1: Based on the equivalent circuit of the three-phase star-chain STATCOM, the mathematical model of the chain STATCOM is obtained, and then discretized by the forward Euler algorithm. After considering the calculation of delay compensation, the optimization objective value function of the model predictive controller is finally obtained. Step S2: Calculate the search step size of the model predictive controller using the output current and reference current of the chained STATCOM and the voltage deadbeat model of the chained STATCOM. Under the control set constraints, traverse the search space to find the control set that minimizes the value function and use it as the output of the model predictive controller. Step S3: To address the issue of unbalanced DC-side capacitor voltage in the chained STATCOM, a three-layer control strategy for DC-side capacitor voltage is adopted, namely global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system's H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM).

[0020] Specifically, in step S1, based on the equivalent circuit of a three-phase star-chain STATCOM, a complex mathematical model is established using basic circuit laws and coordinate transformation theory. Then, the model is discretized using the forward Euler algorithm, taking into full account the impact of computational delay compensation, thus carefully constructing the optimal objective value function of the model predictive controller. In step S2, utilizing the difference between the output current and reference current of the chain STATCOM, combined with its voltage deadbeat model, the search step size of the model predictive controller is accurately calculated. Under strict control set constraints, the search space is fully traversed to find the control set that minimizes the value function, which is then used as the output of the model predictive controller, achieving precise control of the control quantity. In step S3, addressing the critical issue of DC-side capacitor voltage imbalance in the chain STATCOM, a three-layer control strategy for DC-side capacitor voltage is adopted, performing equalization control at the global, inter-phase, and intra-phase levels. Carrier phase-shift pulse width modulation (CPS-PWM) technology is used to accurately transmit the control signal to the system's H-bridge switching devices. Through this series of closely coordinated steps, efficient compensation of static synchronous reactive power and significant improvement in power quality are achieved, effectively enhancing the stability and reliability of the power grid operation.

[0021] Furthermore, in step S1, based on the equivalent circuit of the three-phase star-connected chain STATCOM, the mathematical model of the chain STATCOM is obtained, and then discretized using the forward Euler algorithm. After considering the calculation of delay compensation, the optimization objective value function of the model predictive controller is finally obtained. The specific steps are as follows: Based on the equivalent circuit of a three-phase star-connected STATCOM and Kirnov's voltage law, the mathematical model of the chained STATCOM system in the abc coordinate system can be written. Using the Clark transformation matrix, the mathematical model of the system in the abc coordinate system can be transformed to the αβ two-phase stationary coordinate system. The specific mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is as follows: Sampling control period in and Let be the instantaneous voltage in the αβ two-phase stationary coordinate system, and and Let α and β be the instantaneous currents in the α and β two-phase stationary coordinate system, L be the filter inductance, and R be the system equivalent resistance.

[0022] Specifically, based on the structural characteristics of the equivalent circuit of a three-phase star-chain STATCOM and Kirnov's voltage law, the relationship between voltage and current in each part of the circuit is analyzed in detail, thus accurately writing the mathematical model of the chain STATCOM system in the abc coordinate system. Since the model analysis in the abc coordinate system is relatively complex, the CLARK transformation matrix is ​​used to cleverly transform it to the αβ two-phase stationary coordinate system, making the analysis and calculation of the model simpler. Then, using the forward Euler algorithm and the principle of difference approximation to replace differentiation, the model in the αβ two-phase stationary coordinate system is discretized, transforming the continuous model into a discrete form, which is convenient for digital control system processing. On this basis, taking into full account the factor of computational delay compensation, the optimization objective value function of the model predictive controller is finally successfully established through multi-step prediction and other methods, providing an important basis for subsequent control decisions.

[0023] Furthermore, in step S2, the search step size of the model predictive controller is calculated using the output current and reference current of the chained STATCOM and the deadbeat voltage model of the chained STATCOM. Under the control set constraints, the search space is traversed to find the control set that minimizes the value function, which is then used as the output of the model predictive controller. The specific steps are as follows: Based on the aforementioned formula and assuming that the predicted current perfectly tracks the reference current, the deadbeat voltage prediction output of the chained STATCOM system can be obtained. The specific mathematical model for deadbeat voltage prediction of the chained STATCOM system is as follows:

[0024] The system output current at time k obtained from sampling , Output voltage , The search step size required for the model predictive controller optimization at time k can be calculated using the system voltage prediction value at time k+1 and the reference current at time k, as calculated above. The specific formula for calculating the search step size is as follows: Where: e is the adaptive adjustment parameter. The magnitude of the system output current. Let be the rated voltage of the DC-side capacitor of the H-bridge in the system, l1 and l2 be weighting coefficients, e be 1, and l1 and l2 be 0.5. The constraints on the search step size are as follows: Where: z represents the z mentioned earlier. ab (k), z max With z min Based on engineering experience, take respectively and .

[0025] Specifically, based on the operating characteristics of the chained STATCOM system and the established mathematical model, and assuming the ideal situation where the predicted current perfectly tracks the reference current, the deadbeat voltage prediction output of the chained STATCOM system is derived, thus obtaining the deadbeat voltage prediction mathematical model. Using this model, combined with the sampled system output current and voltage at time k, and the calculated system voltage prediction value at time k+1 and the reference current at time k, a series of rigorous mathematical calculations are performed to accurately calculate the search step size required for the model predictive controller to optimize at time k. During the calculation of the search step size, adaptive adjustment parameters and weighting coefficients are also set to improve the accuracy and adaptability of the search step size. After obtaining the search step size, under strict control set constraints, the search space is fully traversed, and the value function corresponding to each possible control set is calculated one by one. By comparing the magnitudes of all value functions, the control set that minimizes the value function is found and used as the output of the model predictive controller, ensuring that the controller can make the optimal control decision based on the real-time state of the system.

[0026] Furthermore, in step S3, a three-layer control strategy for the DC-side capacitor voltage is adopted, namely global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM). The specific steps are as follows: The active power reference current of the system is obtained by proportional-integral (PI) regulation control based on the difference between the three-phase total voltage and the rated value of the DC-side capacitor voltage of the system H-bridge. This is to achieve the balance of the overall active power of the system, and thus realize the balanced control of the global DC voltage.

[0027] Specifically, by monitoring the three-phase total voltage in real time and comparing it with the rated voltage of the DC-side capacitor of the system H-bridge, the difference between the two is obtained. This difference is used as the input signal of the proportional-integral (PI) regulator. Utilizing the PI regulator's rapid response and precise adjustment capability to error signals, the difference is adjusted and controlled. After PI regulation, the system active power reference current is obtained. By controlling the active power reference current, the overall active power of the system is precisely balanced. When the overall active power of the system is balanced, the charging and discharging process of the DC-side capacitor reaches a stable state, thereby achieving balanced control of the global DC voltage. This ensures the stability of the DC-side voltage of the chain-type STATCOM and provides a strong guarantee for the reliable operation of the system.

[0028] Furthermore, step S3 employs an additional control signal superimposed after the modulation wave is generated to perform intra-phase voltage equalization control. The specific method for generating the modulation wave signal is as follows: Where: x = a, b, c, j = 1, 2, 3, ..., N, mx is the modulation wave of phase x. The final modulated wave signal mxj is obtained by superimposing the additional control signal on the x-phase voltage output by the control system in the previous steps. Where: mxj is the modulation signal of the j-th H-bridge unit in phase x. The control signal is obtained by passing the difference between the DC side capacitor voltage and the rated capacitor voltage of each H-bridge through the PI regulator. KCHG-x is the charging and discharging coefficient of phase x, and its value is equal to the positive or negative sign of the output current of the x-phase chained STATCOM system, taking only -1, 0, and 1. The modulated wave signal and its inverted signal are compared with a series of triangular carrier signals with phase angles of π / N, generating two sets of PWM waves to drive the left and right arms of the N H-bridges of the system respectively.

[0029] Specifically, a modulation wave signal is first generated according to a specific formula. This modulation wave signal reflects the control requirements during normal system operation. To achieve phase-to-phase voltage equalization control, an additional control signal is superimposed on the modulation wave. The additional control signal is obtained by the difference between the DC-side capacitor voltage and the rated capacitor voltage of each H-bridge through a PI regulator, and then combined with the charge-discharge coefficient. The charge-discharge coefficient is determined according to the positive and negative signs of the output current of the x-phase chained STATCOM system, and only takes three values: -1, 0, and 1. This allows for flexible adjustment of the H-bridge's operating state according to the current direction, achieving phase-to-phase capacitor voltage equalization. After generating the final modulation wave signal, the modulation wave signal and its inverse signal are compared with a series of triangular carrier signals with a phase angle of π / N. Based on the comparison results, two sets of PWM waves are generated. These two sets of PWM waves are used to drive the left and right arms of the N H-bridges in the system, thereby achieving precise control of the H-bridge switching devices and achieving phase-to-phase voltage equalization control, effectively solving the problem of phase-to-phase DC voltage imbalance.

[0030] Furthermore, the search step size calculated in step S2 and the control set S at time k-1 are... MPC (k-1)=[u cα (k-1),u cβ From (k-1)], we can obtain the control set at time k. The specific control set at time k is as follows: in, m is the optimization range, which can generally be any integer.

[0031] The control set constraints considered during the optimization process are as follows: ; Calculate the predicted current based on the current control set. and Then, the value function J is calculated using the reference current obtained from the multi-step prediction and the aforementioned value function calculation formula. The above steps are repeated until all possible control sets SMPC(k) at time k are traversed. At this time, the model predicts the controller output of the control set SMPC-opt that minimizes the value function J.

[0032] Specifically, using the search step size calculated in claim 3, combined with the control set SMPC(k-1) = [ucα(k-1), ucβ(k-1)] at time k-1, the control set at time k is obtained according to a specific calculation formula. In this process, the optimization range m is an important parameter, generally taking any integer value, which determines the search range of the control set. During the optimization process, the constraints of the control set are fully considered. These constraints are set according to the actual operating requirements and safety limits of the system to ensure that the value of the control set is within a reasonable range. Based on the current control set, the predicted current i(k+2) and i(k+2) are calculated using the mathematical model of the system. Then, combined with the reference current obtained from multi-step prediction and the value function calculation formula established in claim 1, the value function J is accurately calculated. The above steps of calculating the control set, predicting the current, and calculating the value function are repeated until all possible control sets SMPC(k) at time k are traversed. By comparing the magnitudes of all value functions J, the control set SMPC-opt that minimizes the value function J is finally found and used as the output of the model predictive controller, thus realizing the optimized selection of the control quantity and improving the control performance of the system.

[0033] Furthermore, in step S1, considering the computational delay of the control system, multi-step prediction is needed to compensate for the computational delay. The specific method is as follows: In the k-th sampling control cycle, the optimal switching state calculated in the (k-1)-th sampling control cycle is applied, and the predicted current value at time k+1 is calculated using the prediction model. Furthermore, the predicted current value at time k+2 is calculated using the predicted current value at time k+1. At this point, the optimization search finds the objective value function. The minimum switching state, which acts on the converter at time k+1, is specifically considered in the prediction model for calculating delay compensation as follows: in, and It can be predicted by the following formula: Where ω is the angular frequency of the grid voltage; Based on the prediction model for calculating delay compensation and the prediction reference values ​​for multi-step prediction, the optimization objective value function of the model predictive controller can be obtained: ,in The reference value for the control system after multi-step prediction is as follows: The specific multi-step prediction method is as follows: .

[0034] Specifically, during the k-th sampling control cycle, due to the computational delay in the control system, the optimal control decision cannot be obtained in real time. Therefore, the optimal switching state calculated during the (k-1)-th sampling control cycle is applied to ensure that the system can maintain a relatively stable operating state during the computational delay. Simultaneously, using the established prediction model, the predicted current value i(k+1) at time k+1 is calculated based on the current system state information. Then, based on the predicted current value at time k+1, the predicted current value i(k+2) at time k+2 is further calculated. Through this series of multi-step steps... The system predicts the future state of the system and then optimizes to find the switching state that minimizes the objective value function. This switching state acts on the converter at time k+1, thereby effectively compensating for the computational delay. In this process, using a specific prediction model calculation formula and combining parameters such as grid voltage and angular frequency, u_scx(k+1) and u_sβ(k+1) are accurately predicted, thus obtaining the optimized objective value function of the model predictive controller. In this way, the impact of computational delay on system control is fully considered, ensuring the stable operation and precise control of the system under complex operating conditions.

[0035] Furthermore, in step S3, the zero-sequence voltage injection method is used to achieve the balance of active power among the three phases, thereby realizing the phase-to-phase DC voltage equalization control. First, the difference between the sampled real-time DC side voltage of each phase and the rated value of the DC side capacitor voltage of the system H-bridge is used for PI regulation control to obtain the changes in active power DPa, DPb, and DPc of each phase. Then, these are transformed to the αβ two-phase stationary coordinate system to obtain DPa and DPb. A low-pass filter needs to be used before the PI regulator to filter out the second harmonic component of the DC side voltage. The characteristic angular frequency of the low-pass filter is 100π. Then, the cosine and sinine components of the zero-sequence voltage are calculated by the formula as follows:

[0036] Where U0 is the magnitude of the zero-sequence voltage, j0 is the initial phase angle of the zero-sequence voltage, and the specific form of the matrix CZSV is as follows: in, and These are the system's active reference current and reactive reference current, respectively. Finally, the zero-sequence voltage u0 is calculated: ; The calculated zero-sequence voltage is directly superimposed on the output of the model predictive controller.

[0037] Specifically, the real-time DC-side voltage of each phase is first accurately sampled. The sampled phase voltage is then compared with the rated value of the DC-side capacitor voltage of the system H-bridge to obtain the difference between the phase voltage and the rated value. These differences are then input into the PI controller for regulation and control. To avoid interference from the second harmonic component of the DC-side voltage during the regulation process, a low-pass filter is used before the PI controller to filter out the second harmonic component. The characteristic angular frequency of the low-pass filter is set to 100π to ensure that the signal input to the PI controller is stable and reliable. After PI regulation, the active power changes DPa, DPb, and DPc of each phase are obtained. These active power changes are then transformed to the αβ two-phase static voltage. In the coordinate system, DPα and DPβ are obtained. Based on these transformed changes in active power, the cosine and sinine components of the zero-sequence voltage are calculated using specific formulas. The formulas involve parameters such as the amplitude U0 of the zero-sequence voltage, the initial phase angle j0, and the active reference current and reactive reference current. Through precise calculation and processing of these parameters, the zero-sequence voltage u0 is finally calculated. The calculated zero-sequence voltage is directly superimposed on the output of the model predictive controller. By injecting the zero-sequence voltage, the active power balance between the three phases is achieved, thereby achieving the purpose of phase-to-phase DC voltage balance control. This effectively solves the problem of phase-to-phase DC voltage imbalance and improves the overall performance of the system.

[0038] Further, in step S1, the forward Euler algorithm uses the difference approximation to replace the differential, and the discrete mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is obtained through the mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system, that is, the prediction model is as follows: in: and It predicts the current output of the chained STATCOM at time k+1. and It is the current value of the chained STATCOM output sampled from the circuit at time k. and This is the measured voltage value of the three-phase power grid at time k. and It is a control variable, and its value is calculated by the controller at time k.s The sampling period.

[0039] Specifically, the forward Euler algorithm is a commonly used numerical calculation method. It uses the principle of difference approximation to replace differential to discretize the continuous mathematical model. In the αβ two-phase stationary coordinate system, the mathematical model of the chained STATCOM system describes the dynamic relationship between variables such as current and voltage in the system. Using the forward Euler algorithm, the mathematical model is processed, and the differential part of the model is expressed in difference form. By analyzing and calculating the values ​​of each variable in the model at different times, the discrete mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is obtained, that is, the prediction model. In this prediction model, the relationship between the predicted current value output by the chained STATCOM at time k+1 and the current value sampled from the circuit at time k, the measured voltage value of the three-phase power grid, and the control variables is clarified, providing an important basic model for subsequent control algorithm design and system state prediction.

[0040] This invention also provides a static synchronous reactive power compensation system based on model predictive control, such as... Figure 2 As shown, the system includes: a computing unit for the equivalent circuit of a three-phase star-connected chain STATCOM, which obtains the mathematical model of the chain STATCOM, discretizes it using the forward Euler algorithm, considers computational delay compensation, and finally obtains the optimization objective value function of the model predictive controller. The output unit is used to calculate the search step size of the model predictive controller by calculating the output current and reference current of the chained STATCOM and the voltage deadbeat model of the chained STATCOM. Under the control set constraints, the search space is traversed to find the control set that minimizes the value function and it is used as the output of the model predictive controller. The control unit employs a three-layer control strategy for the DC-side capacitor voltage imbalance problem of the chained STATCOM: global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system's H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM).

[0041] Specifically, the computational unit, based on the equivalent circuit of a three-phase star-chain STATCOM, meticulously establishes the optimization objective value function of the model predictive controller using a series of complex techniques, including circuit analysis, coordinate transformation, discretization, and compensation for computational delays. This provides a core evaluation index for the system's control decisions. The output unit utilizes real-time data from the chain STATCOM's output and reference currents, combined with a deadbeat voltage model, to accurately calculate the search step size of the model predictive controller. Under strict control set constraints, it comprehensively and meticulously traverses the search space to find the control set that minimizes the value function, and uses this set as the basis for the model predictive controller. The controller output enables precise selection of control quantities. Addressing the challenge of unbalanced DC-side capacitor voltage in chain-type STATCOM systems, the control unit employs a three-layer control strategy for DC-side capacitor voltage, performing comprehensive balancing control at the global, inter-phase, and intra-phase levels. Through carrier phase-shift pulse width modulation (CPS-PWM) technology, the control signal is accurately transmitted to the system's H-bridge switching devices, achieving precise control of the H-bridge switching state. Through the close cooperation of the computing unit, output unit, and control unit, efficient compensation of static synchronous reactive power and significant improvement in power quality are achieved, ensuring stable and reliable grid operation.

[0042] To verify the effectiveness and superiority of this invention, a control method was designed according to the above process, and simulation experiments were conducted using MATLAB / Simulink. The results were compared with a chain-type STATCOM system based on the traditional FCS-MPC. The simulation parameters are shown in Table 1.

[0043] like Figure 4 As shown, the three-phase current waveforms of the power grid before and after compensation are compared between the chained STATCOM system and the chained STATCOM system based on the traditional FCS-MPC. It can be seen that before compensation, the initial phase of the three-phase current of the power grid is significantly lagging. After compensation, both methods of controlling the chained STATCOM achieve the compensation effect. However, the power grid current waveform after compensation by the chained STATCOM system based on the traditional FCS-MPC is significantly distorted. The power grid current waveform after compensation by the chained STATCOM system of the present invention is still a good sine waveform after a short dynamic response process, indicating that the compensation effect of the present invention is better and the dynamic response is faster.

[0044] like Figure 5As shown, the FFT analysis results of the compensated grid current of the chained STATCOM system and the chained STATCOM system based on the traditional FCS-MPC show that the total harmonic distortion (THD) of the compensated grid current of the chained STATCOM system based on the traditional FCS-MPC reaches 6.50%, and the content of low-order harmonics exceeds 5%. In contrast, the THD of the compensated grid current of the chained STATCOM system of this invention is only 2.68%, which is lower than the 5% design requirement of general reactive power compensators, and the content of each harmonic is less than 0.55%. This indicates that the chained STATCOM system of this invention has low harmonic pollution of the grid current after compensation and can suppress the harmonics of the grid current to a certain extent.

[0045] To verify the reactive power compensation effect of this invention under high voltage conditions, a control method was designed according to the above process, and simulation experiments were conducted using MATLAB / Simulink. The simulation parameters are shown in Table 2.

[0046] like Figure 6 As shown, the power factor of the chain-type STATCOM system before and after compensation under high voltage conditions is as follows. It can be seen that the power factor of the grid before compensation is about 0.707, which is relatively low. After compensation, it reaches about 0.99, indicating that the present invention can play a good compensation role under high voltage and large capacity conditions and effectively improve the power factor of the grid.

[0047] like Figure 7 As shown, the grid current waveforms before and after compensation of the chained STATCOM system under high voltage conditions show that the dynamic process after the reactive power compensation system is connected is about 0.01s. Subsequently, the current stabilizes and the phase no longer lags. The stable current waveform is almost a sine wave. This shows that the compensation effect, dynamic performance and steady-state performance of the present invention are still very good under high voltage and a large number of cascaded H-bridges.

[0048] like Figure 8 As shown in the figure, the FFT analysis results of the grid current after compensation under high voltage conditions of the chained STATCOM system show that the THD of the grid current after compensation by the chained STATCOM system of the present invention is 0.12%. At this time, there are basically no harmonics in the grid current, indicating that the present invention has a good compensation effect under high voltage conditions and does not generate additional harmonics. It can suppress some harmonics of the grid to a certain extent.

[0049] To verify the reactive power compensation effect of the present invention under nonlinear load conditions, the control method was designed according to the above process, and simulation experiments were conducted using MATLAB / Simulink. The simulation parameters are shown in Table 2.

[0050] like Figure 9 As shown, the three-phase current waveforms of the power grid before and after compensation under the nonlinear load connection of the chained STATCOM system can be seen. It can be seen that the power grid current exhibited significant distortion before the reactive power compensation system was connected. However, after the chained STATCOM system of the present invention was connected, not only was the compensation effect achieved and the power grid current no longer exhibited phase lag, but the distortion rate of the current waveform also decreased, becoming close to a sine wave. This demonstrates that the present invention can suppress harmonics in the power grid current and effectively compensate reactive power under the large-scale connection of nonlinear loads.

[0051] like Figure 10 As shown, the FFT analysis results of the grid current before and after compensation under nonlinear load access in the chained STATCOM system show that the THD of the grid current before compensation is 3.64%, with high levels of 5th, 7th, 11th, and 13th harmonics, all exceeding 0.7% and reaching a maximum of 2.5%. After compensation, the THD of the grid current is 1.47%, with the odd harmonics of 5th, 7th, 11th, and 13th, which have a significant impact on power quality, effectively suppressed, with their levels all below 0.16%. This demonstrates that the present invention can achieve the suppression effect of 5th, 7th, 11th, and 13th harmonics in the grid current under nonlinear load access.

[0052] In summary, firstly, based on the equivalent circuit of a three-phase star-connected STATCOM and Kirchhoff's voltage law, a mathematical model of the chained STATCOM system in the abc coordinate system is derived. To simplify subsequent calculations, the CLARK transformation matrix is ​​used to transform this mathematical model to the αβ two-phase stationary coordinate system, obtaining a mathematical model related to parameters such as instantaneous voltage, current, filter inductance, and system equivalent resistance in the αβ two-phase stationary coordinate system. Next, using the forward Euler algorithm to approximate the differential with a difference approximation, and based on the mathematical model in the αβ two-phase stationary coordinate system, a discrete mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system, i.e., the predictive model, is further derived. The model is used to predict the current value output by the chained STATCOM at time k+1. Considering the computational delay in the control system, multi-step prediction is used to compensate for the computational delay in order to ensure the accuracy of the control. In the kth sampling control cycle, the optimal switching state calculated in the (k-1)th sampling control cycle is applied to calculate the predicted current value at time k+1 using the prediction model, and then the predicted current value at time k+2 is calculated. By optimization, the switching state that minimizes the objective value function is found. This switching state acts on the converter at time k+1. Finally, based on the prediction model that considers computational delay compensation and the prediction reference value of multi-step prediction, the optimized objective value function of the model predictive controller is successfully obtained.

[0053] Assuming the predicted current perfectly tracks the reference current, based on the previously derived formula, a deadbeat voltage prediction output mathematical model for a chained STATCOM system is obtained. In actual operation, the system output current and voltage at time k are obtained by sampling. Combined with the previously calculated predicted system voltage at time k+1 and the reference current at time k, the search step size required for the model predictive controller to optimize at time k can be calculated according to a specific calculation formula. The search step size is subject to certain constraints, which are set based on engineering experience. Based on the calculated search step size and the control set at time k-1, the control set at time k can be obtained. During the optimization process, considering the constraints of the control set, the predicted current is calculated based on the current control set. Then, combined with the reference current obtained from multiple predictions and the previously obtained value function calculation formula, the value function J is calculated. The above calculation and optimization steps are repeated until all possible control sets at time k are traversed. Finally, the model predictive controller outputs the control set that minimizes the value function J, which is used as the control output at the current time.

[0054] Subsequently, a three-layer control strategy for DC-side capacitor voltage is adopted. For global DC voltage balance control, proportional-integral (PI) regulation is applied to the difference between the three-phase total voltage and the rated value of the DC-side capacitor voltage of the system H-bridge, thereby obtaining the system's active power reference current. This achieves overall system active power balance and ultimately global DC voltage balance control. For inter-phase DC voltage balance control, a zero-sequence voltage injection method is used. First, PI regulation is applied to the difference between the sampled real-time DC-side voltage of each phase and the rated value of the DC-side capacitor voltage of the system H-bridge, obtaining the change in active power of each phase. This change is then transformed into the αβ two-phase stationary coordinate system. During this process, a low-pass filter is used before the PI regulator to filter out the second harmonic component of the DC-side voltage (the characteristic angular frequency of the low-pass filter is 100π). Then, the cosine and sinine components of the zero-sequence voltage are calculated according to a specific formula. The zero-sequence voltage is obtained and directly superimposed on the output of the model predictive controller to achieve the balance of active power among the three phases and the purpose of phase-to-phase DC voltage equalization control. In terms of phase-to-phase DC voltage equalization control, an additional control signal is superimposed after the modulation wave is generated. First, the modulation wave signal is generated according to a specific formula. Then, the control signal obtained by the difference between the DC side capacitor voltage and the rated capacitor voltage of each H-bridge is superimposed through the PI regulator. Then, the charging and discharging coefficient of phase x (whose value is equal to the positive and negative signs of the output current of the x-phase chained STATCOM system, taking only -1, 0, 1) is combined to obtain the final modulation wave signal. Finally, the final modulation wave signal and its inverse signal are compared with a series of triangular carrier signals with a phase angle of π / N to generate two sets of PWM waves, which are used to drive the left and right arms of the N H-bridges of the system to achieve phase-to-phase DC voltage equalization control.

[0055] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0056] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

[0057] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A static synchronous reactive power compensation method based on model predictive control, characterized in that, The method includes the following steps: Step S1: Based on the equivalent circuit of the three-phase star-chain STATCOM, obtain the mathematical model, discretize it using the forward Euler algorithm, consider the calculation delay compensation, and obtain the model predictive controller optimization objective value function. Step S2: Calculate the search step size using the chained STATCOM output, reference current and voltage deadbeat model, and traverse the control set under control set constraints to find the control set that minimizes the value function as the controller output; Step S3: To address the voltage imbalance of the DC-side capacitors in the chained STATCOM, a three-layer DC-side voltage balancing control strategy of global, phase-to-phase, and phase-to-phase is adopted. The control signal of the system H-bridge switching device is obtained through carrier phase-shifted pulse width modulation (CPS-PWM).

2. The static synchronous reactive power compensation method based on model predictive control according to claim 1, characterized in that, In step S1, based on the equivalent circuit of the three-phase star-connected chain STATCOM, the mathematical model of the chain STATCOM is obtained, and then discretized using the forward Euler algorithm. After considering the calculation of delay compensation, the optimization objective value function of the model predictive controller is finally obtained. The specific steps are as follows: Based on the equivalent circuit of a three-phase star-connected STATCOM and Kirnov's voltage law, the mathematical model of the chained STATCOM system in the abc coordinate system is written. The mathematical model can be transformed to the αβ two-phase stationary coordinate system using the Clark transformation matrix. The specific mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is as follows: Sampling control period in and Let be the instantaneous voltage in the αβ two-phase stationary coordinate system, and and Let α and β be the instantaneous currents in the α and β two-phase stationary coordinate system, L be the filter inductance, and R be the system equivalent resistance.

3. The static synchronous reactive power compensation method based on model predictive control according to claim 2, characterized in that, In step S2, the search step size of the model predictive controller is calculated using the output current and reference current of the chained STATCOM and the deadbeat voltage model of the chained STATCOM. Under the control set constraints, the search space is traversed to find the control set that minimizes the value function, which is then used as the output of the model predictive controller. The specific steps are as follows: Based on the aforementioned formula and assuming that the predicted current perfectly tracks the reference current, the deadbeat voltage prediction output of the chained STATCOM system can be obtained. The specific mathematical model for deadbeat voltage prediction of the chained STATCOM system is as follows: The system output current at time k obtained from sampling , Output voltage , The search step size required for the model predictive controller optimization at time k can be calculated using the system voltage prediction value at time k+1 and the reference current at time k, as calculated above. The specific formula for calculating the search step size is as follows: Where e is the adaptive adjustment parameter. The magnitude of the system output current. Let be the rated voltage of the DC-side capacitor of the H-bridge in the system, l1 and l2 be weighting coefficients, e be 1, and l1 and l2 be 0.

5. The constraints on the search step size are as follows: Where z represents the z mentioned earlier. ab (k), z max With z min Based on engineering experience, take respectively and .

4. The static synchronous reactive power compensation method based on model predictive control according to claim 1, characterized in that, In step S3, a three-layer control strategy for the DC-side capacitor voltage is adopted, namely global DC voltage equalization control, inter-phase DC voltage equalization control, and intra-phase DC voltage equalization control. The control signals for the system H-bridge switching devices are obtained through carrier phase-shift pulse width modulation (CPS-PWM). The specific steps are as follows: The active power reference current of the system is obtained by proportional-integral (PI) regulation control based on the difference between the three-phase total voltage and the rated value of the DC-side capacitor voltage of the system H-bridge. .

5. The static synchronous reactive power compensation method based on model predictive control according to claim 4, characterized in that, Step S3 employs an intra-phase voltage equalization control method by superimposing an additional control signal after generating the modulation wave. The specific method for generating the modulation wave signal is as follows: Where: x = a, b, c, j = 1, 2, 3, ..., N, mx is the modulation wave of phase x. The final modulated wave signal mxj is obtained by superimposing the additional control signal on the x-phase voltage output by the control system in the previous steps. Where: mxj is the modulation signal of the j-th H-bridge unit in phase x. The control signal is obtained by passing the difference between the DC side capacitor voltage and the rated capacitor voltage of each H-bridge through the PI regulator. KCHG-x is the charging and discharging coefficient of phase x, and its value is equal to the positive or negative sign of the output current of the x-phase chained STATCOM system, taking only -1, 0, and 1. The modulated wave signal and its inverted signal are compared with a series of triangular carrier signals with phase angles of π / N, generating two sets of PWM waves to drive the left and right arms of the N H-bridges of the system respectively.

6. The static synchronous reactive power compensation method based on model predictive control according to claim 3, characterized in that, The search step size and the control set S at time k-1 calculated in step S2 are described above. MPC (k-1)=[u cα (k-1),u cβ From (k-1)], we can obtain the control set at time k. The specific control set at time k is as follows: in m represents the search range, which can generally take any integer value. The control set constraints considered during the optimization process are as follows: ； Calculate the predicted current based on the current control set. and Then, the value function J is calculated using the reference current obtained from the multi-step prediction and the aforementioned value function calculation formula. The above steps are repeated until all possible control sets SMPC(k) at time k are traversed. At this time, the model predicts the controller output of the control set SMPC-opt that minimizes the value function J.

7. The static synchronous reactive power compensation method based on model predictive control according to claim 2, characterized in that, In step S1, considering the calculation delay of the control system, multi-step prediction is needed to compensate for the calculation delay. The specific method is as follows: In the k-th sampling control cycle, the optimal switching state calculated in the (k-1)-th sampling control cycle is applied, and the predicted current value at time k+1 is calculated using the prediction model. Furthermore, the predicted current value at time k+2 is calculated using the predicted current value at time k+1. At this point, the optimization search finds the objective value function. The minimum switching state, which acts on the converter at time k+1, is specifically considered in the prediction model for calculating delay compensation as follows: in and It can be predicted by the following formula: , where ω is the angular frequency of the grid voltage; Based on the prediction model for calculating delay compensation and the prediction reference values ​​for multi-step prediction, the optimization objective value function of the model prediction controller can be obtained: ,in The reference value for the control system after multi-step prediction is as follows: The specific multi-step prediction method is as follows: 。 8. The static synchronous reactive power compensation method based on model predictive control according to claim 4, characterized in that, In step S3, the zero-sequence voltage injection method is used to achieve the balance of active power among the three phases, thereby realizing the phase-to-phase DC voltage equalization control. First, the difference between the sampled real-time DC side voltage of each phase and the rated value of the DC side capacitor voltage of the system H-bridge is used for PI regulation control to obtain the changes in active power DPa, DPb, and DPc of each phase. Then, these are transformed to the αβ two-phase stationary coordinate system to obtain DPa and DPb. A low-pass filter needs to be used before the PI regulator to filter out the second harmonic component of the DC side voltage. The characteristic angular frequency of the low-pass filter is 100π. Then, the cosine and sinine components of the zero-sequence voltage are calculated by the formula as follows: Where U0 is the magnitude of the zero-sequence voltage, j0 is the initial phase angle of the zero-sequence voltage, and the specific form of the matrix CZSV is as follows: in, and These are the system's active reference current and reactive reference current, respectively. Finally, the zero-sequence voltage u0 is calculated: ； The calculated zero-sequence voltage is directly superimposed on the output of the model predictive controller.

9. The static synchronous reactive power compensation method based on model predictive control according to claim 2, characterized in that, In step S1, the forward Euler algorithm uses the difference approximation to replace the differential, and the discrete mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system is obtained through the mathematical model of the chained STATCOM system in the αβ two-phase stationary coordinate system. That is, the prediction model is as follows: in and It predicts the current output of the chained STATCOM at time k+1. and It is the current value of the chained STATCOM output sampled from the circuit at time k. and This is the measured voltage value of the three-phase power grid at time k. and It is a control variable, and its value is calculated by the controller at time k. s The sampling period.

10. A static synchronous reactive power compensation system based on model predictive control, characterized in that, The system includes: a computing unit, used to obtain a mathematical model based on the equivalent circuit of a three-phase star-chain STATCOM, discretize it using the forward Euler algorithm, consider computational delay compensation, and obtain the model predictive controller optimization objective value function; The output unit is used to calculate the search step size using the chained STATCOM output, reference current and voltage deadbeat model, and to traverse under control set constraints to find the control set that minimizes the value function as the controller output. The control unit adopts a three-layer DC-side voltage balancing control strategy (global, phase-to-phase, and phase-to-phase) to address the voltage imbalance of the DC-side capacitors in the chained STATCOM. The control signals for the system's H-bridge switching devices are obtained through carrier phase-shifted pulse width modulation (CPS-PWM).

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