Three-vector-based low-complexity model prediction control method

Abstract

The invention discloses a three-vector-based low-complexity model prediction control method. The method comprises the following steps: S1, designing a cost function; s2, sector judgment and vector selection; and S3, calculating the duty ratio. According to the invention, only one PI controller is used in a voltage outer loop. Compared with seven PI controllers in a traditional PI control loop, the method has the advantages that the number of the PI controllers is greatly reduced, the complexity of parameter design is reduced, and meanwhile, compared with the high-precision requirement of traditional sliding mode control on system parameters and high sampling frequency and large output harmonic waves of hysteresis control, the method has the advantage that the control precision is greatly improved. The method provided by the invention can realize a simpler control process and has better performance.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent distribution networks, and particularly to a low-complexity model predictive control method based on three vectors. Background Art

[0002] Nowadays, more and more renewable energy sources (such as solar energy and wind energy) and loads such as new energy vehicles have been connected to the distribution network, which has seriously affected the stable and safe operation of the distribution network. Therefore, due to its advantages of flexible connection between feeders of different voltage levels, improving power supply reliability, and continuously adjusting power, the Soft Open Point (SOP) is used more and more frequently in the distribution network. The two ports of the SOP can be regarded as an AC / DC / AC converter composed of Voltage Source Converters (VSCs). Through corresponding control, power exchange can be achieved at the two ports.

[0003] In terms of control methods, existing research has adopted droop control and designed a proportional-integral (PI) controller to achieve closed-loop control of the outer power loop and the inner current loop. There has also been research on reducing the number of PI controllers through sliding mode control, or combining sliding mode control and feedback linearization control to adapt to different operating modes. However, if a large number of PI coefficients need to be adjusted or numerous controller parameters need to be selected, the control application will become difficult. Model Predictive Control (MPC) has been widely applied in power electronic converters due to its simple implementation and fast dynamic response. According to different control purposes, MPC can be subdivided into Model Predictive Current Control (MPCC) and Model Predictive Power Control (MPPC), and has been applied in rectifiers, inverters, modular multilevel converters, induction motors, and permanent magnet synchronous motors.

[0004] However, the traditional single-vector MPC can only control one voltage vector at each sampling time, which leads to large current ripples and power fluctuations, thus affecting the control effect. To improve the control performance, researchers have proposed various improved MPC methods, such as implementing delay compensation, multi-step prediction, improving the cost function, and increasing the number of voltage vectors at each sampling time. Among them, increasing the number of voltage vectors is the main method to improve the control performance. In these methods, some project the current error vector onto the active voltage vectors, and some define virtual vectors of different magnitudes and select the virtual vector that minimizes the cost function to reduce the computational burden.

[0005] Specifically:

[0006] 1. Large current ripple and power fluctuation:

[0007] In the traditional single-vector model predictive control (SV-MPC), only one voltage vector can be selected in each sampling period, resulting in large current ripple and harmonic power fluctuation, which affect the power quality and system stability.

[0008] 2. High computational complexity:

[0009] SV-MPC needs to perform a large amount of calculations in each sampling period to predict and optimize the control strategy, increasing the computational burden and possibly leading to control delay.

[0010] 3. Unfixed switching frequency:

[0011] The switching frequency of the traditional MPC method is not fixed, which may increase the stress of power electronic devices, shorten the equipment life, and affect the electromagnetic compatibility of the system.

[0012] 4. Difficult parameter adjustment:

[0013] A large number of PI controller parameters need to be adjusted or numerous controller parameters need to be selected, making the design and adjustment of the control strategy complex, especially when the system parameters change or there are uncertainties.

[0014] Further analysis:

[0015] 1. Establishment of two-port SOP mathematical model:

[0016] Figure 1 Shows the topological structure of the two-port SOP, where the rectifier side and the inverter side are interconnected through the capacitor on the DC side. According to Kirchhoff's law, the state equations of the rectifier side and the inverter side in the stationary reference frame can be obtained as follows:

[0017] For the rectifier side:

[0018]

[0019] For the inverter side:

[0020]

[0021] Where, V x and i x1 are the grid voltage and input current of the rectifier side respectively; e x and i x2 are the load back electromotive force and output current of the inverter side respectively; the subscripts a, b, c represent the three phases of the SOP; Ls and Rs are the filter inductance and resistance; L l and R lare the inductor and resistor on the inverter side. The switching states of the SOP are defined as:

[0022]

[0023] After introducing the definition of the switching states, the output voltage value of each converter can be determined as:

[0024]

[0025] where u dc is the capacitor voltage V a1N , V b1N , V c1N are the output voltages of each side in phases a, b, and c respectively; i = 1 represents the rectifier side; i = 0 represents the inverter side. As Figure 2 shown, in a two-port SOP system, eight VSC voltage vectors can be selected, six of which are effective voltage vectors (V 1 , V 2 , V 3 , V 4 , V 5 , V 6 ) and two are zero vectors (V 0 , V 7 ). According to the instantaneous reactive power theory, neglecting the line losses and self-losses of the SOP, the output active power P and reactive power Q of each SOP port can be obtained:

[0026]

[0027] where P1 and Q1 are the active and reactive powers of the rectifier side respectively, while P2 and Q2 are the active and reactive powers of the inverter side. Vα, Vβ, i1α, Vα, Vβ, i1α, and i1β are the grid-side voltage and harmonic current in the stationary αβ reference frame of the rectifier side, while eα, eβ, i2α, and i2β are the load back electromotive force and harmonic current in the αβ reference frame of the inverter side. When the SOP is operating normally, the output active power Ps of the rectifier side can be calculated by the power conservation theorem:

[0028] P s = P dc + P l (6)

[0029] where Pdc is the active power obtained from the DC-side capacitor, and Pl is the active power obtained from the inverter-side load.

[0030] 2. Traditional MPC Analysis

[0031] 2.1 Outer-Loop Control Mode Selection

[0032] Each port of the SOP can operate in different control modes, namely PQ mode, UdcQ mode, and Udcf mode. A VSC port is required to control the stability of the DC-side voltage. When the SOP is operating normally, its two ports usually operate in PQ mode and UdcQ mode. To ensure normal operation and meet the load power supply requirements during feeder faults, the Udcf mode is set and usually used in SOP systems with three or more ports. In this study, the outer loop of the rectifier side selects the UdcQ mode, and the inner loop selects the direct power model predictive control (DPMPC). The outer loop of the inverter side selects the PQ mode, and the inner loop selects MPCC to reduce the load current error.

[0033] 2.2 Analysis of the DPMPC Method on the Rectifier Side

[0034] Through the Clark transformation, Equation (1) can be transformed into the stationary αβ reference frame as follows:

[0035]

[0036] where i 1αβ is the input current vector of the rectifier side; V αβ is the grid voltage vector of the rectifier side; V 1Nαβ is the voltage vector of the VSC on the rectifier side. Using the forward Euler discretization method to predict the current in the next control cycle in (7), the predicted current at the (k + 1) instant can be calculated as:

[0037]

[0038] where i 1αβ (k) and V αβ (k) are the input current and grid voltage at the k instant, respectively; V 1Nαβ (k) is the voltage vector of the VSC on the rectifier side at the k instant; Ts is the sampling time. In the UdcQ mode, the rectifier side uses part of the power obtained from the grid to exchange with other ports, and the other part is used to adjust the DC-side voltage. The outer loop uses PI control, and the reference value of the active power of this port Pref is as follows:

[0039] P ref = k p (u deref - u dc ) + k i ∫(u deref - u dc )dt + Re{e - i 2ref} (9)

[0040] where kp and ki are the proportional and integral coefficients of the PI control, respectively; u dcref and u dcare the reference voltage and the sampled voltage on the DC side; e i2ref is the conjugate load reference current on the inverter side. The first two terms calculate the power required to adjust the DC side voltage, and the last term calculates the active power obtained by the inverter side load. The voltage vector and the predicted current vector can be used to calculate the predicted instantaneous input active power and reactive power as follows:

[0041]

[0042] In (10), when the sampling time is small enough, it can be assumed that V αβ (k + 1) ≈ V αβ (k), but if the sampling time is not short enough to ignore the change in the grid voltage during the sampling time, vector angle compensation can be used to calculate the grid voltage at the (k + 1)-th instant as follows:

[0043] V αβ (k + 1) = V aβ (k)e jωT , (11)

[0044] where ω is the pulsation of the grid voltage. Then, Equation (12) can be used as a cost function to evaluate the prediction error generated by each switch, as described below:

[0045] f = |P ref - P 1 (k + 1)| + |Q ref - Q 1 (k + 1)| (12)

[0046] In DPMPC, all eight voltage vectors are substituted into (8) to predict the current at the (k + 1)-th instant, the predicted power is substituted into (12) to calculate the error, and the switch with the minimum cost function is selected as the optimal switch and applied to the SOP rectifier side at the next moment.

[0047] 2.3 Analysis of the MPCC Method on the Inverter Side

[0048] MPCC is used on the inverter side to compare the predicted load current with the reference load current and select the voltage with the minimum cost function to apply in the next control cycle. After transforming (2) to the stationary αβ reference frame and adopting the forward Euler discretization method, the predicted load current at the (k + 1)-th instant is as follows:

[0049]

[0050] where i 2αβ (k) is the load current at the k-th instant; e αβ (k is the load back electromotive force at the k-th instant on the inverter side; V 2Nαβ(k) is the voltage vector of the VSC on the inverter side at the k-th instant. To adjust the load current, the cost function is used to find the optimal switching state:

[0051] g = |i 2αref -i 2α (k + 1)| + |i 2βref -i 2β (k + 1)| (14)

[0052] Figure 3 Shows the traditional SOP MPC block diagram. At each sampling time, the cost function values of all switching states on both sides are calculated using equations (12) and (14). The switching state that minimizes the cost function is selected to drive the SOP. Summary of the Invention

[0053] Aiming at the above technical problems, the present invention provides a three-vector-based low-complexity model predictive control method.

[0054] To achieve the above object, the technical solution of the present invention is as follows:

[0055] A three-vector-based low-complexity model predictive control method includes the following steps:

[0056] S1. Cost function design

[0057] In the three-vector-based MPC, the cost functions (12) and (14) are improved as follows:

[0058] f = (P ref -P 1 (k + 1)) 2 +(Q ref -Q 1 (k + 1)) 2 (15)

[0059] g = (i 2αref -i 2α (k + 1)) 2 +(i 2βref -i 2β (k + 1)) 2 (16)

[0060] In the above improved cost function, comparing the error between the predicted value and the reference value helps to select the optimal switching value. Six vector combinations are obtained by using adjacent effective vectors for vector synthesis: (V 1 , V 2 , V 0 , 7), (V 2 , V 3 , V 0 , 7), (V3 , V 4 , V 0 , 7), (V 4 , V 5 , V 0 , 7), (V 5 , V 6 , V 0 , 7), and (V 6 , V 1 , V 0 , 7);

[0061] In the three - vector - based MPC, since three vectors are synthesized within one sampling time, an additional cost function is designed to comprehensively evaluate the errors of the three vectors within the sampling time Ts. That is, a new cost function is designed using the weighted root - mean - square error:

[0062]

[0063] where e 1 , e 2 and e 0 are the corresponding cost function values of two effective voltage vectors and the zero vector respectively; d 1 , d 2 , and d 0 are the operating times of the three voltage vectors within the sampling time Ts;

[0064]

[0065] Taking (18) as the new cost function, the voltage vector time allocation obtained by minimizing the weighted root - mean - square error is the optimal vector that makes the system prediction value closest to the reference value;

[0066] S2. Sector Judgment and Vector Selection

[0067] To improve the control accuracy and fix the switching frequency, before calculating the duty cycle, it is necessary to judge the reference vector sectors on both sides of the SOP to select the port voltage vector. On the inverter side, current predictive control is adopted. From the perspective of tracking the reference current, the dead - beat control principle is adopted on the inverter side, and the derivation is as follows:

[0068]

[0069] where V 2Nαβref and i 2αβref are the reference voltage vector and reference current of the VSC respectively. After obtaining the reference voltage, the selection of the sector depends on the phase angle θref of the reference voltage. The phase angle of the reference voltage in the stationary αβ reference frame is calculated as follows:

[0070]

[0071] According to the phase angle θ ref As shown in the selected sector and vector table below, by judging the sector, two effective vectors and zero vectors determined by the inverter side effectively reduce the calculation amount:

[0072]

[0073] On the rectifier side, power prediction control is adopted. In order to achieve power tracking, the variables affecting the value of the cost function (15) are analyzed, and the derivative of (5) is obtained as follows:

[0074]

[0075]

[0076] For a three-phase balanced grid voltage, the differential of the grid voltage is expressed as follows:

[0077]

[0078] Substituting (22) and (7) into (21), (21) is rewritten as:

[0079]

[0080]

[0081] Discretizing (23) using the forward Euler method, the power prediction control for the next sampling period is obtained:

[0082]

[0083] where f p and f q are the derivatives of the active power P 1 and the reactive power Q 1 respectively. For the power reference values P 1ref and Q 1ref , the corresponding voltage vector V 1Nref is an unknown quantity and is obtained from (24) as follows:

[0084]

[0085]

[0086] After substituting (25) and (24) into the cost function (15), (15) is rewritten as:

[0087]

[0088] where, is a constant. Therefore, the values of the cost functions f and f are only related to (V 1Nαref - V 1Nα ) 2 +(V 1Nβref - V 1Nβ ) 2 . Assuming that the voltage reference value V 1Nref is in the first sector, the Euclidean distance between the reference voltage and each effective voltage vector is as Figure 4 shown. The two voltage vectors that minimize (V 1Nαref - V 1Nα ) 2 +(V 1Nβef - V 1Nβ ) 2 are V 1 and V 2 . Both V 1 and V 2 are in the first sector. Therefore, it shows that the two effective voltage vectors that minimize the cost functions f and f must be in the same sector as the reference voltage vector V 1Nref . To ensure that the combination of the two effective voltage vectors that minimizes the cost function is within the six vector combinations listed in step S1. In the traditional three-vector-based MPC, using the traversal optimization theory, it is necessary to calculate all combinations formed by two active vectors and a zero vector. For the six vector combinations, each side of the SOP needs to be calculated 15 times to find the best combination and action time of each vector at each sampling time. In this step, only the reference predicted voltage needs to be calculated once on the inverter side, while on the rectifier side, it is only necessary to prove that the two active voltage vectors with the minimum value of the active vector in the cost function are the optimal active vector combination, which requires calculating six cost functions and one action time;

[0089] S3. Calculation of the duty cycle

[0090] In (18), it is necessary to minimize the cost function GG to obtain the responsible vector combination; e 1 , e 2 , and e 0 are regarded as known quantities in the cost function, and d 1 , d 2 , and d 0 are regarded as unknown quantities. This is an extreme value problem of a multivariable function with constraints. The constraints are as follows:

[0091]

[0092] For the extreme value problem of a multivariable function with constraints, the Lagrange multiplier method is used to construct the function as follows:

[0093]

[0094] where μ is the Lagrange multiplier. Taking the partial derivatives of the three variables in (28) respectively and setting them to 0, the following calculations are obtained:

[0095]

[0096] After sector judgment and vector selection, the minimum value of the newly constructed cost function F(d 1 , d 2 , d 0 ) is obtained from (29), and the action time of each vector is calculated. These action times will be applied to the switch control in the next sampling period.

[0097] The beneficial effects of the present invention are as follows:

[0098] 1. By selecting two effective voltage vectors and one zero voltage vector within each sampling time, the present invention increases the selection range of voltage vectors, thereby reducing current ripple and power fluctuation. In addition, the present invention also proposes a method for voltage vector selection and action time allocation to further optimize the control performance. Through this method, the performance of the SOP in the distribution network can be improved, enabling it to better serve the stable and safe operation of the distribution network in the context of the continuous connection of new loads such as renewable energy and new energy vehicles;

[0099] 2. The present invention increases the number of switch states within one sampling time to reduce current ripple and power fluctuation. A method for judging sectors and selecting vectors is provided to reduce the calculation amount and the complexity of control;

[0100] 3. The present invention aims to solve the problems existing in the prior art, especially the model predictive control (MPC) problem of the soft open point (SOP) in the distribution network system;

[0101] 4. In traditional MPC, the VSCs on both sides adopt single-vector predictive control, and the vector selection is very limited. The voltage vector output cannot reach the entire spatial circular trajectory range. Therefore, the current ripple and power fluctuation on both sides become larger. To improve the control accuracy, it is necessary to increase the sampling frequency of the system, thereby increasing the computational burden of the processor. Another problem is that the switching frequency is not fixed. To reduce current ripple and harmonic power fluctuation while fixing the switching frequency, the present invention adopts a low-complexity MPC based on three vectors at both port sides;

[0102] 5. Compared with the seven PI controllers in the traditional PI control loop, the method used in the present invention greatly reduces the number of PI controllers, thereby reducing the complexity of parameter design. At the same time, compared with the high-precision requirements for system parameters in traditional sliding mode control and the high sampling frequency and large output harmonics of hysteresis control, the method proposed in this paper can achieve a simpler control process and has better performance. In the traditional MPC method, a large amount of calculation is required at each sampling time, resulting in system control delay, while the low-complexity algorithm only requires a small amount of calculation at each sampling time. At the same time, using the vector angle compensation of the reference voltage can improve the control accuracy and has better real-time performance when the sampling time is large;

[0103] 6. The present invention selects two effective voltage vectors and a zero voltage vector within one sampling period to reduce current ripple and power fluctuation; an innovative method for voltage vector selection and action time allocation is proposed, and the working time of each voltage vector within the sampling period is determined through an optimization algorithm to achieve the best control effect; by simplifying the method of judging sectors and selecting vectors, the present invention reduces the amount of calculation, reduces the complexity of the control algorithm, and improves the real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 is the schematic diagram of the existing two-port SOP equivalent model;

[0105] Figure 2 is the voltage vector diagram in the existing stationary coordinate system;

[0106] Figure 3 is the traditional SOP MPC block diagram;

[0107] Figure 4 is the schematic diagram of the Euclidean distance between the reference voltage of the present invention and each effective voltage vector;

[0108] Figure 5 is the control block diagram of the model predictive control of the present invention;

[0109] Figure 6 is the power fluctuation diagram of the present invention and the comparative example;

[0110] Figure 7 is the schematic diagram of the total harmonic distortion rate of the present invention and the comparative example;

[0111] Figure 8 is the schematic diagram of the current waveform during bidirectional power flow operation. DETAILED DESCRIPTION OF THE INVENTION

[0112] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the descriptions of well-known structures and technologies are omitted to avoid unnecessarily confusing the concepts of the present invention.

[0113] As Figure 4 and Figure 5 shown, a low-complexity model predictive control method based on three vectors is characterized by comprising the following steps:

[0114] S1. Cost function design

[0115] In the MPC based on three vectors, the cost functions (12) and (14) are improved as follows:

[0116] f = (P ref - P 1 (k + 1)) 2 + (Q ref - Q 1 (k + 1)) 2 (15)

[0117] g = (i 2αref - i 2α (k + 1)) 2 + (i 2βref - i 2β (k + 1)) 2 (16)

[0118] In the above improved cost functions, comparing the error between the predicted value and the reference value helps to select the optimal switching value. Using adjacent effective vectors for vector synthesis, six vector combinations are obtained: (V 1 , V 2 , V 0 , 7), (V 2 , V 3 , V 0 , 7), (V 3 , V 4 , V 0 , 7), (V 4 , V 5 , V 0 , 7), (V 5 , V 6 , V 0 , 7), and (V 6 , V 1 , V 0 , 7);

[0119] In the three-vector-based MPC, since three vectors are synthesized within one sampling time, an additional cost function is designed to comprehensively evaluate the errors of the three vectors within the sampling time Ts. That is, a new cost function is designed using the weighted root mean square error:

[0120]

[0121] where e 1 , e 2 and e 0 are the corresponding cost function values of two effective voltage vectors and the zero vector respectively; d 1 , d 2 , and d 0 are the operating times of the three voltage vectors within the sampling time Ts;

[0122]

[0123] Taking (18) as the new cost function, the voltage vector time allocation obtained by minimizing the weighted root mean square error is the optimal vector that makes the system prediction value closest to the reference value;

[0124] S2. Sector Judgment and Vector Selection

[0125] To improve the control accuracy and fix the switching frequency, before calculating the duty cycle, it is necessary to judge the sectors of the reference vectors on both sides of the SOP to select the port voltage vectors. On the inverter side, current predictive control is adopted. From the perspective of tracking the reference current, the deadbeat control principle is adopted on the inverter side, and the derivation is as follows:

[0126]

[0127] where V 2Nαβref and i 2αβref are the reference voltage vector and reference current of the VSC respectively. After obtaining the reference voltage, the selection of the sector depends on the phase angle θref of the reference voltage. The phase angle of the reference voltage in the stationary αβ reference frame is calculated as follows:

[0128]

[0129] According to the phase angle θ ref The selected sectors and vectors are shown in the following table. By judging the sectors, the two effective vectors and the zero vector determined on the inverter side effectively reduce the calculation amount:

[0130]

[0131] On the rectifier side, power predictive control is adopted. To achieve power tracking, the variables affecting the value of the cost function (15) are analyzed, and the derivative of (5) is obtained as follows:

[0132]

[0133]

[0134] For a three - phase balanced grid voltage, the differential of the grid voltage is expressed as follows:

[0135]

[0136] Substituting (22) and (7) into (21), (21) is rewritten as:

[0137]

[0138]

[0139] Discretizing (23) using the forward Euler method, the power predictive control for the next sampling period is obtained:

[0140]

[0141] where f p and f q are the derivatives of the active power P 1 and the reactive power Q 1 respectively. For the power reference values P 1ref and Q 1ref , the corresponding voltage vector V 1Nref is an unknown quantity and is obtained from (24) as follows;

[0142]

[0143]

[0144] After substituting (25) and (24) into the cost function (15), (15) is rewritten as:

[0145]

[0146] where, is a constant. Therefore, the values of the cost functions f, f only depend on (V 1Nαref - V 1Nα ) 2 +(V 1Nβref - V 1Nβ ) 2 Assuming that the voltage reference value V 1Nref is in the first sector, the Euclidean distance between the reference voltage and each effective voltage vector is as Figure 4 shown. Minimizing (V 1Nαref - V 1Nα ) 2 +(V1Nβref -V 1Nβ ) 2 The two voltage vectors of 1 are V 2 and V 1 and V 2 Both are in the first sector. Therefore, it shows that the two effective voltage vectors for minimizing the cost functions f and f must be in the same sector as the reference voltage vector V 1Nref To ensure that the two effective voltage vector combinations for minimizing the cost function are within the six vector combinations listed in step S1. In traditional three-vector-based MPC, using traversal optimization theory, all combinations formed by two active vectors and zero vectors need to be calculated. For the six vector combinations, each side of the SOP needs to be calculated 15 times to find the best combination and action time of each vector at each sampling time. In this step, only the reference predicted voltage needs to be calculated once on the inverter side, while on the rectifier side, it only needs to be proved that the two active voltage vectors with the minimum value of the active vectors in the cost function are the optimal active vector combination, which requires calculating six cost functions and one action time;

[0147] S3. Calculation of duty cycle

[0148] In (18), it is necessary to minimize the cost function GG to obtain the responsible vector combination; e 1 ,e 2 , and e 0 are regarded as known quantities in the cost function, and d 1 ,d 2 and d 0 are regarded as unknown quantities. This is an extreme value problem of a multivariable function with constraints. The constraints are as follows:

[0149]

[0150] For the extreme value problem of a multivariable function with constraints, the Lagrange multiplier method is used to construct the function as follows:

[0151]

[0152] where μ is the Lagrange multiplier. The partial derivatives of the three variables in (28) are taken separately and set to 0 to obtain the following calculations:

[0153]

[0154] After sector judgment and vector selection, the newly constructed cost function F(d 1 ,d 2 ,d 0) minimum value, and calculate the action time of each vector, and these action times will be applied to the switching control in the next sampling period.

[0155] The feasibility of the present invention has been verified through simulation experiments on the MATLAB / Simulink platform. The simulation results show that the simulation parameters are as follows:

[0156]

[0157] In order to verify the effectiveness and correctness of the present invention, a simulation experiment platform based on MATLAB / Simulink was constructed. By comparing the simulation results in steady state and dynamic state with the single-vector model predictive control (SV-MPC), the effectiveness of the proposed method was proved. The specific results are as follows:

[0158] 1. Reduction of current ripple and power fluctuation:

[0159] As Figures 6 to 8 shown, the simulation results show that compared with the traditional SV-MPC, the TV-MPC method, that is, the present invention, effectively reduces the current ripple and harmonic power fluctuation. The total harmonic distortion (THD) of the current is significantly reduced, from 2.08% of SV-MPC to 0.91% of TV-MPC.

[0160] Among them, Figure 6 and Figure 7 in, (a) SV-MPC, (b) the present invention.

[0161] 2. Dynamic response performance:

[0162] In practical applications, the SOP needs to meet the requirements of bidirectional power flow operation. The simulation results show that when the reference current on the inverter side suddenly changes from 40A to -20A, the TV-MPC method can quickly respond and stabilize the system, showing good dynamic characteristics. The DC-side voltage can quickly stabilize to 800V after a short-term fluctuation, and the active power and reactive power can effectively track the reference power, meeting the conservation of power exchange at both ports.

[0163] 3. Stability and reliability:

[0164] The simulation results also show that under steady-state conditions, the TV-MPC method has better stability than the single-vector method, which proves the effectiveness of the present invention in improving the stability and reliability of the system.

[0165] It should be understood that the above specific embodiments of the present invention are only for illustrative or explanatory purposes of the principles of the present invention and do not constitute a limitation to the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention shall be included within the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all variations and modifications that fall within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A three-vector based low-complexity model predictive control method, characterized in that: The following steps are involved: S1. Cost function design In the three-vector based MPC, the cost functions (12) and (14) are improved as follows: f=(P ref -P1(k+1)) 2 +(Q ref -Q1(k+1)) 2 (15) g=(i 2αref -i 2α (k+1)) 2 +(i 2βref -i 2β (k+1)) 2 (16) In the above improved cost function, comparing the error between the predicted value and the reference value helps to select the optimal switching value. Using adjacent valid vectors for vector synthesis, six vector combinations are obtained: (V1, V2, V0, 7), (V2, V3, V0, 7), (V3, V4, V0, 7), (V4, V5, V0, 7), (V5, V6, V0, 7), and (V6, V1, V0, 7); In the three-vector based MPC, since three vectors are synthesized within one sampling time, an additional cost function is designed to comprehensively evaluate the errors of the three vectors within the sampling time Ts, that is, a new cost function is designed using the weighted root mean square error: Where e1, e2 and e0 are the corresponding cost function values ​​of the two effective voltage vectors and the zero vector respectively; d1, d2, and d0 are the operation times of the three voltage vectors within the sampling time Ts; Taking (18) as the new cost function, the voltage vector time allocation obtained by minimizing the weighted RMS error is the optimal vector that makes the system prediction value closest to the reference value; S2. Sector judgment and vector selection In order to improve the control accuracy and fix the switching frequency, before calculating the duty cycle, it is necessary to judge the reference vector sectors on both sides of the SOP to select the port voltage vector. On the inverter side, current prediction control is adopted. From the perspective of tracking the reference current, the inverter side adopts the dead zone control principle, which is derived as follows: Where V 2Nαβref and i 2αβref are the reference voltage vector and reference current of VSC respectively. After obtaining the reference voltage, the selection of the sector depends on the phase angle θref of the reference voltage. The phase angle of the reference voltage in the stationary αβ reference frame is calculated as follows: According to the phase angle θ ref The selected sectors and vectors are shown in the table below. By judging the sectors, the two valid vectors and the zero vector determined by the inverter side effectively reduce the amount of calculation: On the rectifier side, power prediction control is adopted. In order to achieve power tracking, the variables affecting the value of the cost function (15) are analyzed, and the derivative of (5) is obtained as follows: For a three-phase balanced grid voltage, the differential of the grid voltage is expressed as follows: Substituting (22) and (7) into (21), (21) can be rewritten as: Using the forward Euler method to discretize (23), the power prediction control of the next sampling period is obtained: where f p and f q They are the derivatives of active power P1 and reactive power Q1 respectively. For the power reference value P 1ref and Q 1ref , the corresponding voltage vector V 1Nref is an unknown quantity, which is obtained from (24) as follows; After substituting (25) and (24) into the cost function (15), (15) can be rewritten as: in, is a constant, so the value of the cost function f, f only depends on (V 1Naref -V 1Nα ) 2 +(V 1Nβref -V 1Nβ ) 2 Assuming the voltage reference value V 1Nref In the first sector, the Euclidean distance between the reference voltage and each effective voltage vector is minimized as shown in Figure 4 (V 1Naref -V 1Nα ) 2 +(V 1Nβref -V 1Nβ ) 2 The two voltage vectors are V1 and V2, both of which are in the first sector. Therefore, the two effective voltage vectors that minimize the cost function f and f must be equal to the reference voltage vector V 1Nref In the same sector, the two valid voltage vector combinations that ensure the minimization of the cost function must be within the six vector combinations listed in step S1. In the traditional three-vector-based MPC, using the ergodic optimization theory, it is necessary to calculate all combinations formed by two active vectors and a zero vector. For the six vector combinations, each side of the SOP needs to be calculated 15 times to find the best combination and action time of each vector within each sampling time. In this step, only the reference predicted voltage needs to be calculated once on the inverter side, and on the rectifier side, it is only necessary to prove that the two active voltage vectors with the minimum value of the active vector in the cost function are the optimal active vector combination, which requires the calculation of six cost functions and one action time. S3. Calculation of duty cycle In (18), the cost function GG needs to be minimized to obtain a responsible vector combination; e1, e2, and e0 are regarded as known quantities in the cost function, and d1, d2, and d0 are regarded as unknown quantities. This is a problem of finding the extreme value of a multivariable function with constraints. The constraints are as follows: For the extreme value problem of multivariable functions with constraints, the Lagrange multiplier method is used to construct the function as follows: Where μ is the Lagrange multiplier. The partial derivatives of the three variables in (28) are calculated and set to 0, and the following calculation is obtained: After sector judgment and vector selection, the minimum value of the newly constructed cost function F(d1, d2, d0) is obtained from (29), and the action time of each vector is calculated, which will be applied to the switch control in the next sampling period.

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