Multivariable model prediction control method of photovoltaic inversion grid-connected system

Abstract

The invention discloses a multivariable model predictive control method for a photovoltaic inverter grid-connected system, which comprises the following steps of: establishing a mathematical model of an inverter under a rotating coordinate system, and setting a discrete mathematical model on the basis of traditional model predictive control to obtain a predictive value of output current; and taking the predicted value, the current error at the sampling moment and the error of the direct current bus voltage as control factors of the value function, and seeking the minimum solution of the value function to achieve the optimal control effect. According to the multivariable model predictive control method for the photovoltaic inverter grid-connected system, through the steps, the photovoltaic grid-connected response efficiency can be improved, the total harmonic distortion rate can be reduced, the stability and the anti-interference performance of the direct-current bus voltage can be enhanced, the grid-side current can be controlled at a lower total harmonic distortion level, and the effect is obvious.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of integrated energy systems, in particular to a multivariable model predictive control method for a photovoltaic inverter grid-connected system. BACKGROUND

[0002] The photovoltaic inverter grid-connected system is a device that converts the direct current generated by the solar power generation system into alternating current of the same frequency and voltage as the power grid for transmission and distribution, and provides it to the power grid to meet the power demand of users. The photovoltaic inverter grid-connected system is one of the most important components in the solar power generation system, and its performance has a crucial impact on the power generation efficiency, stability and safety of the entire system.

[0003] In recent years, although the application of the photovoltaic inverter grid-connected system has developed rapidly, its large-scale development has been restricted to some extent, one of the main reasons being the energy fluctuation of the existing power grid caused by large-scale grid connection. The research on the control method of the photovoltaic inverter grid-connected system is mainly to improve the photoelectric conversion efficiency of the photovoltaic cell and provide stable and reliable power to the existing power grid. Therefore, developing efficient and high-performance inverter control technology is the breakthrough for the photovoltaic inverter grid-connected problem. At present, the existing inverter control technology has the disadvantages of low photovoltaic grid connection efficiency, high total harmonic distortion rate, poor voltage stability and poor anti-interference performance. SUMMARY

[0004] The purpose of the present application is to provide a multivariable model predictive control method for a photovoltaic inverter grid-connected system to solve the above problems.

[0005] In order to achieve the above purpose, the present application provides the following technical scheme:

[0006] A multivariable model predictive control method for a photovoltaic inverter grid-connected system, comprising the following steps:

[0007] S1, constructing a mathematical model of a three-phase full-bridge voltage type grid-connected inverter in a rotating coordinate system, and combining SVPWM modulation technology with model predictive algorithm to improve the output current quality of the grid-connected inverter;

[0008] S2, using the derivative approximation principle to derive and deduce the discrete-time model of the predicted current at k+1 time in the AC / DC converter rectification and inverter modes, and bringing it into the calculation equation to obtain the current discrete prediction model;

[0009] S3, designing a proper value function to seek the minimum solution of the value function, thereby obtaining the switching state of the converter.

[0010] Preferably, in the step S1, the mathematical model of the three-phase full-bridge voltage type grid-connected inverter is constructed as follows:

[0011] The three-phase full-bridge voltage type grid-connected inverter is selected as the research object, and the mathematical model in the three-phase stationary coordinate system is continuously rotated and transformed to obtain the mathematical model in the rotating coordinate system.

[0012] Preferably, in the S1 step, the mathematical model of the three-phase full-bridge voltage type grid-connected inverter is constructed in detail as follows:

[0013] 1) The three-phase full-bridge voltage type grid-connected inverter is selected as the research object, and in the design of the control system of the three-phase grid-connected inverter, the mathematical model of the three-phase grid-connected inverter device is usually represented by a switching function; the switching of the three-phase grid-connected inverter is represented as:

[0014]

[0015]

[0016] In the formula, S i (i=a, b, c) represents the switching tube corresponding to the three bridge arms of the three-phase inverter, and the working state of the switching tube has only two working states of "on" and "off. The working states of the upper and lower switching tubes on the same bridge arm cannot be the same, and for convenience, the number "1" represents that the switching tube is in the "on" state, and the number "0" represents that the switching tube is in the "off state. S is the total state of the three-phase inverter; the unit vector a=e j2π / 3 represents a 120° phase difference between phases;

[0017] Because the upper and lower power switching tubes of each phase bridge arm of the three-phase grid-connected inverter cannot be turned on at the same time, when the upper bridge arm power switching tube of the i phase is turned on, then u iN = u dc , S i = 1; when the lower bridge arm of the i phase is turned on, then u iN = 0, S i = 0; therefore, the formula (16) can be used to represent the three-phase grid-connected inverter AC end output voltage value, switching state and DC end input voltage;

[0018] u iN = s i U dC (16),

[0019] In the formula, u iN represents the i-phase AC end output voltage, S i represents the i-phase lower bridge arm conduction state, S i is 0 if it is turned on, and vice versa, U dC represents the DC end input voltage;

[0020] 2) Three-phase voltage type grid-connected inverter adopts Kirchhoff's law, and the formula (17) is obtained by adding three-phase voltage equations on both sides, specifically as follows:

[0021]

[0022] It can be concluded that the mathematical model of three-phase grid-connected inverter in abc stationary coordinate system is as formula (18), specifically as follows:

[0023]

[0024] 3) Three-phase to two-phase transformation matrix C abc / αβ The transformation from abc coordinate system to αβ coordinate system can be realized;

[0025] According to formula (18), the mathematical model of three-phase grid-connected inverter in three-phase abc stationary coordinate system is transformed into three-phase to two-phase, and the mathematical model of three-phase grid-connected inverter in αβ coordinate system is as formula (19) shown:

[0026]

[0027] In formula (19), e α , e β , i α , i β are the components of three-phase grid voltage and three-phase output current in αβ coordinate system; u α , u β are the components of three-phase grid-connected inverter output voltage in two-phase αβ stationary coordinate system;

[0028] 4) The relevant parameters in αβ coordinate system can be transformed into dq coordinate system by Park transformation, and the formula is as formula (20) shown,

[0029]

[0030] The mathematical model of three-phase grid-connected inverter in αβ coordinate system is transformed by formula (20), and the mathematical model in dq coordinate system is as formula (21) shown:

[0031]

[0032] In formula (21), e d , e q , i d , i q are the components of three-phase grid voltage and three-phase grid-connected inverter output current in dq axis; u d , u q are the components of three-phase voltage in two-phase dq axis; s d , sq Represents the components of the inverter switching function in the two-phase dq axis.

[0033] Preferably, the specific steps of step S2 are as follows:

[0034] 1) Converter output current i a 、i b 、i c The current i in the stationary coordinate system is obtained by Clack transformation α 、i β ; As shown in formulas (22) and (23),

[0035]

[0036]

[0037] Where: i α 、i β is the current component in αβ coordinates;

[0038] 2) For the current component i α 、i β By taking the derivative and using the forward difference theorem, we can get the discrete mathematical model of the converter output current, as shown in formula (24):

[0039]

[0040] 3) Using the derivative approximation principle, the discrete-time model of the predicted current at time k+1 in both the rectification and inversion modes of the AC / DC converter is derived, and Equation (24) is substituted into the voltage-current vector equation of the converter to obtain the current discrete prediction model shown in Equation (25);

[0041]

[0042] Where: i α (k+1), i β (k+1) is the predicted current component at time k+1 under αβ coordinates; V α 、V β is the inverter output voltage component under αβ coordinates; E α 、E β is the grid voltage component under αβ coordinates; T s is the sampling time.

[0043] Preferably, the specific steps of step S3 are as follows:

[0044] The main goal of model predictive control is to minimize the designed value function g, and the current reference value is obtained through the non-static tracking of the DC bus voltage command as shown in formula (26), (27) and (28); the dynamic response error between the discretized current prediction value and the reference value is calculated through the designed value function as shown in formula (30);

[0045]

[0046]

[0047]

[0048]

[0049] In the formula, i * α (k), i * β (k) is the reference current component at the moment k in the alpha-beta coordinate; V * dc (k) is the DC reference voltage at the moment k; V dc (k) is the DC sampling voltage at the moment k; i * α (k+1), i * β (k+1) is the reference current component at the moment k+1 in the alpha-beta coordinate; K p , K i The proportional coefficient and the integral coefficient of the PI controller are respectively;

[0050] In order to improve the control accuracy and the grid electromotive force does not change greatly during the period, the next step and the test can also be estimated by formula, considering the fluctuation of the charging pile DC bus voltage, in order to improve the system robustness, the DC bus voltage error is multiplied by a certain weight coefficient and added to the value function.

[0051] The beneficial effects of the application are:

[0052] (1) The multivariable model predictive control method of the photovoltaic inverter grid-connected system, by establishing the mathematical model of the grid-connected inverter, simplifying the model predictive control, and studying the control problem of the grid-connected inverter, the model predictive current control can be realized in the alpha-beta coordinate, without using the traditional PWM modulator and current inner loop control, only the coordinate transformation is needed, the optimal switching state can be calculated, the calculation amount is small, and the method is easy to realize.

[0053] (2) The multivariable model predictive control method of the photovoltaic inverter grid-connected system can quickly make the inverter output current value approach the given reference value by establishing a predictive current mathematical model in the alpha-beta coordinate, obtaining the possible predictive current value of the inverter under the action of different voltage vectors at the next moment through a prediction function, and selecting the optimal vector according to an evaluation function.

[0054] (3) The PI parameters need to consider system stability and response speed, and the parameter setting process is complex and tedious. The multivariable model predictive control method of the photovoltaic inverter grid-connected system can make the overshoot, peak time and stable time of the alternating current under MPC control less than the corresponding values of PI feedforward control, which shows that the MPC control effect is better than PI feedforward.

[0055] (4) The multivariable model predictive control method of the photovoltaic inverter grid-connected system can improve the photovoltaic grid-connected response efficiency and reduce the total harmonic distortion rate, enhance the stability and anti-interference of the DC bus voltage, and control the grid-side current at a lower total harmonic distortion level, and the effect is obvious. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 : The main circuit model diagram of the photovoltaic grid-connected inverter in the application;

[0057] Figure 2 : The equivalent circuit diagram of the photovoltaic cell in the application;

[0058] Figure 3 : The relationship diagram of output power and voltage when the light intensity changes in the application;

[0059] Figure 4 : The relationship diagram of output power and voltage when the temperature changes in the application;

[0060] Figure 5 : The boost circuit model diagram of the photovoltaic system in the application;

[0061] Figure 6 : The topology structure diagram of the three-phase grid-connected inverter in the application;

[0062] Figure 7 : The alpha-beta stationary coordinate system diagram in the application;

[0063] Figure 8 : The two-phase rotating alpha-beta coordinate system diagram in the application;

[0064] Figure 9 : The voltage sector and vector distribution diagram in the application;

[0065] Figure 10 : The disturbance observation method flow chart in the application;

[0066] Figure 11 : The minimum value selection principle of the value function in the application;

[0067] Figure 12 : The output curve of the photovoltaic cell in the application;

[0068] Figure 13 : The model predictive current control flow chart in the application;

[0069] Figure 14 : The illumination intensity curve under the MPC method in the application;

[0070] Figure 15 : The comparison between the actual power and the theoretical maximum power under the MPC method in the application;

[0071] Figure 16 : The efficiency diagram under the MPC method in the application;

[0072] Figure 17 : The direct current diagram under the MPC method in the application;

[0073] Figure 18 : The grid current diagram (0.65-0.95s) under the MPC method in the application;

[0074] Figure 19 : The grid current diagram (1.45s-1.75s) under the MPC method in the application;

[0075] Figure 20 : The A-phase voltage and current diagram (0.65-0.95s) under the MPC method in the application;

[0076] Figure 21 : The A-phase voltage and current diagram (1.45s-1.75s) under the MPC method in the application;

[0077] Figure 22 : The current frequency analysis diagram under the MPC method in the application;

[0078] Figure 23 : The PI feedforward method control block diagram in the application;

[0079] Figure 24 : The illumination intensity curve under the PI feedforward method;

[0080] Figure 25 : The comparison between the actual power and the theoretical maximum power under the PI feedforward method;

[0081] Figure 26 : The efficiency diagram under the PI feedforward method;

[0082] Figure 27 : The direct current diagram under the PI feedforward method;

[0083] Figure 28 Grid current chart under PI feedforward method (0.65-0.95s);

[0084] Figure 29 Grid current chart under PI feedforward method (1.45s-1.75s);

[0085] Figure 30 A phase voltage and current chart under PI feedforward method (0.65-0.95s);

[0086] Figure 31 A phase voltage and current chart under PI feedforward method (1.45s-1.75s);

[0087] Figure 32 Current frequency analysis chart under PI feedforward method.DETAILED DESCRIPTION

[0088] The present application is further described in conjunction with the following examples, it should be noted that the following examples are only examples and illustrations of the present application, those skilled in the art can make various modifications or supplements to the described specific examples or use similar ways to replace, as long as they do not deviate from the concept of the present application or exceed the scope defined by the present claims, they should be considered to fall within the scope of the present application.

[0089] Embodiment:

[0090] Referring to Figure 1 and Figure 11 , a multivariable model predictive control method of a photovoltaic inverter grid-connected system includes the following steps:

[0091] S1, construct a mathematical model of a three-phase full-bridge voltage type grid-connected inverter in a rotating coordinate system, and combine SVPWM modulation technology with model predictive algorithm to improve the quality of grid-connected inverter output current, which is as follows:

[0092] S1.1, Figure 1 is a photovoltaic grid-connected inverter main circuit model diagram, as Figure 1 shown, the photovoltaic inverter grid-connected system is composed of a photovoltaic panel, a DC / DC converter, a DC / AC inverter, a filter module, an alternating current grid and related control equipment. This design separates the MPPT and unit power factor grid-connected functions, which helps to improve the stability of the system.

[0093] S1.2, the photovoltaic cell is one of the key components of the photovoltaic system. By studying and analyzing its output characteristics, understanding its working principle and physical characteristics and adjusting it through corresponding means, it can provide corresponding basis for reliable tracking of the maximum power point of the photovoltaic system in the following.

[0094] Figure 2 The equivalent circuit diagram of the photovoltaic cell, wherein Iph is the photo-generated current, Ipv and Upv are the output current and output voltage of the photovoltaic cell respectively, Id is the diode forward conduction current, Rs and Rsh are the series resistance and parallel resistance of the photovoltaic cell respectively, q is the charge constant, A is the ideal coefficient of the diode, K is the Boltzmann constant, and T is the ambient temperature of the photovoltaic panel.

[0095] Figure 3 The output power-voltage relationship diagram when the light intensity changes, Figure 4 The output power-voltage relationship diagram when the temperature changes. As shown in Figure 3 , when the light intensity rises, the output power of the photovoltaic cell also rises, and there is a nonlinear relationship between the two, indicating that the output power of the photovoltaic cell will be affected by the light intensity. As shown in Figure 4 , the output power of the photovoltaic cell decreases with the increase of the temperature, and the P-U characteristic curve of the photovoltaic cell appears to be adjusted. It shows that the temperature is also a key external factor affecting the output characteristics of the photovoltaic cell.

[0096] 1) Let the diode reverse saturation current be I0, and according to the model, the Kirchhoff law can be obtained:

[0097]

[0098] In the formula, I pv , U pv represents the output current of the photovoltaic cell single-diode model; the photovoltaic cell is equivalent to an ideal current source; I ph is the photo-generated current; I d is the diode current; I o is the diode reverse saturation current; I sh is the parallel resistance current. n is the ideal factor of the diode; R s is the equivalent series resistance of the photovoltaic cell; and R sh is the equivalent parallel resistance of the photovoltaic cell.

[0099] Substitute I d and I sh into the above formula:

[0100]

[0101] The value of R sh is generally large, and Rsh>>Rs, so the third term of formula (10) is approximately zero and can be ignored, and the above formula can be simplified as:

[0102]

[0103] Let I0 = C1I sc , AKT = qC2U oc (q is the charge constant (1.6021*10 -19 C), when the environmental factors and battery parameters are constant, C1 and C2 can be considered as constants, and substituting equation (11) can obtain:

[0104]

[0105] wherein,

[0106]

[0107] In the formula, I sc is the short-circuit current;

[0108] 2) In the photovoltaic system, the front-stage DC / DC converter adopts the Boost voltage circuit, the Boost circuit model is shown in Figure 5 , PV is the photovoltaic array, L is the boost inductance, C1 and C2 are input and output capacitors respectively.

[0109] S1.3, select the three-phase full-bridge voltage type grid-connected inverter as the research object. Figure 6 is the three-phase grid-connected inverter topology structure diagram, as shown in Figure 6 , in the figure, u dc is the three-phase grid-connected inverter input DC voltage, C is the DC parallel capacitor, L is the AC energy storage inductance, R is the linear resistance, e is the grid voltage, and n is the neutral point of the three-phase grid voltage.

[0110] (1) Select the three-phase full-bridge voltage type grid-connected inverter as the research object, when designing the control system of the three-phase grid-connected inverter, the switching function is usually used to represent the mathematical model of the three-phase grid-connected inverter device; let the three-phase grid-connected inverter switch be represented as:

[0111]

[0112]

[0113] In the formula, S i (i = a, b, c) represents the switch tube corresponding to the three bridge arms of the three-phase inverter, the working state of the switch tube only has "on" and "off" two working states, and the working states of the upper and lower switch tubes on the same bridge arm cannot be the same, for convenience, the number "1" represents that the switch tube is in "on" state, and the number "0" represents that the switch tube is in "off" state; S is the total state of the three-phase inverter; the unit vector a = e j2π / 3 represents the 120° phase difference between phases;

[0114] Because the upper and lower power switch tubes of each phase bridge arm of the three-phase grid-connected inverter cannot be turned on at the same time, when the upper power switch tube of the i phase bridge arm is turned on, then u iN = u dc , S i = 1; when the lower power switch tube of the i phase bridge arm is turned on, then u iN = 0, S i = 0; therefore, the three-phase grid-connected inverter AC end output voltage value, switch state and DC end input voltage can be represented by formula (16);

[0115] u iN = s i U dC (16),

[0116] In the formula, u iN represents the i phase AC end output voltage, S i represents the i phase lower bridge arm conduction state, if conduction S i is 0, otherwise 1, U dC represents the DC end input voltage;

[0117] 2) The three-phase voltage grid-connected inverter adopts Kirchhoff's law, and the three-phase voltage equation is added on both sides to obtain formula (17), which is as follows:

[0118]

[0119]

[0120] It can be deduced that the mathematical model of the three-phase grid-connected inverter in the abc stationary coordinate system is as formula (18), which is as follows:

[0121]

[0122] 3) The three-phase to two-phase transformation matrix C abc / αβ can realize the transformation from the abc coordinate system to the αβ coordinate system;

[0123] According to formula (18), the three-phase to two-phase transformation of the mathematical model of the three-phase grid-connected inverter in the three-phase abc stationary coordinate system can obtain the mathematical model of the three-phase grid-connected inverter in the αβ coordinate system, which is as formula (19) shown:

[0124]

[0125] In formula (19), e α , e β , i α , i β are the components of the three-phase grid voltage and the three-phase output current in the αβ coordinate system; u α , uβ is the component of the output voltage of the three-phase grid-connected inverter in the two-phase αβ stationary coordinate system;

[0126] 4) The spatial position relationship between the stationary αβ coordinate system and the two-phase dq rotating coordinate system is as follows: Figure 8 shown. Figure 8 Where w is the angular frequency of the power grid, the spatial positions of the d-axis and the q-axis rotate counterclockwise at an angular velocity of wt, and the d-axis lags behind the q-axis by 90°.

[0127] The Park transformation can transform the relevant parameters in the αβ coordinate system into the dq coordinate system. The formula is shown in Equation (20):

[0128]

[0129] By using formula (20) to transform the mathematical model of the three-phase grid-connected inverter in the αβ coordinate system, the mathematical model in the dq coordinate system can be obtained as shown in formula (21);

[0130]

[0131] In formula (21), e d 、e q 、i d 、i q are the components of the three-phase grid-side AC voltage and the three-phase grid-connected inverter output current on the d and q axes respectively; u d 、u q is the component of the three-phase voltage in the two-phase dq axis; s d 、s q Represents the components of the inverter switching function in the two-phase dq axis.

[0132] 5) SVPWM modulation technology was first proposed by Japanese scholars in the 1980s to solve the problem of variable frequency control of AC motor drive control. Its main advantages are improved DC voltage utilization (for inverters) and a quasi-circular rotating magnetic field obtained through space vector synthesis. It has better control performance than SPWM modulation. Its principle is vector synthesis. Through two adjacent basic vectors and the zero vector in the sector, the rotating reference vector is synthesized within one switching cycle to achieve tracking of the reference vector.

[0133] The three-phase grid-connected inverter in this technology uses SVPWM modulation technology combined with a model prediction algorithm to improve the output current quality of the grid-connected inverter.

[0134] Figure 9 is the voltage sector and vector distribution diagram, such as Figure 9As shown, there are 8 switch states, which are set as u0(000), u1(110), u2(110), u3(010), u4(011), u5(001), u6(101), and u7(111). Figure 9 It can be seen that the effective voltage vectors u1~u6 divide the complex plane into 6 sectors 1~6; the voltage vector amplitude is 2udc / 3. When Us moves into any sector, it is synthesized by the two adjacent voltage vectors in the sector and the zero vector; Figure 9 Here, u0 and u7 are both zero vectors with an amplitude of 0.

[0135] S2. Using the derivative approximation principle, derive the discrete-time model of the predicted current at time k+1 in both the rectification and inversion modes of the AC / DC converter, and substitute it into the relevant equations to obtain the current discrete prediction model, as follows:

[0136] S2.1, Figure 10 This is the flow chart of the perturbation and observation method. Figure 10 As shown, when ΔP / ΔU>0, it means that the operating point is on the left side of the maximum power point and the voltage needs to be increased; conversely, when ΔP / ΔU<0, it means that the operating point is on the right side of the maximum power point and the voltage needs to be reduced; when ΔP / ΔU>0, it means that the operating point is on the left side of the maximum power point and the voltage needs to be increased; conversely, when ΔP / ΔU<0, it means that the operating point is on the right side of the maximum power point and the voltage needs to be reduced.

[0137] S2.2. Effective control of the AC / DC converter is key to maintaining the inverter. The converter has a limited number of switching states, and the optimal switching state must be selected according to certain criteria. By properly designing the value function of the model predictive control, efficient control of the AC / DC converter can be achieved, thereby meeting actual needs.

[0138] 1) Converter output current i a 、i b 、i c The current i in the stationary coordinate system is obtained by Clack transformation α 、i β ; As shown in formulas (22) and (23),

[0139]

[0140]

[0141] Where: i α 、i β is the current component in αβ coordinates;

[0142] 2) For the current component i α 、iβ The derivative is taken, and the discrete mathematical model of the inverter output current can be obtained according to the forward difference theorem, as shown in equation (24),

[0143]

[0144] 3) The derivative is taken to derive the discrete-time model of the predicted current at time k+1 in the AC / DC converter rectification and inversion modes using the derivative approximation principle, and equation (24) is substituted into the voltage-current vector equation of the inverter to obtain the current discrete prediction model as shown in equation (25);

[0145]

[0146] In the formula: i α (k+1) is the predicted current component at time k+1 in the αβ coordinate; V β (k+1) is the predicted current component at time k+1 in the αβ coordinate; V α (k+1) is the predicted current component at time k+1 in the αβ coordinate; V β (k+1) is the predicted current component at time k+1 in the αβ coordinate; V α (k+1) is the predicted current component at time k+1 in the αβ coordinate; V β (k+1) is the predicted current component at time k+1 in the αβ coordinate; V s is the sampling time.

[0147] S3, a proper value function is designed to find the minimum solution of the value function, so as to obtain the switching state of the inverter, and the specific steps are as follows:

[0148] S3.1, the main goal of model predictive control is to minimize the designed value function g, and the current reference value is obtained by PI modulation of the error between the DC bus voltage command and V * dc (k) and V dc (k) as shown in equations (26), (27), and (28);

[0149] The value function designed in the present technology is the dynamic response error between the discrete current prediction value and the reference value, as shown in equation (29);

[0150]

[0151]

[0152]

[0153]

[0154] In the formula: i * α (k+1) is the predicted current component at time k+1 in the αβ coordinate; V * β(k) is the reference current component at time k in αβ coordinates; V * dc (k) is the DC reference voltage at time k; V dc (k) is the DC sampling voltage at time k; i * α (k+1), i * β (k+1) is the reference current component at time k+1 in αβ coordinates; K p , K i are the proportional coefficient and integral coefficient of the PI controller respectively;

[0155] The cost function is used to measure the error or distance between the reference vector and the predicted vector. In order to complete the optimal switch state calculation for a sampling period, the system uses different switch functions (a total of 2 3 = 8 kinds). From another perspective, the selection of the optimal voltage vector can be based on Figure 9 Each voltage vector generates a corresponding predicted current, which in turn generates a corresponding cost function value. This approach plays a key role in system optimization, ensuring that the system selects the optimal voltage vector at each moment to achieve optimal performance.

[0156] Formula (29) is a value function established based on the current prediction value at time k+1. In order to further improve the control accuracy of the converter, the value function is corrected using the current prediction value at time k+2. s When the time is small enough, it is generally believed that the future value of the current reference is approximately equal to the current value, that is, formula (30):

[0157]

[0158] Where i * α (k+2), i * β (k+2) is the reference current component at time k+2 in the αβ coordinates.

[0159] However, in a very short time, the grid electromotive force will not change much, and the next prediction value can be estimated by formula (31);

[0160]

[0161] Where, E α (k+1), E β (k+1) is the predicted component of the power grid electromotive force at time k+1 under the αβ coordinates.

[0162] S3.2, the k+2 time model predictive controller of the converter (i.e., finite set model predictive control) can be expressed by equations (32) and (33);

[0163]

[0164]

[0165] Considering the fluctuation of the charging pile DC bus voltage, to improve system robustness, the DC bus voltage error is multiplied by a certain weight coefficient and added to the value function of Equation (33). After multiple tests and comparisons, the optimal weight coefficient λ is 0.03. The comparison results of the weight coefficient selection test are shown in Table 1.

[0166] Table 1 Comparison results of weight coefficient selection test

[0167]

[0168] The final reconstructed value function is shown in formula (34).

[0169]

[0170] Figure 11 For the minimum value of the value function, select the principle diagram. For the minimum solution of the value function, from the example Figure 11 Analysis shows that vector v2 and vector v6 can make the current i α The error between the predicted value and the reference value is the smallest, while vector v2 and vector v3 are the same when the current i β The predicted value and reference value are optimal. Therefore, when considering both optimization objectives, the voltage vector that minimizes the cost function g is v2. Ultimately, the optimal switching state corresponding to vector v2 is applied to the inverter to achieve optimal system performance. This comprehensive optimization approach helps achieve a comprehensive balance in voltage vector selection, thereby improving overall system performance.

[0171] Figure 12 is the output curve of photovoltaic cells, Figure 13 Predict the current control flow graph for a finite set model, such as Figure 13 As shown in Figure 1, we first establish a high-order nonlinear dynamic model for current prediction at time k+1 by sampling the voltage, current, and electromotive force at high frequency. Next, we use this model to predict the current at time k+2, taking into account different switch states. Next, we introduce a cost function g that comprehensively considers factors such as current error and voltage harmonics. By minimizing this cost function, we select the optimal voltage vector and generate the corresponding switch state signals. Finally, we update the switch states and loop back to the program's initial state to continuously achieve optimal control in each sampling cycle.

[0172] Example description and simulation result analysis:

[0173] In order to verify its effectiveness, the overall structure of the photovoltaic grid-connected inverter is built based on MATLAB / Simulink software; the value of R of the grid-side RL filter should not be too large, and in this technology, 0.1Ω is selected, wherein the value of the inductance L needs to consider the grid harmonic performance and the transient current tracking effect. The minimum value of the inductance value is determined by the grid harmonic requirement, and the maximum value of the inductance value is determined by the transient current tracking requirement.

[0174] In the formula, V dc is the DC bus voltage; E m is the effective value of the grid voltage; Δi max is the maximum harmonic current ripple value allowed by the grid; ω is the angular frequency of the AC side; I m is the maximum current effective value of the grid side; finally, the grid inductance value L is selected as 20mH.

[0175] Table 2 System simulation parameters

[0176]

[0177] The AC / DC converter uses MPC, the DC / DC converter uses Boost structure, and the disturbance observation method is used; the simulation parameters and the grid-side equivalent resistance R required for FCS-MPC calculation, the grid-side filter inductance L, the sampling time T s , etc. are shown in Table 2 System simulation parameters.

[0178] The simulation results of the MPC method adopted by the application include: the illumination intensity curve, the comparison diagram of the actual power and the theoretical maximum power, the efficiency diagram, the DC voltage diagram, the grid current (0.65-0.95s), the grid current (1.45s-1.75s), the A-phase voltage and current (0.65-0.95s), the A-phase voltage and current (1.45s-1.75s), and the current frequency analysis diagram, as shown in Figures 14-22 .

[0179] In order to fully reflect and verify the effectiveness of the method proposed in the application, another case is set up for comparative simulation analysis:

[0180] Comparative case 1: simulation results of the PI feedforward method.

[0181] The core of the PI feedforward method is: voltage and current double closed loop control is adopted, and three-phase voltage and current are sampled on the AC side. Park is used for coordinate transformation, and three-phase voltage and current signals are transformed from abc coordinate system to synchronous rotating dq axis coordinate system. Then, the driving signals of each bridge arm of the converter can be obtained through SVPWM modulation.

[0182] Figure 14 PI feedforward method control block diagram, Figure 23 Eabc represents the alternating side fundamental electromotive force, iabc represents the alternating side three-phase current value, u d , u q represents the dq0 coordinate system dq axis alternating side voltage value, Vdc represents the DC side voltage value, V * dc represents the reference voltage value of the DC side, i d , i q represents the dq0 coordinate system dq axis alternating side current value, i * d , i * q represents i d , i q The given current reference value of i

[0183] The simulation results obtained under the PI feedforward method include: the light intensity curve, the comparison diagram of the actual power and the theoretical maximum power, the efficiency diagram, the DC voltage diagram, the grid current (0.65-0.95s), the grid current (1.45s-1.75s), the A-phase voltage and current (0.65-0.95s), the A-phase voltage and current (1.45s-1.75s), and the current frequency analysis diagram, as shown in Figures 24-32

[0184] Figures 14-22 And Figures 24-32 It can be known from the comparison shown in the figure that the overshoot of the MPC of the application is smaller than that of the PI feedforward control, and the response speed is fast; the overshoot, peak time and stable time of the alternating current under the MPC control are smaller than the corresponding values of the PI feedforward control, which indicates that the MPC control effect is better than the PI feedforward.

[0185] (1) The multivariable model predictive control method of the photovoltaic inverter grid-connected system of the application can realize model predictive current control under the alpha-beta coordinate, without using the traditional PWM modulator and current inner loop control, and only needs to perform coordinate transformation to calculate the optimal switching state, so that the calculation amount is small and easy to realize.

[0186] (2) The multivariable model predictive control method of the photovoltaic inverter grid-connected system of the application establishes a predictive current mathematical model under the alpha-beta coordinate, obtains the possible predictive current values of the inverter under the action of different voltage vectors at the next moment through the prediction function, selects the optimal vector according to the evaluation function, and makes the inverter output current value quickly approach the given reference value.

[0187] ​​(3) The PI parameter needs to consider the system stability and response speed, and the parameter setting process is complex and tedious. The multivariable model predictive control method of the photovoltaic inverter grid-connected system can control the overshoot, peak time and stable time of the alternating current under the MPC control to be less than the corresponding values of the PI feedforward control, which indicates that the MPC control effect is better than the PI feedforward.

[0188] (4) The multivariable model predictive control method of the photovoltaic inverter grid-connected system can improve the photovoltaic grid-connected response efficiency and reduce the total harmonic distortion rate, enhance the stability and anti-interference of the direct current bus voltage, control the grid-side current at a lower total harmonic distortion level, and the effect is obvious.

[0189] The above is an exemplary description of the application, and obviously, the specific implementation of the application is not limited by the above method. As long as the method concept and technical solution of the application are used for non-essential improvement or direct application in other occasions without improvement, it is within the protection scope of the application.

Claims

1. A multivariable model predictive control method for a photovoltaic inverter grid-connected system, characterized in that: The following steps are involved: S1. Construct a mathematical model of a three-phase full-bridge voltage-type grid-connected inverter in a rotating coordinate system, and combine SVPWM modulation technology with a model prediction algorithm to improve the output current quality of the grid-connected inverter. S2. Using the derivative approximation principle, derive the discrete-time model of the predicted current at time k+1 in both the rectification and inversion modes of the AC / DC converter, and substitute it into the calculation equation to obtain the current discrete prediction model; S3. By designing an appropriate value function, the minimum solution of the value function is sought to obtain the switching state of the converter.

2. The multivariable model predictive control method for a photovoltaic inverter grid-connected system according to claim 1, characterized in that: In step S1, the mathematical model of the three-phase full-bridge voltage-type grid-connected inverter is constructed as follows: The three-phase full-bridge voltage-type grid-connected inverter is selected as the research object. Based on the mathematical model of the three-phase stationary coordinate system, continuous rotation and transformation are performed to obtain the mathematical model of the rotating coordinate system.

3. The multivariable model predictive control method for a photovoltaic inverter grid-connected system according to claim 1 or 2, characterized in that: In step S1, the mathematical model of the three-phase full-bridge voltage-type grid-connected inverter is constructed in the following detailed process: 1) A three-phase full-bridge voltage-type grid-connected inverter is selected as the research object. When designing the control system of a three-phase grid-connected inverter, a switching function is usually used to represent the mathematical model of the three-phase grid-connected inverter device; let the switch of the three-phase grid-connected inverter be represented as: Where S i (i=a, b, c) represents the switch tubes corresponding to the three bridge arms of the three-phase inverter. The working states of the switch tubes are only "on" and "off". The working states of the upper and lower switches of the same bridge arm cannot be the same. For convenience, the number "1" is used to represent the switch tube in the "on" state, and the number "0" is used to represent the switch tube in the "off" state; S is the total state of the three-phase inverter; the unit vector a=e j2π / 3 represents a 120° phase difference between phases; Because the upper and lower power switches of each phase bridge arm of the three-phase grid-connected inverter cannot be turned on at the same time, when the upper bridge arm power switch of phase i is turned on, there is u iN =u dc , S i =1; When the lower bridge arm of phase i is turned on, there is u iN =0, S i =0; so formula (16) can be used to express the AC output voltage value, switch state and DC input voltage of the three-phase grid-connected inverter; in iN =with i IN dc (16), Where u iN Indicates the output voltage of phase i AC terminal, S i Indicates the conduction state of the lower bridge arm of phase i. If the conduction S i is 0, otherwise it is 1, U dC Indicates the DC input voltage; 2) The three-phase voltage type grid-connected inverter adopts Kirchhoff's law and adds both sides of the three-phase voltage equation to obtain formula (17), which is: The mathematical model of the three-phase grid-connected inverter in the abc stationary coordinate system can be derived as formula (18), specifically: 3) The three-phase to two-phase transformation matrix C is obtained by formula (18): abc / αβ It can realize the transformation from abc coordinate system to αβ coordinate system; According to formula (18), the mathematical model of the three-phase grid-connected inverter in the three-phase abc stationary coordinate system is transformed from three phases to two phases, and the mathematical model of the three-phase grid-connected inverter in the coordinate system αβ is shown in formula (19); In formula (19), e α 、e β 、i α 、i β are the components of the three-phase grid voltage and the three-phase output current in the αβ coordinate system; u α 、u β is the component of the output voltage of the three-phase grid-connected inverter in the two-phase αβ stationary coordinate system; 4) The relevant parameters in the αβ coordinate system can be transformed into the dq coordinate system through Park transformation, as shown in formula (20): By using formula (20) to transform the mathematical model of the three-phase grid-connected inverter in the αβ coordinate system, the mathematical model in the dq coordinate system can be obtained as shown in formula (21); In formula (21), e d 、e q 、i d 、i q are the components of the three-phase grid-side AC voltage and the three-phase grid-connected inverter output current on the d and q axes respectively; u d 、u q is the component of the three-phase voltage in the two-phase dq axis; s d 、s q Represents the components of the inverter switching function in the two-phase dq axis.

4. The multivariable model predictive control method for a photovoltaic inverter grid-connected system according to claim 3, characterized in that: The specific steps of the S2 step are as follows: 1) Converter output current i a 、i b 、i c The current i in the stationary coordinate system is obtained by Clack transformation α 、i β ; As shown in formulas (22) and (23), Where: i α 、i β is the current component in αβ coordinates; 2) For the current component i α 、i β By taking the derivative and using the forward difference theorem, we can get the discrete mathematical model of the converter output current, as shown in formula (24): 3) Using the derivative approximation principle, the discrete-time model of the predicted current at time k+1 in both the rectification and inversion modes of the AC / DC converter is derived, and Equation (24) is substituted into the voltage-current vector equation of the converter to obtain the current discrete prediction model shown in Equation (25); Where: i α (k+1), i β (k+1) is the predicted current component at time k+1 under αβ coordinates; V α 、V β is the inverter output voltage component under αβ coordinates; E α 、E β is the grid voltage component under αβ coordinates; T s is the sampling time.

5. The multivariable model predictive control method for a photovoltaic inverter grid-connected system according to claim 4, characterized in that: The specific steps of the S3 step are as follows: The main goal of model predictive control is to minimize the designed value function g. The current reference value is obtained by tracking the DC bus voltage command without static error, as shown in Equations (26), (27), and (28). The dynamic response error between the discretized current prediction value and the reference value is calculated using the designed value function, as shown in Equation (30). Where i * α (k), i * β (k) is the reference current component at time k in αβ coordinates; V * dc (k) is the DC reference voltage at time k; V dc (k) is the DC sampling voltage at time k; i * α (k+1), i * β (k+1) is the reference current component at time k+1 in αβ coordinates; K p , K i are the proportional coefficient and integral coefficient of the PI controller respectively; During this period, in order to improve the control accuracy and the grid electromotive force will not change greatly, the next step and test can also be estimated by the formula. Taking into account the fluctuation of the DC bus voltage of the charging pile, in order to improve the robustness of the system, the DC bus voltage error is multiplied by a certain weight coefficient and added to the value function.

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