An improved variational iterative simulation method based on event triggering

Abstract

The invention discloses an improved variational iteration simulation method based on event triggering. The simulation method establishes a mathematical model by using the variational iteration method according to the variable relationship of distributed photovoltaics in a modern active distribution network. For a grid-connected inverter module in a two-stage photovoltaic power station, based on the state space correlation principle, a numerical stability analysis of the system is performed on the basis of establishing a state space expression, and the analysis is compared with a traditional simulation algorithm. An improved method for applying the variational iteration method to photovoltaic solution is proposed, and the error generated by updating the analytical expression with a fixed step length and its numerical stability are analyzed. The simulation method is based on the event triggering principle, and an inequality relationship is established according to the error norm of the state quantity after the locked value, and the triggering condition of the locked value is derived. The simulation method is based on the event triggering theory and takes the variational iteration method as the basic algorithm, so as to provide a basis for the design of an efficient simulation method for distributed photovoltaic power stations, achieve the goal of taking both accuracy and efficiency into consideration, and improve the speed of active distribution network simulation.

Description

Technical Field

[0001] The invention relates to the field of simulation algorithms for distributed power sources in a distribution network, and in particular to an improved variational iterative simulation method based on event triggering. Background Art

[0002] The modern distribution network with high-density distributed generation is a complex nonlinear rigid system. The solution method of this type of model, namely the dynamic simulation algorithm, has always been the focus of attention in the field of power system simulation. The accuracy and efficiency of numerical calculation in dynamic simulation are of great significance for the planning, operation, and control of modern active distribution networks with high randomness and uncertainty in power generation characteristics. At present, the solution method of differential equations (ODEs) is conventional numerical integration algorithm such as trapezoidal method, which is difficult to meet the requirements of fast and stable simulation at the same time. Compared with traditional distribution networks, the components in active distribution networks have large differences in dynamic characteristics; the time scales are obviously different, and there are rigidity problems; the corresponding mathematical models have higher order, higher dimension, and stronger nonlinear characteristics. Based on the above, the dynamic simulation of large-scale distribution networks faces more severe challenges. Therefore, it is necessary to propose a more efficient and fast simulation algorithm under the premise of ensuring accuracy and stability.

[0003] In recent years, the variational iteration method (VIM) has stood out among various approximate analytical methods due to its outstanding advantages, and has been widely used in solving various nonlinear problems including ODEs. When this method is applied to the simulation of distributed power sources in distribution networks, it improves efficiency compared to the traditional implicit trapezoidal algorithm. When applied, the essence is to obtain the variable parameter calculation formula of the system and update the state quantity expression once at each step. It will cause a waste of computing resources during steady-state operation, and there is still room for optimization. Therefore, an improved variational iteration simulation method based on event triggering is proposed. Summary of the invention

[0004] The purpose of the present invention is to provide an improved variational iterative simulation method based on event triggering, a variational iterative approximate analytical method based on differential equations, and apply it to an active distribution network containing high-density distributed photovoltaics, and perform numerical stability analysis on it. According to the relevant theory of event triggering, some state variables in the variational model are locked, and fixed-step updates are adopted or when the error vector norm meets certain conditions, updates are made to improve the simulation solution rate of the photovoltaic power station, thereby improving the simulation operation efficiency of the active distribution network.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] An improved variational iterative simulation method based on event triggering, the simulation method comprises the following steps:

[0007] Step 1: According to the relevant steps of the variational iteration method, a variational mathematical model is established for the two-stage photovoltaic power station, and then proceed to step 2.

[0008] Step 2: Calculate the state space expression corresponding to the model, and perform numerical stability analysis on the system based on the state space stability judgment theory. Compare the maximum allowed simulation step size with the trapezoidal method and improved Euler method, and then proceed to step 3.

[0009] Step 3: Update some higher-order analytical expressions with a fixed step size, perform numerical stability analysis and error propagation on the method, expand the maximum equivalent step size of the variational method, and then proceed to step 4.

[0010] Step 4: Based on the event triggering related theory, the norm of the error vector is used as the trigger judgment condition to obtain the error threshold, improve the original variational iterative method, and further improve the operation efficiency of the simulation system.

[0011] Furthermore, in the step 1, in the modeling of the two-stage photovoltaic power station, according to the relevant steps of the variational iteration method calculation, a mathematical model of the two-stage photovoltaic including the photovoltaic array, the boost chopper circuit, and the grid-connected inverter is established, and the specific operation includes the following steps:

[0012] S11: The variational iteration method is introduced to solve the general form of the differential equation in the two-stage photovoltaic power station. The format is as follows:

[0013] Ly(t)+Ny(t)=f(t) Formula (1)

[0014] Among them, y(t) is the function to be solved, L and N are linear operators and nonlinear operators respectively. According to the VIM principle, the correction functional corresponding to this equation is:

[0015]

[0016] Where n is the number of iterations, λ(τ) is the Lagrangian operator, which is an undetermined function. Represents y n The restricted variation of (τ) is performed, and the result of the variation operation is 0.

[0017] S12: Mathematical modeling is performed on the photovoltaic array, boost chopper, and grid-connected inverter in the two-stage photovoltaic power station respectively. The corresponding algebraic-differential equation (D-Es) model of each part is as follows:

[0018] Photovoltaic array:

[0019]

[0020] Among them, u PV 、i PVare photovoltaic voltage and current, i Boost,L is the boost chopper input current, C PV is the photovoltaic equivalent capacitance;

[0021] Boost Chopper:

[0022]

[0023] Among them, u Boost is the output voltage, i Boost is the output current, D is the chopping duty cycle, L Boost , C Boost are the inductance and capacitance in the chopper, u M is the voltage corresponding to the maximum power point of photovoltaic, k p1 , k i1 are the controller parameters of the Boost circuit.

[0024] Grid-connected inverter (single-loop PQ control, when performing Park transformation, the d-axis is consistent with the phase of one phase):

[0025]

[0026]

[0027] u Boost i Boost =u id i d +u iq i q Formula (14)

[0028] Among them, u mdq 、u idq 、u sdq 、i dq are the modulation wave voltage, inverter output voltage, grid connection point voltage, and dq components of current, respectively, and k0 is the modulation ratio. p2 , k i2 is the controller parameter of the inverter circuit. When the SPWM modulation method is adopted, k0 is If u Boost 800V, U AC is 380V, then m=2.227.

[0029] S13: Use the variational iteration method to solve all differential equations in equations (3)-(13). Take equation (8) as an example to calculate its variational iteration format. According to equation (2), its correction functional is:

[0030]

[0031] Considering the alternating solution of algebraic-differential equations, when calculating differential equations, usd 、u id , L f Since they are all known quantities, they are combined into parameter 1 and the variation operation is performed on equation (15):

[0032]

[0033] According to the variational principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, so for the right side, there are restrictions:

[0034]

[0035] λ = -1, substituting into equation (15) we can get the iteration format of id, substituting into the initial function, and obtaining its approximate analytical solution through iteration. Similarly, we can get the variational iteration format corresponding to equations (4)-(11).

[0036] Furthermore, in step 2, based on the state space theory, the state space expression corresponding to the grid-connected inverter is calculated, and its numerical stability is analyzed. The specific steps include:

[0037] S21: List the mathematical model corresponding to the grid-connected inverter after applying variational iteration. The inverter adopts PQ single-loop control and the variational iteration method adopts the second-order expression. The model is as follows:

[0038]

[0039] Among them, the subscript containing 0 indicates that the variable is the initial value after update.

[0040] S22: Alternating solution is used for simulation calculation on a single simulation step. md1 、u md2 There is no coupling of state quantities in the integral equation, so it can be directly discretized using the Euler method. The remaining variables are in variational format. d 、i q 、u md1 、u mq1 As state variables, after sorting, we can get the state space expression of the system:

[0041]

[0042] Among them, Δt is the simulation step size, C is the constant matrix related to the input and output parameters of the inverter. m is the ratio of the inverter output voltage to the modulation voltage. According to the state space theory, when the state matrix spectrum radius is less than 1, the system can be stable. Therefore, when the parameters in the matrix are known, it is possible to calculate whether the system is stable. Therefore, when the remaining unknown parameters are known, the state iteration matrix can be used to determine the maximum simulation step size.

[0043] Furthermore, the step 3 updates the analytical expression by a fixed step length to improve the simulation speed to a certain extent, according to the following formula:

[0044]

[0045] The state space expression corresponding to the fixed step size update is obtained. By this method, the equivalent step size can be expanded to nΔt. For the numerical stability of this improved form, the spectral radius of the state matrix ' can be used to judge the numerical stability.

[0046] Furthermore, the fourth step is based on the event triggering theory, and locks i when the system state quantity meets certain conditions. dq The value of , thereby omitting the calculation of the quadratic expression in the simulation calculation time step, the specific operation steps include:

[0047] S41: The state space expression corresponding to equation (19) is simplified as follows:

[0048] y(k+1)=Ay(k)+C1 Formula (21)

[0049] And assume that its steady-state value is y ∞ , there is a deviation e0 between the state quantity and the steady-state value when the value is locked, and the state matrix after locking the value is -1, then the new state space expression is:

[0050] y ∞ +e(k+1)=A1[y ∞ +e(k)]+C2 Formula (22)

[0051] Note that -1=-+Δ-, and substitute it into formula (26) to transform it, that is:

[0052]

[0053] Eliminating the steady-state components on both sides, the iterative expression of the error is:

[0054] e(k+1)=A1e(k)+ΔAy ∞ +C2-C1=A1e(k)+C3 Formula (24).

[0055] S42: Convert the error iteration format of the above formula (24) into a continuous form for solving, according to the conversion relationship between the discrete form and the continuous form:

[0056]

[0057] Taking the norm, we can obtain the inequality constraint:

[0058]

[0059] By solving this differential inequality, we can obtain the event triggering condition, that is, the constraint condition of the error norm is:

[0060]

[0061] Beneficial effects of the present invention:

[0062] 1. The simulation method of the present invention combines the variational iterative method in the mathematical field with the distributed photovoltaic in the active distribution network through numerical stability verification, error calculation and event triggering method, and compares this method with the traditional numerical integration algorithm, thereby establishing a simulation algorithm combining the variational method with the traditional numerical integration method, and utilizing the variational method to approximate the analytical characteristics to improve the efficiency of simulation calculation;

[0063] 2. The simulation method of the present invention uses state space theory to perform numerical stability analysis on the mathematical model established by the variational method, thereby obtaining the maximum simulation step length allowed by the simulation method as the basis for simulation design;

[0064] 3. The simulation method of the present invention improves the existing variational simulation method that updates the expression once per step, and proposes an improved form based on event triggering, which further improves the simulation efficiency of the system.

[0065] 4. The algorithm iteration format in the simulation method of the present invention is simple to construct and has high versatility;

[0066] 5. The simulation method of the present invention has a precision close to that of the traditional simulation algorithm, allows a larger step size, and has a faster simulation speed. It has certain application prospects in modern active distribution networks with high-density distributed power access. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The present invention will be further described below in conjunction with the accompanying drawings.

[0068] Figure 1 is a flow chart of the simulation method of the present invention;

[0069] Figure 2 It is a grid-connected inverter simulation system used in the simulation method of the present invention;

[0070] Figure 3 It is a comparison diagram of the active power of the variational modeling under different step lengths of the simulation method of the present invention;

[0071] Figure 4 It is a simulation result diagram of active power comparison of three algorithms under near-limit step length in the simulation method of the present invention;

[0072] Figure 5 It is a comparison diagram of the active power output by the inverter under different triggering modes in the simulation method of the present invention;

[0073] Figure 6 is a voltage comparison diagram of the inverter output under different triggering modes in the simulation method of the present invention;

[0074] Figure 7 It is a structural diagram of an improved IEEE-33 node active distribution network test system used in the simulation method of the present invention;

[0075] Figure 8 It is a comparison diagram of active power waveforms of different simulation methods of test system node 8 in the simulation method of the present invention;

[0076] Fig. 9 It is a comparison diagram of reactive power waveforms of different simulation methods of test system node 8 in the simulation method of the present invention;

[0077] Fig.10 It is a comparison diagram of voltage waveforms of different simulation methods of test system node 8 in the simulation method of the present invention. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] In the description of this specification, reference is made to an improved variational iterative simulation method based on event triggering, such as Figure 1 As shown, the simulation method includes the following steps:

[0080] Step 1: According to the relevant steps of the variational iteration method, a variational mathematical model is established for the two-stage photovoltaic power station, and then proceed to step 2.

[0081] In the modeling of the two-stage photovoltaic power station, according to the relevant steps of the variational iteration method calculation, a mathematical model of the two-stage photovoltaic including the photovoltaic array, the boost chopper circuit, and the grid-connected inverter is established. The specific steps include:

[0082] S11: The variational iteration method is introduced to solve the general form of the differential equation in the two-stage photovoltaic power station. The format is as follows:

[0083] Ly(t)+Ny(t)=f(t) Formula (1)

[0084] Among them, y(t) is the function to be solved, L and N are linear operators and nonlinear operators respectively. According to the VIM principle, the correction functional corresponding to this equation is:

[0085]

[0086] Where n is the number of iterations, λ(τ) is the Lagrangian operator, which is an undetermined function. Represents y n The restricted variation of (τ) is performed, and the result of the variation operation is 0.

[0087] S12: Mathematical modeling is performed on the photovoltaic array, boost chopper, and grid-connected inverter in the two-stage photovoltaic power station respectively. The corresponding algebraic-differential equation (D-Es) model of each part is as follows:

[0088] Photovoltaic array:

[0089]

[0090] Among them, u PV 、i PV are photovoltaic voltage and current, i Boost,L is the boost chopper input current, C PV is the photovoltaic equivalent capacitance.

[0091] Boost Chopper:

[0092]

[0093] Among them, u Boost is the output voltage, i Boost is the output current, D is the chopping duty cycle, L Boost , C Boost are the inductance and capacitance in the chopper, u M is the voltage corresponding to the maximum power point of photovoltaic, k p1 , k i1 are the controller parameters of the Boost circuit.

[0094] Grid-connected inverter (single-loop PQ control, when performing Park transformation, the d-axis is consistent with the phase of one phase):

[0095]

[0096] u Boost i Boost =u id i d +u iq i q Formula (14)

[0097] Among them, u mdq 、u idq 、u sdq 、i dq are the modulation wave voltage, inverter output voltage, grid connection point voltage, and dq components of current, respectively, and k0 is the modulation ratio. p2, k i2 is the controller parameter of the inverter circuit. When the SPWM modulation method is adopted, k0 is If u Boost 800V, U AC is 380V, then m=2.227.

[0098] S13: Use the variational iteration method to solve all differential equations in equations (3)-(13), and take equation (8) as an example to calculate its variational iteration format. According to equation (2), its correction functional is:

[0099]

[0100] Considering the alternating solution of algebraic-differential equations, when calculating differential equations, u sd 、u id , L f Since they are all known quantities, they are combined into parameter 1 and the variation operation is performed on equation (15):

[0101]

[0102] According to the variational principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, so for the right side, there are restrictions:

[0103]

[0104] It is further known that λ = -1, and the iterative format of id can be obtained by substituting it into equation (15). Substituting it into the initial function, its approximate analytical solution can be obtained through iteration. Similarly, the variational iterative format corresponding to equations (4)-(11) can be obtained. For other distributed power generation equipment in the active distribution network, such as turbines and fans, the same method can be used to obtain the corresponding variational iterative format and expressions of each order.

[0105] Step 2: Calculate the state space expression corresponding to the model, and perform numerical stability analysis on the system based on the state space stability judgment theory. Compare the maximum allowed simulation step size with the trapezoidal method and improved Euler method, and then proceed to step 3.

[0106] Based on the state space theory, the state space expression corresponding to the grid-connected inverter is calculated and its numerical stability is analyzed. The specific operations include the following:

[0107] S21: List the mathematical model corresponding to the grid-connected inverter after applying variational iteration. The inverter adopts PQ single-loop control and the variational iteration method adopts the second-order expression. The model is as follows:

[0108]

[0109] Among them, the subscript containing 0 indicates that the variable is the initial value after update.

[0110] S22: Alternating solution is used for simulation calculation on a single simulation step. md1 、u md2 There is no coupling of state quantities in the integral equation, so it can be directly discretized using the Euler method. The remaining variables are in variational format. d 、i q 、u md1 、u mq1 As state variables, after sorting, we can get the state space expression of the system:

[0111]

[0112] Among them, Δt is the simulation step size, C is the constant matrix related to the input and output parameters of the inverter. m is the ratio of the inverter output voltage to the modulation voltage. According to the state space theory, when the state matrix spectrum radius is less than 1, the system can be stable. Therefore, when the parameters in the matrix are known, it is possible to calculate whether the system is stable. Therefore, when the remaining unknown parameters are known, the state iteration matrix can be used to determine the maximum simulation step size.

[0113] Step 3: Update some higher-order analytical expressions with a fixed step size, perform numerical stability analysis and error propagation on the method, expand the maximum equivalent step size of the variational method, and then proceed to step 4.

[0114] By updating the analytical expression with a fixed step length, the simulation speed can be improved to a certain extent, according to the following formula:

[0115]

[0116] The state space expression corresponding to the fixed step size update is obtained. Through this method, the equivalent step size can be expanded to nΔt. For the numerical stability of this improved form, the spectral radius of the state matrix ' can be used to judge the numerical stability.

[0117] Step 4: Based on the event triggering related theory, the norm of the error vector is used as the trigger judgment condition to obtain the error threshold, improve the original variational iterative method, and further improve the operation efficiency of the simulation system.

[0118] Based on the event triggering theory, the system state quantity is locked when certain conditions are met. dq The value of can be used to omit the calculation of the quadratic expression in the simulation time step, which can not only suppress the increase of errors but also improve the simulation efficiency.

[0119] S41: The state space expression corresponding to equation (19) is simplified as follows:

[0120] y(k+1)=Ay(k)+C1 Formula (21)

[0121] And assume that its steady-state value is y ∞ , there is a deviation e0 between the state quantity and the steady-state value when the value is locked, and the state matrix after locking the value is -1, then the new state space expression is:

[0122] y ∞ +e(k+1)=A1[y ∞ +e(k)]+C2 Formula (22)

[0123] Note that -1=-+Δ-, and substitute it into formula (26) to transform it, that is:

[0124]

[0125] Eliminating the steady-state components on both sides, the iterative expression of the error is:

[0126] e(k+1)=A1e(k)+ΔAy ∞ +C2-C1=A1e(k)+C3 Formula (24)

[0127] S42: Convert the error iteration format of the above formula (24) into a continuous form for solving, according to the conversion relationship between the discrete form and the continuous form:

[0128]

[0129] Taking the norm, we can obtain the inequality constraint:

[0130]

[0131] By solving this differential inequality, we can obtain the event triggering condition, that is, the constraint condition of the error norm is:

[0132]

[0133] Applying the above simulation method to practice, the simulation system is as follows Figure 2 As shown, the DC side circuit on the left side of the converter is connected to 800V DC input, and the right side of the converter is connected to the filter inductor and connected to the grid through the line. The effective value of the grid line voltage is 380V, and the frequency is 50Hz. The filter inductor L f is 4mH, the line resistance R line is 0.1Ω, inductance L line The system simulation time is 5s, the converter adopts PQ control, and the power reference value P ref 20kw, which becomes 15kw in 2-3s, Q ref 20kV-R. Controller parameter setting k p=1.5, k i = 30. According to the improved variational iterative simulation method based on event triggering in the embodiment of the present invention, a distributed photovoltaic grid-connected inverter is designed, and a simulation model is built based on the M-TL-2 platform to simulate the stability of each algorithm and the event triggering effect to verify the feasibility of the method of the present invention.

[0134] According to the active power comparison diagram modeled by the variational method under different step lengths, 1ms, 1.7ms, 1.73ms, and 1.74ms are used as simulation step lengths for comparison. The inverter output active power is shown in Figure 3 As shown, when the simulation step size is less than 1.73ms, the system can converge and oscillate around the steady-state value at 1.73ms. However, when the step size is 1.74ms, the system gradually diverges from the beginning of the calculation. The simulation results are consistent with the theoretical maximum simulation step size.

[0135] At the beginning of operation, the reference active power of each inverter is 20kW. The power is reduced to 15kW at 2 seconds and restored to 20kW at 3 seconds. The simulation results of the active power comparison of the three algorithms under the near-limit step size are as follows: Figure 4 As shown in the figure, the waveform comparison shows that the trapezoidal method can no longer guarantee accuracy when it approaches the limit step size, while the variational method has large oscillations at a step size of 1.7ms, and its convergence performance is better than the other three cases at 1.5ms. The total time consumption of 100 5-second simulations using each simulation algorithm is shown in Table 1. Since the variational method allows a larger step size for simulation calculation, the simulation efficiency is significantly improved.

[0136]

[0137] Table 1

[0138] At the beginning of operation, the reference active power of each inverter is 20kW, the power is reduced to 15kW after 2 seconds, and restored to 20kW after 3 seconds. Figure 5 The following is a comparison chart of the active power output of the inverter under different triggering modes. Figure 6 The voltage comparison diagram of the inverter output under different triggering modes is shown in Figure 2. Figure 5 It can be seen that when the steady-state trigger method is used, the current value at the moment of current reference value update is still the value of the previous steady state, so the difference is entered into the modulation wave calculation formula, which will cause large fluctuations, which is not allowed in simulation. The accuracy and convergence speed of fixed-step trigger are not as good as event trigger, and event trigger can basically achieve the same effect as the original method.

[0139] like Figure 7The structure diagram of the improved IEEE-33 node active distribution network test system in this embodiment is shown. Among them: the distributed photovoltaic power generation system is connected to the load nodes 8, 13, 25, and 33 in the system. The total load of the system is 5084.26+j2547.32kV. The simulation step size is 10μs. During normal operation, the initial environmental condition of the photovoltaic power generation system is 1000W / m 2 and 25℃, and all operate at unity power factor. Line parameters: C PV =10 -4 F, L 二oost =50mH, C 二oost =5mF, L f =5mH. Controller parameters: k p1 =k p2 =1.5, k i1 =k i2 =30. The total simulation time is 5s. When the system runs to 2.5s, all photovoltaic irradiance drops to 800W / m 2 , and recover to 1000W / m in 3s 2 .

[0140] like Figures 8 to 10 As shown in the figure, the simulation methods respectively use the improved variational method based on event triggering, the variational method without triggering the lock value, and the trapezoidal integration method to perform simulation results, and compare the per-unit values ​​of the active power, reactive power and node voltage effective value of node 8. The accuracy of the basic variational method and the trapezoidal method is similar, while the improved variational method has an error of about 0.1% when calculating the bus voltage. The error magnitude is small and basically meets the accuracy requirements. The simulation time of each algorithm is shown in Table 2. The simulation time is mainly composed of distributed photovoltaic calculations and power flow calculations. It can be seen from Table 2 that the improved variational method reduces the photovoltaic calculation time by about 29% compared with the trapezoidal method, which has certain advantages.

[0141]

[0142] Table 2

[0143] The present invention proposes an improved variational iterative simulation method, and provides numerical stability verification, error calculation and event triggering methods. This method is compared with a traditional numerical integration algorithm, and the variational iterative method in the mathematical field is combined with distributed photovoltaics in an active distribution network, thereby establishing a simulation algorithm that combines the variational method with the traditional numerical integration method, and utilizing the approximate analytical characteristics of the variational method to improve the efficiency of simulation calculations; the state space theory is used to perform numerical stability analysis on the mathematical model established by the variational method, thereby obtaining the maximum simulation step length allowed by the simulation method, which is used as the basis for simulation design.

[0144] The simulation method of the present invention improves the existing variational simulation method that updates the expression once per step, and proposes an improved form based on event triggering, which further improves the simulation efficiency of the system. The algorithm iteration format is simple to construct and has high versatility. The simulation method of the present invention has a precision close to that of the traditional simulation algorithm, allows a larger step size, and has a faster simulation speed. It has certain application prospects in modern active distribution networks with high-density distributed power access.

[0145] The description of "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0146] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. An improved variational iterative simulation method based on event triggering, characterized in that: The simulation method comprises the following steps: Step 1: According to the relevant steps of the variational iterative method, a variational mathematical model is established for the two-stage photovoltaic power station, and then proceed to step 2; Step 2: Calculate the state space expression corresponding to the model, and perform numerical stability analysis on the system based on the stability judgment theory of the state space, compare the maximum simulation step allowed with the trapezoidal method and the improved Euler method, and then proceed to step 3; Step 3: Update the state space expression with a fixed step length, perform numerical stability analysis and error propagation on the updated system, expand the maximum equivalent step length of the variational method, and then proceed to step 4; Step 4: Based on the event triggering related theory, the norm of the error vector is used as the trigger judgment condition to obtain the error threshold, improve the original variational iterative method, and further improve the operation efficiency of the simulation system.

2. The improved variational iterative simulation method based on event triggering according to claim 1, characterized in that: In the step 1, in the modeling of the two-stage photovoltaic power station, according to the relevant steps of the variational iteration method calculation, a mathematical model of the two-stage photovoltaic including the photovoltaic array, the boost chopper circuit, and the grid-connected inverter is established, and the specific operation includes the following steps: S11: The variational iteration method is introduced to solve the general form of the differential equation in the two-stage photovoltaic power station. The format is as follows: Ly(t)+Ny(t)=f(t) Formula (1) Among them, y(t) is the function to be solved, L and N are linear operators and nonlinear operators respectively. According to the VIM principle, the correction functional corresponding to this equation is: Where n is the number of iterations, λ(τ) is the Lagrangian operator, which is an undetermined function. Represents y n The restricted variation of (τ) is 0. S12: Mathematical modeling is performed on the photovoltaic array, boost chopper, and grid-connected inverter in the two-stage photovoltaic power station. The algebraic-differential equation model corresponding to each part is shown below: Photovoltaic array: Among them, u PV 、i PV are photovoltaic voltage and current, i Boost,L is the boost chopper input current, C PV is the photovoltaic equivalent capacitance; Boost Chopper: Among them, u Boost is the output voltage, i Boost is the output current, D is the chopping duty cycle, L Boost , C Boost are the inductance and capacitance in the chopper, u M is the voltage corresponding to the maximum power point of photovoltaic, k p1 , k i1 is the controller parameter of the Boost circuit; Grid-connected inverter, single-loop PQ control, when performing Park transformation, the d-axis is consistent with one phase: u Boost i Boost = u id i d + u iq i q Equation (14) Among them, u mdq 、u idq 、u sdq 、i dq are the modulation wave voltage, inverter output voltage, grid connection point voltage, and dq components of current respectively. k0 is the modulation ratio, k p2 , k i2 is the controller parameter of the inverter circuit. When the SPWM modulation method is adopted, k0 is If u Boost 800V, U AC is 380V, then m=2.227; S13: Use the variational iteration method to solve all differential equations in equations (3)-(13). Take equation (8) as an example to calculate its variational iteration format. According to equation (2), its correction functional is: Considering the alternating solution of algebraic-differential equations, when calculating differential equations, u sd 、u id , L f Since they are all known quantities, they are combined into parameter 1 and the variation operation is performed on equation (15): According to the variational principle, as the iteration proceeds, the left side of equation (16) gradually approaches 0, so for the right side, there are restrictions: λ = -1, substituting into equation (15) we can get the iterative format of id, substituting into the initial function, and obtaining its approximate analytical solution through iteration. Similarly, we can get the variational iterative format corresponding to equations (4)-(11).

3. The improved variational iterative simulation method based on event triggering according to claim 1 is characterized in that: In the second step, based on the state space theory, the state space expression corresponding to the grid-connected inverter is calculated and its numerical stability is analyzed. The specific steps include: S21: List the mathematical model corresponding to the grid-connected inverter after applying variational iteration. The inverter adopts PQ single-loop control and the variational iteration method adopts the second-order expression. The model is as follows: Among them, the subscript contains 0 to indicate that the variable is the initial value after the update; S22: Alternating solution is used for simulation calculation on a single simulation step. md1 、u md2 There is no coupling of state quantities in the integral equation, so it can be directly discretized using the Euler method. The remaining variables are in variational format. d 、i q 、u md1 、u mq1 As state variables, after sorting, we can get the state space expression of the system: Among them, Δt is the simulation step, C is the constant matrix related to the inverter input, output and other parameters, m is the ratio of the inverter output voltage to the modulation voltage. According to the state space theory, when the state matrix spectrum radius is less than 1, the system can be stable. Therefore, when the parameters in the matrix are known, it can be calculated whether the system is stable. Therefore, when the other unknown parameters are known, the state iteration matrix can be used to determine the maximum simulation step.

4. The improved variational iterative simulation method based on event triggering according to claim 1, characterized in that: The step 3 updates the analytical expression by a fixed step length to improve the simulation speed to a certain extent, according to the following formula: The state space expression corresponding to the fixed-step update is obtained. This method can be used to expand the equivalent step size to nΔt. For the numerical stability of the improved system, the spectral radius of the state matrix can be used to judge the numerical stability.

5. The improved variational iterative simulation method based on event triggering according to claim 3 is characterized in that: The fourth step is based on the event triggering theory, and locks i when the system state quantity meets the triggering condition. dq The value of , thereby omitting the calculation of the quadratic expression in the simulation calculation time step, the specific operation steps include: S41: The state space expression corresponding to equation (19) is simplified as follows: y(k+1)=Ay(k)+C1 Formula (21) And assume that its steady-state value is y ∞ , there is a deviation e0 between the state quantity and the steady-state value when the value is locked, and the state matrix after locking the value is -1, then the new state space expression is: y ∞ +e(k + 1)= A1[y ∞ +e(k)]+ C2 Equation (22) Note that -1=-+Δ-, and substitute it into formula (26) to transform it, that is: Eliminating the steady-state components on both sides, the iterative expression of the error is: e(k + 1) = A1e(k) + ΔAy ∞ + C2 - C1 = A1e(k) + C3 Equation (24); S42: Convert the error iteration format of the above formula (24) into a continuous form for solving, according to the conversion relationship between the discrete form and the continuous form: Taking the norm, we can obtain the inequality constraint: By solving this differential inequality, we can obtain the event triggering condition, that is, the constraint condition of the error norm is:

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