State-space equation discretization method based on characteristics of capacitance and inductance elements

Abstract

The invention relates to the technical field of circuit state-space equation solving in the field of real-time simulation, and discloses a state-space equation discretization method based on capacitor and inductor element characteristics, which comprises the following steps of: A) establishing a state-space differential equation of a circuit; b) establishing characteristic equations of capacitance and inductance elements, determining a numerical integration method used by each capacitance and inductance element in the circuit, and obtaining a characteristic equation of a discrete time domain by using the numerical integration method; c) combining the discrete time domain characteristic equation in the step B) and the state space differential equation in the step A) to obtain a state space discrete equation of the circuit; and D) loop simulation. According to the state-space equation discretization method based on the characteristics of the capacitance and inductance elements, the real-time simulation speed and precision of a circuit system are improved by independently discretizing the characteristic equation of each capacitance and inductance element and optimizing the discretization process of the state-space equation.

Description

Technical Field

[0001] The present invention relates to the technical field of solving circuit state space equations in the field of real-time simulation, and in particular to a state space equation discretization method based on the characteristics of capacitor and inductor components. Background Art

[0002] With the continuous expansion of the scale of power systems and the adoption of new power electronic devices, the dynamic characteristics of the system have become increasingly complex. Unlike traditional power equipment such as generators and motors, power electronic equipment has the characteristics of high frequency and rapid response. Systems that introduce power electronic equipment also have the characteristics of numerous components and complex dynamic characteristics, which brings new challenges to the development and testing of power systems.

[0003] Real-time simulation can study the electromagnetic transient behavior characteristics of the system, facilitate the design of system control methods, replace physical experiments with hardware-in-the-loop testing, and reduce scientific research costs, R&D cycles, and experimental risks. Therefore, real-time simulation is an important tool for studying power systems containing power electronic equipment. In this context, real-time simulation of power electronics has attracted widespread attention from scholars.

[0004] Based on the current situation of increasingly complex systems and considering that the time step of real-time simulation is a fixed value, the optimization goals of power electronics real-time simulation are concentrated on simulation speed and calculation accuracy, mainly including: reducing the amount of calculation and improving the real-time simulation speed; improving the real-time simulation accuracy while ensuring the real-time performance of the simulation.

[0005] To achieve the above goals, one of the key means to solve the problem is to optimize the discrete process of the system equations, reduce the amount of calculation and improve the calculation accuracy.

[0006] Taking the trapezoidal method as an example, the traditional state-space equation discretization method focuses on using the numerical integration method to directly discretize the state-space equation as a whole, ignoring the characteristics of different capacitors and inductors in the circuit. It has the disadvantages of large amount of calculation and inflexible numerical integration method. Summary of the invention

[0007] The purpose of the present invention is to address the deficiencies of the above-mentioned technologies and to provide a state-space equation discretization method based on the characteristics of capacitor and inductor components. By independently discretizing the characteristic equations of each capacitor and inductor component and optimizing the discretization process of the state-space equation, the speed and accuracy of real-time simulation of the circuit system are improved.

[0008] To achieve the above object, the state space equation discretization method based on the characteristics of capacitor and inductor components designed in the present invention comprises the following steps:

[0009] A) Establish the state space differential equation of the circuit;

[0010] B) establishing characteristic equations of capacitors and inductors, determining the numerical integration method used for each capacitor and inductor in the circuit, and using the numerical integration method to obtain the characteristic equation in the discrete time domain;

[0011] C) combining the discrete time domain characteristic equation of step B) and the state space differential equation of step A) to obtain a state space discrete equation of the circuit;

[0012] D) Cycle simulation.

[0013] Preferably, in the step C), the relationship equation between the non-state quantity, state quantity and input is established according to the characteristic equations of the capacitor and the inductor, and the relationship equation between the non-state quantity of the capacitor, the non-state quantity of the inductor, the state quantity of the capacitor, the state quantity of the inductor and the historical source is established according to the solution of the step B), and then the relationship equation between the state quantity, the historical source and the input is established, and finally the state space discrete equation based on the characteristics of the capacitor and the inductor components is established.

[0014] Preferably, in step A), the state space differential equation of the circuit is:

[0015]

[0016] Where A and B are state space matrices, t is the time, and X is the state quantity, including the current i flowing through the inductor L and the voltage u across the capacitor C , Include U is the system input.

[0017] Preferably, in step B), the characteristic equations of capacitance and inductance are respectively:

[0018]

[0019] In the formula, i C represents the current flowing through the capacitor, u L Represents the voltage across the inductor, and solves the characteristic equation of the capacitor using the trapezoidal method to obtain:

[0020]

[0021] In the formula, Δt is the simulation step size, and the characteristic equation of the inductor is solved using the third-order Adams-Moulton method:

[0022]

[0023] After calculation, we get:

[0024] In the formula,

[0025] Preferably, in step C), i is defined C 、u L For the non-state quantity X′, establish the relationship equation between the non-state quantity X′, state quantity X and input U:

[0026] X′(t)=EAX(t)+EBU(t) (3)

[0027] Where E is a diagonal matrix containing capacitance values ​​C and inductance values ​​L;

[0028] Then establish the non-state quantity X of the capacitor C ′、non-state quantity X of inductance L ′、Capacitor state quantity X C , the state quantity of inductance X L The relationship equation with the historical source h is:

[0029]

[0030] Historical source h is i history 、u history The column vector composed of (7) and (3) is used to establish the relationship between the state quantity X, the historical source h and the input U:

[0031] FX(t)-h(t)=EAX(t)+EBU(t) (8)

[0032] In the formula, F is the C , Z L The diagonal array composed of

[0033] Finally, the state space discrete equation based on the characteristics of capacitor and inductor components is established:

[0034] X(t)=Ph(t)+QU(t) (9)

[0035] Where, P = (F-EA) -1 , Q = (F-EA) -1 EB.

[0036] Preferably, in the step D), when performing the loop simulation, the state quantity X(t) at the initial time t and the historical source h at the current time are calculated, and then t=t+1 until the simulation is completed.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. Abandoning the traditional method of directly discretizing the state space equation as a whole, so that each state quantity in the system can flexibly choose the numerical integration method;

[0039] 2. When all state quantities are discretized using the same third-order or higher implicit numerical integration method, the computational complexity of the method provided by the present invention is less than that of the traditional state space discretization method;

[0040] 3. When numerical integration is selected for partition, that is, most of the capacitors and inductors in the system select low-order numerical integration methods and the remaining capacitors and inductors select high-order numerical integration methods, the accuracy can be significantly improved at the cost of a small increase in the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a simulation flow chart of the state space equation discretization method based on the characteristics of capacitor and inductor components of the present invention;

[0042] Figure 2 is a schematic diagram of a certain RLC circuit system;

[0043] Figure 3 This is a comparison chart of the target center distances of the four schemes calculated using the gray target method in Experiment 2. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with specific embodiments.

[0045] like Figure 1 As shown, a state space equation discretization method based on the characteristics of capacitor and inductor components includes the following steps:

[0046] A) Establish the state space differential equation of the circuit;

[0047] B) establishing characteristic equations of capacitors and inductors, determining the numerical integration method used for each capacitor and inductor in the circuit, and using the numerical integration method to obtain the characteristic equation in the discrete time domain;

[0048] C) combining the discrete time domain characteristic equation of step B) and the state space differential equation of step A) to obtain a state space discrete equation of the circuit;

[0049] D) Cycle simulation.

[0050] Among them, in step C), the relationship equation between non-state quantity, state quantity and input is established according to the characteristic equation of capacitance and inductance, and the relationship equation between the non-state quantity of capacitance, the non-state quantity of inductance, the state quantity of capacitance, the state quantity of inductance and historical source is established according to the solution of step B), and then the relationship equation between state quantity, historical source and input is established, and finally the state space discrete equation based on the characteristics of capacitance and inductance components is established.

[0051] by Figure 2 Taking the RLC circuit system shown in the figure as an example, in step A), the state space differential equation of the circuit is:

[0052]

[0053] Where A and B are state space matrices, t is the time, and X is the state quantity, including the current i flowing through the inductor L and the voltage u across the capacitor C , Include U is the system input.

[0054] In step B), the characteristic equations of capacitance and inductance are:

[0055]

[0056] In the formula, i C represents the current flowing through the capacitor, u L Represents the voltage across the inductor, and solves the characteristic equation of the capacitor using the trapezoidal method to obtain:

[0057]

[0058] In the formula, Δt is the simulation step size, and the characteristic equation of the inductor is solved using the third-order Adams-Moulton method:

[0059]

[0060] After calculation, we get:

[0061] In the formula,

[0062] In step C), define i C 、u L For the non-state quantity X′, establish the relationship equation between the non-state quantity X′, state quantity X and input U:

[0063] X′(t)=EAX(t)+EBU(t) (3)

[0064] Where E is a diagonal matrix containing capacitance values ​​C and inductance values ​​L;

[0065] Then establish the non-state quantity X of the capacitor C ′、non-state quantity X of inductance L ′、Capacitor state quantity X C , the state quantity of inductance X L The relationship equation with the historical source h is:

[0066]

[0067] Historical source h is i history 、uhistory The column vector composed of (7) and (3) is used to establish the relationship between the state quantity X, the historical source h and the input U:

[0068] FX(t)-h(t)=EAX(t)+EBU(t) (8)

[0069] In the formula, F is the C , Z L The diagonal array composed of

[0070] Finally, the state space discrete equation based on the characteristics of capacitor and inductor components is established:

[0071] X(t)=Ph(t)+QU(t) (9)

[0072] Where, P = (F-EA) -1 , Q = (F-EA) -1 EB.

[0073] In step D), when performing a loop simulation, the state quantity X(t) at the initial time t and the historical source h at the current time are calculated, and then t=t+1 until the simulation is completed.

[0074] In order to verify the correctness of the present invention, the following comparative experiments were performed:

[0075] Experiment 1

[0076] Purpose: To verify that when all state quantities are discretized using the same third-order or higher implicit numerical integration method, the computational complexity of the method provided by the present invention is less than that of the traditional state space discretization method.

[0077] Solution 1: Using the state space equation discretization method based on the characteristics of capacitor and inductor components of the present invention, all capacitor and inductor components select the third-order Adams-Moulton numerical integration method;

[0078] Solution 2: Use the traditional state-space equation discretization method and select the third-order Adams-Moulton numerical integration method.

[0079] The experimental results are as follows:

[0080] take add Solution 1 50 40 Solution 2 58 52

[0081] Therefore, the computational complexity of the state space equation discretization method based on the characteristics of capacitor and inductor components of the present invention is less than that of the traditional discretization method.

[0082] Experiment 2

[0083] Purpose: To verify that when numerical integration is selected by partition, that is, most of the capacitors and inductors in the system select low-order numerical integration methods and the remaining capacitors and inductors select high-order numerical integration methods, the accuracy can be significantly improved at the cost of a small increase in the amount of calculation.

[0084] Scheme 1: All state quantities use the third-order Adams-Multon numerical integration method;

[0085] Solution 2: L1 uses the 4th-order Adams-Multon numerical integration method, and the rest use the 3rd-order Adams-Multon numerical integration method.

[0086] Solution 3: C2 uses 4th-order Adams-Multon, and the rest use 3rd-order Adams-Multon

[0087] Solution 4: C1 and C2 use 4th-order Adams-Multon, and the rest use 3rd-order Adams-Multon

[0088] The experimental results are as follows:

[0089] take add Simulation result error Solution 1 50 40 <![CDATA[2.2338*10 -7 ]]> Solution 2 51 41 <![CDATA[1.3729*10 -7 ]]> Solution 3 51 41 <![CDATA[1.4258*10 -7 ]]> Solution 4 52 42 <![CDATA[1.0380*10 -7 ]]>

[0090] The number of multiplications and additions and the error of simulation results are the targets, such as Figure 3 As shown in the figure, the grey target method is used to calculate the bull's-eye distances of the four solutions. The smaller the bull's-eye distance, the better the solution.

[0091] As can be seen from the above figure, Schemes 2, 3, and 4 are all better than Scheme 1. Therefore, when using the state space equation discrete method based on the characteristics of capacitors and inductors to select numerical integration by partition, it is determined that most of the capacitors and inductors in the system select low-order numerical integration methods and the remaining capacitors and inductors select high-order numerical integration methods. This can achieve the goal of significantly improving accuracy at the cost of increasing a small amount of calculation, which is superior.

Claims

1. A state space equation discretization method based on the characteristics of capacitor and inductor components, characterized in that: The steps include: A) Establish the state space differential equation of the circuit; B) establishing characteristic equations of capacitors and inductors, determining the numerical integration method used for each capacitor and inductor in the circuit, and using the numerical integration method to obtain the characteristic equation in the discrete time domain; C) combining the discrete time domain characteristic equation of step B) and the state space differential equation of step A) to obtain a state space discrete equation of the circuit; D) Cycle simulation.

2. The state space equation discretization method based on the characteristics of capacitor and inductor components according to claim 1, characterized in that: In the step C), the relationship equation between the non-state quantity, state quantity and input is established according to the characteristic equation of the capacitor and the inductor, and the relationship equation between the non-state quantity of the capacitor, the non-state quantity of the inductor, the state quantity of the capacitor, the state quantity of the inductor and the historical source is established according to the solution of the step B), and then the relationship equation between the state quantity, the historical source and the input is established, and finally the state space discrete equation based on the characteristics of the capacitor and the inductor components is established.

3. The state space equation discretization method based on the characteristics of capacitor and inductor components according to claim 1, characterized in that: In step A), the state space differential equation of the circuit is: Where A and B are state space matrices, t is the time, and X is the state quantity, including the current i flowing through the inductor L and the voltage u across the capacitor C , Include U is the system input.

4. The state space equation discretization method based on the characteristics of capacitor and inductor components according to claim 3 is characterized in that: In step B), the characteristic equations of capacitance and inductance are respectively: In the formula, i C represents the current flowing through the capacitor, u L Represents the voltage across the inductor, and solves the characteristic equation of the capacitor using the trapezoidal method to obtain: In the formula, Δt is the simulation step size, and the characteristic equation of the inductor is solved using the third-order Adams-Moulton method: After calculation, we get: In the formula, 5. The state space equation discretization method based on the characteristics of capacitor and inductor components according to claim 4, characterized in that: In the step C), define i C 、u L For the non-state quantity X′, establish the relationship equation between the non-state quantity X′, state quantity X and input U: X′(t)=EAX(t)+EBU(t) (3) Where E is a diagonal matrix containing capacitance values ​​C and inductance values ​​L; Then establish the non-state quantity X of the capacitor C ′、non-state quantity X of inductance L ′、Capacitor state quantity X C , the state quantity of inductance X L The relationship equation with the historical source h is: Historical source h is i history 、u history The column vector composed of (7) and (3) is used to establish the relationship between the state quantity X, the historical source h and the input U: FX(t)-h(t)=EAX(t)+EBU(t) (8) In the formula, F is the C , Z L The diagonal array composed of Finally, the state space discrete equation based on the characteristics of capacitor and inductor components is established: X(t)=Ph(t)+QU(t) (9) Wherein, P = (F - EA) -1 , Q = (F - EA) -1 EB.

6. The state space equation discretization method based on the characteristics of capacitor and inductor components according to claim 5, characterized in that: In the step D), when performing the loop simulation, the state quantity X(t) at the initial time t and the historical source h at the current time are calculated, and then t=t+1 until the simulation is completed.

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