Constant admittance electromagnetic transient simulation method
By equating power electronic switches to binary resistors and generating constant admittance port equivalent equations, the problem of low power system simulation efficiency is solved, efficient power electronic converter system simulation is achieved, the modeling process is simplified, and the simulation accuracy is improved.
Patent Information
- Application Number
- CN202510581957.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-07
- Publication Date
- 2025-09-05
AI Technical Summary
Existing power system simulation methods have the problem of low simulation efficiency when dealing with large-scale power electronic equipment. Especially when using the node elimination method, the serial solution steps are numerous and the simulation time is too long.
The constant admittance electromagnetic transient simulation method is adopted. The power electronic switch is equivalent to a binary resistor. The constant admittance port equivalent equation is generated by processing the state matrix in blocks and introducing the injected current of the capacitor port. The discretization is performed by combining trapezoidal and forward Euler integration to simplify the modeling process.
It improves simulation efficiency, reduces calculation amount and modeling complexity, and is suitable for large-scale power electronic converter systems, with high simulation accuracy and simplified modeling process.
Smart Images
Figure CN120597481A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of power system simulation, in particular to a constant admittance electromagnetic transient simulation method. Background Art
[0002] The expansion of new power systems has led to an increasing integration of power electronics into these systems. Given the rapid dynamic characteristics of power electronics, accurate descriptions of their dynamic behavior are inextricably linked to electromagnetic transient (EMT) simulation technology. EMT simulation is a primary method for assessing power system stability and safe operation. Simulating complex systems using detailed models is often hampered by efficiency issues. For example, using the simulation software PSCAD / EMTDC with a 10-μs simulation step size to simulate a 100-MW photovoltaic power plant for 1 second would take over 3 hours, significantly reducing research efficiency.
[0003] Extensive research efforts are underway both domestically and internationally on this technology. The most popular approach uses node elimination, which eliminates internal nodes while retaining external port nodes to reduce the dimension of the admittance matrix during circuit solution, thereby improving simulation efficiency. This method has been applied in many scenarios, such as modular multilevel converters, power electronic transformers, and voltage source converters, achieving significant acceleration. However, a drawback of this approach is the excessive number of serial solution steps. While this approach maintains accuracy, there is still room for improvement in simulation efficiency. Therefore, based on current research progress, there is a lack of efficient port equivalence simulation methods. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a constant admittance electromagnetic transient simulation method. This method has the characteristic of constant admittance, that is, it does not require the inversion of the changing admittance matrix during solution, thus greatly reducing the computational complexity. The method is characterized by a constant admittance matrix, which facilitates direct connection to external circuits, low time complexity, and a simple modeling process. In addition, it has certain versatility for modular and unitized electrical equipment, providing theoretical guidance and technical reference for the efficient simulation of systems including large-scale power electronic converters.
[0005] The present invention adopts the following technical solutions to solve the above technical problems:
[0006] A constant admittance electromagnetic transient simulation method proposed in the present invention includes:
[0007] Step 1: The power electronic circuit includes a power electronic switch, a capacitor, and an inductor. The power electronic switch is equivalent to a binary resistor, and a state equation is written for the power electronic circuit.
[0008] Step 2: Introduce the injection current of the port where the capacitor is located and perform block processing on the state matrix in the state equation;
[0009] Step 3: discretize the processed state equation, and combine the state matrix in the discretized state equation with the port current equation to generate a constant admittance port equivalent equation;
[0010] Step 4: Inversely solve the state quantity of the power electronic circuit according to the port node voltage;
[0011] Step 5: Obtain the node voltage according to the constant admittance port equivalent equation, and update the historical current source according to the node voltage and the state quantity obtained in step 4.
[0012] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, in step 2, the state matrix after block processing includes a diagonal block matrix of constant admittance and a non-diagonal matrix of variable admittance.
[0013] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, the state equation in step 1 is:
[0014] The nonlinear power electronic switch is equivalent to a binary resistor. For a linear power electronic circuit, its state equation is expressed as
[0015]
[0016] Among them, the state variables include the capacitor voltage u C (t) and the inductor current i L (t), C represents the matrix including capacitors, L represents the matrix including inductors, A is the state matrix of a power electronic circuit, and U is the input matrix of the state equation. is the capacitor voltage u C The differential of (t), is the inductor current i L The differential of (t), A 11 is the diagonal block matrix of the upper left part of the A matrix, A 12 is the diagonal block matrix of the upper right part of the A matrix, A 21 is the diagonal block matrix of the lower left part of the A matrix, A 22 is the diagonal block matrix of the lower right part of the A matrix, and t is the time.
[0017] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, the state matrix after processing in step 2 is:
[0018] When there is a capacitive element at the DC port of the power electronic circuit, the matrix of the injected current is added to the equation in formula (1), and the state equation is shown in formula (2);
[0019]
[0020] in, is the differential of the matrix of injected current, i d (t) is the matrix of injected current, I is the coefficient matrix consisting of 0 or 1 elements, B1 is the upper half matrix of input matrix B, B2 is the lower half matrix of input matrix B, u n (t) is the node voltage matrix of the external port at time t;
[0021] Decompose A, and express formula (2) as the equivalent form of formula (3);
[0022]
[0023] in, is the differential of x(t), x(t) is the state matrix after block processing, A α is a constant matrix, and the time-varying matrix A β Represents the on-off state of the power electronic switch, and M is a coefficient matrix including capacitance and inductance values.
[0024] As a further optimization scheme for the constant admittance electromagnetic transient simulation method described in the present invention, in step 3, discretization refers to: discretizing the non-diagonal matrix product part of the variable admittance using the forward Euler method, and discretizing the non-diagonal matrix product part of the state matrix excluding the variable admittance using the trapezoidal integration method to generate the constant admittance port equivalent equation.
[0025] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, step 3 includes:
[0026] i s (t+Δt)=Px(t+Δt) (4)
[0027] Among them, i s (t+Δt) is the matrix of the external port injection current, P is a coefficient matrix consisting of 0 or 1 elements, Δt represents the simulation step size, and x(t+Δt) is the state matrix at time t+Δt after block processing. Equation (4) represents the relationship between the port injection current and the state matrix.
[0028] The formula (3) is discretized by combining trapezoidal and forward Euler integration, and the following results are obtained:
[0029]
[0030] Among them, u n (t+Δt) is the node voltage matrix of the external port at time t+Δt;
[0031] By combining equations (4) and (5), while retaining the electrical variables of the port and eliminating x(t+Δt), we obtain equation (6);
[0032] i s (t+Δt)=Y n u n (t+Δt)+i h (t) (6)
[0033] Among them, Y n is the admittance matrix, i h (t) is the historical current source matrix;
[0034]
[0035] Among them, Q is a constant coefficient matrix, and R is a variable coefficient matrix;
[0036] According to formula (6), the equivalent equation of the constant admittance port is obtained, and then the power electronic equivalent circuit is obtained.
[0037] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, the conductance between adjacent nodes of the power electronic equivalent circuit is determined by Y n Calculation, and the injection current of each node of the power electronic equivalent circuit is calculated by i h (t) Export.
[0038] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, step 4 includes: after solving the port node voltage, solving x(t+Δt) using equation (8);
[0039]
[0040] Among them, K is the coefficient matrix containing constant intermediate variables, is a matrix containing intermediate variables.
[0041] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention,
[0042]
[0043] As a further optimization scheme of the constant admittance electromagnetic transient simulation method described in the present invention, according to formula (7), the historical current source is composed of x(t) and u n (t) composition; x(t+Δt) and u solved in formulas (6) and (8) n (t+Δt) is directly given to the history current source of the next simulation time step.
[0044] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:
[0045] (1) This method can simulate large-scale power electronic converter systems more accurately and efficiently, and improves simulation efficiency compared to traditional node elimination methods;
[0046] (2) This method can achieve modeling with fewer serial steps and has a simpler modeling process;
[0047] (3) This method has the characteristic of constant admittance and has high simulation efficiency;
[0048] (4) The method of this embodiment can improve the simulation efficiency of a system containing large-scale power electronic converters. Compared with the existing node elimination method, the simulation efficiency is further improved, and it has theoretical guiding significance for power system simulation. BRIEF DESCRIPTION OF THE DRAWINGS
[0049] Figure 1 This is a specific method of an embodiment of the present invention;
[0050] Figure 2 A diagram of a power electronic converter used in an embodiment of the present invention;
[0051] Figure 3 The comparison diagram of the simulation results in the embodiment of the present invention is shown in FIG. 1 , wherein (a) is the active power of the converter 1, and (b) is Figure 3 (a) is a partial enlarged view, (c) is the active power of converter 2, and (d) is Figure 3 (c) is a partial enlarged view of the grid, (e) is the grid-connected point A phase voltage, (f) is Figure 3 (e) is the partial enlarged view of the grid, (g) is the grid side A phase current, (h) is Figure 3 A partial enlarged view of (g). DETAILED DESCRIPTION
[0052] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
[0053] In the simulation platform, Figure 2 The three converters in parallel system shown in the figure verify the effectiveness of the proposed method. The system adopts active power P / reactive power Q control strategy, and the system parameters are: DC voltage is 25kV, 50kV and 22kV respectively, operating frequency is 2kHz, 1kHz and 5kHz respectively, and load is 10+jω0.01 and 15+jω0.01 respectively. RM is the reference model built in the simulation software, and EM is the proposed model. The two models are compared to verify the simulation accuracy of the proposed model. The system simulation step size is set to 10μs and the simulation time is 1s. Working condition setting: at 0.5s, the AC bus phase A is set to grounded, and the fault duration is 0.01s. The simulation results are shown in Figure 3 shown.
[0054] like Figure 1 As shown, an embodiment of the present invention provides a constant admittance electromagnetic transient simulation method based on state quantity elimination, comprising the following steps:
[0055] Step 10) The power electronic circuit includes a power electronic switch, a capacitor, and an inductor. The power electronic switch is equivalent to a binary resistor, and a state equation is written for the power electronic circuit.
[0056] Step 20) introducing the injection current of the port where the capacitor is located, and performing block processing on the state matrix in the state equation;
[0057] Step 30) discretizing the processed state equation, combining the state matrix in the discretized state equation with the port current equation to generate a constant admittance port equivalent equation;
[0058] Step 40) inversely solving the state quantity of the power electronic circuit according to the port node voltage;
[0059] Step 50) Obtain the node voltage according to the constant admittance port equivalent equation, and update the historical current source according to the node voltage and the state quantity obtained in step 4.
[0060] In the above embodiment, step 10) includes:
[0061] Equivalently treating the nonlinear power electronic switch as a binary resistor, the state equation for a linear power electronic circuit is expressed as
[0062]
[0063] Among them, the state variables include the capacitor voltage u C (t) and the inductor current i L (t), C represents the matrix including capacitors, L represents the matrix including inductors, A is the state matrix of a power electronic circuit, and U is the input matrix of the state equation. is the capacitor voltage u C The differential of (t), is the inductor current i L The differential of (t), u C (t) is the capacitor voltage, i L (t) is the inductor current A 11 is the diagonal block matrix of the upper left part of the A matrix, A 12 is the diagonal block matrix of the upper right part of the A matrix, A 21 is the diagonal block matrix of the lower left part of the A matrix, A 22 is the diagonal block matrix of the lower right part of the A matrix, and t is the time.
[0064] In the above embodiment, the step 20) includes:
[0065] When there is a capacitive element at the DC port of the power electronic circuit, the matrix of the injected current is added to the equation in formula (1), and the state equation is shown in formula (2);
[0066]
[0067] in, is the differential of the matrix of injected current, i d (t) is the matrix of injected current, I is the coefficient matrix consisting of 0 or 1 elements, B1 is the upper half matrix of input matrix B, B2 is the lower half matrix of input matrix B, u n (t) is the node voltage matrix of the external port at time t;
[0068] Decompose A, and express formula (2) as the equivalent form of formula (3);
[0069]
[0070] in, is the differential of x(t), x(t) is the state matrix after block processing, A α is a constant matrix, and the time-varying matrix A β Represents the on-off state of the power electronic switch, and M is a coefficient matrix including capacitance and inductance values.
[0071] In the above embodiment, step 30) includes:
[0072] i s (t+Δt)=Px(t+Δt) (4)
[0073] Among them, i s (t+Δt) is the matrix of the external port injection current, P is a coefficient matrix consisting of 0 or 1 elements, Δt represents the simulation step size, and x(t+Δt) is the state matrix at time t+Δt after block processing. Equation (4) represents the relationship between the port injection current and the state matrix.
[0074] The formula (3) is discretized by combining trapezoidal and forward Euler integration, and the following results are obtained:
[0075]
[0076] Among them, u n (t+Δt) is the node voltage matrix of the external port at time t+Δt;
[0077] By combining equations (4) and (5), while retaining the electrical variables of the port and eliminating x(t+Δt), we obtain equation (6);
[0078] i s (t+Δt)=Y n u n (t+Δt)+i h (t) (6)
[0079] Among them, Y n is the admittance matrix, i h (t) is the historical current source matrix;
[0080]
[0081] Among them, Q is a constant coefficient matrix, and R is a variable coefficient matrix;
[0082] According to formula (6), the equivalent equation of the constant admittance port is obtained, and then the power electronic equivalent circuit is obtained.
[0083] In the above embodiment, step 40) includes:
[0084] After solving the port node voltage, use equation (8) to solve x(t+Δt);
[0085]
[0086] Among them, K is the coefficient matrix containing constant intermediate variables, is a matrix containing intermediate variables.
[0087]
[0088] In the above embodiment, the step 50) includes:
[0089] According to formula (7), the historical current source is composed of x(t) and u n (t) composition; x(t+Δt) and u solved in formulas (6) and (8) n (t+Δt) is directly given to the history current source of the next simulation time step.
[0090] Depend on Figure 3 It can be seen that Figure 3 (a) is the active power of converter 1, Figure 3 (b) in Figure 3 A partial enlarged view of (a) in FIG. Figure 3 (c) in the equation is the active power of converter 2, Figure 3 (d) in Figure 3 A partial enlarged view of (c) in FIG. Figure 3 (e) is the phase A voltage at the grid connection point, Figure 3 (f) in Figure 3 A partial enlarged view of (e) in FIG. Figure 3 (g) is the current of phase A on the grid side, Figure 3 (h) in Figure 3 A partial enlargement of (g) in Figure 1. During a short-circuit fault, the active power P1 of converter 1 and the active power P2 of converter 2 decrease, the grid-connection point phase A voltage Ua drops to zero, and the grid-side phase A current Iga increases. The MRE of the test results is less than 1.95%, demonstrating the high simulation accuracy of the EM. Simulation results show that the PM model has higher accuracy than the DM model and is highly similar to the RM model, demonstrating the high simulation accuracy of the PM model.
[0091] This embodiment of the present invention provides a constant admittance electromagnetic transient simulation method based on state elimination. This method utilizes a three-layer architecture: network-node voltage-historical current source. Low-order equivalent node voltage equations are generated by matrix splitting and adding output equations. This method features a constant admittance matrix, facilitating direct connection to external circuits, low time complexity, and a simple modeling process. Furthermore, it is applicable to modular and unitized electrical equipment.
[0092] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.
Claims
1. A constant admittance electromagnetic transient simulation method, characterized in that: include: Step 1: The power electronic circuit includes a power electronic switch, a capacitor, and an inductor. The power electronic switch is equivalent to a binary resistor, and a state equation is written for the power electronic circuit. Step 2: Introduce the injection current of the port where the capacitor is located and perform block processing on the state matrix in the state equation; Step 3: discretize the processed state equation, and combine the state matrix in the discretized state equation with the port current equation to generate a constant admittance port equivalent equation; Step 4: Inversely solve the state quantity of the power electronic circuit according to the port node voltage; Step 5: Obtain the node voltage according to the constant admittance port equivalent equation, and update the historical current source according to the node voltage and the state quantity obtained in step 4.
2. The constant admittance electromagnetic transient simulation method according to claim 1, characterized in that: In step 2, the state matrix after block processing includes a diagonal block matrix of constant admittance and a non-diagonal matrix of variable admittance.
3. The constant admittance electromagnetic transient simulation method according to claim 1, characterized in that: The state equation in step 1 is: The nonlinear power electronic switch is equivalent to a binary resistor. For a linear power electronic circuit, its state equation is expressed as Among them, the state variables include the capacitor voltage u C (t) and the inductor current i L (t), C represents the matrix including capacitors, L represents the matrix including inductors, A is the state matrix of a power electronic circuit, and U is the input matrix of the state equation. is the capacitor voltage u C The differential of (t), is the inductor current i L The differential of (t), A 11 is the diagonal block matrix of the upper left part of the A matrix, A 12 is the diagonal block matrix of the upper right part of the A matrix, A 21 is the diagonal block matrix of the lower left part of the A matrix, A 22 is the diagonal block matrix of the lower right part of the A matrix, and t is the time.
4. The constant admittance electromagnetic transient simulation method according to claim 3, characterized in that: The state matrix after processing in step 2 is: When there is a capacitive element at the DC port of the power electronic circuit, the matrix of the injected current is added to the equation in formula (1), and the state equation is shown in formula (2); in, is the differential of the matrix of injected current, i d (t) is the matrix of injected current, I is the coefficient matrix consisting of 0 or 1 elements, B1 is the upper half matrix of input matrix B, B2 is the lower half matrix of input matrix B, u n (t) is the node voltage matrix of the external port at time t; Decompose A, and express formula (2) as the equivalent form of formula (3); in, is the differential of x(t), x(t) is the state matrix after block processing, A α is a constant matrix, and the time-varying matrix A β Represents the on-off state of the power electronic switch, and M is a coefficient matrix including capacitance and inductance values.
5. The constant admittance electromagnetic transient simulation method according to claim 2, characterized in that: In step 3, discretization refers to: discretizing the non-diagonal matrix product part of the variable admittance using the forward Euler method, and discretizing the non-diagonal matrix product part of the state matrix excluding the variable admittance using the trapezoidal integration method to generate the constant admittance port equivalent equation.
6. The constant admittance electromagnetic transient simulation method according to claim 4, characterized in that: Step 3 includes: i s (t+Δt)=Px(t+Δt) (4) Among them, i s (t+Δt) is the matrix of the external port injection current, P is a coefficient matrix consisting of 0 or 1 elements, Δt represents the simulation step size, and x(t+Δt) is the state matrix at time t+Δt after block processing. Equation (4) represents the relationship between the port injection current and the state matrix. The formula (3) is discretized by combining trapezoidal and forward Euler integration, and the following results are obtained: Among them, u n (t+Δt) is the node voltage matrix of the external port at time t+Δt; By combining equations (4) and (5), while retaining the electrical variables of the port and eliminating x(t+Δt), we obtain equation (6); i s (t+Δt)=Y n u n (t+Δt)+i h (t) (6) Among them, Y n is the admittance matrix, i h (t) is the historical current source matrix; Among them, Q is a constant coefficient matrix, and R is a variable coefficient matrix; According to formula (6), the equivalent equation of the constant admittance port is obtained, and then the power electronic equivalent circuit is obtained.
7. The constant admittance electromagnetic transient simulation method according to claim 6, characterized in that: For the power electronic equivalent circuit, the conductance between adjacent nodes is represented by Y n Calculation, and the injection current of each node of the power electronic equivalent circuit is calculated by i h (t) Export.
8. The constant admittance electromagnetic transient simulation method according to claim 6, characterized in that: Step 4 includes: after solving the port node voltage, solving x(t+Δt) using equation (8); Among them, K is the coefficient matrix containing constant intermediate variables, is a matrix containing intermediate variables.
9. The constant admittance electromagnetic transient simulation method according to claim 8, characterized in that:
10. The constant admittance electromagnetic transient simulation method according to claim 6, characterized in that: According to formula (7), the historical current source is composed of x(t) and u n (t) composition; x(t+Δt) and u solved in formulas (6) and (8) n (t+Δt) is directly given to the history current source of the next simulation time step.