Electromagnetic transient simulation numerical oscillation suppression method and system based on eigenvalue analysis

Abstract

The invention relates to the field of power systems, and discloses an electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis, which comprises the following steps that: an electromagnetic transient model discretizes a characteristic formula of a memorable element in a circuit into linear conductance and a historical current source, and during normal simulation calculation, the linear conductance and the historical current source are converted into linear conductance; calculating a state variable and a characteristic value of the electromagnetic transient model by using an implicit trapezoid method; after the circuit breaker is operated, an electromagnetic transient characteristic value of a circuit under discretization of a backward Euler method is calculated, and on the basis of the characteristic value, the number of steps of half-step backward Euler method calculation which needs to be carried out can be calculated to completely suppress the numerical oscillation phenomenon; the simulation step size is reduced to 1 / 2 of the original simulation step size, and k-step half-step-size backward Euler method calculation is carried out; and after k-step half-step backward Euler method calculation is completed, the implicit trapezoid method is switched back to continue calculation, and electromagnetic transient simulation numerical oscillation suppression is completed. According to the invention, the numerical oscillation phenomenon after the operation of the circuit breaker can be more effectively inhibited.

Description

Technical Field

[0001] The present invention relates to the field of power systems, and in particular to an electromagnetic transient simulation numerical oscillation suppression method and system based on eigenvalue analysis. Background Art

[0002] Electromagnetic transient simulation is an important tool for studying the dynamic characteristics of power systems. Compared with electromechanical transient simulation, electromagnetic transient simulation can more accurately describe the dynamic characteristics of power electronic power systems. At present, the more mature electromagnetic transient simulation analysis software includes EMTP, PSCAD / EMTDC developed by the Manitoba DC Research Center in Canada, NETOMAC developed by Siemens in Germany, and CLOUDPSS developed by the Institute of Digital Twins of Energy and Power Systems of the Sichuan Energy Internet Research Institute of Tsinghua University.

[0003] The implicit trapezoidal integration method is widely used in electromagnetic transient simulation calculations. It is a very effective, highly stable and accurate numerical integration method. However, when there is a circuit breaker operation in the network, this method will cause abnormal swings in the non-state variables, a phenomenon called numerical oscillation. This is an abnormal oscillation phenomenon. If measures are not taken to eliminate it, it will affect the accuracy of subsequent simulations. The fundamental reason for the numerical oscillation is that when a certain form of disturbance occurs in the network (such as circuit breaker operation, etc.), the non-state variables in the network undergo a sudden change. However, since the non-state variables after the mutation are difficult to obtain, the variables before the mutation are often used to calculate the equivalent current source after the mutation. The equivalent current source calculated in this way is obviously incorrect, which is reflected in the calculation results as abnormal swings of the non-state variables. Generally, numerical oscillations are easily generated when the circuit breaker is operated, and studies have shown that in some cases, short-circuit faults may also cause numerical oscillations.

[0004] At present, the most widely used method to suppress numerical oscillation is the critical damping adjustment (CDA) method, which is to switch the numerical integration method to the backward Euler method at the moment of circuit breaker operation and perform two-step simulation calculations. The reason why the backward Euler method does not cause numerical oscillation is that there are no non-state variables at the moment in its differential equation, so the sudden change of non-state variables will not form an unreasonable equivalent injection source. However, the accuracy of the backward Euler method is not as good as the trapezoidal method, and it is not suitable for calculating the entire simulation process. Usually, after the disturbance such as circuit breaker operation, the backward Euler method is used to calculate for several steps, and then the trapezoidal method is switched to continue the calculation.

[0005] Although the CDA method can suppress the occurrence of numerical oscillation to a certain extent, it also has obvious defects. To suppress the numerical oscillation of different circuit networks, different numbers of backward Euler calculations are required. The CDA method performs two-step backward Euler calculations on all circuit networks. For circuit networks with less than 2 steps of backward Euler calculations, the accuracy of the simulation calculation will be reduced; for circuit networks with more than 2 steps, the numerical oscillation cannot be effectively suppressed. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide an electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis, comprising the following steps: Step 1: The electromagnetic transient model discretizes the characteristic formula of the components with memory in the circuit into linear conductance and historical current source. In normal simulation calculation, the implicit trapezoidal method is used to calculate the state variables and eigenvalues ​​of the electromagnetic transient model; the circuit state variables at the previous moment and the eigenvalues ​​of the electromagnetic transient model determine the value of the historical current source; Step 2: After the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, the half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size. , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation; Step 3: After performing k steps of half-step backward Euler method calculation, switch back to the implicit trapezoidal method to continue the calculation and complete the numerical oscillation suppression of the magnetic transient simulation.

[0007] Furthermore, the circuit contains memory elements, and the memory elements include inductors and capacitors.

[0008] Furthermore, during normal simulation calculation, the implicit trapezoidal method is used to calculate the eigenvalue of the electromagnetic transient model. After the circuit breaker is operated, the backward Euler method is used to calculate the eigenvalue of the electromagnetic transient model. The circuit state variables at the previous moment and the eigenvalue of the electromagnetic transient model determine the value of the historical current source, including: In the RL circuit, for the resistor R have For inductance L have For inductance L The trapezoidal method discretizes, get in Then the characteristic equation of the inductor L after discretization using the implicit trapezoidal method is: The calculation formula of the historical current source is: Then there is get but get Then the implicit trapezoidal method electromagnetic transient characteristic value of the RL circuit is: Eigenvalues ​​under the discretization of the backward Euler method RL circuit For resistors R have For inductance L have Discretization using the backward Euler method Arranged in ; Then the characteristic equation of the inductor L after discretization using the backward Euler method is: in have Arranged but get That is, the backward Euler electromagnetic transient eigenvalue of the RL circuit is: .

[0009] Furthermore, after the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, a half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation, including: If used After the first half-step backward Euler method, the numerical oscillation is effectively suppressed. The historical current source value after the first half-step backward Euler method is: The historical current source value after the second half-step backward Euler method is: After k-step backward Euler method calculation, the historical current source value is: when Decay to of Times, ,Right now but get but The minimum number of steps for: The oscillating voltage after k steps of half-step backward Euler method calculation is: Then proceed The numerical oscillation voltage after the backward Euler method with a half-step length is: .

[0010] The electromagnetic transient simulation numerical oscillation suppression system based on eigenvalue analysis applies the electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis, and includes an electromagnetic transient simulation module, a data processing module and a data storage module; the electromagnetic transient simulation module and the data storage module are respectively connected to the data processing module.

[0011] The beneficial effect of the present invention is that: based on eigenvalue analysis, this patent proposes a new method that is more effective than the traditional method for suppressing numerical oscillation of electromagnetic transient simulation and can affect the calculation accuracy to a lesser extent. Compared with the traditional method for suppressing numerical oscillation of electromagnetic transient simulation, this method can more effectively suppress the numerical oscillation phenomenon after the circuit breaker operation and can affect the calculation accuracy to a lesser extent, perfect and improve the electromagnetic transient simulation algorithm, and improve the practicality and universality of electromagnetic transient simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flow chart of the numerical oscillation suppression method of electromagnetic transient simulation based on eigenvalue analysis; Figure 2 is the schematic diagram of RL circuit; Figure 3 This is the RL circuit diagram after the trapezoidal method is discretized; Figure 4 This is the discrete circuit diagram after R is disconnected; Figure 5 This is a schematic diagram of the voltage value across the inductor calculated using the implicit trapezoidal method; Figure 6 Schematic diagram of the inductor historical current source value calculated using the implicit trapezoidal method; Figure 7 A schematic diagram of the voltage value across the inductor calculated using the traditional numerical oscillation suppression method; Figure 8 A schematic diagram of the inductor historical current source value calculated using the traditional numerical oscillation suppression method; Fig. 9 A schematic diagram of the voltage value across the inductor calculated by the numerical oscillation suppression method for electromagnetic transient simulation based on eigenvalue analysis; Fig.10 The inductor historical current source value calculated by the numerical oscillation suppression method for electromagnetic transient simulation based on eigenvalue analysis. DETAILED DESCRIPTION

[0013] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0014] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.

[0015] like Figure 1 As shown, the numerical oscillation suppression method for electromagnetic transient simulation based on eigenvalue analysis includes the following steps: Step 1: The electromagnetic transient model discretizes the characteristic formula of the components with memory in the circuit into linear conductance and historical current source. In normal simulation calculation, the implicit trapezoidal method is used to calculate the state variables and eigenvalues ​​of the electromagnetic transient model; the circuit state variables at the previous moment and the eigenvalues ​​of the electromagnetic transient model determine the value of the historical current source; Step 2: After the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, the half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size. , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation; Step 3: After performing k steps of half-step backward Euler method calculation, switch back to the implicit trapezoidal method to continue the calculation and complete the numerical oscillation suppression of the magnetic transient simulation.

[0016] The circuit contains memory elements, which include inductors and capacitors.

[0017] During normal simulation calculation, the implicit trapezoidal method is used to calculate the eigenvalue of the electromagnetic transient model. After the circuit breaker is operated, the backward Euler method is used to calculate the eigenvalue of the electromagnetic transient model. The circuit state variables at the previous moment and the eigenvalue of the electromagnetic transient model determine the value of the historical current source, including: In the RL circuit, for the resistor R have For inductance L have For inductance L The trapezoidal method discretizes, get in Then the characteristic equation of the inductor L after discretization using the implicit trapezoidal method is: The calculation formula of the historical current source is: Then there is get but get Then the implicit trapezoidal method electromagnetic transient characteristic value of the RL circuit is: Eigenvalues ​​under the discretization of the backward Euler method RL circuit For resistors R have For inductance L have Discretization using the backward Euler method Arranged in ; Then the characteristic equation of the inductor L after discretization using the backward Euler method is: in have Arranged but get That is, the backward Euler electromagnetic transient eigenvalue of the RL circuit is: .

[0018] After the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, a half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation, including: If used After the first half-step backward Euler method, the numerical oscillation is effectively suppressed. The historical current source value after the first half-step backward Euler method is: The historical current source value after the second half-step backward Euler method is: After k-step backward Euler method calculation, the historical current source value is: when Decay to of Times, ,Right now but get but The minimum number of steps for: The oscillating voltage after k steps of half-step backward Euler method calculation is: Then proceed The numerical oscillation voltage after the backward Euler method with a half-step length is: .

[0019] The electromagnetic transient simulation numerical oscillation suppression system based on eigenvalue analysis applies the electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis, and includes an electromagnetic transient simulation module, a data processing module and a data storage module; the electromagnetic transient simulation module and the data storage module are respectively connected to the data processing module.

[0020] Specifically, in order to solve the problem of how many steps of backward Euler method are needed for different circuit networks after the circuit breaker operation, we consider using the eigenvalue of the electromagnetic transient model to solve this problem. The electromagnetic transient model discretizes the characteristic formula of memory components such as inductors and capacitors into a linear conductance and a historical current source. The value of the historical current source is determined by the circuit state variables at the previous moment and the eigenvalue of the electromagnetic transient model. The eigenvalue of the electromagnetic transient model reflects the change process of the historical current source and the system characteristics during the simulation process.

[0021] Eigenvalues ​​under the discretization of the backward Euler method Figure 2The circuit shown in derives and analyzes the historical current source eigenvalues ​​obtained by discretizing the RL circuit using the backward Euler method.

[0022] For resistors R have (1-1) For inductance L have (1-2) Because the voltage value across the resistor is only related to the current value at this moment, and has nothing to do with the current value at the previous moment, and the two are linearly related, the historical current source of the resistor is always 0, that is, The inductance characteristic formula of equation (1-2) is discretized using the backward Euler method. (1-3) Arranged (1-4) in Then the characteristic equation of the inductor L after discretization using the backward Euler method is: (1-5) in (1-6) like Figure 3 Discretized RL circuit diagram, using Kirchhoff's law for node 1, we have (1-7) Arranged (1-8) Since the right end of the inductor is grounded, the voltage across the inductor is equal to the voltage at node 1. (1-9) Substituting (1-9) into (1-6) we get (1-10) That is, the backward Euler electromagnetic transient eigenvalue of the RL circuit is (1-11) Eigenvalues ​​under implicit trapezoidal discretization by Figure 2 The circuit shown in the derivation and analysis uses the implicit ladder method to discretize the RL circuit to obtain the historical current source eigenvalues.

[0023] For resistors R have (1-12) For inductance L have (1-13) and Figure 2 Because the voltage value across the resistor is only related to the current value at this moment, and has nothing to do with the current value at the previous moment, and the two are linearly related, so the historical current source of the resistor is always 0, that is, .

[0024] Discretizing the inductor trapezoidal method of equation (1-13), we have: (1-14) (1-15) Arranged (1-16) in ; Then the characteristic equation of the inductor L after discretization using the implicit trapezoidal method is: (1-17) The calculation formula of the historical current source is (1-18) like Figure 3 The RL circuit diagram after the trapezoidal method is discretized. Using Kirchhoff's law for node 1, we have (1-19) Arranged (1-20) Since the right end of the inductor is grounded, the voltage across the inductor is equal to the voltage at node 1. (1-21) Substituting (1-21) into (1-18) we get (1-22) That is, the implicit trapezoidal electromagnetic transient characteristic value of the RL circuit is (1-23) The relationship between eigenvalues ​​and numerical oscillation phenomena is Figure 3 In the circuit breaker operation, R is equivalent to an infinite value, the resistance is disconnected, and there is only inductance L in the circuit; Backward Euler method eigenvalues ​​and numerical oscillations (2-1) set up is a constant, from (1-11) we get From the switch characteristics, we know that when hour Substituting into formula (1-5) we get (2-2) From the above formula, we can see that the voltage value across the inductor decays rapidly to 0, and no numerical oscillation occurs. Therefore, the essence of the circuit breaker operator not generating numerical oscillation under the backward Euler method discretization is: the characteristics of the update matrix of the historical current source , the historical current source decays rapidly to 0.

[0025] This essence can also be seen in the circuit diagram of the discretized historical current source. Figure 4 This is the discrete circuit diagram after R is disconnected. The resistor is disconnected, and only the inductor L is in the circuit. At this time, there is only one power source in the circuit, the historical current source, according to Ohm's law. (2-3) Implicit Trapezoidal Method Eigenvalues ​​and Numerical Oscillations set up is a constant, and from (1-23) we get (2-4) From the switch characteristics, we know that when hour Substituting into formula (1-17) we get (2-5) From the above formula we can see Will be The amplitude swings up and down, generating numerical oscillation. The essence of the circuit breaker operator not generating numerical oscillation under the post-implicit trapezoidal method discretization is: the characteristics of the update matrix of the historical current source , the historical current source direction is It changes into periodic oscillation.

[0026] Similarly, this essence can also be seen from the circuit diagram that carries the historical current source after discretization. The resistor is disconnected and there is only inductance L in the circuit. Figure 4 This is the discrete circuit diagram after R is disconnected. At this time, there is only one power source in the circuit, the historical current source. According to Ohm's law: (2-6) Method for determining the number of steps used in the backward Euler method when numerical oscillation occurs Set the circuit breaker at Operation at all times, the initial value of the historical current source is , generating numerical oscillation. The electromagnetic transient simulation calculation is switched to the backward Euler method.

[0027] From equations (2-4) and (2-16), we know that when the step size of the backward Euler method is When the equivalent conductance of the backward Euler method is equal to the step size of the trapezoidal method, Therefore, to simplify programming, when a disturbance occurs in the network, the simulation step size can be reduced to the original , and then calculate the historical current source of each component using the backward Euler method. After that, the trapezoidal method is used to continue the calculation. Since the step size is reduced by half, the accuracy of the backward Euler method is improved, and the calculation is quickly transferred back to the trapezoidal method, so the error caused by the backward Euler method can be ignored.

[0028] For distributed parameter transmission lines, it can be seen from the Berelon equivalent circuit that its equivalent conductance has nothing to do with the step size, so there is no need to modify its equivalent conductance after using the backward Euler method.

[0029] Assume use k After using the half-step backward Euler method, the numerical oscillation is effectively suppressed.

[0030] The historical current source value after the first half-step backward Euler method is known from equation (2-10): (3-1) The historical current source value after the second half-step backward Euler method is (3-2) After k-step backward Euler method calculation, the historical current source value is (3-3) when Decay to of times, it can be considered , from (2-3), we know that the numerical oscillation has been effectively suppressed at this time.

[0031] Right now (3-4) but (3-5) Taking the base 10 logarithm of both sides, we get (3-6) but (3-7) The minimum number of steps is: (3-8) Oscillating voltage after k-step half-step backward Euler method calculation (3-9) (3-10) Then proceed The numerical oscillation voltage after the backward Euler method with a half-step length is (3-11) From formula (3-11), we can see that After the step-backward Euler method, the numerical oscillation voltage can be suppressed to approximately equal to 0, and the accuracy of the simulation calculation is minimally affected.

[0032] In this example, the circuit parameters and calculation parameters are shown in Table 1.

[0033] Table 1 Circuit parameters and calculation parameters The calculation results using the implicit trapezoidal method, as analyzed above, produce the amplitude , the frequency is The abnormal numerical oscillation seriously affects the calculation results. Figure 5 is the voltage across the inductor calculated using the implicit trapezoidal method; Figure 6 is the inductor history current source value calculated using the implicit trapezoidal method.

[0034] Calculation results using traditional numerical oscillation suppression methods The traditional critical damping adjustment (CDA) method is used to suppress numerical oscillations, that is, after the circuit breaker S is operated, the backward Euler method is used for calculation with two and a half steps and then the trapezoidal method is used for calculation. Figure 7 and Figure 8 It can be seen that using this method, the voltage oscillation amplitude is suppressed to a certain extent, but not completely. After exiting the backward Euler method, the voltage value across the inductor and the historical current source value continue to oscillate.

[0035] The calculation results using the method proposed in this patent Substituting the data in Table 1 into equation (3-8), we can see that the number of steps of the half-step backward Euler method to be used is from Fig. 9 and Fig.10 The results show that the use of this patented method can suppress the voltage across the inductor and the historical current source to approximately 0, effectively suppressing the numerical oscillation phenomenon and minimizing the impact on the calculation accuracy.

[0036] In summary: The results show that this patented method can more effectively suppress the numerical oscillation phenomenon in electromagnetic transient simulation by accurately judging the number of steps of the backward Euler method, and can avoid the influence of simulation calculation accuracy caused by excessive use of the backward Euler method. The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A numerical oscillation suppression method for electromagnetic transient simulation based on eigenvalue analysis, characterized in that: The following steps are involved: Step 1: The electromagnetic transient model discretizes the characteristic formula of the components with memory in the circuit into linear conductance and historical current source. In normal simulation calculation, the implicit trapezoidal method is used to calculate the state variables and eigenvalues ​​of the electromagnetic transient model; the circuit state variables at the previous moment and the eigenvalues ​​of the electromagnetic transient model determine the value of the historical current source; Step 2: After the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, the half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size. , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation; Step 3: After performing k steps of half-step backward Euler method calculation, switch back to the implicit trapezoidal method to continue the calculation and complete the numerical oscillation suppression of the magnetic transient simulation.

2. The electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis according to claim 1 is characterized in that: The circuit contains memory elements, which include inductors and capacitors.

3. The electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis according to claim 1 is characterized in that: During normal simulation calculation, the implicit trapezoidal method is used to calculate the eigenvalues ​​of the electromagnetic transient model. After the circuit breaker is operated, the backward Euler method is used to calculate the eigenvalues ​​of the electromagnetic transient model. The circuit state variables at the last moment and the characteristic values ​​of the electromagnetic transient model determine the value of the historical current source, including: In the RL circuit, for the resistor R have For inductance L have For inductance L The trapezoidal method discretizes, get in Then the characteristic equation of the inductor L after discretization using the implicit trapezoidal method is: The calculation formula of the historical current source is: Then there is get but get Then the implicit trapezoidal method electromagnetic transient characteristic value of the RL circuit is: Eigenvalues ​​under the discretization of the backward Euler method RL circuit For resistors R have For inductance L have Discretization using the backward Euler method Arranged in ; Then the characteristic equation of the inductor L after discretization using the backward Euler method is: in have Arranged but get That is, the backward Euler electromagnetic transient eigenvalue of the RL circuit is: 。 4. The method for suppressing numerical oscillation in electromagnetic transient simulation based on eigenvalue analysis according to claim 3 is characterized in that: After the circuit breaker is operated, the electromagnetic transient characteristic value of the circuit under the backward Euler method discretization is calculated, and based on the electromagnetic transient characteristic value, a half-step backward Euler method calculation of k steps that completely suppresses the numerical oscillation phenomenon is obtained; the simulation step size is reduced to the original simulation step size , calculate the historical current source of each component according to the backward Euler method, where the linear conductance value remains unchanged, and perform k steps of half-step backward Euler method calculation, including: If used After the first half-step backward Euler method, the numerical oscillation is effectively suppressed. The historical current source value after the first half-step backward Euler method is: The historical current source value after the second half-step backward Euler method is: After k-step backward Euler method calculation, the historical current source value is: when Decay to of Times, ,Right now but get but The minimum number of steps for: The oscillating voltage after k steps of half-step backward Euler method calculation is: Then proceed The numerical oscillation voltage after the backward Euler method with a half-step length is: 。 5. The electromagnetic transient simulation numerical oscillation suppression system based on eigenvalue analysis is characterized by: The electromagnetic transient simulation numerical oscillation suppression method based on eigenvalue analysis described in any one of claims 1-4 includes an electromagnetic transient simulation module, a data processing module and a data storage module; the electromagnetic transient simulation module and the data storage module are respectively connected to the data processing module.

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