Parallel Simulation Method for Power-Electronic Power Systems Based on Improved Euler Method

Abstract

The present invention discloses a parallel simulation method for an electrified power system based on the improved Euler method. A large-scale electrified power system contains a large number of power electronic switching devices. Such a high-order nonlinear system greatly increases the computational amount within a single simulation step. Therefore, it is necessary to decouple the entire system to achieve parallel simulation. The present invention establishes a state-space equation describing the coupling relationship of subsystems for the topological structure of passive components at the connection of converters to the grid, discretizes the AC inductor current and DC capacitor voltage of the converter based on the improved Euler method, and constructs an adjoint equivalent circuit of the discrete equation. The present invention can eliminate the delay between the equivalent circuit and the global solution of the system and achieve high-precision delay-free parallel simulation.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic transient simulation, and specifically to a parallel simulation method for power electronic power systems based on the improved Euler method. Background Art

[0002] Large-scale power electronic power systems have a huge number of switches and fast-slow coupled dynamic characteristics. The transient process of the new power system has a large time scale span and coexists fast and slow dynamic characteristics, and its requirements for numerical calculation stability and accuracy are higher than those of traditional power system simulations. Since there are hundreds of switching devices in the system, as the number of switches and the simulation scale increase, the time required for simulation calculation will also increase significantly. The real-time simulation platform of power systems is generally developed based on the Central Processing Unit (CPU) and Field Programmable Gate Array (FPGA). As the system scale increases, a large number of power electronic switching devices make the overall calculation amount increase significantly, while the internal logic calculation resources of a single FPGA are limited and cannot meet the real-time simulation requirements of power systems with a high proportion of power electronic converters. The decoupling of traditional power systems generally uses the propagation delay of transmission lines to decompose the system into different subsystems, but there will be delays between the decoupled subsystems. Based on the multi-port Thevenin equivalent to cut the system at the nodes, the scale of the nodal admittance matrix can be effectively reduced, but it needs to be calculated in multiple steps, and the simulation scale is limited. Summary of the Invention

[0003] The technical problem to be solved by the present invention is:

[0004] The existing parallel simulation methods achieve the decoupling purpose by inserting delays or splitting nodes between subsystems. Calculating in two steps increases the complexity of the operation, and the delays between subsystems will also cause simulation errors. Especially in the case of faults, the accumulation of delay errors caused by the sharp change of current will cause system oscillation. In addition, in order to ensure the accuracy of the simulation, the simulation step size will also be strictly limited.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] For the passive element topology at the connection of the converter to the grid, a state space equation describing the coupling relationship of the subsystems is established. Based on the improved Euler method, the state space equation is discretized, and after being converted into the form of nodal equations, Norton and Thevenin equivalent circuits are established for the inductor current and capacitor voltage respectively to eliminate the delay between the equivalent circuits and the global solution of the system.

[0007] As a further improvement of the present invention, for the passive components inductance and capacitance at the connection of subsystems, a second-order state-space equation is written, and the state-space equation is:

[0008]

[0009] Wherein, v c and i L are the capacitor voltage and inductor current respectively, C and L are the capacitance value and inductance value respectively, i 1 and v 2 are the port current of subsystem 1 and the port voltage of subsystem 2 respectively.

[0010] As a further improvement of the present invention, the improved Euler method is used to discretize the state-space equation with a step size T s to obtain:

[0011]

[0012] Where is the next-step predicted value, and the matrices A and B are expressed as and Therefore, both matrices A and B are constant admittance matrices and are related to the inductance value and capacitance value;

[0013] Writing the above equation in the form of a nodal admittance matrix gives:

[0014]

[0015] Where the historical terms v c_his and i i_his are expressed as:

[0016]

[0017] Where and

[0018] Since matrix B is a diagonal matrix, the inductor current and capacitor voltage are solved independently as follows:

[0019]

[0020] As a further improvement of the present invention, the capacitor voltage value at the current moment is only related to the current value of subsystem 1, and the influence of subsystem 2 and inductor current is reflected in the historical terms; the inductor current value at the current moment is related to the voltage value of subsystem 2, and the influence of subsystem 1 and capacitor voltage is reflected in the historical terms; the capacitor and subsystem 1 are calculated together, and the inductor and subsystem 2 are calculated together, realizing the non-delay parallel simulation of different subsystems.

[0021] As a further improvement of the present invention, the constant admittance matrix in the form of the nodal equation is a diagonal matrix, and the coefficient values are related to the inductance value and capacitance value at the connection.

[0022] As a further improvement of the present invention, the second-order constant admittance matrix in the form of the nodal equation can be solved independently, and the inductor current and capacitor voltage can be respectively equivalent to the Norton and Thevenin adjoint circuits.

[0023] Compared with the prior art by adopting the above technical solutions, the present invention has the following technical effects:

[0024] The present invention proposes a parallel simulation method for a power electronic power system based on the improved Euler method, which realizes natural decoupling between subsystems through passive components without inserting a delay, and does not need to be calculated in multiple steps to realize parallel simulation, eliminates the delay in solving between the power electronic converter subsystems, and improves the accuracy of parallel simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a traditional decoupling method based on one-step delay insertion.

[0026] Figure 2 is a delay-free decoupling method based on the improved Euler method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] The technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings:

[0028] As Figure 1 shown, the traditional parallel simulation decoupling method decouples the system on the inductor and capacitor sides by equivalently replacing the inductor current with a current source and the capacitor voltage with a voltage source. Its principle is to assume that the inductor current and capacitor voltage do not change abruptly after one step, and use the previous step values to achieve decoupling. However, inserting a one-step delay will affect the system simulation accuracy and solution stability.

[0029] As Figure 2 shown, the present invention proposes a parallel simulation of a power electronic power system based on the improved Euler method. By writing the state space equations for the capacitor voltage and inductor current at the connection between subsystems, we can obtain

[0030]

[0031] where, v c and i L are the capacitor voltage and inductor current respectively, C and L are the capacitance value and inductance value respectively, i 1 and v 2 are the port current of subsystem 1 and the port voltage of subsystem 2 respectively.

[0032] Similarly, the improved Euler method is used to discretize the state - space equation with a step size of T s and we can obtain

[0033]

[0034] where is the predicted value for the next step, and the matrices A and B can be expressed as and Therefore, both A and B are constant admittance matrices and are related to the inductance value and capacitance value.

[0035] Writing the above - mentioned equation in the form of a nodal admittance matrix, we can get

[0036]

[0037] where the historical terms \(v\) c_his and \(i\) i_his can be expressed as

[0038]

[0039] where and

[0040] Since matrix B is a diagonal matrix, the inductor current and capacitor voltage can be solved independently as follows

[0041]

[0042] Based on the discrete results, the Norton and Thevenin equivalent circuits are derived as Figure 2 shown. The value of the capacitor voltage at the current moment is only related to the current value of subsystem 1, and the influence of subsystem 2 and the inductor current is reflected in the historical terms. Similarly, the value of the inductor current at the current moment is related to the voltage value of subsystem 2, and the influence of subsystem 1 and the capacitor voltage is reflected in the historical terms. Therefore, the capacitor and subsystem 1 are calculated together, and the inductor and subsystem 2 are calculated together, realizing the non - delay parallel simulation of different subsystems.

Claims

1. A parallel simulation method for power electronic power system based on improved Euler method, characterized by: Firstly, the state-space equations describing the coupling relationship of the subsystems are established according to the topological structure of the passive components at the grid-connected connection of the converter. Then, the state-space equations are discretized based on the improved Euler method. After being converted into node equations, the Norton and Thevenin equivalent circuits are established for the inductor current and capacitor voltage respectively, eliminating the delay between the equivalent circuit and the global solution of the system. The second-order state-space equations are written for the passive component inductances and capacitances at the subsystem connections, and the state-space equations are: Among them, v c and i L are the capacitor voltage and inductor current, C and L are the capacitance and inductance values, i1 and v2 are the subsystem 1 port current and subsystem 2 port voltage, respectively; The state space equation is solved by using the improved Euler method with a step size T s Discretize to get: in For the next prediction value, matrices A and B are expressed as and Therefore, both matrices A and B are constant admittance matrices and are related to the inductance and capacitance values; Write the above formula into the form of node admittance matrix: The historical term v c_his and i i_his It is expressed as: in and Since matrix B is a diagonal matrix, the inductor current and capacitor voltage are solved independently as follows:

2. The method for parallel simulation of power electronic power system based on improved Euler method according to claim 1, characterized in that: The capacitor voltage value is only related to the current value of subsystem 1 at the current moment, and the influence of subsystem 2 and inductor current is reflected in the history item; the inductor current value is related to the voltage value of subsystem 2 at the current moment, and the influence of subsystem 1 and capacitor voltage is reflected in the history item; the capacitor is calculated together with subsystem 1, and the inductor is calculated together with subsystem 2, realizing delay-free parallel simulation of different subsystems.

3. The power electronic power system parallel simulation method based on the improved Euler method according to claim 1, characterized in that: The constant admittance matrix expressed in the form of a node equation is a diagonal matrix, and the coefficient values ​​are related to the inductance and capacitance values ​​at the connection.

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