CN103440374A - Electromagnetic transient simulation modeling method based on state variable nodal analysis combination frame - Google Patents

Abstract

The invention discloses an electromagnetic transient simulation modeling method based on a state variable nodal analysis combination frame. The method comprises the steps that an electric system is divided into a research system and an external system according to the nature of research questions, the external system is modeled through a state equation to acquire an output equation, a trapezoidal method is adopted to conduct differencing on the acquired state equation, the research system is modeled through nodal equations, and the calculation equation Gglobalu=iglobal of the state variable-nodal analysis combination frame is calculated to acquire a nodal voltage instantaneous value u (t) of the whole system; a nodal conductance matrix Gglobal of the whole system is regenerated, the nodal voltage instantaneous value u (t) of the whole system is acquired through a combination frame interpolation algorithm; an equivalent node injection current source column vector iN_hist of a next-moment state equation is calculated, and a node injection current source column vector iglobal based on the whole state variable-nodal analysis combination frame system is updated. The electromagnetic transient simulation modeling method based on a state variable nodal analysis combination frame achieves electric system state variable-nodal analysis combination simulation through interface variables.

Description

The state-based variable node is analyzed the electromagnetic transient simulation modeling method of combination frame

Technical field

The present invention relates to a kind of electric system simulation modeling method.Particularly relate to a kind of state-based variable node and analyze the electromagnetic transient simulation modeling method of combination frame.

Background technology

In the research of Power System Time Domain Simulation Under, developed corresponding digital simulation method for electromagnetic transient and electromechanical transient process respectively, be electromagnetical transient emulation method and electromechanical transient simulation method, the two mathematical model from element all has diverse feature to emulated computation method.The change procedure of the electric current and voltage of the generation that influences each other in electric field and magnetic field in mainly reflection system of electromagnetic transient in power system emulation, electromechanical transient simulation is mainly paid close attention to the change procedure of fault generation rear motor rotor mechanical motion.The present invention proposes a kind of state-based variable node and analyze the electromagnetic transient simulation modeling method of combination frame, the method not only is suitable for conventional electric power system electromagnetic transient simulation, is applicable to too calculate containing the active distribution system of various distributed power sources and energy storage device and the transient emulation of local islet operation electrical network.With respect to conventional electric power system electromagnetic transient simulation, the transient emulation of active power distribution network and local islet operation electrical network requires higher to the diversity of component type, the complicacy of model, but aspect the system method for solving, the two is consistent, and put forward the methods of the present invention has generality.

Electromagnetic transient in power system emulation can be summed up as asking for the dynamical system time domain response in essence, it comprises the mathematical model of system itself and the numerical algorithm adapted with it, its fundamental simulation framework can be divided into two classes, i.e. nodal analysis (Nodal Analysis) and State-Variable Analysis Method (State-space Analysis).Electromagnetical transient emulation method based on node analysis can be summarized as and first adopts certain numerical integration method (being generally trapezoidal integration) by the characteristic equation differencing of dynamic element in system, obtain the Equivalent Calculation electricity and lead the equivalent circuit with history entries current source parallel form, now the element characteristic equation of the whole electrical system of simultaneous forms nodal-admittance matrix, as the formula (1), solve the instantaneous value of each node voltage in the system of obtaining.

Gu=i （1）

Nodal analysis is widely used in, in the electromagnetic transient in power system simulated program of the specialties such as EMTP, PSCAD/EMTDC, also claiming on engineering that the electromagnetic transient simulation instrument based on the node analysis framework is the EMTP class method.The main advantage of nodal analysis is embodied in program and realizes difficulty and simulation calculation efficiency aspect, but because the modal equation itself shown in formula (1) combines numerical integration method and system model together, cause the EMTP class method to lack dirigibility with open aspect the derivation algorithm selection, same up-to-date style (1) can not provide the characteristic information of system itself.

Different from nodal analysis, State-Variable Analysis Method belongs to general modeling method (general purpose modeling), not only is suitable for circuit and electric system simulation, equally also is suitable for the modeling and simulation of the dynamical system of other form.Matlab/SimPowerSystems software is the Typical Representative of transient emulation program under the state variable analytical framework.With the node analysis framework, compare, state equation has opening and the dirigibility of height aspect solving in the calculating of model, can provide the abundant information about the various features of system (as the eigenwert of system) simultaneously, and then can understand from overall angle the dynamic perfromance of system, for various fast, the exploitation of simulation algorithm accurately and efficiently and the test job condition of providing convenience.

$\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}$ （2）

The basis of application state variable analysis is the State-output equation that forms canonical form shown in formula (2), and now the power supply in system is as input u.The state equation of above-mentioned canonical form can directly obtain A, B, C, tetra-matrixes of D by Matlab software.For example, to the circuit shown in Fig. 1, build circuit diagram as shown in Figure 2 on the Matlab/SimPowerSystems platform, circuit parameter R is set ₁=1 Ω, R ₂=4 Ω, L=0.1H, C=0.1mF, choose capacitance current i by the use of measuring sensor _cwith inductive drop u _lfor output quantity, its capacitance voltage v _cwith inductive current i _lfor state variable, supply voltage v _sfor input quantity, the state equation of canonical form shown in contrast (2), we obtain

$x=\left[\begin{array}{c}{v}_C\\ i_L\end{array}\right],$ u＝[v _S]、 $y=\left[\begin{array}{c}{v}_L\\ i_C\end{array}\right],$

Fundamental equation by the row write circuit, obtain

$A=\left[\begin{array}{cc}-\frac{1}{C(R_1+R_2)}& -\frac{R_2}{C(R_1+R_2)}\\ \frac{R_2}{L(R_1+R_2)}& -\frac{R_1{R}_2}{L(R_1+R_2)}\end{array}\right],$ $B=\left[\begin{array}{c}\frac{1}{C(R_1+R_2)}\\ \frac{R_1}{L(R_1+R_2)}\end{array}\right],$ $C=\left[\begin{array}{cc}\frac{R_2}{R_1+R_2}& -\frac{R_1{R}_2}{R_1+R_2}\\ -\frac{1}{R_1+R_2}& -\frac{R_2}{R_1+R_2}\end{array}\right],$ $D=\left[\begin{array}{c}\frac{R_1}{R_1+R_2}\\ \frac{1}{R_1+R_2}\end{array}\right],$ Utility command sps=power_analyze in Matlab (' sys', ' structure'), just can obtain $A=\left[\begin{array}{cc}-2000& -8000\\ 8& -8\end{array}\right],$ $B=\left[\begin{array}{c}2000\\ 2\end{array}\right],$ $C=\left[\begin{array}{cc}0.8& -0.8\\ -0.2& -0.8\end{array}\right],$ $D=\left[\begin{array}{c}0.2\\ 0.2\end{array}\right]$ Four matrixes, and can use various explicit or implicit expression integration methods to be solved.

Two kinds of basic skills all can be used for the particularly realization of the transient emulation of active power distribution network and local islet operation electrical network of electric system, for nodal analysis, modal equation itself has been considered real background and the physical significance of Circuits System, and the formation that the most important thing is modal equation is also very simple with easily.With nodal analysis, compare, State-Variable Analysis Method has more opening and dirigibility in the calculating of model aspect solving, can provide the abundant information about the various features of system (as the eigenwert of system) simultaneously, and then can understand from overall angle the dynamic perfromance of system, for various fast, the exploitation of simulation algorithm accurately and efficiently and the test condition of providing convenience.

In electromagnetic transient in power system emulation, two kinds of emulation modes are respectively had its own advantage and limitation, often both needed to use nodal analysis to carry out Accurate Model quickly and easily to the distributed power source of access, power electronic equipment etc., and wished again to adopt the various means of the advanced technology towards the state variable analysis to be analyzed and researched to system.Obviously, the electromagnetic transient simulation program of tradition based on single framework can't meet this demand, and the electromagnetic transient simulation modeling method of developing a kind of state-based variable node analysis combination frame is very necessary.

Summary of the invention

Technical matters to be solved by this invention is, provide a kind of state-based variable node to analyze the electromagnetic transient simulation modeling method of combination frame, be dissolved in the electromagnetic transient simulation program under the conventional node simulation frame by State-Variable Analysis Method and realized the two simultaneous solution, program is had concurrently the advantage of two kinds of simulation frames, can either be to distributed power source, the complex nonlinear elements such as power electronic equipment carry out fast accurate model solution, can utilize again the various means of the advanced technology towards the state variable analysis analyzed and researched or simplify processing the specific part in system, greatly promoted the opening of simulated program, expanded the modeling of program, the simulation and analysis ability, containing distributed power source, significant in the active power distribution network of energy storage device and microgrid and the application of the transient emulation of local islet operation electrical network.

The technical solution adopted in the present invention is: a kind of state-based variable node is analyzed the electromagnetic transient simulation modeling method of combination frame, comprises the steps:

1) electric system is divided into to Study system and external system according to the character studied a question, determines the interface node of Study system and external system, emulation is t=0 constantly;

2) external system is adopted state equation carry out modeling, obtain the State-output equation of canonical form $\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}$ , determine the interface node variable, take interface node voltage as input quantity, the grouting socket node current is output quantity;

3) adopting trapezoidal method and set simulation step length is △ t, by the state equation differencing obtained, obtains state equation equivalent node conductance matrix

with equivalent node Injection Current source column vector , wherein $\hat{A}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}(I+\frac{\mathrm{\Δt}}{2}A),\hat{B}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}\left(\frac{\mathrm{\Δt}}{2}B\right),$ I is unit matrix;

4) Study system is adopted modal equation carry out modeling, the equivalent node conductance matrix W that will be obtained by state equation _swith equivalent node Injection Current source column vector i _{n_hist}insert nodal-admittance matrix G and the node Injection Current source column vector i formed by modal equation according to node serial number, obtain the state-based variable node and analyze the system-wide nodal-admittance matrix G of combination frame _globalwith node Injection Current source column vector i _global;

5) simulation time is pushed ahead a step-length, t=t+ Δ t;

6) the accounting equation G of solving state variable-node analysis combination frame _globalu=i _global, calculate system-wide node voltage instantaneous value u (t);

7) judge whether switch motion, if switch motion is arranged, continued next step, if there is no switch motion, entered the 9th step;

8) regenerate system-wide nodal-admittance matrix G _global, application mix framework interpolation algorithm, obtain system-wide node voltage instantaneous value u (t);

9) solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist};

10) upgrade the state-based variable-system-wide node Injection Current of node analysis combination frame source column vector i _global;

11) judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory, emulation finishes, otherwise returns to the 5th step.

The described system-wide node voltage instantaneous value u (t) that obtains of step 8), specifically first to combination frame, use the method for linear interpolation to be interpolated into action constantly, use again the backward Euler method of half step-length to reinitialize, finally integration be synchronized to action constantly again.

Described next the state equation equivalent node Injection Current source column vector i constantly that solves of step 9) _{n_hist}, be the interface node voltage e in the node voltage instantaneous value u (t) will calculated _n(t) as input quantity substitution state equation

solving state variable x (t), by the interface node voltage e calculated _nand state variable x (t) substitution output equation (t)

in, solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist}.

State-based variable node of the present invention is analyzed the electromagnetic transient simulation modeling method of combination frame, realized that by interface variables the POWER SYSTEM STATE variable node analyzes hybrid simulation, can realize the transient emulation of in large scale, complex structure and highly asymmetric active power distribution network and local islet operation electrical network.The present invention has good feasibility and applicability, for solving electromagnetic transient in power system emulation, particularly containing the extensive active power distribution network of distributed power source and the transient emulation of local islet operation electrical network, provides a kind of good solution thinking.

The accompanying drawing explanation

Fig. 1 is examples of circuits;

Fig. 2 is the Matlab/SimPowerSystems analogous diagram of Fig. 1;

Fig. 3 is the process flow diagram of the electromagnetic transient in power system emulation modelling method based on combination frame of the present invention;

Fig. 4 is IEEE123 node power distribution network example structural drawing;

Fig. 5 is IEEE123 node example PV_1 photovoltaic system A phase output voltage curve map;

Fig. 6 is IEEE123 node example PV_1 photovoltaic system A phase output current curve map.

Embodiment

The electromagnetic transient simulation modeling method of state-based variable node of the present invention being analyzed to combination frame below in conjunction with embodiment and accompanying drawing is described in detail.

State-based variable node of the present invention is analyzed the electromagnetic transient simulation modeling method of combination frame, belong to the electric system simulation field, be specially adapted to the various active power distribution networks containing distributed power source, energy storage device and microgrid and the transient emulation of local islet operation electrical network.TSDG(Transient Simulator for Distributed Generation Systems and Microgrid) be a kind of calculation procedure of Based on Distributed generating micro-grid system transient emulation, the present invention has realized the electromagnetic transient in power system emulation modelling method of state-based variable node analysis combination frame on the basis of this program.Below using IEEE123 node distribution example as embodiment, and its system architecture as shown in Figure 4.This network voltage grade is 4.16kV, at node 150 places, by the large electrical network of transformer station and 115kV, is connected, and that inside is provided with is single-phase, three-phase load and circuit, is an asymmetric radial supply network of complexity.Three stage photovoltaic single system PV_1, PV_2 and PV_3 are grid-connected by step-up transformer respectively at node 47, node 65, node 76 3 places, and each photovoltaic capacity is 10kW, all adopts the maximal power tracing control mode.The Simulation Example set of time is 0.6s, and simulation step length is 10us, and when 0.3s, A phase ground short circuit fault occurs in PV_1 photovoltaic system combining inverter exit, failure removal during 0.35s, and by reference to the accompanying drawings 3, detailed description comprises the steps:

1) electric system is divided into to Study system and external system according to the character studied a question, determine the interface node of Study system and external system, the present embodiment is that distributed power source using the distribution network of IEEE123 node distribution example part as external system, access is as Study system, between the two, by node 47, node 65, node 76, interrelate, emulation is t=0 constantly;

2) external system is adopted state equation carry out modeling, obtain the State-output equation of canonical form $\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}$ , determine the interface node variable, take interface node voltage as input quantity, the grouting socket node current is output quantity;

3) adopting trapezoidal method and set simulation step length is △ t, by the state equation differencing obtained, obtains state equation equivalent node conductance matrix

with equivalent node Injection Current source column vector

, wherein $\hat{A}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}(I+\frac{\mathrm{\Δt}}{2}A),\hat{B}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}\left(\frac{\mathrm{\Δt}}{2}B\right),$ I is unit matrix;

4) Study system is adopted modal equation carry out modeling, the equivalent node conductance matrix W that will be obtained by state equation _swith equivalent node Injection Current source column vector i _{n_hist}insert nodal-admittance matrix G and the node Injection Current source column vector i formed by modal equation according to node serial number, obtain the state-based variable node and analyze the system-wide nodal-admittance matrix G of combination frame _globalwith node Injection Current source column vector i _global;

5) simulation time is pushed ahead a step-length, t=t+ Δ t;

6) the solving state variable node is analyzed the accounting equation G of combination frame _globalu=i _global, calculate system-wide node voltage instantaneous value u (t);

7) judge whether switch motion, if switch motion is arranged, continued next step, if there is no switch motion, entered the 9th step;

8) regenerate system-wide nodal-admittance matrix G _globalapplication mix framework interpolation algorithm, obtain system-wide node voltage instantaneous value u (t), specifically first to combination frame, uses the method for linear interpolation to be interpolated into action constantly, use again the backward Euler method of half step-length to reinitialize, finally integration be synchronized to action constantly again;

9) solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist}, specifically by the interface node voltage e in the node voltage instantaneous value u (t) calculated _n(t) as input quantity substitution state equation

$x\left(t\right)=\hat{A}x(t-\mathrm{\Δt})+\hat{B}{e}_N(t-\mathrm{\Δt})+\hat{B}{e}_N\left(t\right)$

Solving state variable x (t), by the interface node voltage e calculated _nand state variable x (t) substitution output equation (t)

$i_{N\_\mathrm{hist}}=C(\hat{A}x\left(t\right)+\hat{B}{e}_N\left(t\right))$

In, solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist}.

10) upgrade the state-based variable node and analyze the system-wide node Injection Current of combination frame source column vector i _global;

11) judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory, emulation finishes, otherwise returns to step 5).

The computer hardware environment of carrying out simulation calculation is Intel Core2 Q8400 2.66GHz CPU, memory size 2GB; Software environment is Windows7 operating system.

Fig. 5 and Fig. 6 have compared the TSDG of employing the inventive method and the simulation result of business simulation software MATLAB/SimPowerSystems.As can be seen from the figure, the simulation result of MATLAB/SimPowerSystems simulation result and TSDG can both fit like a glove in stable state and transient state process, it is highly consistent that the dynamic response characteristic of the two has kept, embody good simulation accuracy, fully verified correctness and the feasibility of the electromagnetic transient simulation modeling method of the state-based variable node analysis combination frame that the present invention proposes.

Above numerical testing proves, the electromagnetic transient simulation modeling method that the state-based variable node that the present invention proposes is analyzed combination frame has good feasibility and applicability, for solving electromagnetic transient in power system emulation, particularly containing the extensive active power distribution network of distributed power source and the transient emulation of local islet operation electrical network, provides a kind of good solution thinking.

Claims (3)

1. the electromagnetic transient simulation modeling method of a state-based variable node analysis combination frame, is characterized in that, comprises the steps:

1) electric system is divided into to Study system and external system according to the character studied a question, determines the interface node of Study system and external system, emulation is t=0 constantly;

2) external system is adopted state equation carry out modeling, obtain the State-output equation of canonical form $\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}$ , determine the interface node variable, take interface node voltage as input quantity, the grouting socket node current is output quantity;

3) adopting trapezoidal method and set simulation step length is △ t, by the state equation differencing obtained, obtains state equation equivalent node conductance matrix

with equivalent node Injection Current source column vector

, wherein $\hat{A}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}(I+\frac{\mathrm{\Δt}}{2}A),\hat{B}={(I-\frac{\mathrm{\Δt}}{2}A)}^{-1}\left(\frac{\mathrm{\Δt}}{2}B\right),$ I is unit matrix;

4) Study system is adopted modal equation carry out modeling, the equivalent node conductance matrix W that will be obtained by state equation _swith equivalent node Injection Current source column vector i _{n_hist}insert nodal-admittance matrix G and the node Injection Current source column vector i formed by modal equation according to node serial number, obtain the state-based variable node and analyze the system-wide nodal-admittance matrix G of combination frame _globalwith node Injection Current source column vector i _global;

5) simulation time is pushed ahead a step-length, t=t+ Δ t;

6) the accounting equation G of solving state variable-node analysis combination frame _globalu=i _global, calculate system-wide node voltage instantaneous value u (t);

7) judge whether switch motion, if switch motion is arranged, continued next step, if there is no switch motion, entered the 9th step;

8) regenerate system-wide nodal-admittance matrix G _global, application mix framework interpolation algorithm, obtain system-wide node voltage instantaneous value u (t);

9) solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist};

10) upgrade the state-based variable-system-wide node Injection Current of node analysis combination frame source column vector i _global;

11) judge whether simulation time reaches emulation and end constantly, as reach emulation and end constantly, releasing memory, emulation finishes, otherwise returns to the 5th step.

2. state-based variable node according to claim 1 is analyzed the electromagnetic transient simulation modeling method of combination frame, it is characterized in that, the described system-wide node voltage instantaneous value u (t) that obtains of step 8), specifically first to combination frame, use the method for linear interpolation to be interpolated into action constantly, use again the backward Euler method of half step-length to reinitialize, finally integration be synchronized to action constantly again.

3. state-based variable node according to claim 1 is analyzed the electromagnetic transient simulation modeling method of combination frame, it is characterized in that described next the state equation equivalent node Injection Current source column vector i constantly that solves of step 9) _{n_hist}, be the interface node voltage e in the node voltage instantaneous value u (t) will calculated _n(t) as input quantity substitution state equation

solving state variable x (t), by the interface node voltage e calculated _nand state variable x (t) substitution output equation (t)

in, solve next state equation equivalent node Injection Current source column vector i constantly _{n_hist}.

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