Wind power system stability domain division method for avoiding boundary crisis under random disturbance

Abstract

The invention discloses a wind power system stability domain division method for avoiding boundary crisis under random disturbance. The method comprises the following steps: S1, establishing a nonlinear dynamic model of a wind power system; s2, establishing a random disturbance model, and introducing a disturbance coefficient; s3, establishing a wind power system nonlinear dynamic model containing random disturbance; s4, performing nonlinear bifurcation analysis, and respectively setting disturbance coefficients to obtain single-parameter bifurcation diagrams F1, F2 and F3; s5, analyzing the influence of the boundary crisis on the stability of the wind power system; s6, dividing a first system stability domain R1 by taking the boundary crisis point as a stability domain boundary; s7, analyzing the influence of random disturbance on the first system stability domain R1; and S8, drawing a second system stability domain R2 based on the analysis of the S7, F2 and F3. According to the method, system stability domains under different random disturbances are divided, so that the system not only has the capability of resisting random disturbances, but also does not lose stability in advance due to boundary crisis.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability analysis, and in particular to a method for dividing a wind power system stability domain for avoiding boundary crises under random disturbances. Background Art

[0002] The large-scale access of wind power has brought new challenges to the stability analysis of power systems. On the one hand, the wind power system is a type of strongly nonlinear system, which is difficult to analyze; on the other hand, wind power is extremely susceptible to the influence of the installation environment, resulting in a strong randomness in the power injected into the system. This change in injected power is regarded as a random disturbance, which may cause power system instability or large-scale power outages. Boundary crisis is a nonlinear phenomenon caused by the collision of the system limit cycle and the system attraction domain, which will cause the system to produce chaotic oscillations and make the system lose stability prematurely. In particular, when the influence of random disturbances is considered, the risk of system instability through boundary crisis is further increased.

[0003] Commonly used analysis methods include eigenvalue analysis, impedance analysis, complex torque coefficient method, etc. This type of linear analysis method ignores the strong nonlinearity of the system, so it is impossible to analyze nonlinear phenomena such as boundary crisis, and the accuracy of the analysis results will be affected. The nonlinear method of time domain simulation has the disadvantages of long solution time and inability to study the oscillation mechanism, and is usually used as an auxiliary tool to verify the results obtained by other methods. Summary of the invention

[0004] In order to solve the problem that the existing analysis methods cannot cope with the impact of random disturbances and boundary crises on the stability of wind power systems, the present invention proposes a method for dividing the stability domain of wind power systems to avoid boundary crises under random disturbances. Based on bifurcation and chaos theory, the stable area of ​​the wind power system under boundary crises and random disturbances is accurately characterized, and the risk of instability of the wind power system is further reduced to solve the above problem.

[0005] The present application discloses a method for dividing a wind power system stability domain to avoid boundary crises under random disturbances, comprising the following steps: S1. System model construction: establish the mathematical model of the components in the wind power system and the mathematical model of the network topology, and finally synthesize a set of nonlinear differential algebraic equations to represent the nonlinear dynamic model of the wind power system; S2. Random disturbance term model construction: a random disturbance model describing the change of wind power injection power is established, and a disturbance coefficient is introduced to simulate random disturbances of different sizes; S3, model modification, based on the nonlinear dynamic model of S1 and the random disturbance model of S2, a nonlinear dynamic model of the wind power system including random disturbance is established; S4, nonlinear dynamic analysis, using the nonlinear dynamic analysis software MATLAB / MATCONT, the nonlinear bifurcation analysis of the nonlinear dynamic model of the wind power system containing random disturbances obtained in S3 is performed, and the disturbance coefficient is set to 0, 10%, and 20% respectively. The obtained single parameter bifurcation diagrams are represented by F1, F2, and F3 respectively; S5. Boundary crisis impact analysis: analyzing the impact of boundary crisis on the stability of wind power system; S6, dividing the first system stability domain R1, based on the single parameter bifurcation diagram F1 obtained in S4, find the boundary crisis point of the wind power system, and divide the first system stability domain R1 with the boundary crisis point as the stability domain boundary; S7, analyzing the influence of random disturbance on the stability region R1 of the first system, analyzing the influence of random disturbance on the stability region R1 of the first system; S8. Division of the second system stability domain R2 under different random disturbances. Based on the analysis of S7 and the single-parameter bifurcation diagram F2 and single-parameter bifurcation diagram F3 obtained in S4, the second system stability domain R2 is drawn.

[0006] Preferably, the nonlinear dynamic model in S1 is:

[0007] in, is the state variable vector, such as node voltage, fan speed, etc. is a vector of algebraic variables, such as synchronous generator voltage, power, etc., is a vector of parameter variables, such as load reactive power, active power generated by wind turbine, etc. is a set of differential equations representing the system state equations dimension column vector, is a system of algebraic equations, representing the system of algebraic equations dimensional column vector.

[0008] Preferably, S2 comprises the following steps: The random perturbations are modeled as:

[0009] in, is the drift of the equation, is the expansion vector of the equation, is a white noise process, is a random disturbance, is the drift component of the random disturbance, is the diffusion component of the random disturbance.

[0010] Then, considering that random disturbances will cause random phenomena in the system, and this random phenomenon is related to the system's own variables and parameters, the random disturbance is further modeled as:

[0011] Consider the random disturbance process caused by the change of wind power injection power, and introduce the disturbance coefficient to represent random disturbances of different sizes:

[0012] in, is the disturbance coefficient of random disturbance caused by wind power input power change, Injecting power into wind power, The initial value of wind power injection power, The power variation injected into wind power, is the pre-set average wind power injection power. is the equation drift in the random disturbance process caused by the change of wind power injection power, is the diffusion tensor in the random disturbance process caused by the change of wind power injection power, is the white noise in the random disturbance process caused by the change of wind power injection power, For time.

[0013] Preferably, the nonlinear dynamic model expression of the wind power system including random disturbance is:

[0014] in, is the system differential equation containing random perturbations, is a system of algebraic equations involving random perturbations.

[0015] Preferably, the impact of the boundary crisis on the stability of the wind power system is analyzed by the following formula:

[0016] in, is an unstable manifold of unstable limit cycles, is the unstable manifold of the unstable equilibrium point, is the stable manifold of the chaotic attractor, is the critical parameter value of the border crisis, is the critical parameter value of the subcritical Hopf bifurcation, is the system parameter.

[0017] Preferably, R1 is expressed in parameter space as:

[0018] in, Representing algebraic equations Algebraic variable vector The Jacobian matrix of is the characteristic value, is the parameter space.

[0019] Preferably, the S7 comprises the following steps: Based on the nonlinear dynamic model of wind power system including random disturbances obtained by S3, we can get:

[0020]

[0021] Among them, among them, express The disturbance coefficient at time .

[0022] The evolution of the system is determined by the same set of equations. The effect of random disturbances depends on their initial values, so when the disturbance coefficient When taking different values, the manifold of the system should remain basically the same; Random perturbations further affect the first system stability region R1 by changing the critical parameter value of the boundary crisis:

[0023] in, is the critical value of system boundary crisis under random disturbance.

[0024] Preferably, the R2 is expressed in parameter space as:

[0025] in, are system parameters under random perturbations, is the disturbance coefficient The value of .

[0026] Beneficial effects of the present invention: (1) Based on the nonlinear analysis method, the present invention explores the influence of boundary crisis and external random disturbance on the stability domain of wind power system, and divides the system stability domain under random disturbances of different sizes. Within the divided stability domain, the system can not only remain stable under the influence of random disturbances, but also avoid losing stability through boundary crisis.

[0027] (2) The present invention can provide a stable domain of a wind power system under random disturbances of different magnitudes, and provide guidance to operation and maintenance personnel for adjusting key parameters of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1A flow chart of a method for dividing a wind power system stability region to avoid a boundary crisis under random disturbances according to an embodiment of the present invention; Figure 2 A schematic diagram of the structure of a wind power system according to an embodiment of the present invention; Figure 3 For the embodiment of the present invention Time system bifurcation diagram; Figure 4 This is a single parameter bifurcation diagram of a wind power system under random disturbances of different sizes according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0030] The embodiment of the present application discloses a method for partitioning the stability domain of a wind power system to avoid boundary crises under random disturbances. The method flow is as follows: Figure 1 As shown, the following steps are included: This embodiment is for Figure 2 The wind power system shown in the figure is divided into stable areas, considering the impact of boundary crises and random disturbances of different sizes on the system stability area, which is determined by the system PU L The single parameter bifurcation diagram is used to reflect this. Figure 2 middle represents wind power injection power, PMSG represents permanent magnet direct drive generator, RSC represents rotor side converter, GSC represents grid side converter, Indicates the voltage of 12 nodes; represents the voltage phase angle of 12 nodes, , They represent the active and reactive power output of PMSG respectively; SG1-SG4 represent 4 synchronous generators respectively. Indicates the voltage of the load, represents the voltage phase angle of the load, and Represent the load active and reactive power respectively.

[0031] S1. System model construction, establish the mathematical model of the components in the wind power system and the mathematical model of the network topology, and finally synthesize a set of nonlinear differential algebraic equations to represent the nonlinear dynamic model of the wind power system. This set of equations includes the mathematical models of components such as wind turbines, synchronous generators, loads, and the mathematical model of the power system network in the wind power system. This set of nonlinear differential algebraic equations is represented by the following formula:

[0032] in, is the state variable vector, such as node voltage, fan speed, etc. is a vector of algebraic variables, such as synchronous generator voltage, power, etc., is a vector of parameter variables, such as load reactive power, active power generated by wind turbine, etc. is a set of differential equations representing the system state equations dimensional column vector, is a system of algebraic equations, representing the system of algebraic equations dimensional column vector.

[0033] S2. Random disturbance term model construction: a random disturbance model describing the change of wind power injection power is established, and a disturbance coefficient is introduced to simulate random disturbances of different sizes.

[0034] First, the random perturbation is modeled as:

[0035] in, is the drift of the equation, is the expansion vector of the equation, is a white noise process, is a random disturbance, is the drift component of the random disturbance, is the diffusion component of the random disturbance.

[0036] Then, considering that random disturbances will cause random phenomena in the system, and this random phenomenon is related to the system's own variables and parameters, the random disturbance is further modeled as:

[0037] Furthermore, the random disturbance process caused by the change of wind power injection power is considered, and the disturbance coefficient is introduced to represent random disturbances of different sizes:

[0038] in, is the disturbance coefficient of random disturbance caused by wind power input power change, Injecting power into wind power, The initial value of wind power injection power, The power variation injected into wind power, is the pre-set average wind power injection power. is the equation drift in the random disturbance process caused by the change of wind power injection power, is the diffusion tensor in the random disturbance process caused by the change of wind power injection power, is the white noise in the random disturbance process caused by the change of wind power injection power, For time.

[0039] S3, model modification, based on the nonlinear dynamic model of S1 and the random disturbance model of S2, a nonlinear dynamic model of the wind power system including random disturbance is established.

[0040]

[0041] in, is the system differential equation containing random perturbations, is a system of algebraic equations involving random perturbations.

[0042] S4. Nonlinear dynamic analysis: nonlinear bifurcation analysis is performed on the nonlinear dynamic model of the wind power system containing random disturbances obtained in S3 using the nonlinear dynamic analysis software MATLAB / MATCONT. The disturbance coefficient is set to 0, and the obtained single parameter bifurcation diagram is represented by F1; the disturbance parameter is set to 10%, and the obtained single parameter bifurcation diagram is represented by F2; the disturbance parameter is set to 20%, and the obtained single parameter bifurcation diagram is represented by F3.

[0043] S5. Analysis of the impact of boundary crisis: Analyze the impact of boundary crisis on the stability of wind power system. Boundary crisis is one of the ways for the system to generate chaotic attractors. This process occurs before the subcritical Hopf bifurcation. hour( is the critical parameter value of boundary crisis), the system enters a chaotic state and becomes unstable.

[0044]

[0045] in, is an unstable manifold of unstable limit cycles, is the unstable manifold of the unstable equilibrium point, is the stable manifold of the chaotic attractor, is the critical parameter value of the border crisis, is the critical parameter value of the subcritical Hopf bifurcation, is the parameter of the system. A boundary crisis will cause the system to lose stability prematurely.

[0046] S6, the first system stability domain R1 is divided. Based on the analysis of S5 and the single parameter bifurcation diagram F1 obtained in S4, the boundary crisis point of the wind power system is found, and the first system stability domain R1 is divided with the boundary crisis point as the boundary of the stability domain. R1 is expressed in the parameter space as:

[0047] in, Representing algebraic equations Algebraic variable vector The Jacobian matrix of is the characteristic value, is the parameter space.

[0048] like Figure 3 The disturbance coefficient is shown At that time is the bifurcation diagram of the bifurcation parameter. The blue solid line and dashed line represent the stable and unstable manifolds of the system respectively, and the blue hollow circle represents the unstable limit cycle of the system. In the figure, A is the Hopf bifurcation point (HB) of the system, and C is the boundary crisis point of the system. The traditional method believes that It is a system stability area. However, this embodiment takes into account the impact of the boundary crisis and takes the boundary crisis point as the boundary of the system stability region. The first system stability region R1 is divided into .

[0049] S7. Analyze the impact of random disturbances on the stability region R1 of the first system, and analyze the impact of random disturbances on the stability region R1 of the first system.

[0050] Based on the nonlinear dynamic model of wind power system including random disturbances obtained by S3, we can get:

[0051]

[0052] in, express The disturbance coefficient at time .

[0053] The evolution of the system is determined by the same set of equations, and the effect of random disturbances depends on their initial values. When taking different values, the manifold of the system should remain basically the same. Random perturbations further affect the first system stability region R1 by changing the critical parameter value of the boundary crisis.

[0054]

[0055] in, is the critical value of system boundary crisis under random disturbance.

[0056] S8, the second system stability region R2 is divided under different random perturbations. Based on the analysis of S7 and the single parameter bifurcation diagram F2 and single parameter bifurcation diagram F3 obtained in S4, the second system stability region R2 is drawn. R2 is expressed in parameter space as:

[0057] in, are system parameters under random perturbations, is the disturbance coefficient The value of .

[0058] like Figure 4 The figure shows the division results of the second system stability region R2 under random perturbations of different sizes. Curves of different colors in the figure represent the system manifold under random perturbations of different sizes. The dashed line indicates that the system is stable, and the dotted line indicates that the system is unstable. Figure 4 It can be seen that the perturbation coefficient The larger it is, the smaller the second system stability region R2 is. When , the second system stability region R2 is: , When , the second system stability region R2 is: .

[0059] In summary, this application explores the impact of boundary crisis and external random disturbance on the stability domain of wind power system based on nonlinear analysis method, and divides the system stability domain under random disturbances of different sizes. The divided stability domain comprehensively considers the impact of boundary crisis and random disturbance. When the system operates in the divided stability domain, the system not only has the ability to resist random disturbances, but also will not lose stability in advance due to boundary crisis.

[0060] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for partitioning the stability region of a wind power system to avoid boundary crises under random disturbances, characterized in that: The following steps are involved: S1. Establish a nonlinear dynamic model of the wind power system using a set of nonlinear differential algebraic equations; S2. Establish a random disturbance model to describe the change of wind power injection power, and introduce disturbance coefficients to simulate random disturbances of different sizes; S3, establishing a nonlinear dynamic model of a wind power system including random disturbances according to the nonlinear dynamic model of S1 and the random disturbance model of S2; S4, performing nonlinear bifurcation analysis on the nonlinear dynamic model of the wind power system including random disturbances obtained in S3, and setting the disturbance coefficient to 0, 10%, and 20%, respectively, and the obtained single parameter bifurcation diagrams are represented by F1, F2, and F3, respectively; S5. Analyze the impact of border crisis on wind power system stability; S6. Based on the single parameter bifurcation diagram F1 obtained in S4, find the boundary crisis point of the wind power system, and divide the first system stability domain R1 with the boundary crisis point as the stability domain boundary; S7, analyzing the impact of random disturbance on the stability region R1 of the first system; S8. Based on the analysis of S7 and the single-parameter bifurcation diagram F2 and single-parameter bifurcation diagram F3 obtained in S4, the stability region R2 of the second system is drawn.

2. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 1 is characterized in that: The nonlinear dynamic model in S1 is: in, is the state variable vector, is a vector of algebraic variables, is the parameter variable vector, is a set of differential equations representing the system state equations dimension column vector, is a system of algebraic equations, representing the system of algebraic equations dimensional column vector.

3. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 2 is characterized in that: The S2 comprises the following steps: The random perturbations are modeled as: in, is the drift of the equation, is the expansion vector of the equation, is a white noise process, is a random disturbance, is the drift component of the random disturbance, is the diffusion component of random disturbance; Random disturbances will cause random phenomena in the system, and this random phenomenon is related to the system's own variables and parameters, so the random disturbance is further modeled as: Consider the random disturbance process caused by the change of wind power injection power, and introduce the disturbance coefficient to represent random disturbances of different sizes: in, is the disturbance coefficient of random disturbance caused by wind power input power change, Injecting power into wind power, The initial value of wind power injection power, The power variation injected into wind power, is the pre-set average wind power injection power. is the equation drift in the random disturbance process caused by the change of wind power injection power, is the diffusion tensor in the random disturbance process caused by the change of wind power injection power, is the white noise in the random disturbance process caused by the change of wind power injection power, For time.

4. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 3 is characterized in that: The nonlinear dynamic model expression of the wind power system including random disturbance is: in, is the system differential equation containing random perturbations, is a system of algebraic equations involving random perturbations.

5. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 4 is characterized in that: The impact of the boundary crisis on the stability of the wind power system can be reflected by the following formula: in, is an unstable manifold of unstable limit cycles, is the unstable manifold of the unstable equilibrium point, is the stable manifold of the chaotic attractor, is the critical parameter value of the border crisis, is the critical parameter value of the subcritical Hopf bifurcation, is the system parameter.

6. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 5 is characterized in that: The R1 is expressed in parameter space as: in, Representing algebraic equations Algebraic variable vector The Jacobian matrix of is the characteristic value, is the parameter space.

7. The method for dividing the stability region of a wind power system to avoid boundary crises under random disturbances according to claim 6 is characterized in that: The S7 comprises the following steps: Based on the nonlinear dynamic model of the wind power system including random disturbances obtained by S3, it can be obtained: in, express The disturbance coefficient at time . The evolution of the system is determined by the same set of equations. The effect of random disturbances depends on their initial values, so when the disturbance coefficient When taking different values, the manifold of the system should remain basically the same; Random perturbations further affect the first system stability region R1 by changing the critical parameter value of the boundary crisis: in, is the critical value of system boundary crisis under random disturbance.

8. The method for dividing the stability region of a wind power system to avoid boundary crisis under random disturbance according to claim 7, characterized in that: The R2 is expressed in parameter space as: in, are system parameters under random perturbations, is the disturbance coefficient The value of .

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