CN110649604B - Damping control method suitable for random fluctuation of new energy - Google Patents

Damping control method suitable for random fluctuation of new energy Download PDF

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CN110649604B
CN110649604B CN201910915548.1A CN201910915548A CN110649604B CN 110649604 B CN110649604 B CN 110649604B CN 201910915548 A CN201910915548 A CN 201910915548A CN 110649604 B CN110649604 B CN 110649604B
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王彤
宓登凯
杨京
王增平
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North China Electric Power University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks

Abstract

The invention discloses a random adaptive new energy resourceA method of damping control of wave activity, the control method comprising the steps of: the method comprises the following steps: establishing a linear variable parameter system model of the new energy power system; step two: expressing the linear variable parameter system model by using a multicellular model; step three: using mixing of H2/H∞Controlling to solve a state feedback matrix for each vertex system; step four: and forming the self-adaptive damping controller according to the variable gain of the feedback matrix designed by the vertex.

Description

Damping control method suitable for random fluctuation of new energy
Technical Field
The invention relates to the technical field of power systems, in particular to a damping control method adaptive to random fluctuation of new energy.
Background
Under the large background of global warming and increasing exhaustion of fossil energy, development and utilization of renewable energy are increasingly paid attention to the international society, and the vigorous development of novel renewable energy is imperative. In recent years, photovoltaic power stations and wind power plants become the most common new energy form for large-scale access to power grids, photovoltaic power generation and wind power generation are rapidly developed in China, and installed capacity is increased day by day. By the end of 2016, the cumulative photovoltaic installed capacity of China reaches 7742 thousands kW, and the generated energy accounts for 1% of the total annual generated energy; the wind power accumulated installed capacity is listed world first, and the wind power installed capacity is expected to reach at least 1.5 hundred million kW by 2020. However, the dynamic characteristic and the operating characteristic of the power grid are changed to a certain extent by the access of new energy, and certain influence is exerted on the stability of the system. The random fluctuation of primary energy such as wind energy determines the random fluctuation of wind power output power, and along with the continuous expansion of the wind power grid-connected scale, the randomness and the fluctuation of a system are more severe, and the random drift phenomenon of a system operating point is increasingly prominent. Under the remote large-scale delivery mode in China, the influence of large-scale wind power access on the stability of a power grid is further exposed and worsened, and the system stability faces unprecedented challenges.
The design of conventional power system controllers is performed under typical operating conditions, i.e., given system component parameters, operating conditions, and disturbance regimes. Because wind power has intermittence and strong random fluctuation, the operation point of the new energy power system has random drift behavior in the operation space, so that the traditional controller designed based on typical operation conditions has the defect of obviously insufficient adaptability, and is difficult to effectively track the random drift behavior of the wind power grid-connected system, thereby being difficult to effectively damp.
Therefore, a damping control method adaptive to the random fluctuation of new energy is expected to solve the problems in the prior art.
Disclosure of Invention
The invention discloses a damping control method adaptive to random fluctuation of new energy, which comprises the following steps:
the method comprises the following steps: establishing a linear variable parameter system model of the new energy power system;
step two: expressing the linear variable parameter system model by using a multicellular model;
step three: using mixing of H2/H∞Controlling to solve a state feedback matrix for each vertex system;
step four: and forming the self-adaptive damping controller according to the variable gain of the feedback matrix designed by the vertex.
Preferably, the step one is to convert the nonlinear model of the power system with the random drift behavior of the operating point into the linear variable parameter system based on a Jacobian linearization method.
Preferably, the state space matrix elements of the linear variable parameter (LPV) system depend on a continuous time-varying parameter vector p (t), the variation of which is obtained by online measurement, the variation range of which is bounded and determined.
Preferably for multiple targets H2/H∞The linear variable parameter (LPV) system of the control problem is represented by a state space equation as formula (1):
Figure BDA0002216013910000021
in the formula: x is a power system state vector; u is a control input vector; w is an external disturbance input vector and is selected according to system disturbance; z is a radical of∞And z2Respectively represent and H∞And H2Performance indexA correlated output vector; a is the system state matrix, B1Is a perturbation gain matrix; b is2Inputting a matrix for control; c∞，D∞1And D∞2Are respectively H∞Coefficient matrixes of performance index related state variables, disturbance inputs and control inputs; c2，D21And D22Are respectively H2Coefficient matrices for performance index related state variables, disturbance inputs and control inputs.
Preferably, in the second step, if there are m parameter variables in the variable parameter p of the linear variable parameter (LPV) system, the corresponding multicellular linear variable parameter system has N-2mSeveral vertexes, the variable parameter rho of the system is in N related vertexes b of the multicellular typekK is 1,2, …, N is constantly changed, i.e. the variable parameter ρ satisfies the formula (2):
Figure BDA0002216013910000022
the state space matrix of the linear variable parameter system also varies within the multicellular matrix of N related vertices according to equation (3):
Figure BDA0002216013910000031
by convex combination of the vertex system matrix by varying the coefficient alpha using a convex decomposition techniquekApproximating the actual system matrix, and measuring the error of the convex combination of the vertex system matrix and the actual system matrix by the difference L2 norm of the two matrixes, as shown in formula (4):
Figure BDA0002216013910000032
αkchanging from 0 to 1, the step size is 0.01, and through the traversal calculation, the coefficient alpha when xi is minimum is selectedkTo represent the actual system matrix, the state space matrix of the multicellular linear variable parameter system is represented by equation (5):
Figure BDA0002216013910000033
preferably, in the third step, when the parameter ρ is determined, the linear variable parameter system is converted into a linear time-invariant system, as shown in formula (6):
Figure BDA0002216013910000034
and (3) substituting a state feedback rule u which is Kx into an open-loop system model formula (6) by adopting a state feedback design controller to obtain a closed-loop system model formula (7):
Figure BDA0002216013910000035
in the formula: a. thec＝A+B2K；C∞c＝C∞+D∞2K；C2c＝C2+D2K；
Introducing a positive definite matrix X, a symmetric matrix Q and a variable replacement Y which is KX to satisfy a system H∞Performance, H2The multi-objective control problem of performance and regional pole allocation is solved by solving the linear inequality of equation (8):
Figure BDA0002216013910000041
in the formula: l, M, gamma0，η0μ and β are parameters given to meet different design goals;
Figure BDA0002216013910000042
is a Kronecker product;
the vertex of the multicellular linear variable parameter system is a linear time-invariant system, and each vertex is connected with a computer
Figure BDA0002216013910000043
Substituting formula (8) to obtain state feedback matrix K of N vertexesk,k＝1,2,…,N。
The invention provides a damping control method adaptive to random fluctuation of new energy, which selects active power of a fan as a variable parameter vector, establishes a linear variable parameter system model of an electric power system and utilizes multicell type representation; based on mixing H2/H∞The control method solves the feedback matrix of each vertex state by using a linear matrix inequality to obtain the subsynchronous oscillation adaptive damping controller with a multi-cell structure. The adaptive damping controller based on the multicellular linear variable parameter system can provide enough damping for the subsynchronous oscillation mode of the system under the condition that the wind power is changed in a large range.
Drawings
FIG. 1 is a flow chart of a damping control method adapted to random fluctuation of new energy according to the present invention;
FIG. 2 is a schematic diagram of a system architecture of a four-machine two-zone system according to an embodiment of the present invention;
fig. 3 is a schematic diagram of active power of a doubly-fed wind turbine in the embodiment of the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the damping control method adapted to the random fluctuation of new energy according to the present invention includes the following steps:
A. establishing a linear variable parameter system model of the new energy power system;
B. expressing the linear variable parameter system model by using a multicellular model;
C. using mixing of H2/H∞Controlling to solve a state feedback matrix for each vertex system;
D. and forming the self-adaptive damping controller according to the variable gain of the feedback matrix designed by the vertex.
The Jacobian linearization method is based on, and a nonlinear model of the power system considering the random drift behavior of the operating point can be converted into a linear variable parameter system. Linear variable parameter systems refer to systems whose state space matrix elements depend on a continuous time-varying parameter vector p (t). The variation of the parameter vector ρ (t) can be obtained by on-line measurement, and the variation range thereof is bounded and can be determined. For multiple targets H2/H∞The LPV system that controls the problem can be represented by a state space equation:
Figure BDA0002216013910000051
in the formula: x is a state vector of the wind power system, and u is a control input vector; w is an external disturbance input vector and is selected according to system disturbance; z is a radical of∞And z2Respectively represent and H∞And H2An output vector associated with the performance indicator; a is the system state matrix, B1Is a perturbation gain matrix; b is2Inputting a matrix for control; c∞，D∞1And D∞2Are respectively H∞Coefficient matrixes of performance index related state variables, disturbance inputs and control inputs; c2，D21And D22Are respectively H2Coefficient matrices for performance index related state variables, disturbance inputs and control inputs.
If there are m parameter variables in the variable parameter rho of the LPV system, the corresponding multicell type LPV system has N-2mAt each vertex, the system variable parameter p is at N related vertices b of the multicellular typekK is 1,2, …, N is constantly changed, that is, the variable parameter ρ satisfies:
Figure BDA0002216013910000061
at the same time, the state space matrix of the LPV system also varies within the multicellular matrix of N related vertices:
Figure BDA0002216013910000062
further using convex decomposition techniques, convex combinations of the vertex system matrices can be formed by varying the coefficient αkApproximating the actual system matrix, the error between the convex combination of the vertex system matrix and the actual system matrix can be measured by the difference L2 norm between the two matrices, as shown in equation (4). Let alphakChanging from 0 to 1, the step size is 0.01, and through the traversal calculation, the coefficient alpha when xi is minimum is selectedkTo represent the actual system matrix. The state space matrix of the multicellular LPV system can be represented by equation (5).
Figure BDA0002216013910000063
Figure BDA0002216013910000064
When the parameter ρ is determined, the LPV system transitions to a linear time invariant system:
Figure BDA0002216013910000065
and (3) substituting a state feedback rule u which is Kx into an open-loop system model formula (6) by adopting a state feedback design controller to obtain a closed-loop system model:
Figure BDA0002216013910000066
in the formula: a. thec＝A+B2K；C∞c＝C∞+D∞2K；C2c＝C2+D2K。
Introducing a positive definite matrix X, a symmetric matrix Q and a variable replacement Y which is KX to satisfy a system H∞Performance, H2The multi-objective control problem of performance and regional pole placement can be solved by solving the following linear inequality:
Figure BDA0002216013910000071
in the formula: l, M, gamma0，η0μ and β are parameters given to meet different design goals;
Figure BDA0002216013910000072
is the Kronecker product.
The vertex of the multicellular LPV system is a linear time-invariant system, and each vertex is connected
Figure BDA0002216013910000073
Substituting formula (8) to obtain state feedback matrix K of N vertexesk,k＝1,2,…,N。
Similar to the convex decomposition structure of LPV model, the vertex state feedback matrix KkAnd K is 1,2, …, wherein N is used as N vertexes of the multi-cell LPV controller, and a state feedback matrix K with global characteristics is obtained at an arbitrary position ρ of the multi-cell by using the idea of robust variable gain and the characteristics of a convex set of a multi-cell model system of the LPV:
Figure BDA0002216013910000074
example 2:
as shown in fig. 2, two doubly-fed wind turbines (DFIGs) are connected to a 4-machine 2-zone test system. The initial output active power of the two DFIGs is 0.3p.u., and small interference stability analysis is carried out on a test system, wherein the main oscillation mode is shown in Table 1. As can be seen from the table, the patterns 1 to 4 are subsynchronous oscillation patterns, and the subsynchronous oscillation is likely to occur because the damping is small. Modes 4-7 are low-frequency oscillation modes, and the damping performance is better.
TABLE 1 mode of system oscillation
Mode(s) Characteristic root Oscillation frequency/Hz Damping ratio
1 -0.3611±119.7502j 19.06 0.0030
2 -0.2848±107.5388j 17.12 0.0026
3 -0.1982±90.3861j 14.39 0.0022
4 -0.3034±74.8455j 11.91 0.0041
5 -3.9387±12.8940j 2.05 0.2921
6 -4.1875±11.8834j 1.89 0.3324
7 -4.0214±4.5343j 0.72 0.6635
Designing a damping controller:
and selecting time-varying parameter vectors capable of reflecting the random drift behavior of the system operating point as the output active power of the two DFIGs. And setting the random fluctuation range of the active power of the two DFIGs to be 0.3p.u. to 0.6p.u. according to the system operation condition. And establishing a multi-cell LPV model corresponding to the wind power system. The number of elements of the time-varying parameter vector of the test system is 2, and thus the number of vertices of the multicellular LPV system is 4. The DFIG active power of the top point 1 is 0.3 p.u.; the active power of DFIG1 in vertex 2 is 0.3p.u., and the active power of DFIG2 is 0.6 p.u.; the active power of DFIG1 in the vertex 3 is 0.6p.u., and the active power of DFIG2 is 0.3 p.u.; the DFIG active power of the top point 4 is 0.6 p.u.;
and adding a control signal of the damping controller to reactive power control and active power control of the fan rotor side converter. Comprehensive consideration of H∞Performance and H2Performance, using hybrid H2/H∞And solving the state feedback matrix of the vertex by the control design method. Calculating the coefficient alpha according to the actual operation point of the systemkAnd after the state feedback matrix of each vertex is obtained, the system self-adaptive damping controller can be obtained by using the formula (9). In a real power system, in generalThe measured values of all state variables of the system cannot be obtained, so that a state observer is designed to complete the estimation of the state variables of the system. The state observer imitates the linear model structure of an actual system and designs a same system to observe state variables.
And (3) damping effect analysis:
the damping controller is designed under the conditions that the active power of DFIG1 is 0.36p.u. and the active power of DFIG2 is 0.53p.u. in a test system. The operating point parameter vector is marked as [ 0.360.53 ], and the solution coefficient vector alpha is [ 0.040.760.20 ]. The subsynchronous oscillation characteristic values of the system before and after the introduction of the state feedback are shown in table 2. As can be seen from table 2, the damping controller improves the damping ratio of the subsynchronous oscillation mode of the system. The damping ratios of the subsynchronous oscillation modes of the closed-loop system are all larger than 0.1, and the controller meets the design requirement.
TABLE 2 SSO eigenvalues for open and closed loop systems
Figure BDA0002216013910000091
To further prove the effectiveness of the proposed adaptive damping controller, a time domain simulation was performed. At 1s, the active reference power of each DFIG is superposed with 5% of disturbance, and the disturbance is cleared after 0.02 s. Fig. 3 shows a time-domain simulation curve of the active power of the DFIG with an adaptive controller and an unadjusted controller. The dashed and solid lines represent the DFIG time domain simulation curves without the controller and with the adaptive controller, respectively. It can be seen that after the adaptive damping controller is put into use, the active power is attenuated quickly, and the system recovers stable operation faster.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (3)

1. A damping control method adapting to random fluctuation of new energy is characterized by comprising the following steps:
the method comprises the following steps: establishing a linear variable parameter system model of the new energy power system;
converting a power system nonlinear model of random drift behavior of an operating point into the linear variable parameter system model based on a Jacobian linearization method;
the state space matrix element of the linear variable parameter (LPV) system depends on a continuous time-varying parameter vector rho (t), the variation of the parameter vector rho (t) is obtained by online measurement, the variation range of the parameter vector rho (t) is bounded and determined;
step two: expressing the linear variable parameter system model by using a multicellular model;
in the second step, if there are m parameter variables in the parameter vector ρ of the linear variable parameter (LPV) system, the corresponding multicellular model of the LPV system has N-2mA system of parameter vectors rho at N associated vertices b of the polytopekK is 1,2, …, N is constantly changing, i.e. the parameter vector ρ satisfies equation (2):
Figure FDA0003150082540000011
the state space matrix of the linear variable parameter system also varies within the multicellular matrix of N related vertices according to equation (3):
Figure FDA0003150082540000012
by convex combination of the vertex system matrix by varying the coefficient alpha using a convex decomposition techniquekApproximating the actual system matrix, wherein the error xi between the convex combination of the vertex system matrix and the actual system matrix is measured by the difference L2 norm between the two matrixes, as shown in the formula (4) Shown in the figure:
Figure FDA0003150082540000013
αkchanging from 0 to 1, the step size is 0.01, and through the traversal calculation, the coefficient alpha when xi is minimum is selectedkTo represent the actual system matrix, the state space matrix of the multicellular linear variable parameter system is represented by equation (5):
Figure FDA0003150082540000021
step three: using mixing of H2/H∞Controlling to solve a state feedback matrix for each vertex system;
for multiple targets H2/H∞The linear variable parameter (LPV) system of the control problem is represented by a state space equation as formula (1):
Figure FDA0003150082540000022
in the formula: x is a power system state vector; u is a control input vector; w is an external disturbance input vector and is selected according to system disturbance; z is a radical of∞And z2Respectively represent and H∞And H2An output vector associated with the performance indicator; a is the system state matrix, B1Is a perturbation gain matrix; b is2Inputting a matrix for control; c∞，D∞1And D∞2Are respectively H∞Coefficient matrixes of performance index related state variables, disturbance inputs and control inputs; c2，D21And D22Are respectively H2Coefficient matrixes of performance index related state variables, disturbance inputs and control inputs;
step four: and forming the self-adaptive damping controller according to the state feedback matrix variable gain designed by the vertex.
2. The damping control method adapting to the random fluctuation of the new energy according to claim 1, characterized in that: in the third step, when p is determined, the linear variable parameter system is converted into a linear time-invariant system, as shown in formula (6):
Figure FDA0003150082540000023
and (3) adopting a state feedback design controller, substituting a state feedback rule u which is Kx and K which is a state feedback matrix into an open-loop system model formula (6) to obtain a closed-loop system model formula (7):
Figure FDA0003150082540000024
in the formula: a. thec＝A+B2K；C∞c＝C∞+D∞2K；C2c＝C2+D22K；
A positive definite matrix X, a symmetrical matrix Q and a variable Y are introduced to satisfy the requirement of a system H∞Performance, H2The multi-objective control problem of performance and regional pole allocation is solved by solving the linear inequality of equation (8):
Figure FDA0003150082540000031
in the formula: l, M, gamma0，η0μ and β are parameters given to meet different design goals;
Figure FDA0003150082540000032
is a Kronecker product;
the vertex of the multicellular linear variable parameter system is a linear time-invariant system, and each vertex is connected with a computer
Figure FDA0003150082540000033
Substituting formula (8) to obtain state feedback matrix K of N vertexesk，k＝1，2，…，N。
3. The damping control method adapting to the random fluctuation of the new energy according to claim 1, characterized in that: in the fourth step, the matrix K is fed back by the vertex statekAnd K is 1,2, …, where N is the N vertices of the controller of the multicellular linear variable parameter system, and at any position ρ of the multicellular system, the state feedback matrix K with global characteristics is obtained by using the robust variable gain and the features of the convex set of the multicellular model system of the linear variable parameter system, as shown in formula (9):
Figure FDA0003150082540000034
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