CN112965377B - Non-fragile robust control method of distributed power generation system - Google Patents

Non-fragile robust control method of distributed power generation system Download PDF

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CN112965377B
CN112965377B CN202110149000.8A CN202110149000A CN112965377B CN 112965377 B CN112965377 B CN 112965377B CN 202110149000 A CN202110149000 A CN 202110149000A CN 112965377 B CN112965377 B CN 112965377B
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孙伟
陶鹏
方昭
李帷韬
李奇越
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Hefei University of Technology
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Abstract

The invention discloses a non-fragile robust control method of a distributed power generation system, which comprises the following steps: aiming at the conditions of system jump, distributed delay and external disturbance of a distributed power generation system, establishing a discrete time distributed power generation system model, and then constructing a Lyapunov-Krasovski function to obtain sufficient conditions of random stability and non-fragile robust controller existence of the distributed power generation system; finally, calculating a controller gain matrix K corresponding to the system stability by continuously reducing the disturbance rejection rate gamma in the stability conditioniWhen the disturbance rejection rate gamma is minimum and the system is stable, the optimal controller gain matrix K is obtainedi *. The invention can improve the robustness of the system to disturbance, thereby ensuring the safe and stable operation of the distributed power generation system.

Description

Non-fragile robust control method of distributed power generation system
Technical Field
The invention relates to a distributed power generation system and a robust control theory, in particular to a non-fragile robust control method of the distributed power generation system.
Background
Distributed power generation is used as a new power generation form, various scattered energy sources including renewable energy sources and locally conveniently-obtained fossil fuels are used for power generation and energy supply, the distributed power generation has the characteristics of flexible configuration and scattering, the power supply reliability of the existing power grid can be effectively improved, and multiple targets of environmental protection, energy diversification and efficient utilization and the like are achieved. However, the distributed power generation system has a complex structure, the control performance of the distributed power generation system is greatly influenced by external disturbance and internal device change, and meanwhile, the distributed power generation system is connected with a user side load and directly supplies power consumption requirements of the user side, so that the distributed power generation system has important significance in ensuring that the distributed power generation system operates in a stable state.
In an actual control process, frequent actions of power electronic devices in the distributed power generation system increase the difficulty of control, and output characteristics of a large number of nonlinear devices in the system also adversely affect the stable operation of the system, so that the reliability and safety of the distributed power generation system are reduced. In addition, because the operating condition is complicated and changeable, the stability of the distributed power generation system can not meet the actual engineering design requirements only by analyzing, after the distributed power generation system is disturbed to be separated from the stable state in the actual operation, if the original stable state can not be recovered in time, the transmission power quality can be influenced, the power supply voltage and the frequency are unstable, the safety of the electrical equipment of a user can be directly influenced, and when the stable state can not be recovered for a long time, the whole power system can be even paralyzed.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a non-fragile robust control method of a distributed power generation system. The problems of system jumping, distributed delay and external disturbance of the distributed power generation system can be solved, so that the distributed power generation system has better robust performance, and the safe and stable operation of the distributed power generation system is ensured.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a non-fragile robust control method of a distributed power generation system, which is characterized by comprising the following steps of:
step 1: the distributed power generation system is subjected to linearization and discretization, so that a distributed power generation system model is obtained by using the formula (1):
Figure GDA0003478953030000011
in the formula (1), x (k) is a state vector containing frequency and voltage information of the distributed power generation system at the time k, u (k) is a control input quantity containing frequency and voltage information of the distributed power generation system at the time k, w (k) is external disturbance at the time k, and z (k) is a control output quantity containing output frequency and output voltage of the distributed power generation system at the time k; r iskThe method comprises the steps that a jump mode of a load is connected when different switches in a distributed power generation system are closed, the jump mode is a Markov chain which is evaluated along with time k in a finite set of lambda {1,2.., N }, and N is a positive integer; the mode transition probability of the mode i at the moment k to the mode j at the moment k +1 is piij＝Pr{rk+1＝j|rkI } and
Figure GDA0003478953030000021
A(rk)、B1(rk)、B2(rk)、C(rk) Is a chain r with MaerkovkCorrelation, four constant matrixes representing the jump characteristic of the distributed power generation system;
step 2: the state feedback controller is constructed using equation (2):
Figure GDA0003478953030000022
in the formula (2), K (r)k) Is a Markov chain rkTaking corresponding controller gain matrix when different values are taken, distributed transmission delay exists in a communication network for data communication, rho (l) is a probability density function of the distributed transmission delay, and x (k-l) isThe state vector of the system at time k-l, where l ∈ [1, h ∈ ]]H is the maximum transmission delay;
and step 3: obtaining a closed-loop distributed power generation system model by using the formula (3):
Figure GDA0003478953030000023
in the formula (3), the reaction mixture is,
Figure GDA0003478953030000024
is a kronecker product of m (l) and an n-dimensional unit matrix, where m (l) is a linearly independent function representing a delay probability density function ρ (l) and ρ (l) ═ bm (l), B is a constant matrix,
Figure GDA0003478953030000025
Figure GDA0003478953030000026
is a constant matrix; denotes the Markov chain r by ikTherefore A isi＝A(rk)、B1i＝B1(rk)、B2i＝B2(rk)、Ci＝C(rk)、Ki＝K(rk)；
And 4, step 4: constructing a function containing Lyapunov-Krasovski with time delay information by using an equation (4)
V(k)＝V1(k)+V2(k)+V3(k) (4)
In the formula (4), V (k) is a scalar function constructed for the distributed power generation system, and is used for checking the change rate of the sampling time k so as to judge the stability of the distributed power generation system, and V (k) is used for judging the stability of the distributed power generation system1(k)、V2(k)、V3(k) Consists of three parts, and comprises:
Figure GDA0003478953030000031
in the formula (5), PiSymmetric positive definite matrix corresponding to Mareckov chain i when different values are taken；
Figure GDA0003478953030000032
In the formula (6), Q1Is a symmetric positive definite matrix;
Figure GDA0003478953030000033
in the formula (7), Z1A symmetric positive definite matrix, wherein delta (k-l) ═ x (k +1-l) -x (k-l) represents the difference of state vectors of the system at the moment k +1-l and the moment k-l;
and 5: according to the Lyapunov stability theory and a linear matrix inequality analysis method, the sufficient conditions of the random stability and the existence of a robust controller of the distributed power generation system are obtained by using the formulas (8) and (9):
Figure GDA0003478953030000034
Pi＞0，Q1＞0，Z1＞0 (9)
in the formula (8), phiiIs a linear matrix containing unknown variables and having:
Φi＝Ξ1+Ξ2-γ2Ψ4 TΨ4 (10)
in the formula (10), γ is a disturbance suppression ratio;
in the formula (8), the reaction mixture is,
Figure GDA0003478953030000035
is a linear matrix containing unknown variables and having:
Figure GDA0003478953030000036
in the formula (11), the reaction mixture is,
Figure GDA0003478953030000037
corresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
in the formula (10), xi1Is a first linear matrix containing unknown variables and having:
Figure GDA0003478953030000038
in the formula (12), the reaction mixture is,
Figure GDA0003478953030000041
representing the following matrix P at different transition probabilities during system jumpiA correspondingly varying symmetric positive definite matrix
Figure GDA0003478953030000042
F represents a constant matrix obtained by summing 1 to h after multiplying m (l) which is linearly independent of the transpose of m by h, and
Figure GDA0003478953030000043
G1is a number 1 constant matrix and has:
Figure GDA0003478953030000044
in the formula (13), IρnIs a rho n dimensional identity matrix, 0nIs an n-dimensional zero matrix, 0ρnIs a rho n-dimensional zero matrix, 0ρn×nIs ρ n × n dimensional zero matrix, M (1) and M (h +1) are constant matrices calculated by function M (l), and M (l +1) -M (l) ═ mm (l), M is constant matrix;
in formula (12), G2Is a number 2 constant matrix and has:
Figure GDA0003478953030000045
in formula (12), G3Is a number 3 constant matrix and has:
G3＝diag(0n,Q1,-Q1,0n,0n) (15)
in the formula (15), diag (·) represents a diagonal matrix;
in formula (12), G4Is a number 4 constant matrix and has:
G4＝[In -I n 0n 0ρn×n 0n] (16)
in formula (12), G5Is a number 5 constant matrix and has:
G5＝[0ρn×n M(1) -M(h+1) M 0ρn×n] (17)
in the formula (10), xi2Is a second linear matrix containing unknown variables and having:
Figure GDA0003478953030000046
in the formula (18), YiSymmetric positive definite matrix corresponding to the Markov chain i with different values1Is a first constant matrix and has:
Ψ1＝[I n 0n 0n 0n×ρn 0n] (19)
in formula (18), Ψ2Is a second constant matrix and has:
Ψ2＝[0n In 0n 0n×ρn 0n] (20)
in formula (18), Ψ3Is a third constant matrix and has:
Ψ3＝[0ρn×n 0ρn×n 0ρn×n Iρn 0ρn×n] (21)
in formula (18), Ψ4Is a fourth constant matrix and has:
Ψ4＝[0n 0n 0n 0n×ρn In] (22)
step 6: judging whether the sufficient condition is satisfied, if so, indicating that a symmetric positive definite matrix exists
Figure GDA0003478953030000051
And matrix YiIf the distributed power generation system is randomly stable and meets the robust performance index, the gain matrix of the controller is
Figure GDA0003478953030000052
And executing step 7; otherwise, the distributed power generation system is not random and stable and does not meet the robust performance index, no controller gain matrix exists, and the calculation is stopped;
and 7: continuously reducing the disturbance suppression rate gamma, and returning to the step 6 for execution until the calculation is stopped, thereby selecting the minimum disturbance suppression rate gamma when the system is kept stable in all the calculation results*The corresponding controller gain matrix is used as the optimal controller gain matrix
Figure GDA0003478953030000053
Thereby utilizing the optimal controller gain matrix
Figure GDA0003478953030000054
And carrying out robust control on the distributed power generation system.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention researches a stable and robust control strategy of the distributed power generation system aiming at the distributed power generation system, simultaneously considers the influences of system parameter jumping, distributed delay and external disturbance, establishes a discrete-time closed-loop distributed power generation system model, and designs a non-fragile robust controller, thereby providing a solution for the stability and non-fragile robust control of the system, so that the distributed power generation system can still keep stable under the conditions and has better robust performance.
2. The distributed delay method has the advantages that the condition that the distributed delay exists in the system is considered, the Lyapunov-Krasovski function with the delay information is established, the distributed delay is analyzed and processed based on a summation inequality, sufficient conditions for stabilizing the distributed power generation system are obtained, the stable operation range of the distributed power generation system is improved, and therefore the conservation is reduced.
3. The optimal controller gain matrix K is obtained by optimizing the minimum disturbance rejection rate gammai *The distributed power generation system has better anti-interference performance to enhance the robustness of the system, so that the output of the distributed power generation system is reasonably controlled, the distributed power generation system can safely and stably operate, and the distributed power generation system has important significance for further development of a power system.
Drawings
FIG. 1 is a schematic diagram of a distributed power generation system;
FIG. 2 is a flow diagram of a closed-loop distributed power generation system non-fragile robust controller solution;
FIG. 3 is a system state response diagram without disturbance;
FIG. 4 is a system state response diagram under the effect of a disturbance.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
Referring to fig. 2, a non-fragile robust control method of a distributed power generation system includes the steps of:
step 1: establishing a discrete time closed-loop distributed power generation system model:
referring to fig. 1, considering that the distributed power generation system has system parameter jumps and external disturbances, its discrete time model is:
Figure GDA0003478953030000061
in the formula (1), x (k) is a state vector containing frequency and voltage information of the distributed power generation system at the time k, u (k) is a control input quantity containing frequency and voltage information of the distributed power generation system at the time k, w (k) is external disturbance at the time k, and z (k) is a control output quantity containing output frequency and output voltage of the distributed power generation system at the time k; r iskThe method represents the jump mode of the access load when different switches are closed in the distributed power generation system, and values are taken in a limited set of lambda (1, 2.., N) along with time kN is a positive integer; the mode transition probability of the mode i at the moment k to the mode j at the moment k +1 is piij＝Pr{rk+1＝j|rkI } and
Figure GDA0003478953030000062
A(rk)、B1(rk)、B2(rk)、C(rk) Is a chain r with MaerkovkCorrelation, four constant matrixes representing the jump characteristic of the distributed power generation system;
step 2: the state feedback controller is constructed using equation (2):
Figure GDA0003478953030000063
in the formula (2), K (r)k) Is a Markov chain rkTaking corresponding controller gain matrixes with different values, wherein distributed transmission delay exists in a communication network for data communication, rho (l) is a probability density function of the distributed transmission delay, x (k-l) is a state vector of a k-l time system, and l belongs to [1, h ∈ time]H is the maximum transmission delay;
and step 3: obtaining a closed-loop distributed power generation system model by using the formula (3):
Figure GDA0003478953030000071
in the formula (3), the reaction mixture is,
Figure GDA0003478953030000072
is a kronecker product of m (l) and an n-dimensional unit matrix, where m (l) is a linearly independent function representing a delay probability density function ρ (l) and ρ (l) ═ bm (l), B is a constant matrix,
Figure GDA0003478953030000073
Figure GDA0003478953030000074
is a constant momentArraying; denotes the Markov chain r by ikTherefore A isi＝A(rk)、B1i＝B1(rk)、B2i＝B2(rk)、Ci＝C(rk)、Ki＝K(rk)；
And 4, step 4: constructing a function containing Lyapunov-Krasovski with time delay information by using an equation (4)
V(k)＝V1(k)+V2(k)+V3(k) (4)
In the formula (4), V (k) is a scalar function constructed for the distributed power generation system, and is used for checking the change rate of the sampling time k so as to judge the stability of the distributed power generation system, and V (k) is used for judging the stability of the distributed power generation system1(k)、V2(k)、V3(k) Consists of three parts, and comprises:
Figure GDA0003478953030000075
in the formula (5), PiCorresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
Figure GDA0003478953030000076
in the formula (6), Q1Is a symmetric positive definite matrix;
Figure GDA0003478953030000077
in the formula (7), Z1A symmetric positive definite matrix, wherein delta (k-l) ═ x (k +1-l) -x (k-l) represents the difference of state vectors of the system at the moment k +1-l and the moment k-l;
and 5: according to the Lyapunov stability theory and a linear matrix inequality analysis method, sufficient conditions of random stability and robust controller existence of the distributed power generation system are obtained, and the method comprises the following steps:
step 5.1: based on the Lyapunov-Krasovski function constructed in the step 4, according to a Lyapunov stability theory and a linear matrix inequality analysis method, the random stability of the distributed power generation system is judged firstly, and sufficient conditions for the random stability of the distributed power generation system are obtained.
Forward differentiating the Lyapunov-Krasovski function V (k) to obtain Δ V (k) and having:
ΔV(k)＝ΔV1(k)+ΔV2(k)+ΔV3(k) (8)
in the formula (8), Δ V (k) is represented by Δ V1(k)、ΔV2(k)、ΔV3(k) Consists of three parts, and comprises:
Figure GDA0003478953030000081
in the formula (9), the reaction mixture is,
Figure GDA0003478953030000082
representing the following matrix P at different transition probabilities during system jumpiA correspondingly varying symmetric positive definite matrix
Figure GDA0003478953030000083
x (k +1-l) is a state vector of the system at the k +1-l moment;
ΔV2(k)＝xT(k)Q1x(k)-xT(k-h)Q1x(k-h) (10)
in the formula (10), x (k-h) is a state vector of a k-h time system;
Figure GDA0003478953030000084
in equation (11), δ (k) ═ x (k +1) -x (k) represents the difference between the state vectors of the system at the time k-l and the time k, δ (k-l) ═ x (k +1-l) -x (k-l) represents the difference between the state vectors of the system at the time k +1-l and the time k-l, F represents a constant matrix obtained by summing a linear independent function m (l) multiplied by its transpose from 1 to h, and F represents a constant matrix obtained by multiplying the linear independent function m (l) by its transpose
Figure GDA0003478953030000085
Defining a zero vector e (k) as:
Figure GDA0003478953030000091
in the formula (12), X1,X2,X3Is an unknown variable matrix;
defining a matrix epsilon (k) containing system state information, delay information and external disturbance as:
Figure GDA0003478953030000092
substituting equation (12) into equation (8) results in:
Figure GDA0003478953030000093
in the formula (14), xi1Is a linear matrix containing unknown variables and having:
Figure GDA0003478953030000094
in formula (15), G1Is a constant matrix and has:
Figure GDA0003478953030000095
in the formula (16), IρnIs a rho n dimensional identity matrix, 0nIs an n-dimensional zero matrix, 0ρnIs a rho n-dimensional zero matrix, 0ρn×nIs ρ n × n dimensional zero matrix, M (1) and M (h +1) are constant matrices calculated by function M (l), and M (l +1) -M (l) ═ mm (l), M is constant matrix;
in formula (15), G2Is a constant matrix and has:
Figure GDA0003478953030000096
in formula (15), G3Is a constant matrix and has:
G3＝diag(0n,Q1,-Q1,0n,0n) (18)
in the formula (18), diag (·) represents a diagonal matrix;
in formula (15), G4Is a constant matrix and has:
G4＝[In -I n 0n 0ρn×n 0n] (19)
in formula (15), G5Is a constant matrix and has:
G5＝[0ρn×n M(1) -M(h+1) M 0ρn×n] (20)
in the formula (14), the compound represented by the formula (I),
Figure GDA0003478953030000101
is a linear matrix containing unknown variables and having:
Figure GDA0003478953030000102
in formula (21), Ψ1Is a constant matrix and has:
Ψ1＝[In 0n 0n 0n×ρn 0n] (22)
in formula (21), Ψ2Is a constant matrix and has:
Ψ2＝[0n In 0n 0n×ρn 0n] (23)
in formula (21), Ψ3Is a constant matrix and has:
Ψ3＝[0ρn×n 0ρn×n 0ρn×n Iρn 0ρn×n] (24)
in formula (21), Ψ4Is a constant matrix and has:
Ψ4＝[0n 0n 0n 0n×ρn In] (25)
when the external disturbance w (k) is 0, if Δ v (k) < 0, Δ v (k) < 0 is equivalent to the following form:
Figure GDA0003478953030000103
according to Lyapunov theory of stability, when the external perturbation w (k) is 0, for a given positive integer h, if a symmetric positive definite matrix P existsi＞0，Q1＞0，Z1> 0 and matrix X1,X2,X3If the formula (26) is established, the closed-loop distributed power generation system shown in the formula (3) is randomly stable, and the step 5.2 is executed; otherwise step 5.2 cannot be performed.
Step 5.2: and judging whether the distributed power generation system has the robust disturbance suppression rate or not to obtain a sufficient condition that the distributed power generation system has the robust disturbance suppression rate gamma.
Under zero initial conditions, when the external disturbance w (k) ≠ 0, z is added to and subtracted from the right side of equation (14)T(k)z(k)-γ2wT(k) w (k), one can obtain:
Figure GDA0003478953030000104
in the formula (27), the reaction mixture is,
Figure GDA0003478953030000111
is a linear matrix containing unknown variables and having:
Figure GDA0003478953030000112
in the formula (28), γ is a disturbance suppression ratio;
in the formula (27), C is a constant matrix and has:
C＝CiΨ2 (29)
according to Schur's theorem, if:
Figure GDA0003478953030000113
and the following inequality holds:
ΔV(k)+zT(k)z(k)-γ2wT(k)w(k)＜0 (31)
according to Lyapunov stability theory, when the external disturbance w (k) ≠ 0, for a given positive integer h, if a symmetric positive definite matrix P existsi＞0，Q1＞0，Z1> 0 and matrix X1,X2,X3If equations (30) and (31) are satisfied, the closed-loop distributed power generation system shown in equation (3) has a robust disturbance rejection rate γ, and step 5.3 is executed; otherwise step 5.3 cannot be performed.
Step 5.3: solving for a non-fragile robust controller:
definition of
Figure GDA0003478953030000114
X is an unknown variable matrix, and X is made equal to X1＝X2＝X3，
Figure GDA0003478953030000115
Figure GDA0003478953030000116
Then it can be obtained from equation (30):
Figure GDA0003478953030000117
in the formula (32), phiiIs a linear matrix containing unknown variables and having:
Φi＝Ξ1+Ξ2-γ2Ψ4 TΨ4 (33)
in the formula (32), the compound represented by the formula (32),
Figure GDA0003478953030000118
is a linear matrix containing unknown variables and having:
Figure GDA0003478953030000119
in the formula (34), the reaction mixture is,
Figure GDA00034789530300001110
corresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
in the formula (33), xi2Is a linear matrix containing unknown variables and having:
Figure GDA00034789530300001111
in the formula (35), YiCorresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
according to Lyapunov's theory of stability, for a given positive integer h, if a symmetric positive definite matrix P existsi＞0，Q1＞0，Z1＞0，
Figure GDA0003478953030000121
And matrix YiIf the formula (32) is satisfied, the distributed power generation system is randomly stable and meets the robust performance index, and the gain matrix of the controller is
Figure GDA0003478953030000122
And executing the step 6; otherwise, the distributed power generation system is not random and stable and does not meet the robust performance index, no controller gain matrix exists, and the calculation is stopped;
step 6: continuously reducing the disturbance suppression rate gamma, and returning to the step 5 for execution until the calculation is stopped, thereby selecting the minimum disturbance suppression rate gamma when the system is kept stable in all the calculation results*The corresponding controller gain matrix is used as the optimal controller gain matrix
Figure GDA0003478953030000123
Thereby utilizing the optimal controller gain matrix
Figure GDA0003478953030000124
And carrying out robust control on the distributed power generation system.
Example (b):
by adopting the non-fragile robust control method of the distributed power generation system, the closed-loop distributed power generation system is randomly stable when w (k) is 0 under the condition of no external disturbance. When external disturbance exists, the system is also random and stable and has certain anti-interference capability. The specific implementation method comprises the following steps:
step 1: the controlled object is a closed-loop distributed power generation system, the state space model of the controlled object is a formula (3), and the system parameters are given as follows:
Figure GDA0003478953030000125
Figure GDA0003478953030000126
Figure GDA0003478953030000127
C1＝[-0.1 0] C2＝[-0.1 0] h＝4
the Markov chain state transition probability matrix is
Figure GDA0003478953030000128
Step 2: when the system has no external disturbance, i.e. w (k) is 0, the initial state is assumed to be x0＝[1 -0.5]T，x1＝[0.5 0.3]T，x2＝[0.2 0.1]T，x3＝[0.3 0.2]T，x4＝[0.1 0.1]TThe controller gain moment can be determinedArray is
K1＝[-4.3078 5.2064] K2＝[0.6358 -0.0044]
Under the action of the controller, the system state response is shown in fig. 3, and it can be seen from fig. 3 that the system state curve rapidly goes to 0, which indicates that the closed-loop system (3) is randomly stable under the action of the controller (2).
And step 3: when the system has external disturbance, the external disturbance is assumed to be
Figure GDA0003478953030000131
And assume an initial state of x0＝[1 -0.5]T，x1＝[0.5 0.3]T，x2＝[0.2 0.1]T，x3＝[0.3 0.2]T，x4＝[0.1 0.1]TThe controller gain matrix can be found as
K1＝[-4.6996 3.7702] K2＝[0.6873 -0.3960]
Under the action of the controller, the state motion track of the controlled system is shown in fig. 4. It can be seen that under the action of non-zero external disturbance, for a given positive real number γ, the closed-loop system (3) is randomly stable under the action of the controller (2) and meets a set robust performance index, and the corresponding robust performance index γ is 1.2.
And 4, step 4: and continuously reducing the disturbance rejection rate gamma, and obtaining an optimal controller gain matrix when the gamma is 1.0001:
K1 *＝[-4.0735 4.4806] K2 *＝[0.8311 -0.3506]
the present invention is not intended to be limited to the particular embodiments shown, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (1)

1. A non-fragile robust control method of a distributed power generation system, comprising the steps of:
step 1: the distributed power generation system is subjected to linearization and discretization, so that a distributed power generation system model is obtained by using the formula (1):
Figure FDA0002931473160000011
in the formula (1), x (k) is a state vector containing frequency and voltage information of the distributed power generation system at the time k, u (k) is a control input quantity containing frequency and voltage information of the distributed power generation system at the time k, w (k) is external disturbance at the time k, and z (k) is a control output quantity containing output frequency and output voltage of the distributed power generation system at the time k; r iskThe method comprises the steps that a jump mode of a load is connected when different switches in a distributed power generation system are closed, the jump mode is a Markov chain which is evaluated along with time k in a finite set of lambda {1,2.., N }, and N is a positive integer; the mode transition probability of the mode i at the moment k to the mode j at the moment k +1 is piij＝Pr{rk+1＝j|rkI } and
Figure FDA0002931473160000012
A(rk)、B1(rk)、B2(rk)、C(rk) Is a chain r with MaerkovkCorrelation, four constant matrixes representing the jump characteristic of the distributed power generation system;
step 2: the state feedback controller is constructed using equation (2):
Figure FDA0002931473160000013
in the formula (2), K (r)k) Is a Markov chain rkTaking corresponding controller gain matrixes with different values, wherein distributed transmission delay exists in a communication network for data communication, rho (l) is a probability density function of the distributed transmission delay, x (k-l) is a state vector of a k-l time system, and l belongs to [1, h ∈ time]H is the maximum transmission delay;
and step 3: obtaining a closed-loop distributed power generation system model by using the formula (3):
Figure FDA0002931473160000014
in the formula (3), the reaction mixture is,
Figure FDA0002931473160000015
is a kronecker product of m (l) and an n-dimensional unit matrix, where m (l) is a linearly independent function representing a delay probability density function ρ (l) and ρ (l) ═ bm (l), B is a constant matrix,
Figure FDA0002931473160000016
Figure FDA0002931473160000017
is a constant matrix; denotes the Markov chain r by ikTherefore A isi＝A(rk)、B1i＝B1(rk)、B2i＝B2(rk)、Ci＝C(rk)、Ki＝K(rk)；
And 4, step 4: constructing a function containing Lyapunov-Krasovski with time delay information by using an equation (4)
V(k)＝V1(k)+V2(k)+V3(k) (4)
In the formula (4), V (k) is a scalar function constructed for the distributed power generation system, and is used for checking the change rate of the sampling time k so as to judge the stability of the distributed power generation system, and V (k) is used for judging the stability of the distributed power generation system1(k)、V2(k)、V3(k) Consists of three parts, and comprises:
Figure FDA0002931473160000021
in the formula (5), PiCorresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
Figure FDA0002931473160000022
in the formula (6), Q1Is a symmetric positive definite matrix;
Figure FDA0002931473160000023
in the formula (7), Z1A symmetric positive definite matrix, wherein delta (k-l) ═ x (k +1-l) -x (k-l) represents the difference of state vectors of the system at the moment k +1-l and the moment k-l;
and 5: according to the Lyapunov stability theory and a linear matrix inequality analysis method, the sufficient conditions of the random stability and the existence of a robust controller of the distributed power generation system are obtained by using the formulas (8) and (9):
Figure FDA0002931473160000024
Pi＞0，Q1＞0，Z1＞0 (9)
in the formula (8), phiiIs a linear matrix containing unknown variables and having:
Φi＝Ξ1+Ξ2-γ2Ψ4 TΨ4 (10)
in the formula (10), γ is a disturbance suppression ratio;
in the formula (8), the reaction mixture is,
Figure FDA0002931473160000025
is a linear matrix containing unknown variables and having:
Figure FDA0002931473160000026
in the formula (11), the reaction mixture is,
Figure FDA0002931473160000031
corresponding symmetric positive definite matrixes are taken for the Markov chain i when different values are taken;
in the formula (10), xi1Is a first linear matrix containing unknown variables and having:
Figure FDA0002931473160000032
in the formula (12), the reaction mixture is,
Figure FDA0002931473160000033
representing the following matrix P at different transition probabilities during system jumpiA correspondingly varying symmetric positive definite matrix
Figure FDA0002931473160000034
F represents a constant matrix obtained by summing 1 to h after multiplying m (l) which is linearly independent of the transpose of m by h, and
Figure FDA0002931473160000035
G1is a number 1 constant matrix and has:
Figure FDA0002931473160000036
in the formula (13), IρnIs a rho n dimensional identity matrix, 0nIs an n-dimensional zero matrix, 0ρnIs a rho n-dimensional zero matrix, 0ρn×nIs ρ n × n dimensional zero matrix, M (1) and M (h +1) are constant matrices calculated by function M (l), and M (l +1) -M (l) ═ mm (l), M is constant matrix;
in formula (12), G2Is a number 2 constant matrix and has:
Figure FDA0002931473160000037
in formula (12), G3Is a number 3 constant matrix and has:
G3＝diag(0n,Q1,-Q1,0n,0n) (15)
in the formula (15), diag (·) represents a diagonal matrix;
in formula (12), G4Is a number 4 constant matrix and has:
G4＝[In -In 0n 0ρn×n 0n] (16)
in formula (12), G5Is a number 5 constant matrix and has:
G5＝[0ρn×n M(1) -M(h+1) M 0ρn×n] (17)
in the formula (10), xi2Is a second linear matrix containing unknown variables and having:
Figure FDA0002931473160000041
in the formula (18), YiSymmetric positive definite matrix corresponding to the Markov chain i with different values1Is a first constant matrix and has:
Ψ1＝[In 0n 0n 0n×ρn 0n] (19)
in formula (18), Ψ2Is a second constant matrix and has:
Ψ2＝[0n In 0n 0n×ρn 0n] (20)
in formula (18), Ψ3Is a third constant matrix and has:
Ψ3＝[0ρn×n 0ρn×n 0ρn×n Iρn 0ρn×n] (21)
in formula (18), Ψ4Is a fourth constant matrix and has:
Ψ4＝[0n 0n 0n 0n×ρn In] (22)
step 6: judging whether the sufficient condition is satisfied, if so, indicating that a symmetric positive definite matrix exists
Figure FDA0002931473160000042
And matrix YiIf the distributed power generation system is randomly stable and meets the robust performance index, the gain matrix of the controller is
Figure FDA0002931473160000043
And executing step 7; otherwise, the distributed power generation system is not random and stable and does not meet the robust performance index, no controller gain matrix exists, and the calculation is stopped;
and 7: continuously reducing the disturbance suppression rate gamma, and returning to the step 6 for execution until the calculation is stopped, thereby selecting the minimum disturbance suppression rate gamma when the system is kept stable in all the calculation results*The corresponding controller gain matrix is used as the optimal controller gain matrix
Figure FDA0002931473160000044
Thereby utilizing the optimal controller gain matrix
Figure FDA0002931473160000045
And carrying out robust control on the distributed power generation system.
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2407664A2 (en) * 2010-06-23 2012-01-18 Vestas Wind Systems A/S Method of Operating a Wind Turbine, Controller Usable for Operating a Wind Turbine, and Wind Turbine
CN104049533A (en) * 2013-03-11 2014-09-17 王岩 Network control system controller design method based on hidden semi-markov model
CN104950676A (en) * 2015-06-12 2015-09-30 华北电力大学 Time-varying electric power system self-adaption control method and device
CN106257873A (en) * 2016-07-16 2016-12-28 江南大学 A kind of uncatalyzed coking H ∞ fault tolerant control method of nonlinear network networked control systems
CN106647253A (en) * 2016-09-28 2017-05-10 南京航空航天大学 Aero-engine distributed control system multi-performance robust tracking control method
CN107947149A (en) * 2016-10-12 2018-04-20 河海大学 Power System Delay dependent robust based on Wirtinger inequality stablizes decision method
CN110212522A (en) * 2019-06-05 2019-09-06 河南理工大学 A kind of time_varying delay wide area power system method for analyzing stability
CN111381501A (en) * 2020-04-10 2020-07-07 杭州电子科技大学 Fault-tolerant control method of asynchronous system based on event trigger

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2407664A2 (en) * 2010-06-23 2012-01-18 Vestas Wind Systems A/S Method of Operating a Wind Turbine, Controller Usable for Operating a Wind Turbine, and Wind Turbine
CN104049533A (en) * 2013-03-11 2014-09-17 王岩 Network control system controller design method based on hidden semi-markov model
CN104950676A (en) * 2015-06-12 2015-09-30 华北电力大学 Time-varying electric power system self-adaption control method and device
CN106257873A (en) * 2016-07-16 2016-12-28 江南大学 A kind of uncatalyzed coking H ∞ fault tolerant control method of nonlinear network networked control systems
CN106647253A (en) * 2016-09-28 2017-05-10 南京航空航天大学 Aero-engine distributed control system multi-performance robust tracking control method
CN107947149A (en) * 2016-10-12 2018-04-20 河海大学 Power System Delay dependent robust based on Wirtinger inequality stablizes decision method
CN110212522A (en) * 2019-06-05 2019-09-06 河南理工大学 A kind of time_varying delay wide area power system method for analyzing stability
CN111381501A (en) * 2020-04-10 2020-07-07 杭州电子科技大学 Fault-tolerant control method of asynchronous system based on event trigger

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
《2004 43rd IEEE Conference on Decision and Control (CDC)》;V.A. Ugrinovskii,et al.;《Decentralized control of power systems via robust control of uncertain Markov jump parameter systems》;20041231;第4卷;全文 *
中立随机马尔科夫跳变系统延迟反馈控制器设计;庄光明 等;《聊城大学学报（自然科学版）》;20181231;第31卷(第4期);全文 *

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