CN105552934B - The networked power system loading control method for frequency that time lag distribution relies on - Google Patents
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Abstract
The invention discloses the networked power system loading control method for frequency that a kind of distribution of time lag relies on.The present invention establishes the networked power system stochastic Time-Delay LFC dynamic model for considering time lag probability distribution, the model has fully considered the non-homogeneous probability density characteristics of time-varying communication delay, the system stability analysis with lower conservative is obtained compared to conventional junction opinion and controls comprehensive related conclusions, and can guarantee to obtain desired control performance.A kind of novel liapunov function is used during carrying out system stability analysis and synthesis, system time lags distribution is obtained using method of convex combination relies on the comprehensive related conclusions of stable analysis and control, it avoids introducing extra free-form curve and surface in calculating process, so that operation time greatly reduces, control and operation efficiency are improved.Significant improvement has been obtained the invention enables the control effect of networked power system loading frequency control and has been promoted.
Description
Technical Field
The invention relates to a load frequency control method of a power system, in particular to a time lag distribution dependent networked power system load frequency control method.
Background
Load Frequency Control (LFC) is an important Control means for ensuring stable operation of an electric power system. In a traditional load frequency control strategy of a power system, a communication connection mode between nodes is a point-to-point private line communication mode, and a measurement and control signal is transmitted in a private line, wherein extremely small delay exists, and the measurement and control signal is generally ignored when an LFC control strategy is designed. With the development of the technology, in a market-oriented power system load frequency control strategy for deregulation, a power communication network based on a transmission control protocol/internet protocol (TCP/IP) is more and more widely applied, and compared with a traditional private line communication mode, the communication strategy of the power communication network based on the TCP/IP protocol can greatly reduce the construction cost of the communication network and has the advantage of more flexibility. However, with the widespread use of power communication networks based on TCP/IP protocol, if the non-negligible time-varying network-induced delay existing in the power communication networks cannot be handled well, the control performance of the power system will be greatly reduced, and even the entire system will be unstable, which brings new challenges to the analysis, synthesis and design of the load frequency control strategy of the power system.
In conventional network control models, it is generally assumed that time-varying communication delays are evenly distributed. In actual network communications, time-varying network delays are typically distributed non-uniformly over a time interval. The highly conservative result obtained based on the traditional assumption is increasingly unable to guarantee the safe and stable operation of the networked power system. How to deal with the problem of non-uniform distribution of time-varying network delay in a networked power system is also a big problem that researchers are dedicated to solve.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a time-lag distribution dependent load frequency control method of a networked power system, aiming at the problem that only time delay or uniformly distributed time-varying delay is considered in the traditional load frequency control of the networked power system, the non-uniform probability distribution characteristic of time-varying communication time delay is fully considered, and a networked random time-lag probability distribution LFC model is established; a novel Lyapunov function is constructed, a system time-lag distribution dependence stability analysis and control comprehensive related conclusion is obtained by utilizing a convex combination method, the conservative property is lower compared with the traditional conclusion, and the introduction of redundant free weight matrixes is avoided in the calculation process, so that the calculation time is greatly reduced, and the control and calculation efficiency is improved.
In order to achieve the above object, the technical solution of the present invention is:
a time lag distribution dependent networked power system load frequency control method comprises the following specific steps:
1. establishing a networked power system random time lag LFC dynamic model considering time lag probability distribution:
(1) establishing a networked power system LFC dynamic model considering communication time lag:
where x (t) is the state vector of the system,is the derivative of x (t) with respect to time t, u (t) Ky t (t)]Is the control input of the system, K is the controller gain matrix of the system, τ (t) is the time varying communication delay in the power communication network, ω (t) is the energy bounded disturbance signal, y (t) is the control output of the system, a, B, F, C are constant coefficient matrices with appropriate dimensions.
(2) Establishing a time lag probability distribution model of network induced delay in a power communication network based on a TCP/IP protocol:
in a power communication network based on a TCP/IP protocol, communication delay is non-uniformly distributed within a certain time interval according to a certain probability. The induced delay tau (t) of the time-varying network is set to conform to the following probability distribution:
Prob[τ(t)∈[τ1,τ2)]＝δ,Prob[τ(t)∈[τ2,τ3)]＝1-δ。
wherein, tau1,τ2,τ3The delay is the lower bound of the delay, the critical value of the delay distribution and the upper bound of the delay of tau (t).
Two successive time intervals are defined: omega1＝{t:τ(t)∈[τ1,τ2)}，Ω2＝{t:τ(t)∈[τ2,τ3)}，
Defining a random variable:
then
Defining:
where 0 ≦ δ ≦ 1, Ε { δ (t) } is the mathematical expectation of δ (t).
(3) Establishing a time-lag probability distribution dependent networked power system LFC dynamic model:
and (2) combining the steps (1) and (2) to obtain the networked power system LFC dynamic model considering the time lag probability distribution.
2. System time lag distribution dependence stability analysis and controller synthesis related conclusion
(1) Given the H of the system∞Performance conditions
Given a normal number τ1,τ2,τ3μ, δ, for a given disturbance rejection level γ > 0 and a control gain matrix K ifThere is a symmetric matrix P > 0, Q of appropriate dimensionsi＞0(i＝0,1,...,4),R0> 0 andso that the wireNature matrix inequalityIt is true that the first and second sensors,
wherein:
a11＝PA+ATP+Q0-R0+CTC,a21＝R0,a31＝δCTKTBTP,a51＝(1-δ)CTKTBTP,a71＝FTP,
a22＝-Q0+Q1-R0-R1,a32＝R1-U1,a42＝U1,a33＝-(1-μ)(Q1-Q2)-2R1+U1+U1 T,a43＝R1-U1,
a44＝-Q2+Q3-R1-R2,a54＝R2-U2,a64＝U2,a55＝-(1-μ)(Q3-Q4)-2R2+U2+U2 T,a65＝R2-U2,
a66＝-R2-Q4,a77＝-γ2I
Γl1＝col{τ1R0Ψl-1,(τ2-τ1)R1Ψl-1,(τ3-τ2)R2Ψl-1}(l＝2,3)
Γ22＝-diag{R0,R1,R2}
Ψ1＝[A,0,δBKC,0,(1-δ)BKC,0,F],Ψ2＝[0,0,BKC,0,-BKC,0,0]
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma.
(2) Determining a controller gain matrix K
Given a normal number τ1,τ2,τ3μ, δ, ε → 0 and disturbance suppression level γ> 0, if symmetry of the appropriate dimension existsMatrix arrayFull rank matrix M of appropriate dimensions and arbitrary momentsArray N makes linear matrix inequalityAndis established
Wherein:
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma. Solving the inequality condition of the matrix can obtain the gain matrix K-NM of the controller-1。
(3) And (c) establishing an output feedback controller u (t) ═ KCx [ t-tau (t) ].
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable technical progress:
the invention establishes a networked power system random time-delay load frequency control dynamic model considering time-delay probability distribution, and the model fully considers the non-uniform probability distribution characteristic of time-varying communication delay in a power communication network based on a TCP/IP protocol; a novel Lyapunov function is constructed in the process of analyzing and synthesizing the system stability, a convex combination method is used for obtaining a system time-lag probability distribution dependence stability analysis and control synthesis related conclusion, and the introduction of redundant free weight matrixes is avoided in the calculation process. Compared with the traditional LFC model and control strategy, the conclusion of the method is lower in conservative property, so that the control efficiency of load frequency control of the networked power system is obviously improved and promoted.
Drawings
Fig. 1 is a networked power system random time-lag load frequency control dynamic model considering time-lag probability distribution.
Fig. 2 is a flow chart of a system control method of the present invention.
Fig. 3 shows the state response curve and the time lag of the dynamic model (3) when τ (t) < 0.8343s, Prob { τ (t) ∈ [0,0.5s) } is 0.3, and Prob { τ (t) ∈ [0.5s,0.8343s) } is 0.7.
Detailed Description
The preferred embodiments of the present invention are described below with reference to the accompanying drawings:
the first embodiment is as follows:
referring to fig. 1 and fig. 2, the time lag distribution dependent networked power system load frequency control method includes the following operation steps:
(1) establishing a networked power system LFC dynamic model considering communication time lag;
(2) establishing a time lag probability distribution model of network induced delay in a power communication network based on a TCP/IP protocol;
(3) establishing a time-lag probability distribution dependent networked power system LFC dynamic model;
(4) given H of the system∞Performance conditions;
(5) a controller gain matrix K is determined.
Example two:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
1. the step (1) is to establish a networked power system LFC dynamic model considering communication time lag:
wherein: x (t) is the state vector of the system,is the derivative of x (t) with respect to time t, u (t) Ky t (t)]Is the control input of the system, K is the gain matrix of the system controller to be solved, τ (t) is the time-varying communication delay in the power communication network based on the TCP/IP protocol, τ (t)1≤τ(t)≤τ3，Is the derivative of τ (t) with respect to time t, τ1，τ3Respectively is a lower delay bound and an upper delay bound of the network communication delay, and mu is a normal number smaller than 1; ω (t) is the energy-bounded disturbance signal, y (t) is the control output of the system, and A, B, F, C are constant coefficient matrices of appropriate dimensions.
2. The step (2) establishes a time lag probability distribution model of network induced delay in the power communication network based on the TCP/IP protocol:
in a power communication network based on a TCP/IP protocol, communication delay is non-uniformly distributed within a certain time interval according to a certain probability. The induced delay tau (t) of the time-varying network is set to conform to the following probability distribution:
Prob[τ(t)∈[τ1,τ2)]＝δ,Prob[τ(t)∈[τ2,τ3)]＝1-δ。
wherein, tau1,τ2,τ3The delay is the lower bound of the delay, the critical value of the delay distribution and the upper bound of the delay of tau (t).
Two successive time intervals are defined: omega1＝{t:τ(t)∈[τ1,τ2)}，Ω2＝{t:τ(t)∈[τ2,τ3)}，
Defining a random variable:
then
Defining:
where 0 ≦ δ ≦ 1, Ε { δ (t) } is the mathematical expectation of δ (t).
3. Establishing a time-lag probability distribution dependence networked power system LFC dynamic model in the step (3):
and (3) combining the steps (1) and (2) to obtain a networked power system LFC dynamic model considering time-lag probability distribution as follows.
4. The step (4) gives H of the system∞Performance conditions were as follows:
given a normal number τ1,τ2,τ3μ, δ, for a given disturbance rejection level γ > 0 and a control gain matrix K ifThere is a symmetric matrix P > 0, Q of appropriate dimensionsi＞0(i＝0,1,...,4),R0> 0 andso that the wireNature matrix inequalityIt is true that the first and second sensors,
wherein:
a11＝PA+ATP+Q0-R0+CTC,a21＝R0,a31＝δCTKTBTP,a51＝(1-δ)CTKTBTP,a71＝FTP,
a22＝-Q0+Q1-R0-R1,a32＝R1-U1,a42＝U1,a33＝-(1-μ)(Q1-Q2)-2R1+U1+U1 T,a43＝R1-U1,
a44＝-Q2+Q3-R1-R2,a54＝R2-U2,a64＝U2,a55＝-(1-μ)(Q3-Q4)-2R2+U2+U2 T,a65＝R2-U2,
a66＝-R2-Q4,a77＝-γ2I
Γl1＝col{τ1R0Ψl-1,(τ2-τ1)R1Ψl-1,(τ3-τ2)R2Ψl-1}(l＝2,3)
Γ22＝-diag{R0,R1,R2}
Ψ1＝[A,0,δBKC,0,(1-δ)BKC,0,F],Ψ2＝[0,0,BKC,0,-BKC,0,0]
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma.
5. The step (5) determines a controller gain matrix K:
given a normal number τ1,τ2,τ3μ, δ, ε → 0 and the perturbation suppression level γ > 0 if symmetry of appropriate dimension existsMatrix arrayFull rank matrix M of appropriate dimensions and arbitrary momentsArray N makes linear matrix inequalityAndwherein:
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma. Solving the inequality condition of the matrix can obtain the gain matrix K-NM of the controller-1；
And (c) establishing an output feedback controller u (t) ═ KCx [ t-tau (t) ].
Example three:
the time lag distribution dependent networked power system load frequency control method comprises the following steps:
firstly, establishing a networked power system random time lag LFC dynamic model considering time lag probability distribution
1. Establishing networked power system LFC dynamic model considering communication time lag
The power system is a complex nonlinear dynamic system, and because the load change of the power system is small during normal operation, a linearized model can be used near the operating point of the power system to represent the system dynamics, and a linearized power system LFC dynamic model considering the communication time lag of the power communication network is shown in FIG. 1. From FIG. 1, the following relationship can be obtained:
the system state equation can then be derived as follows:
wherein,ω(t)＝ΔPd，
wherein the state variables Δ f, Δ Pm，ΔPvAnd Δ PdFrequency deviation, mechanical power deviation, regulating valve position and load of the networked LFC control system are respectively; r, M, D, Tch,TgThe control method comprises the steps of respectively obtaining a speed drop coefficient, a generator rotational inertia, a damping coefficient, a steam capacity time constant and a speed regulator time constant, β is a conversion coefficient of system power and frequency, and ACE is a regional control error signal of the system.
Taking ACE as a control input of a PI controller to be solved, then:
u(t)＝KPACE(t)+KI∫ACE(t)
KP,KIrespectively, the proportional gain and the integral gain of the PI controller to be solved.
Definition ofy(t)＝[ACE(t) ∫ACE(t)]T，K＝[KP KI]And establishing a networked power system LFC output feedback dynamic model considering communication time lag according to the basis:
wherein:
x (t) is the state vector of the system,is the derivative of x (t) with respect to time t, u (t) Ky t (t)]Is the control input of the system, K is the gain matrix of the system controller to be solved, τ (t) is the time-varying communication delay in the power communication network based on the TCP/IP protocol, τ (t)1≤τ(t)≤τ3，Is the derivative of τ (t) with respect to time t, τ1,τ3Respectively is a lower delay bound and an upper delay bound of the network communication delay, and mu is a normal number smaller than 1; ω (t) is the energy-bounded disturbance signal, y (t) is the control output of the system, and A, B, F, C are constant coefficient matrices of appropriate dimensions.
2. Establishing a time lag probability distribution model of network induced delay in a power communication network based on a TCP/IP protocol
In a conventional LFC control model of a networked power system, network-induced delays in a communication network are generally assumed to be constant delays or uniformly distributed time-varying communication delays. Network-induced delay in a power communication network based on a TCP/IP protocol is generally time-varying and has a non-uniform distribution characteristic, and the time-varying communication delay is non-uniformly distributed according to a certain probability in a certain time interval.
In the embodiment, the power communication network experiment platform based on the TCP/IP protocol, which is constructed in the automation key laboratory of the power station of the university in the Shanghai, is used for measuring and researching the communication delay of 25000 data packets, and the data shown in fig. 2, fig. 3 and table 1 are obtained. The graph and the table show that 62.532% of the data packets have communication delay within a time interval [0.15s 0.79s), 95.472% of the data packets have communication delay within a time interval [0.15s 1.11s), and analysis results show that the time-varying communication delay of the data packets transmitted in the power communication network based on the TCP/IP protocol has strong non-uniform distribution characteristics.
According to the invention, the non-uniform distribution characteristic of time-varying communication delay is fully considered in the modeling and analyzing process of the LFC of the networked power system, so that the conclusion that the result has lower conservatism compared with the result based on the traditional hypothesis is expected to be obtained.
In a power communication network based on a TCP/IP protocol, communication delay is non-uniformly distributed within a certain time interval according to a certain probability. The induced delay tau (t) of the time-varying network is set to conform to the following probability distribution:
Prob[τ(t)∈[τ1,τ2)]＝δ,Prob[τ(t)∈[τ2,τ3)]＝1-δ。
wherein, tau1,τ2,τ3The delay is the lower bound of the delay, the critical value of the delay distribution and the upper bound of the delay of tau (t).
Two successive time intervals are defined: omega1＝{t:τ(t)∈[τ1,τ2)}，Ω2＝{t:τ(t)∈[τ2,τ3)}，
Defining a random variable:
then
Defining:
where 0 ≦ δ ≦ 1, Ε { δ (t) } is the mathematical expectation of δ (t),
3. establishing LFC dynamic model of time-lag probability distribution dependent networked power system
Based on the LFC dynamic model and the time-lag probability distribution model of the networked power system, the following time-lag distribution dependent feedback control law can be obtained:
u(t)＝δ(t)Ky[t-τ1(t)]+[1-δ(t)]Ky[t-τ2(t)]
and combining the networked power system LFC dynamic model (2) considering the communication time lag as described above to obtain the following time lag probability distribution dependence networked power system LFC dynamic model:
the purpose of this embodiment is to utilize the proposed time lag probability distribution to rely on the networked power system LFC dynamic model (3) to analyze and design, reduce the traditional conclusion conservatism and ensure to obtain the expected control performance.
Second, the design principle and method of PI controller in this embodiment
The present embodiment aims to provide a time lag distribution dependent networked power system load frequency control method, which obtains a system time lag distribution dependent stability analysis and control comprehensive related conclusion, has lower conservatism compared with a conventional conclusion, and improves control and operation efficiency while ensuring to obtain a desired control performance. For this reason, the following theorem is given to determine the controller gain matrix K.
1. Given H of the system∞Performance conditions
Theorem 1: given a normal number τ1,τ2,τ3Mu, delta, for a given disturbance rejection level gamma > 0 and a control gain matrixK, Q if there is a symmetric matrix P > 0 of appropriate dimensionsi＞0(i＝0,1,...,4),R0> 0 andmake the linear matrix inequalityIt is true that the first and second sensors,
wherein:
a11＝PA+ATP+Q0-R0+CTC,a21＝R0,a31＝δCTKTBTP,a51＝(1-δ)CTKTBTP,a71＝FTP,
a22＝-Q0+Q1-R0-R1,a32＝R1-U1,a42＝U1,a33＝-(1-μ)(Q1-Q2)-2R1+U1+U1 T,a43＝R1-U1,
a44＝-Q2+Q3-R1-R2,a54＝R2-U2,a64＝U2,a55＝-(1-μ)(Q3-Q4)-2R2+U2+U2 T,a65＝R2-U2,
a66＝-R2-Q4,a77＝-γ2I
Γl1＝col{τ1R0Ψl-1,(τ2-τ1)R1Ψl-1,(τ3-τ2)R2Ψl-1}(l＝2,3)
Γ22＝-diag{R0,R1,R2}
Ψ1＝[A,0,δBKC,0,(1-δ)BKC,0,F],Ψ2＝[0,0,BKC,0,-BKC,0,0]
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma.
In the embodiment, a novel Lyapunov function is adopted, a convex combination method is utilized to obtain a system time-lag distribution dependence stability analysis and control comprehensive related conclusion, and compared with the traditional conclusion, the method has lower conservatism, and redundant free weight matrixes are avoided from being introduced in the calculation process, so that the calculation time is greatly reduced, and the control and calculation efficiency is improved.
2. Determining a controller gain matrix K
Definition of X ═ P-1To, forLinear matrix inequalityDiagonal matrix with two sides respectively taking left and taking rightAnd transposing, the following theorem can be obtained:
theorem 2: for a given normal number τ1,τ2,τ3Mu, delta and disturbance suppression level gamma > 0, if appropriate dimensionedSymmetric matrixAndmake the linear matrix inequalityIs established
Wherein:
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma.
Note the linear matrix inequalityContains coupled nonlinear term BKCX, theorem 2The controller gain matrix K cannot be directly found.
Definition ofThe following theorem can be obtained:
theorem 3: given a normal number τ1,τ2,τ3μ, δ, ε → 0 and the perturbation suppression level γ > 0 if the appropriate dimension existsOf the symmetric matrixFull rank matrix M of appropriate dimension andarbitrary matrix N makes linear matrix inequalityAndis established
Wherein:
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma. Solving the inequality condition of the matrix can obtain the gain matrix K-NM of the controller-1。
Establishing an output feedback controller u (t) ═ KCx [ t- τ (t) ]
Third, example analysis
An example analysis was performed on the single-area networked power system shown in fig. 1.
Relevant parameters of the single-area networked power system shown in fig. 1 are shown in table 1:
| Tch(s) | Tg(s) | R | D | β | M(s) |
| 0.3 | 0.1 | 0.05 | 1.0 | 21.0 | 10 |
TABLE 1 Single-regional networked Power System related parameters
Take tau1＝0,τ2When the theorem 3 is used, the upper time delay bound τ can be obtained by 0.4, 0.5 μ, 0.3 δ, 10 γ, and 0.01 ═ γ30.8491, the controller gain matrix K is 0.00060.0774]Compared with the traditional control method which does not consider the probability distribution of the network communication delay time lag, the method of the embodiment has lower conservatism.
Is provided with
For 0 ≦ τ (t) < 0.8343s, Prob { τ (t) ∈ [0,0.5s) } 0.3, Prob { τ (t) ∈ [0.5s,0.8343s) } 0.7, K ≦ 0.00020.0786]，||y(t)||2＝1.3499×10-7,||ω(t)||20.04, thus γ*0.0018 < gamma 10, the invention is proved to be capable of ensuring that the expected control performance is obtained while the conservation of the traditional conclusion is reduced.
According to the invention, a networked power system random time delay LFC dynamic model considering time delay probability distribution is established, the model fully considers the non-uniform probability distribution characteristic of time-varying communication time delay, compared with the traditional conclusion, the system stability analysis and control comprehensive related conclusion with lower conservatism is obtained, and the expected control performance can be ensured to be obtained. A novel Lyapunov function is adopted in the process of analyzing and synthesizing the system stability, a convex combination method is utilized to obtain a system time-lag distribution dependence stability analysis and control synthesis related conclusion, and redundant free weight matrixes are avoided from being introduced in the calculation process, so that the calculation time is greatly reduced, and the control and calculation efficiency is improved. The invention obviously improves and promotes the control effect of the load frequency control of the networked power system.
Claims (5)
1. A time lag distribution dependent networked power system load frequency control method is characterized by comprising the following operation steps:
(1) establishing a networked power system LFC dynamic model considering communication time lag, wherein the LFC dynamic model comprises the following steps:
wherein: x (t) is the state vector of the system,is the derivative of x (t) over time t, u (t) ═ Ky [ t- τ (t)]Is the control input of the system, K is the gain matrix of the system controller to be solved, τ (t) is the time-varying communication delay in the power communication network based on the TCP/IP protocol, τ (t)1≤τ(t)≤τ3， Is the derivative of τ (t) with respect to time t, τ1,τ3Respectively is a lower delay bound and an upper delay bound of the network communication delay, and mu is a normal number smaller than 1; ω (t) is the energy-bounded disturbance signal, y (t) is the control output of the system, A, B, F, C are constant coefficient matrices of appropriate dimensions, specifically:
R,M,D,Tch,Tgthe speed drop coefficient, the generator rotational inertia, the damping coefficient, the steam capacity time constant and the speed regulator time constant are respectively β which is the conversion coefficient of the system power and frequency;
(2) establishing a time lag probability distribution model of network induced delay in a power communication network based on a TCP/IP protocol;
(3) establishing a time-lag probability distribution dependent networked power system LFC dynamic model;
(4) given H of the system∞Performance conditions;
(5) a controller gain matrix K is determined.
2. The time lag distribution dependent networked power system load frequency control method according to claim 1, wherein the step (2) establishes a time lag probability distribution model of network-induced delay in the power communication network based on the TCP/IP protocol: in a power communication network based on a TCP/IP protocol, communication delay is non-uniformly distributed within a certain time interval according to a certain probability; the induced delay tau (t) of the time-varying network is set to conform to the following probability distribution:
Prob[τ(t)∈[τ1,τ2)]＝δ,Prob[τ(t)∈[τ2,τ3)]＝1-δ
wherein, tau1,τ2,τ3Respectively is a delay lower bound, a delay distribution critical value and a delay upper bound of tau (t);
two successive time intervals are defined: omega1＝{t:τ(t)∈[τ1,τ2)}，Ω2＝{t:τ(t)∈[τ2,τ3)}，
Defining a random variable:
then
Defining:
where 0 ≦ δ ≦ 1, Ε { δ (t) } is the mathematical expectation of δ (t).
3. The time-lag distribution dependent networked power system load frequency control method according to claim 2, wherein the step (3) establishes a time-lag probability distribution dependent networked power system LFC dynamic model:
combining the steps (1) and (2) to obtain the networked power system LFC dynamic model considering the time-lag probability distribution;
δ (t) is a random variable.
4. The time lag distribution dependent networked power system load frequency control method of claim 1, wherein said step (4) gives the H of the system∞Performance conditions were as follows:
given a normal number τ1,τ2,τ3Mu, delta, for a given disturbance rejection level gamma > 0 and a control gain matrix K, Q if a symmetric matrix P > 0 of appropriate dimensions existsi＞0(i＝0,1,...,4),R0> 0 andmake the linear matrix inequalityIt is true that the first and second sensors,
wherein:
a11＝PA+ATP+Q0-R0+CTC,a21＝R0,a31＝-δCTKTBTP,a51＝(δ-1)CTKTBTP,a71＝FTP,
a22＝-Q0+Q1-R0-R1,a32＝R1-U1,a42＝U1,a33＝-(1-μ)(Q1-Q2)-2R1+U1+U1 T,a43＝R1-U1,
a44＝-Q2+Q3-R1-R2,a54＝R2-U2,a64＝U2,a55＝-(1-μ)(Q3-Q4)-2R2+U2+U2 T,a65＝R2-U2,
a66＝-R2-Q4,a77＝-γ2I
Γl1＝col{τ1R0Ψl-1,(τ2-τ1)R1Ψl-1,(τ3-τ2)R2Ψl-1}(l＝2,3)
Γ22＝-diag{R0,R1,R2}
Ψ1＝[A,0,-δBKC,0,(δ-1)BKC,0,F],Ψ2＝[0,0,-BKC,0,BKC,0,0]
the above-described networked power system considering the time-lag probability distribution is asymptotically stable and has H∞Norm bound gamma.
5. The time lag distribution dependent networked power system load frequency control method of claim 1, wherein said step (5) determines a controller gain matrix K:
given a normal number τ1,τ2,τ3μ, δ, ε → 0 and the disturbance rejection level γ > 0 if a symmetric matrix of appropriate dimensions existsThe full-rank matrix M and the arbitrary matrix N of appropriate dimensions make the linear matrix inequalityAndit is true that the first and second sensors,
wherein:
then the above considerations applyNetworked power system with time-lag probability distribution is asymptotically stable and has H∞The norm boundary gamma, and the controller gain matrix K is obtained by solving the inequality condition of the matrix-1；
And (4) establishing an output feedback controller u (t) -KCx [ t-tau (t) ].
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