Non-Vulnerable Fault-Tolerant Load Frequency Control Method for Multi-Area Power System

Abstract

The present invention discloses a non-fragile fault-tolerant load frequency control method for a multi-area power system. To address the issue that faults in a multi-area power system can affect actual production and life, we introduce an important control method in the power system, namely load frequency control, and make corresponding improvements. First, based on the distribution characteristics of minor faults and severe faults, a stochastic distribution model of local faults is established. Then, considering the specific situation of controller gain perturbation, we take into account both multiplicative perturbation and additive perturbation in controller design. Next, considering different transmission delays, the multi-area power system is modeled as a multi-delay system, and a new non-fragile H ∞ A fault-tolerant load frequency control scheme is proposed, and the problem of handling coupling terms is transformed into the W problem in the fault-tolerant load frequency controller. Finally, the feasibility of the method is verified through numerical examples.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control of electronic systems, and specifically refers to a non-fragile fault-tolerant load frequency control method for a multi-area power system. Background Art

[0002] The power system is one of the most important parts in the development of modern society, and is closely related to both people's daily life and the production and operation of enterprises and factories. With the development of society and the progress of science and technology, the power system has become the basis for the survival of mankind. Due to external disturbances and various related uncertain factors, the power system often deviates from the normal state, affecting social production and life. With the expansion of the power grid scale and the deepening of structural complexity, the power system is developing towards the direction of multi-area interconnection, and more and more targets need to be processed compared with before. Obviously, the traditional centralized control method can no longer meet the needs of the power system well and is difficult to produce significant effects. In addition, once serious problems occur in the control center, the entire power system will be paralyzed, leading to a series of serious problems such as power supply accidents. In an interconnected power system, the load change in one area will cause frequency imbalance and chaos in the exchange power of the tie lines in different areas. To ensure the stability of the multi-area power system, load frequency control has become one of the effective control methods. It maintains the stability of the system by feeding back the deviation values caused by load fluctuations and the like in the control area to the controller.

[0003] Multi-area power systems need to frequently transmit a large amount of information through communication networks, which makes them face a huge risk of network congestion or cyber attacks. However, the power system is an interconnected and inseparable whole. As we all know, the existence of faults is inevitable, and any abnormality in any part may cause the power system to fail to operate normally or even stop, resulting in economic losses of varying degrees and further affecting the quality of human life and production efficiency. Therefore, it is of great significance to apply the idea of fault-tolerant control to load frequency control, which is becoming an increasingly concerned topic. So far, there are few papers on the fault-tolerant control of power systems. Some literatures apply robust control and adaptive control methods to power systems to solve the problem of actuator faults. Inspired by these literatures, in practice, failures often show the characteristics of probability distribution. In most cases, minor faults often occur, and only in a few cases will serious faults occur. The idea of fault partitioning is to divide faults into different regions according to the probability distribution for further research, which is a new direction for the fault-tolerant control of power systems.

[0004] In practical applications, parameter perturbations often make it difficult for the designed controller to precisely achieve its goal. The vulnerability of the controller will lead to a decline in system performance and even loss of stability. Therefore, non-fragile control has gradually become a hot topic. In addition to the interference factors mentioned above, there is also a certain degree of uncertainty in load frequency control in power systems. Currently, there is little research on this aspect in power systems. The gain perturbation of the controller is usually expressed as additive perturbation and multiplicative perturbation. Existing non-fragile control methods usually only consider specific cases. In fact, the perturbation situation of the controller often exhibits diversity and uncertainty, which requires the non-fragile control scheme to have a certain degree of integrity and systematicness.

[0005] The present invention relates to a fault-tolerant load frequency controller for a multi-area power system. To solve the problem that faults in the multi-area power system affect actual production and life, we introduce an important control method in the power system, namely load frequency control, and make corresponding improvements. First, according to the distribution characteristics of small faults and severe faults, a stochastic distribution model of local faults is established. Then, considering the specific situation of controller gain perturbation, we simultaneously consider multiplicative perturbation and additive perturbation in the controller design. Next, considering different transmission delays, the multi-area power system is modeled as a multi-delay system, and a new non-fragile H ∞ A fault-tolerant load frequency control scheme is proposed, and the problem of dealing with coupling terms is transformed into the W problem in the fault-tolerant load frequency controller. Finally, the feasibility of the method is verified through numerical examples. Summary of the Invention

[0006] Based on the fact that there is still little research in this direction at present, in order to achieve the goal that the system can still operate stably and has an H ∞ interference level γ in the case of certain faults, the present invention designs a non-fragile fault-tolerant load frequency control method for a multi-area power system, so that the power system still has stability when partial failure faults occur.

[0007] The present invention provides a non-fragile fault-tolerant load frequency control method for a multi-area power system, including the following steps:

[0008] Step 1: Specify an application area power system to obtain the i-th control area model of the multi-area power system under partial failure faults in this area;

[0009] This power system mainly consists of four parts, namely the controller: governor: turbine: generator: where S refers to the complex variable in the Laplace transform.

[0010]

[0011]

[0012]

[0013]

[0014] ACE i = βΔf i + ΔP tie-i . (5)

[0015] Δf i 、ΔP mi 、ΔP vi and ΔP di respectively represent the frequency change, the mechanical power output of the turbine, the valve position, and the load of the i-th control area of a power system with a load frequency control scheme, while T gi 、T chi 、M i 、D i and R i These parameters respectively represent the governor time constant, the turbine time constant, the generator inertia moment, the generator damping coefficient, and the speed droop rate of the i-th control area of a multi-area power system. ΔP tie-i represents the power exchange of the tie line in the i-th control area, and T ij represents the tie line synchronizing torque coefficient between the i-th and j-th control areas.

[0016] Step 2, reconstruct the actuator fault model;

[0017] ρ i (t) is the local failure coefficient of the i-th control area of a multi-area power system, which satisfies

[0018] 0 < ρ i min ≤ ρ i (t) ≤ ρ i max ≤ 1, i = 1, 2,..., n, (6)

[0019] ρ i min and ρ i max respectively represent the lower bound and the upper bound of ρ i (t). In a multi-area power system, each area has different fault distribution characteristics. Generally speaking, they all follow such a rule: the probability of a severe fault occurring is small, while the probability of a minor fault occurring is large. Based on this situation, we reconstruct the actuator fault model as:

[0020] ρi (t) = δ i (t)ρ i1 (t)+(1-δ i (t))ρ i2 (t), (7)

[0021] in

[0022]

[0023] is a known calibrator. Assume that δ i (t)(i=1,2,…,n) follows the Bernoulli distribution law, E{δ i (t) = 1} = δ′ i ,δ′ i is a constant in the range [0,1].

[0024] Step 3: Design of fault-tolerant controller;

[0025] The controller of the i-th area in a multi-area power system can be expressed as ρ i (t) is the fault model in step 2, ACE i (t) represents the ACE signal of the i-th region in the multi-regional power system, which can be regarded as the sum of the frequency deviation and power exchange of the inter-regional tie lines, that is:

[0026] ACE i =β i Δf i +ΔP tie-i . (8)

[0027] Taking ACE as the input signal, considering the proportional-integral controller and the non-fragile H ∞ The fault-tolerant controller of the ith control area can be designed as:

[0028]

[0029] Where K Pi and K Ii represents the proportional and integral gains of the designed controller in the ith control region, ΔK Pi and ΔK Ii is the corresponding gain disturbance. The entire system sends the ACE signal to the controller in the form of output feedback. The system output y(t) = [ACE i (t) ∫ACE i (t)] T In fact, the communication delay from ACE signal to controller is inevitable, indicating that K i =[K Pi KIi and ΔK i = [ΔK Pi ΔK Ii , combining (7) and (9), the controller can be redesigned as:

[0030]

[0031] Step Four, based on the above steps, establish a closed-loop multi-area power system model:

[0032]

[0033] x(t) = [x1(1) x2(1) … x n (1)] T ,

[0034] x i (t) = [Δf i ΔP mi ΔP vi ∫ACE i ΔP tie-i T ,

[0035] u F (t) = [u1 F (t) u2 F (t) … u n F (t)] T , ω(t) = [ΔP d1 (t) ΔP d2 (t) … ΔP dn (t)] T ,

[0036] y(t) = [y1(t) y2(t) … y n (t)] T , y i (t) = [ACE ∫ACE] T ,

[0037]

[0038]

[0039] B = diag[B1 B2 … B n , C = diag[C1 C2 … C n , D = diag[D1 D2 … D n , ​

[0040] In a multi - area power system, due to the existence of different system parameters and generator models, it is not realistic to assume that all areas have the same time delay, which may increase the conservatism of the designed controller. Therefore, the existence of multiple time delays is more reasonable. Substituting (10) into (11), the closed - loop multi - area power system model can be further summarized as:

[0041]

[0042]

[0043] Advantages of the present invention: The stability of the closed - loop multi - area power system and the H ∞ disturbance level γ, while maintaining the system stability, has H ∞ disturbance level γ. To ensure the reliability and security of the operation of the multi - area power system, a controller for implementing a fault - tolerant load frequency control method is designed, enabling the system to still operate stably in the case of partial failure faults. Moreover, the additive perturbation and multiplicative perturbation of the controller gain are discussed separately, and the H ∞ meets the performance requirements and the verification is completed. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The design process of the non - fragile fault - tolerant load frequency controller for the multi - area power system;

[0045] Figure 2 The probability distribution of partial failure faults in different areas;

[0046] Figure 3 The state response of the system (12) in Area 1 with multiplicative perturbation of the controller;

[0047] Figure 4 The state response of the system (12) in Area 2 with additive perturbation of the controller. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0049] The following further describes the present invention in detail with reference to the examples shown in the drawings

[0050] This embodiment provides a non - fragile fault - tolerant load frequency control method for a multi - area power system, as Figure 1 shown, including the following steps:

[0051] Step (1) Obtain the multi - area power system under partial failure faults;

[0052] As Figure 1 shown, first specify a multi - area power system under partial - failure faults. This power system mainly consists of four parts, namely: controller: governor: turbine: generator:

[0053] where Δf i , ΔP mi , ΔP vi and ΔP di respectively represent the frequency change, mechanical power output of the turbine, valve position, and load of the i - th control area of a power system with a load - frequency control scheme. And T gi , T chi , M i , D i and R i These parameters respectively represent the governor time constant, turbine time constant, generator inertia moment, generator damping coefficient, and speed - drop rate of the i - th control area of the multi - area power system. ΔP tie-i represents the power exchange of the tie - line in the i - th control area, and T ij represents the tie - line synchronizing torque coefficient between the i - th and j - th control areas.

[0054] Step (2) Reconstruct the actuator fault model;

[0055] ρ i (t) is the local failure coefficient of the i - th control area of the multi - area power system, and it satisfies

[0056] 0 < ρ i min ≤ ρ i (t) ≤ ρ i max ≤ 1, i = 1, 2,..., n, (6)

[0057] ρ i min and ρ i max respectively represent the lower bound and upper bound of ρ i (t). In a multi - area power system, each area has different fault - distribution characteristics. Generally, they all follow such a rule: the probability of a severe fault occurring is small, while the probability of a minor fault occurring is large. Based on this situation, we reconstruct the actuator fault model as:

[0058] ρ i (t) = δ i (t)ρ i1 (t)+(1 - δ i (t))ρi2 (t), (7)

[0059] where

[0060]

[0061] is a known scaler. Assume that δ i (t) (i = 1, 2, …, n) follows the Bernoulli distribution law, and E{δ i (t) = 1} = δ′ i , where δ′ i is a constant belonging to [0, 1].

[0062] Step (3), design a fault-tolerant controller based on Steps (1) and (2);

[0063] The controller of the i-th area in the multi-area power system can be expressed as ρ i (t) is the fault model in Step 2, and ACE i (t) represents the ACE signal of the i-th area in the multi-area power system, which can be regarded as the sum of the frequency deviation and power exchange of the inter-area tie line, that is:

[0064] ACE i = β i Δf i + ΔP tie-i . (8)

[0065] Taking ACE as the input signal, considering a proportional-integral type controller and non-fragile H ∞ The fault-tolerant controller of the i-th control area can be designed as:

[0066]

[0067] where K Pi and K Ii represent the proportional and integral gains of the designed controller in the i-th control area, and ΔK Pi and ΔK Ii are the corresponding gain perturbations. The entire system sends the ACE signal to the controller in the form of output feedback, and the output of the system y(t) = [ACE i (t) ∫ACE i (t)] T . In fact, the communication delay from the ACE signal to the controller is inevitable. Let K i = [K Pi K Ii and ΔK i = [ΔK Pi ΔK Ii, combining (7) and (9), the controller can be redesigned as:

[0068]

[0069] Step (4) obtains the final model of the system

[0070]

[0071] x(t) = [x1(1) x2(1) … x n (1)] T , x i (t) = [Δf i ΔP mi ΔP vi ∫ACE i ΔP tie-i T ,

[0072] u F (t) = [u1 F (t) u2 F (t) …u n F (t)] T , ω(t) = [ΔP d1 (t) ΔP d2 (t) … ΔP dn (t)] T ,

[0073] y(t) = [y1(t) y2(t) … y n (t)] T , y i (t) = [ACE ∫ACE] T ,

[0074]

[0075]

[0076] B = diag[B1 B2 … B n , C = diag[C1 C2 … C n , D = diag[D1 D2 … D n ,

[0077] ​In a multi - area power system, due to the existence of different system parameters and generator models, assuming that all areas have the same time delay is not in line with the actual situation and may increase the conservatism of the designed controller. Therefore, the existence of multiple time delays is more reasonable. Substituting (10) into (11), the closed - loop multi - area power system can be further summarized as:

[0078]

[0079]

[0080]

[0081] Step (5) Based on the system model obtained in step (4), Theorem 1 is given and a suitable Lyapunov - Krasovskii function is constructed:

[0082] First, assume ΔK = 0, and the following theorem is given. Theorem 1. For some given positive constants δ′, μ, d i 、 the variable ρ i1 (t), ρ i2 (t) and an appropriate controller matrix K, the system (12) is mean - square stable with a H ∞ disturbance attenuation level γ if there exist positive definite matrices P > 0, Q i > 0, W i > 0, V i > 0 (i = 1…n), a symmetric matrix S and with appropriate dimensions and a positive scalar γ > 0 such that the following inequalities hold:

[0083]

[0084]

[0085] ψ2 = P - S+A T S - 2T1+U1+U1 T ,

[0086]

[0087]

[0088] ψ6 = diag[(μ - 1)Q1 (μ - 1)Q2 … (μ - 1)Q n , ψ7 = diag[-V1 -V2 … -V n ,

[0089] ψ8 = diag[V1 V2 … V n ,

[0090] ψ 91 = diag[-W1 - V1 - W2 - V2 … -W n-2 -V n-2 ,

[0091]

[0092]

[0093] The Lyapunov - Krasovskii function is constructed as follows:

[0094]

[0095] By dealing with the derivative of (19), we can obtain:

[0096]

[0097] Based on E{δ i (t)=1}=δ i ′ and Lemma 1, we can obtain:

[0098]

[0099] Combining the free - weight - matrix technique, for any given symmetric matrix S, the following equality holds:

[0100]

[0101] where

[0102] Then the following inequality including the performance requirements can be achieved:

[0103]

[0104] where

[0105]

[0106] In other words, if ψ < 0 holds, then also holds, so J < 0 also holds. Given V(0)=0, integrating both sides of (23) from 0 to t, when t → ∞:

[0107]

[0108] Step (6) is based on step (5), considering the following factors, the local failure coefficient ρ i1 (t) and ρ i2(t) is unknown in advance, ΔK≠0, and the following theorem is given to handle these problems.

[0109] Theorem 2 For some given positive constants δ i ′, ρ′ i1 , ρ′ i2 , μ, d i , controller gain matrix K, the system (12) is mean-square stable H ∞ disturbance attention level γ, if there exist positive definite matrices P>0, Q i >0, W i >0, V i >0 (i=1…n), σ m >0 (m=1…2n), symmetric matrix S and positive scalar γ>0, the following inequalities hold:

[0110]

[0111] where

[0112]

[0113]

[0114] Ω2 = P - S + A T S + Y - 2T1 + U1 + U1 T ,

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] λ i = diag{O 5(i-1)×5(i-1) , B i (K i +ΔK i )C i , O 5(n-i)×5(n-i)}

[0121] Y = σ1SY 11 (SY 11 ) T +σ2SY 12 (SY 12 )T +…+σ 2n-1 SY n1 (SY n1 ) T +σ 2n SY n2 (SY n2 ) T ,

[0122] Y ik =diag{O 5(i-1)×5(i-1) ,y ik ,O 5(n-i)×5(n-i)},

[0123]

[0124] a i =-δ′ i ρ′ i1 Z i1 ,a′ i =-(1-δ′ i )ρ′ i2 Z i2 ,ρ′ i =δ′ i ρ′ i1 +(1-δ′ i )ρ′ i2 ,

[0125]

[0126]

[0127] ρ i1 (t) and ρ i2 (t) are unknown in practice. Therefore, to reduce the conservatism of the designed controller, we adopt the fault characteristics analyzed before. We give the definition of ρ ik (t), ρ ik (t) = ρ′ ik (t)(1 + G ik )(i = 1,…n, k = 1, 2), where

[0128]

[0129]

[0130] Then we can obtain the following equation:

[0131]

[0132] Substituting (27) into (18), (18) can be divided into two parts. Γ refers to the constant part and can be expressed as:

[0133]

[0134] where

[0135]

[0136] ΔΓ represents the uncertain part and can be expressed as:

[0137]

[0138] where

[0139] ΔΓ i1 =[γ i1 S T γ i1 S T , ΔΓ i2 =[γ i2 S T γ i2 S T ,

[0140] γ i1 =diag{O 5n(i-1)×5(i-1) , d i1 , O 5n(n-i)×5(n-i)},

[0141] d i1 =diag{-δ′ i ρ′ i1 , -δ′ i ρ′ i1 , -δ′ i ρ′ i1 , -δ′ i ρ′ i1 , -δ′ i ρ′ i1},

[0142] γ i2 =diag{O 5n(i-1)×5(i-1) , d i2 , O 5n(n-i)×5(n-i)},

[0143] d i2 =diag{-(1 - δ′ i )ρ′ i2 , -(1 - δ′ i )ρ′ i2 , -(1 - δ′ i )ρ′ i2 , -(1 - δ′ i )ρ′ i2 , -(1 - δ′ i )ρ′i2}

[0144] By combining Lemma 2 and Lemma 3, Theorem 2 can be obtained.

[0145] Step (7) is based on step (6), and the multiplicative perturbation and additive perturbation of the controller gain are discussed separately. Theorem 3.1 and Theorem 3.2 are used to solve the multiplicative perturbation, while Theorem 4.1 and Theorem 4.2 are used to handle the additive perturbation.

[0146] The form of the multiplicative perturbation is ΔK i =H i F i (t)E i ΔK i and the additive perturbation can be expressed as ΔK i =H i F i (t)E i , where K i is the controller gain designed by us, H i and E i represent known constant matrices with appropriate dimensions, and F i (t) represents a time-varying perturbation matrix that satisfies F i T (t)F i (t) ≤ I.

[0147] Theorem 3.1. For some given positive constants δ′ i , ρ′ i1 , ρ′ i2 , μ, d i , For the controller gain matrix K, by choosing the given matrices H i and E i , the system (12) is mean-square stable with an H ∞ disturbance attenuation level γ. If there exist positive definite matrices P > 0, Q i > 0, W i > 0, V i > 0, σ′ i > 0 (i = 1,..., n), σ m > 0 (m = 1... 2n), a symmetric matrix S and a positive scalar γ > 0, the following inequalities hold:

[0148]

[0149] where

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] λ′ i = diag{O 5(i-1)×5(i-1) , B i K i C i , O 5(n-i)×5(n-i)},

[0157] Ψ1 = [Ψ 11 Ψ 12 … Ψ 1n ,

[0158] Ψ2 = diag{a1, a2, …, a n},Ψ 1i = [ψ i1 ψ i2 ,

[0159]

[0160]

[0161] α ik = [O n×5(i-1) α′ ik O n×5(n-i) (k = 1, 2),

[0162] α′ i1 = [O 5×(i-1) B i H i O 5×(n-i) T ,

[0163] α′ i2 = [O 5×(i-1) E i K i C i O 5×(n-i) T ,

[0164]

[0165] First, the controller gain perturbation is regarded as multiplicative perturbation, and then Hypothesis 2 and Lemma 3 are combined with such problems. ​​The specific part ΔΛ is the uncertain part with respect to the controller gain perturbation and can be written as:

[0166]

[0167] where

[0168] Δ i = diag{O (i-1)×(i-1) , F i (t), O (n-i)×(n-i)},

[0169]

[0170] Then, by using Lemma 2, the matrix inequality (30) is obtained, and the proof of Theorem 3.1 is completed.

[0171] So far, we have solved the controller gain perturbation problem, but there are still some coupling terms in (30). Then we develop Theorem 3.2.

[0172] Theorem 3.2. For some given positive constants δ′ i , ρ′ i1 , ρ′ i2 , μ, d i , and a sufficiently small scalar ò, matrices H i and E i with appropriate dimensions are designed, and the non-fragile H ∞ fault-tolerant controller gain K = MN -1 N, where N is a full-rank matrix, and the system (12) is mean-square stable with an H ∞ disturbance attenuation level γ. If there exist positive definite matrices P a > 0, Q ia > 0, W ia > 0, V ia > 0, σ′ i > 0 (i = 1,..., n), σ m > 0 (m = 1,..., 2n),

[0173] symmetric matrix X and a positive scalar γ > 0, the following inequalities hold:

[0174]

[0175]

[0176] where

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] At this time, especially for the case where both matrices B and C are non-invertible, the traditional idea of variable substitution cannot play an effective role. Therefore, we set X = S -1 , XPX = P a , XQ i X = Q ia , XW i X = W ia , XV i X = V ia , XT j X = T ja , XU j X = U ja (j = 1, 2), and the left and right multiplications of its transpose (30). Then we can obtain the new coupling term Ami X.

[0197]

[0198] In a multi - area power system (12), the method can be further expressed as:

[0199]

[0200] By using the Schur complement, the corresponding results (32) and (33) are obtained, and the controller gain K can be solved from K = MN -1 Solve.

[0201] On the other hand, study the controller gain perturbation as multiplicative perturbation and give the following theorem.

[0202] Theorem 4.1. For some given positive constants δ′ i , ρ′ i1 , ρ′ i2 , μ, d i , and the controller gain K, matrices H i1 , H i2 , E i1 , E i2 with appropriate dimensions, the system (12) is mean - square stable H ∞ disturbance attenuation level γ, if there exist positive definite matrices P > 0, Q i > 0, W i > 0, V i > 0 (i = 1…n), σ m > 0, ε m > 0 (m = 1,…2n), symmetric matrix S and positive scalar γ > 0, the following inequalities hold:

[0203]

[0204] where

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] βik = [O 2n×5(i-1) β′ ik O 2n×5(n-i) (k = 1, …, 4),

[0212] β′ i1 = [O 5×2(i-1) B i [H i1 0] O 5×2(n-i) T ,

[0213] β′ i2 = [O 5×2(i-1) diag{F i1 , 0}C i O 5×2(n-i) T ,

[0214] β′ i3 = [O 5×2(i-1) B i [0 H i2 O 5×2(n-i) T ,

[0215] β′ i4 = [O 5×2(i-1) diag{0, F i2}C i O 5×2(n-i) T ,

[0216] α′ i2 = [O 5×(i-1) E i K i C i O 5×(n-i) T ,

[0217] b m = diag{-ε m I, -ε m I}(m = 1, …, 2n).

[0218] (25) can be divided into two parts and written as denotes the constant part, and the uncertain part is as follows:

[0219]

[0220] where

[0221]

[0222] ​​​​​

[0223]

[0224]

[0225] Then, by using Lemma 2, we can obtain Theorem 4.1.

[0226] To eliminate the coupling terms, we develop Theorem 4.2 and can obtain a non-fragile controller considering multiplicative perturbations.

[0227] Theorem 4.2. For some given positive constants δ′ i , ρ′ i1 , ρ′ i2 , μ, d i , and a sufficiently small scalar ò, matrices H i1 , H i2 , E i1 , E i2 have appropriate dimensions. Design a non-fragile H ∞ fault-tolerant controller gain K = MN -1 . The system (12) is mean-square stable with an H ∞ disturbance attenuation level γ. If there exist positive definite matrices P a > 0, Q ia > 0, W ia > 0, V ia > 0 (i = 1…n), σ m > 0, ε m > 0 (m = 1,…2n), symmetric matrix X and a positive scalar γ > 0, the following inequalities hold:

[0228]

[0229]

[0230] where

[0231]

[0232]

[0233]

[0234]

[0235]

[0236] ​​​Theorem 4.2 can be obtained by using a method similar to the proof of Theorem 3.2.

[0237] Figure 1 It represents the design process of the fault-tolerant load frequency controller for a multi-area power system. The present invention studies the fault-tolerant load frequency control method for a multi-area power system under partial failure faults.

[0238] Figure 2 It shows the probability distribution of partial failures in different areas. Since the present invention mainly focuses on the fault-tolerant load frequency control method for a multi-area power system under partial failure faults, the functions of the non-fragile controller need to be verified separately.

[0239] Figure 3 It represents the state response of the multi-area power system (12) under multiplicative perturbation of the controller. In the case of faults and perturbations, each component gradually tends to 0, that is, the power system achieves mean-square stability and has an H ∞ interference level γ.

[0240] Figure 4 It represents the state response of the multi-area power system (12) under additive perturbation of the controller. In the case of faults and perturbations, each component gradually tends to 0, that is, the power system achieves mean-square stability and has an H ∞ interference level γ.

[0241] Through the above technical solutions, a non-fragile fault-tolerant load frequency control method for a multi-area power system provided in this embodiment is to solve the problem that a multi-area power system fails and affects actual production and life. We introduce the important load frequency control method in the power system and make corresponding improvements. First, according to the distribution characteristics of small faults and severe faults, a stochastic distribution model of local faults is established. Then, considering the specific situation of controller gain perturbation, we consider both multiplicative perturbation and additive perturbation in the controller design. Then, considering different transmission delays, the multi-area power system is modeled as a multi-delay system, and a new non-fragile H ∞ A fault-tolerant load frequency control scheme is proposed, and the problem of dealing with coupling terms is transformed into the W problem in the fault-tolerant load frequency controller. Finally, the feasibility of the method is verified through numerical examples.

[0242] The above has described the embodiments of the present invention in detail with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principles and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments including components still fall within the protection scope of the present invention.

Claims

1. A non-fragile fault-tolerant load frequency control method for a multi-area power system, characterized in that, It includes the following steps: Step 1: Specify an application area power system to obtain a model of the multi-area power system under partial failure faults in this area; Step 2: Construct a closed-loop multi-area power system model (1) Construct an actuator fault model In the multi-area power system, each area has different fault distribution characteristics. Following the rule that the probability of a severe fault occurring is very small, while the probability of a minor fault occurring is very large, the actuator fault model is constructed as: ρ i (t) = δ i (t)ρ i1 (t) + (1 - δ i (t))ρ i2 (t), Where is a known scaler, δ i (t)(i = 1, 2, …, n) follows the Bernoulli distribution law, δ i ′ is a constant belonging to [0, 1], ρ i ρ(t) is the local failure coefficient of the i-th control area of the multi-area power system, and it satisfies 0 < ρ i min ≤ ρ i (t) ≤ ρ i max ≤ 1, i = 1, 2,..., n, ρ i min and ρ i max represent the lower bound and the upper bound of ρ i (t), respectively; (2) Design a fault-tolerant controller according to the actuator fault model; The design method of the fault-tolerant controller is: Design an initial controller, and the expression is as follows: u F u(t) = -ρ(t)u(t), 0 < ρ min ≤ ρ(t) ≤ ρ max ≤ 1 The ACE signal of the i-th area in the multi-area power system can be regarded as the sum of the frequency deviation and power exchange of the inter-area tie line, that is: ACE i = β i Δf i + ΔP tie-i Taking ACE as the input signal, considering the proportional-integral type controller and non-fragile H ∞ The fault-tolerant controller for the i-th control area can be designed as follows: where \(K\) Pi and \(K\) Ii represent the proportional and integral gains of the designed controller in the \(i\)-th control area, \(\Delta K\) Pi and \(\Delta K\) Ii are the corresponding gain perturbations. The entire system sends the ACE signal to the controller in the form of output feedback. The output of the system \(y(t)=[ACE\) i (t)\int ACE\) i (t)] T . In fact, the communication delay from the ACE signal to the controller is inevitable. Denote \(K\) i =[K\) Pi K\) Ii and \(\Delta K\) i =[\Delta K\) Pi \Delta K\) Ii . Combining the initial controller and the proportional-integral type controller and the fault-tolerant \(H\) ∞ fault-tolerant controller for the \(i\)-th control area, the fault-tolerant controller is redesigned as: (3) Design the state-space expression of the multi-power system, and its expression is: Where A, B, C, and D are parameter matrices respectively, and x(t) refers to the state variable Where each specific parameter is expressed as: x(t) = [x1(1) x2(1) ··· x n (1)] T ,x i (t) = [Δf i ΔP mi ΔP vi ∫ACE i ΔP tie-i T ,​ u F (t) = [u1 F (t) u2 F (t) ··· u n F (t)] T , ω(t) = [ΔP d1 (t) ΔP d2 (t) ··· ΔP dn (t)] T , y(t) = [y1(t) y2(t) ··· y n (t)] T ,y i (t) = [ACE∫ACE] T , Among them, T gi represents the governor time constant of the i-th control area of the multi-area power system; β i represents the frequency change parameter; M i represents the generator inertia moment; Obtain the closed-loop multi-area power system model Substitute the fault-tolerant controller into the state-space expression of the multi-power system to obtain a closed-loop multi-area power system model; Step 3: Apply the closed-loop multi-area power system model to the specific non-fragile fault-tolerant load frequency control in the multi-area power system.

2. The non-fragile fault-tolerant load frequency control method for a multi-area power system according to claim 1, characterized in that The multi-area power system model includes Controller: Governor: Turbine: Generator: ACE i = βΔf i + ΔP tie-i Δf i , ΔP mi , ΔP vi and ΔP di denote the frequency change, mechanical power output of the turbine, valve position and load of the ith control area of the power system with load frequency control scheme, respectively, and T gi 、T chi 、M i , D i and R i These parameters represent the governor time constant, turbine time constant, generator inertia moment, generator damping coefficient and speed drop rate of the i-th control area of the multi-area power system, ΔP tie-i represents the power exchange of the tie line in the ith control area, T ij Represents the synchronous torque coefficient of the tie line between the i-th and j-th control areas.

3. The non-fragile fault-tolerant load frequency control method for a multi-area power system according to claim 1 or 2, characterized in that, In Step 2, the method for obtaining the closed-loop multi-area power system model is: In the multi-area power system, due to the existence of different system parameters and generator models, assuming that all areas have the same time delay does not conform to the actual situation and may increase the conservativeness of the designed controller. Therefore, the existence of multiple time delays is more reasonable. Substitute the fault-tolerant controller into the state-space expression of the multi-power system to obtain a closed-loop multi-area power system model:

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