Fault-tolerant load frequency control method for single-area power system based on fault distribution

Abstract

The present invention relates to a fault-tolerant load frequency controller for a single-area power system. Considering the distribution characteristics of faults, a new random fault model is proposed. By constructing a suitable Lyapunov function, sufficient conditions for ensuring the mean square stability of the single-area power system are obtained. Then, we transform the problem of dealing with coupling terms into a W problem, and use the corresponding lemma to split the matrix into two parts, one containing uncertain terms and the other not containing uncertain terms, and eliminate the uncertain terms. Then, using an equivalent iterative algorithm, the coupling terms containing the inverse matrix in the matrix inequality are processed and the gain of the fault-tolerant load frequency controller is solved. Finally, the feasibility of the method is verified by numerical examples.

Description

Technical Field

[0001] The invention relates to a fault-tolerant load frequency control method of a single-area power system based on fault distribution, and belongs to the field of fault-tolerant control. Background Art

[0002] The power system is one of the most important parts in the development of modern society. It is closely related to people's daily life and the production and operation of enterprises and factories. The power system is an electric energy system composed of power plants, transmission lines, substations, distribution stations, and power users. Thermal power generation uses the heat energy generated by the combustion of fuel, hydropower generation uses the potential energy generated by water falling from a high place, and nuclear power generation uses the heat energy generated by nuclear fission in atomic reactors. Power plants convert these various forms of energy in nature into electrical energy. According to the needs of different users, substations adjust the voltage of the transmitted electrical energy and then distribute it to each user through distribution stations. For such a unified whole, any accident in any link may cause the normal transmission of electrical energy. Especially in the face of today's electronic and information society, people are increasingly dependent on electrical energy. The complex structure and huge scale of the power grid make the requirements for electrical energy more stringent, and the problems faced are more difficult. If the problem is not solved in a timely and effective manner, it will not only undermine the stability of the system, but also very likely bring devastating consequences. The economic and other losses caused are incalculable.

[0003] The loss of power system stability will bring a devastating blow to the safe operation of the system. With the rapid development of power systems, modern power grids are characterized by large units, large power grids, ultra-high voltage, long distances, heavy loads, large regional networking, and AC / DC combination. Although they strongly guarantee the growing electricity demand of society, they are also facing many increasingly complex and thorny problems. The consequence of losing frequency stability is the collapse of the system frequency, causing a total power outage in the system. For modern power systems, if a fault occurs in the power grid, its transient process is extremely fast. If it is not handled in time, it will quickly spread to the entire system. In severe cases, it may even cause a system collapse accident, causing a large-scale power outage and huge economic and social losses. Therefore, modern power grids have high requirements for the safe and economic operation of the system, that is, the system is required to have a strong anti-interference ability, and to maintain sufficient safe and stable operation margin for the power system. It is also an important task for system planning and design and power grid dispatching and operation. Frequency stability is one of the most important performances in the power system. According to the actual situation of electricity consumption, the power load is in a state of change at any time, and any sudden change may cause fluctuations in the system frequency and deviations in the exchange power of the interconnection lines between systems.

[0004] Therefore, we introduced one of the most important control methods in the power system, namely load frequency control. It is a very important link in the design and operation of the power system. Its main goal is to adjust the frequency of the system to the rated value and keep the power exchange in the neighboring areas at the predetermined value, so as to provide users with safe and high-quality electricity. Since the object of this paper is a single-area power system, it is not necessary to consider the power exchange of the interconnection line but only the change of frequency. Therefore, in order to ensure the quality of power, it is necessary to maintain the system frequency at the nominal value and minimize the unplanned interconnection line exchange power between the control areas as much as possible. However, in the process of power system operation, the occurrence of faults is inevitable. Therefore, it is of certain practical significance to enable the power system to maintain the expected performance and stable operation in the event of a fault.

[0005] As we all know, the operation of the system is inevitably accompanied by failures. Due to the uncertainty of its own parameters and the influence of external interference, power system failures often occur. Partial failure is a type of actuator failure in the power system. However, scholars from all walks of life have relatively little research on this aspect, so we put forward a new view on fault partitioning. In general, the partial failure factor is an uncertain value in the range of [0,1]. When it is close to 1, it indicates that the fault is very small at this time; on the contrary, when it is close to 0, it means that the fault at this time is very serious. We can realize that when the fault is small, the probability of occurrence is relatively large, and when the fault is more serious, the probability of occurrence is small. The above content inspired the research of this paper. Summary of the invention

[0006] Since there is still little research in this direction, in order to ensure that the system can still operate stably and have H ∞ For the purpose of interference level γ, the present invention designs a fault-tolerant load frequency controller for a single-area power system based on fault distribution, so that the power system still has stability when a partial failure occurs.

[0007] The present invention provides a fault-tolerant load frequency control method for a single-area power system based on fault distribution, comprising the following steps:

[0008] Step 1, specify an application area power system, and obtain a structural block diagram of a single area power system under partial failure of the area;

[0009] ΔP v , ΔP m , ΔP d The four changes of , Δf represent the change of valve opening, the change of turbine mechanical output, the change of power load and the change of system frequency, while R, T g 、T ch, M, D are a series of parameters representing the speed drop rate of the speed governor, the time constant of the speed governor, the time constant of the turbine, the moment of inertia of the generator and the damping coefficient. The ACE signal is used as the regional control error. The whole system tracks it to control the power generation so as to maintain the constant system frequency. ρ(t) is a partial failure, which affects the proportional integral controller and the speed governor link. These two parts need to be considered when designing the controller later.

[0010] Step 2: Establish a preliminary system model based on step 1:

[0011]

[0012] represents the state variable of the system, u(t) represents the input signal of the system, w(t)=ΔP d It indicates that the system is subject to interference signals from the outside world, and the output of the system is in Respectively represent the matrices corresponding to each parameter:

[0013]

[0014] Step 3: Construct a suitable fault model; the fault model can be expressed as:

[0015] u F (t)=ρ(t)u(t),0<ρ min ≤ρ(t)≤ρ max ≤1 (2)

[0016] Among them, the failure factor ρ is an unknown number within a certain range and cannot be 0. min represents the lower bound of the fault factor, ρ max Indicates the upper bound of the failure factor.

[0017] The whole system sends the ACE signal to the controller in the form of output feedback. In the design of the controller, a more conventional proportional-integral controller is selected, which can be further expressed as:

[0018]

[0019] In order to facilitate subsequent derivation and calculation, it is necessary to redefine K and y(t):

[0020]

[0021] So we can get:

[0022] u F(t)=-ρ(t)Ky(td(t)) (5)

[0023] The variable time delay meets the following conditions:

[0024]

[0025] Considering the distribution characteristics of faults, define:

[0026] ρ(t)=δ(t)ρ1(t)+(1-δ(t))ρ2(t) (7)

[0027] Where δ(t) takes the value of 0 or 1 and satisfies:

[0028]

[0029] Step 4: Get the final model of the system:

[0030] Combining the previous results, we can redefine x(t) = [ΔfΔP m ΔP v ∫ACE] Τ , we can get:

[0031]

[0032] in:

[0033]

[0034] Step 5: Apply the system model in step 4 to the regional power system specified in step 1.

[0035] The present invention provides the following verification steps to verify that the system model obtained in step 4 is combined with the system described in the present invention and can still operate stably and have H under certain fault conditions. ∞ The purpose of the interference level γ.

[0036] Verify step 1. According to the system model obtained in step 4, construct a suitable Lyapunov function:

[0037] Choose a suitable Lyapunov function as follows:

[0038]

[0039] We set E{δ(t)=1}=δ', in the classic H ∞ In the theory, the zero initial condition should be taken into account, and H ∞ Performance index J:

[0040]

[0041] make After processing, we can get the given normal quantity d , μ,δ', variables ρ1(t), ρ2(t), scalar γ>0 and a suitable controller gain matrix K. If there exists a matrix of suitable dimensions P>0, Q>0, W>0, V>0 so that the following linear matrix inequality holds, then the system in step 4 can remain mean square stable and have H ∞ Interference level γ.

[0042]

[0043] in:

[0044]

[0045] Verification step 2 is based on step verification step 1, let X = P -1 , And multiply the left and right sides by diag{X,X,X,X,I,I,I,I} and its transpose respectively. This can better deal with the coupling term PBKC and facilitate subsequent calculations.

[0046] Given a normal quantity d , μ,δ', variables ρ1(t),ρ2(t), scalar γ>0 and a suitable controller gain matrix K, if there is a matrix X>0 of suitable dimension, If the following matrix inequality holds, then the system is mean square stable and has H ∞ Interference level γ.

[0047]

[0048] in:

[0049] Verification step 3 is to further solve the coupling term BKCX based on verification step 2. Since C is irreversible, Y=KCX cannot be used directly to solve K. Here is a method, defined as:

[0050]

[0051] Available (NC-CX) Τ (NC-CX) = 0, and then use the Schur complement theorem to further transform the problem of solving the coupling term BKCX into an optimization problem:

[0052]

[0053] Then we can get that, given the normal quantity d , μ,δ', variables ρ1(t),ρ2(t), scalar γ>0 and ε→0, design controller K=MN -1 , if there exists a matrix X>0, and a full-rank matrix N and a matrix M of appropriate dimensions such that matrix inequalities (15) and (16) hold, then the system is mean-square stable and has H ∞ Interference level γ.

[0054]

[0055] in:

[0056]

[0057]

[0058] Verification step 4 Based on verification step 3, considering that the specific values ​​of ρ1(t) and ρ2(t) are unknown, define:

[0059]

[0060]

[0061] Then, we can get:

[0062] ρ1(t)=ρ 10 (1+G1),|G1|≤Z1≤1,

[0063] ρ2(t)=ρ 20 (1+G2),|G2|≤Z2≤1 (18)

[0064] Substitute (18) into (16) and use the relevant lemma to split (16) into two parts with and without definite terms, eliminate the uncertain terms G1 and G2, and then merge them to obtain the following theorem.

[0065] Given a normal quantity d , μ,δ',ρ 10 ,ρ 20 , scalar γ>0 and ε→0, if there exists σ i >0,i=1,2,3,...,12,matrixX>0, and a full-rank matrix N and a matrix M of appropriate dimension such that matrix inequalities (15) and (19) hold, then the system is mean-square stable and has H ∞ Interference level γ.

[0066]

[0067] in:

[0068]

[0069]

[0070] Ω2=diag{-σ1I,-σ2I,-σ3I,-σ4I,-σ5I,-σ6I,-σ7I,-σ8I,-σ9I,-σ 10 I,-s 11 I,-s 12 I}, Λ2=-ρ0BMC,

[0071] Λ4=-γ 2 I,ρ0=δ'ρ 10 +(1-s')p 20,

[0072]

[0073] a1=σ1(δ'ρ 10 Z1) 2 +σ2[(1-δ')ρ 20 Z2] 2 ,

[0074] a2=σ3(δ'ρ 10 Z1) 2 +σ4[(1-δ')ρ 20 Z2] 2 ,

[0075] a3=σ5(δ'ρ 10 Z1) 2 +σ6[(1-δ')ρ 20 Z2] 2 ,

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] The beneficial effect of the present invention: system stability (9) and H∞ The disturbance level γ has H while maintaining system stability ∞ Interference level γ. In order to ensure the reliability and safety of the single-region power system operation, a fault-tolerant load frequency controller is designed so that the system can still operate stably in the event of partial failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 : Single-area power system under partial failure;

[0084] Figure 2 : The state response curve of the system to the first component and the second component;

[0085] Figure 3 : The state of the system responds to the curves of the third and fourth components;

[0086] Figure 4 : Output response curve of the system. DETAILED DESCRIPTION

[0087] The present invention will be described in further detail below in conjunction with the examples shown in the accompanying drawings.

[0088] Step (1) obtains the structural block diagram of a single-area power system under partial failure

[0089] Depend on Figure 1 It can be seen that ΔP v , ΔP m , ΔP d The four changes of , Δf represent the change of valve opening, the change of turbine mechanical output, the change of power load and the change of system frequency, while R, T g 、T ch , M, D are a series of parameters representing the speed drop rate of the speed governor, the time constant of the speed governor, the time constant of the turbine, the moment of inertia of the generator and the damping coefficient. The ACE signal is used as the regional control error. The whole system tracks it to control the power generation so as to maintain the constant system frequency. ρ(t) is a partial failure, which affects the proportional integral controller and the speed governor link. These two parts need to be considered when designing the controller later.

[0090] Step (2) builds a preliminary model of the system based on step (1):

[0091]

[0092] represents the state variable of the system, u(t) represents the input signal of the system, w(t)=ΔP dIt indicates that the system is subject to interference signals from the outside world, and the output of the system is in Respectively represent the matrices corresponding to each parameter:

[0093]

[0094] Step (3) constructs a suitable fault model. The fault model can be expressed as:

[0095] u F (t)=ρ(t)u(t),0<ρ min ≤ρ(t)≤ρ max ≤1 (2)

[0096] Among them, the failure factor ρ is an unknown number within a certain range and cannot be 0. min represents the lower bound of the fault factor, ρ max Indicates the upper bound of the failure factor.

[0097] As can be seen from the figure, the entire system sends the ACE signal to the controller in the form of output feedback. In the design of the controller, a more conventional proportional-integral controller is selected, which can be further expressed as:

[0098]

[0099] In order to facilitate subsequent derivation and calculation, it is necessary to redefine K and y(t):

[0100]

[0101] So we can get:

[0102] u F (t)=-ρ(t)Ky(td(t)) (5)

[0103] The variable time delay meets the following conditions:

[0104]

[0105] Considering the distribution characteristics of faults, define:

[0106] ρ(t)=δ(t)ρ1(t)+(1-δ(t))ρ2(t) (7)

[0107] Where δ(t) takes the value of 0 or 1 and satisfies:

[0108]

[0109] Step (4) Obtain the final model of the system

[0110] Combining the previous results, we can redefine x(t) = [Δf ΔP m ΔP v ∫ACE] Τ , we can get:

[0111]

[0112] in:

[0113]

[0114] Step (5) constructs a suitable Lyapunov function based on the system model obtained in step (4):

[0115] Choose a suitable Lyapunov function as follows:

[0116]

[0117] We set E{δ(t)=1}=δ', in the classic H ∞ In the theory, the zero initial condition should be taken into account, and H ∞ Performance index J:

[0118]

[0119] make After processing, we can get the given normal quantity d , μ, δ', variables ρ1(t), ρ2(t), scalar γ>0 and a suitable controller gain matrix K. If there exists a matrix of suitable dimensions P>0, Q>0, W>0, V>0 so that the following linear matrix inequality holds, then the system in step (4) can remain mean square stable and have H ∞ Interference level γ.

[0120]

[0121] in:

[0122]

[0123] Step (6) is based on step (5), and X = P -1 , And multiply the left and right sides by diag{X,X,X,X,I,I,I,I} and its transpose respectively. This can better deal with the coupling term PBKC and facilitate subsequent calculations.

[0124] Given a normal quantity d , μ,δ', variables ρ1(t),ρ2(t), scalar γ>0 and a suitable controller gain matrix K, if there is a matrix X>0 of suitable dimension, If the following matrix inequality holds, then the system is mean square stable and has H ∞ Interference level γ.

[0125]

[0126] in:

[0127]

[0128] Step (7) is to further solve the coupling term BKCX based on step (6). Since C is irreversible, K cannot be solved directly using Y=KCX. Here is a method, which is defined as:

[0129]

[0130] Available (NC-CX) Τ (NC-CX) = 0, and then use the Schur complement theorem to further transform the problem of solving the coupling term BKCX into an optimization problem:

[0131]

[0132] Then we can get that, given the normal quantity d, μ,δ', variables ρ1(t),ρ2(t), scalar γ>0 and ε→0, design controller K=MN -1 , if there exists a matrix X>0, and a full-rank matrix N and a matrix M of appropriate dimensions such that matrix inequalities (15) and (16) hold, then the system is mean-square stable and has H ∞ Interference level γ.

[0133]

[0134] in:

[0135]

[0136]

[0137] Step (8) Based on step (7), considering that the specific values ​​of ρ1(t) and ρ2(t) are unknown, define:

[0138]

[0139]

[0140] Then, we can get:

[0141] ρ1(t)=ρ 10 (1+G1),|G1|≤Z1≤1,

[0142] ρ2(t)=ρ 20 (1+G2),|G2|≤Z2≤1 (18)

[0143] Substitute (18) into (16) and use the relevant lemma to split (16) into two parts with and without definite terms, eliminate the uncertain terms G1 and G2, and then merge them to obtain the following theorem.

[0144] Given a positive constant d, μ,δ',ρ 10 ,ρ 20 , scalar γ>0 and ε→0, if there exists σ i >0,i=1,2,3,...,12,matrixX>0, and a full-rank matrix N and a matrix M of appropriate dimension such that matrix inequalities (15) and (19) hold, then the system is mean-square stable and has H ∞ Interference level γ.

[0145]

[0146] in:

[0147]

[0148]

[0149] Ω2=diag{-σ1I,-σ2I,-σ3I,-σ4I,-σ5I,-σ6I,-σ7I,-σ8I,-σ9I,-σ 10 I,-σ 11 I,-σ 12 I},

[0150] Λ2=-ρ0BMC,

[0151] Λ4=-γ 2 I,ρ0=δ'ρ 10 +(1-δ')ρ 20 ,

[0152]

[0153] a1=σ1(δ'ρ 10 Z1) 2 +σ2[(1-δ')ρ20 Z2] 2 ,

[0154] a2=σ3(δ'ρ 10 Z1) 2 +σ4[(1-δ')ρ 20 Z2] 2 ,

[0155] a3=σ5(δ'ρ 10 Z1) 2 +σ6[(1-δ')ρ 20 Z2] 2 ,

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] For ease of understanding, step (8) is now explained as follows: Design a fault-tolerant load frequency controller to keep the single-area power system mean square stable under fault conditions and have H ∞ Interference level γ.

[0163] First, a digital simulation example is used to verify the effectiveness of the fault-tolerant control design method:

[0164] First give the parameters of digital simulation:

[0165]

[0166]

[0167]

[0168] d =0.1, μ=0.5

[0169] ε=0.01,θ=0.01,δ'=0.3

[0170] ρ min =0.1,ρ max =1,

[0171] γ=0.8

[0172] Using an iterative algorithm to deal with coupling terms and make use and Replace these two terms respectively. If there is no feasible solution, let use and Replace again and Repeat this step until the controller gain K = MN is obtained. -1 .

[0173] Through step (8), the gain of the fault-tolerant load frequency controller of the present invention can be obtained:

[0174] K = [0.0495, 0.7056]

[0175] Next, we solve the simulation image and find the time point when the partial failure fault ρ(t) begins to appear: a random moment t∈[20,50].

[0176] The variable time delay takes random numbers and satisfies:

[0177] d(t)∈[0.1,0.8]

[0178] External disturbances:

[0179]

[0180] Figure 1 It represents the overall structure of a single-area power system under an actuator fault. The present invention studies a fault-tolerant load frequency control method for a single-area power system under a partial failure.

[0181] Figure 2 The curves representing the first and second components of x(t) in the system state response. In the case of faults and disturbances, each component gradually tends to 0, that is, the power system achieves mean square stability and has H ∞ Interference level γ.

[0182] Figure 3 The curves representing the third and fourth components of x(t) in the system state response. In the case of faults and disturbances, the components gradually tend to 0, that is, the power system achieves mean square stability and has H ∞ Interference level γ.

[0183] Figure 4 A curve that represents the output response of a system.

[0184] The present invention studies the fault-tolerant control method of the load frequency control scheme of a single-region power system under partial failure conditions. First, considering the distribution characteristics of the fault, a new random fault model is proposed. By constructing a suitable Lyapunov function, sufficient conditions to ensure the mean square stability of the single-region power system are obtained. Next, we transform the problem of dealing with coupling terms into a W problem, and use the corresponding lemma to split the matrix into two parts containing uncertain terms and excluding uncertain terms and eliminate the uncertain terms. Then, using an equivalent iterative algorithm, the coupling terms containing the inverse matrix in the matrix inequality are processed and the gain of the fault-tolerant load frequency controller is solved. Finally, the feasibility of this method is verified by numerical examples.

Claims

1. A fault-tolerant load frequency control method for a single-area power system based on fault distribution, characterized in that: The following steps are involved: Step 1, specify an application area power system, and obtain a structural block diagram of a single area power system under partial failure of the area; Step 2: Establish a preliminary system model based on step 1: represents the state variable of the system, u(t) represents the input signal of the system, w(t)=ΔP d It indicates that the system is subject to interference signals from the outside world, and the output of the system is in Respectively represent the matrices corresponding to each parameter: Step 3: construct a fault model; u F (t)=ρ(t)u(t),0<ρ min ≤ρ(t)≤ρ max ≤1 (2) Among them, the failure factor ρ is an unknown number with a limited range and not equal to 0, ρ min represents the lower bound of the fault factor, ρ max Indicates the upper bound of the fault factor value; The whole system sends the ACE signal to the controller in the form of output feedback. In the design of the controller, a proportional-integral controller is selected, which can be further expressed as: In order to facilitate subsequent derivation and calculation, it is necessary to redefine K and y(t): So we can get: u F (t)=-ρ(t)Ky(td(t)) (5) The variable time delay meets the following conditions: Considering the distribution characteristics of faults, define: ρ(t)=δ(t)ρ1(t)+(1-δ(t))ρ2(t) (7) Where δ(t) takes the value of 0 or 1 and satisfies: Step 4: Get the final model of the system Redefine x(t) = [ΔfΔP m ΔP v ∫ACE] Τ , we can get: in: Step 5: Apply the system model in step 4 to the regional power system specified in step 1.

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