Design method of load frequency control power system non-uniform sampling controller based on demand response

Abstract

The invention relates to the field of power systems, in particular to a load frequency control power system non-uniform sampling controller design method based on demand response. Comprising the following steps: establishing a multi-region load frequency control power system with demand response under non-uniform sampling control; constructing an integral quadratic constraint operator to quantify uncertainty caused by non-uniform sampling data and time delay; an original system is converted into a feedback interconnection system; a corresponding consistent index stability condition is given by using an integral quadratic constraint operator and a KYP lemma; designing a controller based on state feedback control and giving a corresponding iterative algorithm; the reliability and feasibility of the controller are verified through numerical simulation.

Description

Technical Field

[0001] The present invention relates to the field of load frequency control power systems, and specifically to a design method for a non-uniform sampling controller of a load frequency control power system based on demand response. Background Art

[0002] With the in-depth application of advanced technologies such as the Internet of Things, big data, cloud computing, and artificial intelligence, the load frequency control power system is gradually realizing an intelligent transformation. These technologies provide more accurate demand forecasting, more flexible energy scheduling and optimization for the power system, thereby improving energy utilization efficiency and reducing losses. When the power system faces challenges such as an increasing proportion of renewable energy generation and the deepening of the electricity market trading mechanism, it requires higher flexibility and stability. By introducing advanced control algorithms and strategies, the load frequency control power system can more effectively address these challenges and ensure the stable operation of the power system. With the acceleration of the construction of the intelligent power system, the load frequency control power system, as one of the key components, plays an irreplaceable role in enhancing the stability and flexibility of the power system. By optimizing energy distribution and scheduling, the system can achieve more efficient and environmentally friendly energy utilization.

[0003] Demand response is a technical means to respond to the changes in power supply and demand of the power system by changing the power consumption pattern. It allows power users to adjust their electricity consumption behavior when the power system needs it, so as to balance the power system load and improve the stability of the power system. In the load frequency control power system, demand response technology has been widely applied. For example, when the power system is affected by factors such as extreme weather, new energy output fluctuations, and reliability events, the demand response technology can be used to organize power customers or load aggregators to participate in interactive responses and adjust the power consumption. Thus, the power system load can be balanced. In addition, demand response technology can also be used to optimize the supply and demand balance of the electricity market and improve the efficiency and fairness of the electricity market.

[0004] Regarding this problem, there are currently many studies. For example, a state feedback controller that meets the optimal conditions is proposed for a periodic sampling load frequency control scheme with delays; a robust time-delay related PI load frequency control scheme is proposed according to the intermittent power generation of renewable energy; for a power system with limited communication bandwidth, an event-triggered load frequency control scheme oriented to decentralized control performance criteria is proposed. A multi-region power system anti-DoS attack load frequency control scheme based on an exchange system is proposed for a power system with a denial-of-service attack.

[0005] Since the load frequency control power system operates in a sampling manner in practice, traditional frequency response control mainly maintains the stability of the system frequency through periodic sampling and fixed control strategies. However, with the complexity of the power system and the large-scale access of new energy, traditional control methods are difficult to meet the requirements of efficient and precise frequency control. Especially when considering demand response, the load changes in the power system are more complex, and more flexible and intelligent control strategies are needed to cope with them.

[0006] With the development of computers and digital controllers, there have been many mature research types in sampled-data control, such as using small-gain integral quadratic constraints to characterize the properties of operators to analyze the stability of sampled-data systems with time-delay signals. There is also the input delay method; the loop-based functional method. To overcome the problems existing in the multi-area load frequency control power system considering demand response, a state feedback control strategy based on aperiodic sampled data is proposed. First, an integral quadratic constraint operator is constructed to quantify the uncertainties caused by sampled data and time delay, and a uniform exponential stability condition is given. Secondly, based on the constructed integral quadratic constraint operator, the model is transformed, and the proposed controller aims to achieve the feedback control of the system. This controller can effectively handle the influence of time-delay signals, improve the control accuracy and stability of the system, and has important practical application value. Finally, through numerical simulation, the delay signal is processed based on aperiodic sampled data combined with integral quadratic constraints, and state feedback is used for control, which can verify the improvement of the system control performance and stability, provide strong support for achieving a higher level of power system frequency stability, and has a higher practical application prospect. Summary of the Invention

[0007] To solve the above problems, the present invention discloses a design method for a non-uniform sampling controller of a load frequency control power system based on demand response.

[0008] The specific scheme is as follows:

[0009] A design method for a non-uniform sampling controller of a load frequency control power system based on demand response includes the following steps.

[0010] Step 1, establish a multi-area load frequency control power system model considering demand response under non-uniform sampling control and its discrete-time model;

[0011] Step 2, construct an integral quadratic constraint operator to quantify the uncertainties caused by non-uniform sampled data and time delay;

[0012] Step 3, for the multi-area load frequency control power system model, substitute the defined quadratic constraint operator into its discrete-time model for transformation, and convert it into a feedback interconnection system model; use the integral quadratic constraint operator and the KYP lemma to give the corresponding uniform exponential stability condition;

[0013] Step 4: Design a controller based on state feedback control and give the corresponding iterative algorithm;

[0014] Step 5: Verify the reliability and feasibility of the controller in Step 4 through numerical simulation.

[0015] Mathematical simulation of the power system is one of the key links in controller design. The goal of establishing a load frequency control power system model is to describe the actual operation effect of the real power system as much as possible. For a multi-area power system, each control area consists of tie-line power, rotating mass and load, steam turbine and governor, and demand response resources. Since the situations of different steam turbines are similar, it is assumed that non-reheat steam turbines are considered in each control area, and a controller is designed for the load frequency control power system. Without considering sampling and delay, the dynamic equation of the i-th control area is given as follows:

[0016]

[0017] Define the state variables A sampling controller design method for state feedback of load frequency control power system based on demand response considered, the specific process of giving the multi-area load frequency control power system model and its discrete-time model in Step 1 is as follows:

[0018] The main objectives of load frequency control power system controller design are to improve the load frequency stability of the power system, the stability of generator output deviation, the stability of tie-line power exchange frequency deviation, the stability of steam turbine valve position deviation, and the stability of area control error. Consider the following performance requirements:

[0019] 1) Load frequency stability: The frequency of the power system is an important indicator of power quality. Under normal circumstances, the frequency of the power system should be maintained near the rated value (such as 50HZ). Deviations or fluctuations in frequency may affect the normal operation of power equipment and the power consumption experience of users. Any change in load may lead to deviations in the tie-line exchange power between systems and fluctuations in the system frequency.

[0020] 2) Generator output deviation stability: The generator is one of the core equipment of the power system, and its output stability is crucial for the stability of the entire system. The stability of generator output deviation helps to maintain the power supply-demand balance of the power system and ensure the stability of power transmission and distribution.

[0021] 3) Tie-line power exchange frequency deviation stability: The stability of tie-line power exchange frequency deviation helps to maintain the coordinated operation between different parts of the power system. In the power system, power is exchanged between different regions through transmission lines. If the exchange frequency deviates, it may affect the efficiency and stability of power transmission.

[0022] 4) Stability of steam turbine valve position deviation: In power production, steam turbines are one of the commonly used power generation equipment. The stability of the steam turbine valve position deviation is crucial for the stable operation of the generator and the stability of the output power. If there is a deviation in the steam turbine valve position, it may cause fluctuations in the generator output power, thereby affecting the stability of the power system. Therefore, measures need to be taken to ensure the stability of the steam turbine valve position.

[0023] 5) Stability of area control error: Area control error refers to the difference between the actual power generation and the load demand in a certain area of the power system. The stability of the area control error helps to maintain the power supply-demand balance and stable operation of the power system.

[0024] Considering the above five constraints and reflecting them in the input and output of the system, the following state space can describe the load frequency control power system:

[0025]

[0026] where

[0027]

[0028] T ij = T ji , i≠j,

[0029] respectively represent the generator control input and the demand response control input.

[0030] Due to the time delay in the signal transmission process, the sensor cannot update the actuator in real time after receiving the signal. To explore the non-periodic sampling data control problem of the load frequency control power system, consider that the sampling sequence {s k} satisfies 0 = s0 < s1 < … < s k < s k+1 < …, and where h and are two real numbers greater than zero, and l k is the time-varying sampling data interval. Due to the influence of transmission delay within the sampling interval, the control input of the system has

[0031]

[0032] At the same time, the following relationship is satisfied between the demand response control input and the generator control input

[0033]

[0034] Therefore, after the state variables affected by time delay are controlled by the state feedback controller, there is

[0035]

[0036] The implementation method of state feedback control is relatively flexible and can be adjusted according to the state requirements of the power system. By adjusting the output of the system, better load frequency control of the power system can be achieved.

[0037] The construction process of the equivalent feedback interconnection of the closed-loop system given in Step 3 is as follows:

[0038] First, in order to cope with the consequences brought by time delay, a feedback interconnection model of the closed-loop system is constructed for the closed-loop system G and the operator generated by sampled data and time delay. For the original system, bring into the feedback interconnection model; therefore, the problem is reduced to the non-periodic sampled data control problem about time delay in the load frequency control power system, design a state feedback controller, and construct a feedback interconnection term.

[0039] Analyze the exponential stability of the closed-loop system based on integral quadratic constraints; considering that the feedback interconnection model is exponentially stable at is equivalent to the feedback interconnection structure:

[0040]

[0041] where Obtain the feedback interconnection structure of G - Ψ; since the feedback interconnection term cannot guarantee the condition that the initial state is zero, the integral quadratic constraint cannot be directly used; to solve this problem, corresponding to the feedback interconnection, a series of transformations are performed on the feedback interconnection using the Bohl-Perron principle to obtain a structure relative to the case where the initial state is zero, and using the integral quadratic constraint, an integral quadratic constraint inequality about the time domain is obtained

[0042]

[0043] The following steps are for the stability of the load frequency control power system:

[0044] Step 1: The closed-loop system G is a linear time-invariant system defined by feedback interconnection, and Ψ is a causal operator such that (G, Ψ) is well-posed; assume that Ψ satisfies Ξ = diag{ΠX, -X} in the time domain through Π, where Π is a given scalar matrix ring and X ∈ R. If there exists a matrix P T = P ∈ R such that

[0045]

[0046] Then (G, Ψ) is uniformly exponentially stable.

[0047] Step 2: For the load frequency control power system, a state feedback controller is designed, and a cyclic iteration algorithm is given. The designed controller can stabilize the system and meet the finite frequency domain requirements. For the given Φ, and Π, the state space of the load frequency control power system can be realized. When there exists a matrix satisfying P T = P > 0 ∈ R, the existence of a controller for the load frequency control power system to be stable and further meet the finite frequency domain index is obtained and

[0048]

[0049] where Υ = [U 0 -I], from which the state feedback control gain matrix can be obtained For the satisfied σ1 and σ2, using the KYP lemma, the above inequality holds, and finally can be used as the desired state feedback control gain matrix.

[0050] Based on the KYP lemma, an iterative algorithm for the state feedback controller is studied. The solution algorithm of this controller adopts a two-stage idea. In the first step, an initial controller is obtained, and there exists a feasible solution as the initial value. In the second step, the state feedback controller is solved, and the optimal solution of the designed iterative algorithm is given. The iterative algorithm of the state feedback controller is given as follows:

[0051] Input: The system parameters of the given power system, and the maximum and minimum sampling intervals h, the upper bound of the transmission delay and the parameter ε = 1;

[0052] Output: The control gain K;

[0053] Step - 1: (Initialization) Let the matrix coupling term K T K = W, solve the controller gain matrix K0 that satisfies the conditions, and solve the linear matrix inequality (3) to obtain the initial controller where σ1 = [I 0], σ2 = [I 0], U = diag{K, K};

[0054] Step - 2.1: (Optimization) If where then the obtained controller gain K = K j , assuming j = 0 at this time;

[0055] Step - 2.2: (Loop) Let Obtain the new control gain by solving the linear matrix inequality (3)

[0056] 1: If and satisfy 2: Then output

[0057] 3: End;

[0058] 4: Otherwise, let j = j + 1,

[0059] 5: If it satisfies

[0060] 7: Then output

[0061] 6: End.

[0062] The beneficial effects of the present invention are as follows: In the background of the gradually expanding scale of the power system, the controller designed by the present invention can still maintain the stability of the system in the case of transmission delay in the power system. At the same time, under the control of demand response, the stability effect of the system can be better. And the sampling efficiency is improved by non-uniform sampling of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is the multi-area load frequency control power system model with demand response in area i of the present invention;

[0064] Figure 2 It is the system frequency response diagram of the present invention under different controllers in a single area;

[0065] Figure 3 It is the system state response diagram of the present invention in area 1 of two areas under different controllers;

[0066] Figure 4 It is the system state response diagram of the present invention in area 2 of two areas under different controllers;

[0067] Figure 5 It is the system sampling needle diagram of the present invention under periodic sampling and aperiodic sampling in a single area;

[0068] Figure 6 It is the system sampling needle diagram of the present invention under periodic sampling and aperiodic sampling in area 1 of two areas;

[0069] Figure 7 It is the system sampling needle diagram of the present invention under periodic sampling and aperiodic sampling in area 2 of two areas;

[0070] Figure 8 It is the system state response diagram of the present invention under periodic sampling and aperiodic sampling in a single area;

[0071] Figure 9Eigenvalue diagram of the present invention under load frequency control of a power system with demand response in a single area as the sampling time h0 decreases from 0.8 to 0.1;

[0072] Figure 10 System state response diagram of the present invention under different weighted scalars α in a single area;

[0073] Figure 11 System state response diagram of the present invention under different weighted scalars α in area 1 of a two - area system;

[0074] Figure 12 System state response diagram of the present invention under different weighted scalars α in area 2 of a two - area system;

[0075] Figure 13 Eigenvalue diagram of the present invention under load frequency control of a power system with demand response in a single area as the weighted scalar α increases from 0.1 to 0.8;

[0076] Figure 14 Interconnected power system structure diagram under the IEEE 39 - bus test system;

[0077] Figure 15 Frequency response diagram obtained under the IEEE 39 - bus test system using the controller designed by the present invention and the PI controller;

[0078] Figure 16 Method flow chart of the present invention. Detailed implementation manners

[0079] The present invention will be further clarified below in conjunction with the accompanying drawings and detailed implementation manners. It should be understood that the following detailed implementation manners are only used to illustrate the present invention and not to limit the scope of the present invention.

[0080] As Figure 1 and 16 shown, the present invention provides a design method for a non - uniform sampling controller of a load frequency control power system based on demand response, which mainly includes the following steps.

[0081] Step 1: Establish a multi - area load frequency control model considering demand response under non - uniform sampling control and its discrete - time model.

[0082] The specific process is as follows: In a multi - area power system, i (i = 1, 2,..., m) is used to represent different power system areas, and each area is interconnected. A simplified dynamic model of a single - area power system is given as follows,

[0083]

[0084] where, in area i, Δf iis the frequency deviation, ΔP si is the supplementary control input deviation, ΔP gi is the generator mechanical output deviation, ΔP li is the load deviation, ΔP vi is the turbine valve position deviation, ΔP tie,i is the distribution power exchange deviation; T ti is the turbine time constant, T gi is the equivalent governor constant, T ij is the tie-line synchronization constant between region i and region j, j = 1, 2, …, m, H i is the equivalent inertia constant, D i is the equivalent load damping coefficient, t represents time, m represents there are m regions in this power system; the area control error Ω i is defined as Ω i = β i Δf i +ΔP tie,i ; where β i is the frequency deviation factor;

[0085] By defining the following state variables output disturbance Then the load frequency control state space model with demand response including m regions can be described as

[0086]

[0087] Among them,

[0088]

[0089]

[0090] T ij = T ji , i ≠ j,

[0091]

[0092] respectively represent the generator set control input and the demand response control input.

[0093] In this embodiment, considering five constraint conditions of load frequency stability, generator output deviation stability, distribution power exchange frequency deviation stability, turbine valve position deviation stability and area control error stability, and reflecting them in the input and output of the load frequency control power system, due to the delay in data sampling and transmission, by setting the sampling sequence {s of the sampler k} satisfying \(0 = s_0 \lt s_1 \lt \cdots \lt s\) k \(\lt s\) k+1 \(\lt \cdots\), and where \(h\) and are two real numbers greater than zero, and \(l\) k is a time-varying sampling data interval.

[0094] Within the sampling interval, due to the influence of transmission delay (the delays generated by the generator transmission signal and the demand response transmission signal are respectively ), the control input of the system has

[0095]

[0096] Meanwhile, the following relationship is satisfied between the demand response control input and the generator control input

[0097]

[0098] Therefore, after the state variables affected by time delay are controlled by the state feedback controller, there is

[0099]

[0100] where \(\alpha\) i \(\in (0, 1]\) is the weight scalar of the demand response and the generator set, represents the state at the sampling sequence moment, respectively represent the generator control input and the demand response control input in region \(i\), and \(K\) i represents the control gain.

[0101] Discretizing the original system can obtain the discrete-time model of the power system under non-periodic sampling data as

[0102]

[0103] where is the system state at the sampling moment \(s\) k ,

[0104] \(\Gamma\) k \( = B\) 11 + B 12 M, \(\Lambda\) k \( = B\) 21 + B 22 M,

[0105]

[0106] \(K = \text{diag}\{K_1, K_2, \cdots, K\) m \},

[0107]

[0108] In Step 2, the non-periodic sampling data and the uncertainties caused by time delay existing in the system are quantified by an integral quadratic constraint operator, and it is defined that:

[0109] Ψ = diag{Ψ1, Ψ1Ψ g , Ψ1Ψ r , Ψ1, Ψ g , Ψ1, Ψ r},

[0110]

[0111] where Ψ1, Ψ gi , Ψ ri represent different integral quadratic constraint operators respectively.

[0112] In Step 3, the original system is transformed. The defined integral quadratic constraint operator is introduced into the discrete system and it is transformed into a feedback interconnection system. By defining the state matrix the feedback interconnection system

[0113]

[0114] where

[0115]

[0116] Ψ = diag{Ψ1, Ψ1Ψ g , Ψ1Ψ r , Ψ1, Ψ g , Ψ1, Ψ r},

[0117] K = diag{K1, K2, …, K m}.

[0118] Using the integral quadratic constraint theory and the KYP lemma, the uniform exponential stability condition of the system is given. The closed-loop system G is a linear time-invariant system defined by feedback interconnection, and Ψ is a causal operator such that (G, Ψ) is well-posed; assume that Ψ satisfies the time domain Ξ = diag{ΠX, -X} through ∏, ∏ is a given scalar matrix ring, X ∈ R. If there exists a matrix P T = P ∈ R such that

[0119]

[0120] then (G, Ψ) is uniformly exponentially stable.

[0121] Design a controller based on state feedback control according to Step 4 and give the corresponding iterative algorithm. For a given Φ, γ, ε, when there exists a matrix P satisfying P > 0, the existence of a controller for the power system stability to further satisfy the finite frequency domain index and

[0122]

[0123] The control gain matrix K = σ1Uσ2 T , where,

[0124] σ1 = [I 0] ∈ R m×2m , σ2 = [I 0] ∈ R 5m×10m

[0125] Υ = [U 0 -I].[[]]END]]

[0126] Thus, the state feedback control gain matrix K can be obtained.[[]]END]]

[0127] To verify the effectiveness of the proposed theoretical results, the parameters of a single - area load frequency control power system with demand response are selected as shown in Table 1

[0128] Table 1

[0129]

[0130] The parameters of a two - area load frequency control power system with demand response are shown in Table 2

[0131] Table 2

[0132] Region <![CDATA[H i (p.u. / s)]]> <![CDATA[D i (p.u. / Hz)]]> <![CDATA[R i (Hz / p.u.)]]> <![CDATA[T gi (s)]]> <![CDATA[T ti (s)]]> <![CDATA[T ij > <![CDATA[β i > 1 5 1 0.05 0.1 0.3 0.2 21 2 6 1.5 0.05 0.17 0.4 0.2 21.5

[0133] The load frequency control power system with demand response in a single area is simulated below. Using the data given in Table 1, the controller gains of the load frequency control power system with demand response in a single area are obtained as [-0.0189 -0.0258 0.0021 -0.0052 0.0101]. Under the condition that the maximum time-varying delay is 2 s and the weight scalar α = 1, this result is compared with the controller results obtained in Reference [1] (Journal: IEEE Journal on Emerging and Selected Topics in Circuits and Systems; Authors: Xin Zhao, Zhongjing Ma, Shouxiang Li, and Suli Zou; Publication Time: 2022; Article Title: Robust LFC of Power Systems With Wind Power Under Packet Losses and Communication Delays; Pages: 135 - 148) and Reference [2] (Journal: IEEE Transactions on Industrial Informatics; Authors: Xing-Chen Shangguan, Chuan-Ke Zhang, Yong He, Li Jin, Lin Jiang, and Joseph W. Spencer; Publication Time: 2021; Article Title: Robust Load Frequency Control for Power System Considering Transmission Delay and Sampling Period; Pages: 5292 - 5303). The state response diagram is as Figure 2 shown. It can be seen from Figure 2 that the controller designed in the present invention can make the frequency response fluctuate less and the stability effect is better.

[0134] The control gains of the load frequency control power system with demand response in a two-area under the controller designed in the present invention are respectively: the controller gain of Area 1 is

[0135] [-0.2631 -0.0795 0.0148 -0.1055 0.0268], and the controller gain of Area 2 is

[0136] [-0.3372 -0.0858 -0.0162 -0.1031 0.0264]. Under the condition that the maximum time-varying delay in the two-area is 1 s and the weight scalars α1 = 1, α2 = 1, the state response diagram of the system is as Figures 3 - 4 shown. It can be seen from Figures 3 - 4It can be seen that the controller designed by the present invention can make the system more stable.

[0137] Uniform sampling and non-uniform sampling of the system are respectively carried out in a single area and a double area, and the obtained sampling needle diagrams are respectively as Figures 5 - 7 shown, and Figure 8 the state response diagrams of the system under periodic and aperiodic sampling are given. Figure 9 It shows that when the sampling time h0 is reduced from 0.8 to 0.1, the eigenvalues of the system are still within the unit circle. Figures 10 - 12 The influence of demand response on the system state response in the power system is respectively described. And it can be seen from Figures 10 - 12 that under the assisted control of demand response, the load frequency control of the power system has a better stability effect. Figure 13 It shows the stability of the system under different proportions of the system control occupied by demand response control. As the weight scalar α increases from 0.1 to 0.8, the eigenvalues of the system gradually become smaller.

[0138] The controller designed by the present invention is simulated and verified by using the IEEE 39bus test system, and the parameters are respectively shown in Table 3

[0139] Table 3

[0140]

[0141] Figure 14 is the structure diagram of the IEEE 39bus interconnected power system. Among them, 1-39 indicates that the system consists of 39 buses, G1-G10 indicate 10 generators, and the symbol arrows indicate 19 load buses. In this system, the 10 generating units are divided into 3 areas for analysis and discussion. The controller gains of the three areas are obtained by the controller method designed by the present invention as K 11 =[-0.2722 -0.0457 -0.0025 -0.0221 0.0916],

[0142] K 12 =[-0.5702 -0.0501 -0.0238 -0.0244 0.2513],

[0143] K 12 =[-0.5702 -0.0501 -0.0238 -0.0244 0.2513],

[0144] By comparing with the controllers obtained from the literature [3] (Journal: Applied Energy; Authors: Xingchen Shang-Guan, Yong He, Chuanke Zhang, Lin Jiang, Joseph William Spencer and Min Wu; Publication Time: 2020; Article Title: Sampled-data based discrete and fast load frequency control for power systems with wind power) [4] (Journal: International Journal of Robust and Nonlinear Control; Authors: Yulong Li, Xiaoqing Li, Jun Cheng, Kaibo Shi and Kun Qiu; Publication Time: 2024; Article Title: Reliable quantized sampled-data lfc for semi-markov jump interconnected multi-area power systems: Dealing with incomplete trs; Page Numbers: 3241-3258), the comparison results are as Figure 15 shown. It can be Figure 15 found that the stability conditions and the designed controller method proposed in the present invention show good stability and fast response ability on the IEEE 39-bus test system. The practical application not only verifies the accuracy of the theoretical analysis, but also fully proves the feasibility and important value of the method in the actual power system.

[0145] The above results show that a design method of a load frequency control power system controller with demand response based on aperiodic sampling control proposed in the present invention can effectively handle the uncertainties brought by aperiodic sampling data and time delay based on integral quadratic constraints, and can make the load frequency control power system stable faster under aperiodic sampling and time-varying delay, and at the same time can also improve the system sampling efficiency. To sum up, compared with the PI controller in the power system, the state feedback control proposed in the present invention has the advantages of robustness, improved control performance, simplified design, etc., and can improve the robustness and control performance of the system.

[0146] This invention studies the stability analysis and controller design of a demand response load frequency modulation power system considering communication delay, integrates demand response resources, and facilitates the provision of auxiliary frequency modulation services. First, the continuous-time model of multi-area load frequency control considering demand response is transformed. By setting reasonable control inputs, it is converted into a multi-area discrete-time model. Then, the uncertainties of communication delay and non-periodic sampling data period in the system are represented by linear operators, and the discrete system is transformed into a feedback interconnection system composed of uncertainty operators and linear time-invariant systems. Using the integral quadratic constraint theory and the Bohl-Perron principle, the conditions for uniform exponential stability of the system are given. On this basis, a new control scheme is designed, and the transmission delay and non-periodic sampling decoupling technology are considered, and the iterative algorithm of the controller is given. Simulation verification shows the effectiveness and superiority of this method in the demand response load frequency control system.

Claims

1. Design method of non-uniform sampling controller for load frequency control power system based on demand response, characterized in that including the following steps, Step 1: Establish a multi-area load frequency control power system model considering demand response under non-uniform sampling control and its discrete-time model; Step 2: Construct an integral quadratic constraint operator to quantify the uncertainties caused by non-uniform sampling data and time delays; Step 3: For the multi-area load frequency control power system model, substitute the defined quadratic constraint operator into its discrete-time model for transformation, and convert it into a feedback interconnection system model; use the integral quadratic constraint operator and the KYP lemma to give the corresponding uniform exponential stability conditions; Step 4: Design a controller based on state feedback control and give the corresponding iterative algorithm; Step 5: Verify the reliability and feasibility of the controller in Step 4 through numerical simulation.

2. The design method of the non-uniform sampling controller for the load frequency control power system based on demand response according to claim 1, characterized in that Step 1 includes first giving the dynamic equation of control area i, where i = 1, 2, …, m: where, in area i, Δf i is the frequency deviation, ΔP si is the supplementary control input deviation, ΔP gi is the generator mechanical output deviation, ΔP li is the load deviation, ΔP vi is the turbine valve position deviation, ΔP tie,i is the tie-line power exchange deviation; T ti is the turbine time constant, T gi is the equivalent governor constant, T ij is the tie-line synchronizing constant between area i and area j, j = 1, 2, …, m, H i is the equivalent inertia constant, D i is the equivalent load damping factor, t represents time, and m represents that there are m areas in the power system; the area control error Ω i is defined as Ω i = β i Δf i + ΔP tie,i ; where β i is the frequency deviation factor; by defining the following state variables output disturbance then the load frequency control power system model with m areas and demand response is described as where, T ij = T ji , i ≠ j, respectively represent the generator set control input and the demand response control input.

3. The design method of the non-uniform sampling controller for a load frequency control power system based on demand response according to claim 2, characterized in that Considering five constraint conditions of load frequency stability, generator output deviation stability, distribution power exchange frequency deviation stability, steam turbine valve position deviation stability, and area control error stability, and reflecting them in the input and output of the load frequency control power system. Due to the delay in data sampling and transmission, considering the sampling sequence {s k} satisfying 0 = s0 < s1 < … < s k < s k+1 < …, and where h and are two real numbers greater than zero, l k is a time-varying sampling data interval; the delays generated by the generator transmission signal and the demand response transmission signal are respectively Therefore, after the state variables affected by time delay are controlled by the state feedback controller, there is Among them, α i ∈(0, 1] is the weight scalar of demand response and generator sets, represents the state at the sampling sequence moment, respectively represent the generator set control input and demand response control input in region i, K i represents the control gain; The discrete-time model of the load frequency control power system considering demand response under the state feedback controller considering the above five constraint conditions is where, Γ k = B 11 + B 12 M, Λ k = B 21 + B 22 M, K = diag{K1, K2, …, K m}, 4. A design method of a non-uniform sampling controller for a load frequency control power system based on demand response according to claim 3, characterized in that, In Step 2, the integral quadratic constraint operator is defined as: Ψ = diag{Ψ1, Ψ1Ψ g , Ψ1Ψ r , Ψ1, Ψ g , Ψ1, Ψ r}, Among them, Ψ1, Ψ gi , Ψ ri represent different integral quadratic constraint operators respectively.

5. A design method of a non-uniform sampling controller for a load frequency control power system based on demand response according to claim 4, characterized in that, In step 3, in order to address the consequences brought about by time delay, a model of a closed-loop feedback interconnection system is constructed for the discrete-time model and the operator Ψ generated by sampled data and time delay, which is G: where Ψ = diag{Ψ1, Ψ1Ψ g , Ψ1Ψ r , Ψ1, Ψ g , Ψ1, Ψ r}, K = diag{K1, K2, …, K m}.

6. A design method for a non-uniform sampling controller of a load frequency control power system based on demand response according to claim 5, characterized in that, The closed-loop system G is a linear time-invariant system defined by feedback interconnection, and Ψ is a causal operator such that (G, Ψ) is well-posed; Suppose Ψ satisfies the time domain Ξ = diag{ΠX, -X} through ∏, where ∏ is a given scalar matrix ring and X ∈ R. If there exists a matrix P T = P ∈ R such that Then (G, Ψ) is uniformly exponentially stable.

7. A design method of a non-uniform sampling controller for a load frequency control power system based on demand response according to claim 6, characterized in that, In step 4, for the load frequency control power system, a state feedback controller is designed and a cyclic iteration algorithm is given. The designed controller stabilizes the system and meets the finite frequency domain requirements. For a given Φ, γ, ε, when there exists a matrix P satisfying P>0, the existence of a controller for the power system stability to further meet the finite frequency domain index is also considered and The control gain matrix K = σ1Uσ2 T , where, σ1 = [I 0] ∈ R m×2m , σ2 = [I 0] ∈ R 5m×10m Υ = [U 0 - I]. Thus, the state feedback control gain matrix K is obtained; Based on the KYP lemma, a heuristic algorithm for the state feedback controller is studied. The solution algorithm of this controller adopts a two-stage idea. The first step is to obtain an initial controller, and there is a feasible solution as the initial value. The second step is to solve the feedback controller and give the optimal solution of the designed iterative algorithm; The following gives the iterative algorithm for solving the state feedback controller: Input: System parameters of a given power system, and the maximum and minimum sampling intervals h, the upper bound of the transmission delay and the parameter ε = 1; Output: Control gain K; Step - 1: Let the matrix coupling term be K T K = W, solve for the controller gain matrix K0 that satisfies the conditions, and solve the linear matrix inequality (3) to obtain the initial controller where σ1 = [I 0], σ2 = [I 0], U = diag{K, K}; Step - 2.1: If where then the obtained controller gain K = K j , assuming j = 0 at this time; Step - 2.2: Let Obtain a new control gain by solving the linear matrix inequality (3) 1: If and satisfy 2: Then the output 3: End; 4: Otherwise, let 5: If satisfied 7: Then output 6: End.

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