A time-delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism

Abstract

The application discloses a time-delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism, and relates to the technical field of micro-grid load frequency control. A new event triggering mechanism based on an adaptive threshold is provided to solve the problem that the control performance of a micro-grid load frequency control system is not ideal due to bandwidth limitation. The application mainly comprises the following steps: step 1, a state space model is established according to the parameters of each distributed power supply and energy storage system of an island micro-grid; step 2, an adaptive event triggering mechanism considering communication delay is introduced into the micro-grid load frequency control; step 3, based on a Lyapunov functional method, a stability criterion of the time-delay island micro-grid is derived; and step 4, a triggering matrix Omega and a minimum performance index gamma are solved min The application introduces the adaptive event triggering mechanism into the island micro-grid load frequency control system, and reduces the loss of communication resources of a communication system and the influence of communication delay.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of micro-grid load frequency control, and particularly relates to a time-delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism. BACKGROUND

[0002] A micro-grid has functions of power generation, power transmission, power transformation and power distribution, and is a small power system integrating distributed power sources, energy storage devices, loads and protection devices. The micro-grid has two operation modes of grid-connected operation and island operation. However, the intermittency and instability of power output of renewable energy may cause frequency fluctuation or instability of the micro-grid, which brings great challenges to load frequency control (LFC) of the micro-grid, especially the island micro-grid. In recent years, how to design an effective scheme to solve the communication problem in load frequency control has become a hot spot.

[0003] With the rapid development of computer technology and communication technology, a shared network is widely used in load frequency control, but this inevitably causes problems such as time delay and bandwidth congestion. In recent years, in order to reduce the consumption of communication resources, an event triggering mechanism has been gradually introduced into the load frequency control scheme. However, the disturbance caused by weather changes is unpredictable, resulting in continuous frequency fluctuation and frequent data transmission. The static threshold cannot be adaptively adjusted according to the change of the frequency response deviation of the system, and part of the unnecessary data is still transmitted. In this case, the static event triggering scheme is difficult to guarantee good working performance under the condition of relatively small number of communications. The adaptive event triggering mechanism has stronger adaptability to the system state and dynamic characteristics of the disturbance of the controlled object, and can also intelligently adjust the control parameters according to the system state and disturbance. On this basis, the system works optimally according to the predetermined standard. The introduction of the adaptive event triggering mechanism can further reduce the consumption of communication resources, while having better frequency response performance. In order to maintain the balance between system dynamic performance and saving of communication resources, we try to combine the adaptive event triggering mechanism with the control scheme to design a more effective controller. SUMMARY

[0004] In order to solve the technical problems in the above background art, the present application provides a time-delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism, which is reasonably designed and greatly saves communication bandwidth.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0006] A time-delay island micro-grid load frequency control system based on an adaptive event triggering mechanism comprises a plurality of distributed generators, a plurality of loads, a plurality of energy storage devices, a plurality of protection devices and a plurality of communication devices. Figure 3As shown, including sensors, event generators, controllers, zero-order holders and actuators;

[0007] Sensors: sample data from the system and transmit the sampled data to the event generator;

[0008] Event generator: receive the signal sent by the sensor, and determine whether the latest measurement output y(t) meets the trigger condition, if it meets, send the measurement output y(t) to the controller to generate a new control signal, if it does not meet, judge the next measurement output y(t);

[0009] Controller: receive the signal sent by the event generator and generate a new control signal, and transmit it to the zero-order holder;

[0010] Zero-order holder: receive the discrete control signal generated by the controller and make it continuous, and transmit it to the actuator;

[0011] Actuator: receive the continuous signal of the zero-order holder and execute the control command;

[0012] By sampling the island micro-grid through the sensor to obtain the measurement output y(t) of the system, then the measurement output y(t) is sent to the event generator and the latest measurement output y(t) is judged whether it meets the trigger condition, if it meets, the measurement output y(t) is sent to the controller, if it does not meet, the next measurement output y(t) is judged, then the discrete signal is converted to continuous signal through the zero-order holder, and the control command is executed by the actuator to restore the frequency of the system.

[0013] The application also provides a time-delay island micro-grid load frequency control method based on an adaptive event triggering mechanism, which can greatly save the consumption of communication resources while maintaining the dynamic performance of the system, mainly including the following steps:

[0014] S1: establishing a state space model of a closed-loop system based on the structural parameters of the island micro-grid;

[0015] S2: introducing an adaptive event triggering mechanism considering communication delay into the micro-grid load frequency control;

[0016] S3: based on the Lyapunov functional method, deriving a stability criterion for the time-delay island micro-grid and excluding the Zeno phenomenon;

[0017] S4: solving the trigger matrix Omega and the minimum performance index gamma using MATLAB / LMI toolbox min ;

[0018] Preferably, the step S1 establishes a closed-loop state space model of the island micro-grid including the controller based on the system parameters of the island micro-grid, and the specific steps are as follows:

[0019] S11: Define state variable x(t), measured output y(t), target vector z(t), system disturbance ω1(t) and measurement bias ω2(t):

[0020]

[0021] ΔP wind (t), ΔP s (t) and ΔP d (t) represent wind speed changes, solar radiation intensity changes and load power changes of the wind generator, respectively, Δf represents the system frequency deviation, ΔP DEG , ΔP MTG , ΔP FC , ΔP V , ΔP WTG , ΔP FESS , ΔP BESS represent the power output changes of the diesel generator, fuel cell, photovoltaic cell, wind generator, flywheel energy storage system and battery energy storage system, respectively, in order to facilitate the representation of the system state, the intermediate variables ΔP DEG1 , ΔP MTG1 , ΔP FC1 , ΔP FC2 and ΔP V1 are introduced, Δf(t) is the system frequency deviation, and z(t) is the target vector;

[0022] S12: Set the PI controller strategy, and use the system frequency deviation Δf(t) as the input signal of the controller:

[0023] u(t) = -K P Δf(t) - K I ∫Δf(t)dt (1)

[0024] Where K P and K I are the proportional and integral coefficients of the system, and u(t) is the PI controller input signal;

[0025] S13: Define the augmented vector

[0026] S14: Establish the closed-loop state space model of the island microgrid:

[0027] The dynamic model of the island microgrid load frequency control system is shown in Figure 2 , and the closed-loop state space model of the island microgrid including the controller can be obtained by combining Figure 1 and the controller (1) as follows:

[0028]

[0029] wherein,

[0030]

[0031] C2=[1 0 0 0 0 0 0 0 0 0 0 0 0],

[0032]

[0033] wherein, H represents the mechanical inertia of the island microgrid, R1, R2 are constants, T WTG , T PV represent the dynamic parameters of the wind turbine and the photovoltaic system, T IC , T t , T FC , T IN all represent the time constant of the converter, T DEG , T MTG , T FC , T FESS , T BESS are the response times of the diesel generator, the microturbine generator, the fuel cell, the flywheel energy storage system and the battery energy storage system, respectively;

[0034] Preferably, the step S2 introduces an adaptive event triggering mechanism to establish a time-delay island microgrid load frequency control system model containing a communication scheme and a controller, and the specific steps are as follows:

[0035] S21: define a delay function τ(t)∈[τ m ,τ M ], wherein: τ=τ M -τ m (τ m ≥0), τ M and τ m represent the upper and lower limits of the communication delay, t k represents the kth triggering time, k represents the kth triggering, h is defined as the sampling period, t k +ih represents the ith sampling time after the kth triggering, and it is assumed that the triggering time s k =t k +τ(t k ), τ(t k )∈[τ m ,τ M ];

[0036] S22: the measured output y(t) can be represented as:

[0037] y(t) = C1x(t k )+Dω2(t k ), t∈[s ks k+1 ) (3)

[0038] S23: The error function can be expressed as:

[0039] e(t) = y(t k )-y(t k +ih) = y(t k )-y(t-τ(t)) (4)

[0040] S24: The control signal of the PI controller is:

[0041] u(t) = u(t k +τ k ) = Ky(t k ), t∈[s k ,s k+1 ) (5)

[0042] S25: The state space model of the microgrid load frequency control system can be rewritten as:

[0043]

[0044] S26: Construct the event-triggered condition:

[0045] An adaptive event-triggering mechanism is introduced to reduce unnecessary data transmission. After the sensor samples the controlled device, it determines whether the transmission condition is met. Only when the event-triggered condition is met will the sampled signal be sent to the controller. Otherwise, it will not be sent and the next sampled signal will be determined. The adaptive event-triggered condition is (7):

[0046]

[0047] where the trigger matrix Ω > 0 and the dynamic threshold σ(t) satisfies the differential equation (8):

[0048]

[0049] where μ > 0 and ρ > 0 are given constants, and 0 < 1 / ρ < σ(t) < 1.

[0050] If μ = 0, i.e. σ(t) becomes a constant, and the adaptive event-triggering mechanism will be reduced to a static event-triggering mechanism.

[0051] If the closed-loop system (6) under the event-triggered condition (7) satisfies the following two conditions, the system is asymptotically stable:

[0052] (3) When ω1(t) = 0, ω2(t) = 0, the system is asymptotically stable.

[0053] (4) for non-zero If there is a positive constant γ > 0 such that the following is satisfied under zero initial conditions:

[0054]

[0055] Preferably, the step S3 derives the stability criterion of the time-delay island microgrid based on the Lyapunov functional method, and excludes Zeno phenomenon, and the specific steps are as follows:

[0056] S31: Select an augmented Lyapunov-Krasovskii functional:

[0057] Select the Lyapunov functional as follows, and perform inequality scaling on it;

[0058]

[0059] V1(t) = x T (t)Px(t) (10a)

[0060]

[0061]

[0062]

[0063]

[0064] Wherein, P > 0, Q1 > 0, Q2 > 0, Q3 > 0, R > 0 and S > 0 are positive definite matrices with appropriate dimensions, τ = τ M -τ m .

[0065] The derivative of V(t) can be obtained as:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] S32: Solve the system asymptotic stability criterion:

[0073] Based on the closed-loop system (6), the following equation is established:

[0074]

[0075] where M,N∈R n×n and ε is a given constant.

[0076] The integral term of (7) can be reduced order as:

[0077]

[0078] where The matrix R>0.

[0079] The integral term of (7) can be reduced order as:

[0080]

[0081] where S>0,ζ T (t)=[x T (t-τ m ),x T (t-τ(t)),x T (t-τ M )].

[0082] When t∈[s k ,s k+1 ), the adaptive event-triggered condition (7) can be obtained as:

[0083] σ(t)y T (t-τ(t))Ωy(t-τ(t))-e T (t)Ωe(t)≥0,t∈[s k ,s k+1 ) (15)

[0084] Further, we can get:

[0085]

[0086] Suppose there is a small enough positive number δ such that:

[0087]

[0088] Inequality (17) can be converted into matrix form:

[0089] η T (t)Ψη(t)≤0 (18)

[0090] When , because is a continuous function, we can integrate (19) from 0 to +∞ on both sides:

[0091]

[0092] When ω1(t)≡0 and ω2(t)≡0, it can be seen from (17) that:

[0093]

[0094] Therefore, the closed-loop system (6) is asymptotically stable while ensuring the performance index γ.

[0095] S33: Islanded microgrid load frequency control system (6) criterion based on linear matrix inequality:

[0096] According to steps S31-S32, the following stability criterion is obtained:

[0097] For a given sampling period h>0, a constant ε>0, 0<1 / ρ<σ(t)<1, μ>0, For a given sampling period h>0, a constant ε>0, 0<1 / ρ<σ(t)<1, μ>0,

[0098]

[0099] In the formula,

[0100]

[0101]

[0102] Ψ 33 = -Q1 + Q2 + Q3 - S - 4R, Ψ 12 = P - M + εA T N T , τ = τ M - τ m ,

[0103]

[0104] Φ 14 = col{ML, εML, 0, 0, 0}, Φ 15 = col{6R, 0, 6R, 0, 0}, Φ 22 = D T ΩD - γ 2 I,

[0105]

[0106] ​Where I represents the identity matrix, and * represents the transpose of the matrix at the pairwise position. All of the above matrices have appropriate dimensions.

[0107] The stability criterion of equation (23) is derived based on h > 0. Another case will be discussed below.

[0108] S34: Analysis of the Zeno Phenomenon:

[0109] When h=0, the load frequency control system (6) of the islanded microgrid may experience Zeno's phenomenon. To avoid Zeno's phenomenon in the islanded microgrid, it is necessary to ensure that the previous signal is received by the controller before the next signal is updated.

[0110] Combining the adaptive event triggering criterion (7) and σ(t)>0, we can obtain:

[0111] ||e(s k+1 )||>σ(t)||y(t)||,t∈[s k ,s k+1 ) (twenty two)

[0112] When ω2(t)≡0, then in t∈[s k ,s k+1 The derivative of e(t) at time t is as follows:

[0113]

[0114] Where p1=||C1BKC1||1||x(t-τ(t))||1+||C1A||1||x(t)||1+||C1A||1||ω1(t)||1, p2=||C1BKC1||1.

[0115] From the definition of e(t), we know that e(s) k ) = 0. Combining (5) and the comparison inequality, we can solve equation (23) to get:

[0116]

[0117] Therefore, there exists a positive number. The minimum execution time T satisfies:

[0118]

[0119] This means that in ensuring While achieving the performance index γ, the islanded microgrid load frequency control system does not exhibit Zeno's behavior at h=0, thus completing the proof. Systems based on continuous event triggering may exhibit Zeno's behavior; to prove that this system does not exhibit Zeno's behavior, the above proof was provided.

[0120] Preferably, the step S4 solves the triggering matrix Omega and the minimum performance index gamma min ;

[0121] S41: solving feasible solution:

[0122] Solving a set of feasible solutions of linear matrix inequality (21) as constraint by using the feasp solver in MATLAB / LMI toolbox

[0123] S42: solving the minimum performance index gamma min :

[0124] When omega1(t) = 0, omega2(t) = 0, the closed-loop system (5) is asymptotically stable according to (20); if there is a non-zero disturbance The closed-loop system is asymptotically stable only when a certain system performance index gamma is met, and the smaller the value of the performance index gamma is, the better the performance is under the condition of meeting the system stability; the minimum performance index gamma is obtained by searching in the interval [gamma1, gamma2] through the least square method min . Set the precision as gamma ac , gamma1 and gamma2 are the lower limit and upper limit of the performance index respectively, and the specific steps of the algorithm are shown in the flow chart. Figure 4

[0125] Compared with the prior art, the beneficial effects of the present application are:

[0126] The application provides a time-delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism, in order to solve the problem that the performance of the island micro-grid load frequency control system is limited by the communication bandwidth. Unlike the static event triggering mechanism which adopts a fixed triggering threshold, the application focuses on adaptive threshold which is adaptively adjusted according to the real-time state of the system, so that unnecessary signal transmission can be further reduced. BRIEF DESCRIPTION OF DRAWINGS

[0127] The drawings accompanying the specification integrated into the present application serve to provide a further understanding of the present application, the illustrative embodiments thereof, and explanations of the present application, and do not constitute an improper limitation of the present application.

[0128] Figure 1 is the island micro-grid connection line model of the present application;

[0129] Figure 2 is the island micro-grid load frequency control dynamic response model of the present application;

[0130] Figure 3 is the flow chart of the adaptive event triggering control scheme of the time-delay island micro-grid of the present application;

[0131] Figure 4 ​is the flow chart for solving the minimum system performance index γ min of the present application;

[0132] Figure 5 is the frequency deviation variation for solving scenario 1 of the present application;

[0133] Figure 6 is the frequency deviation variation for solving scenario 2 of the present application;

[0134] Figure 7 is the frequency deviation variation for solving scenario 3 of the present application. DETAILED DESCRIPTION

[0135] The present application is further described below in conjunction with the accompanying drawings and examples.

[0136] It should be noted that the following detailed description is illustrative only and is not intended to limit the application as described herein. Other embodiments of the present application will be apparent to those of ordinary skill in the art in view of the detailed description that follows, including appended claims as well as accompanying drawings.

[0137] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application.

[0138] Terminology:

[0139] Sensor: sampling data of the system and transmitting the sampled data to the event generator;

[0140] Event generator: receiving the signal sent by the sensor and determining whether the latest measurement output y(t) satisfies the trigger condition, if yes, sending the measurement output y(t) to the controller to generate a new control signal, if no, determining the next measurement output y(t);

[0141] Controller: receiving the signal sent by the event generator and generating a new control signal, and transmitting it to the zero-order holder;

[0142] Zero-order holder: receiving the discrete control signal generated by the controller and making it continuous, and transmitting it to the actuator;

[0143] Actuator: receiving the continuous signal of the zero-order holder and executing the control command;

[0144] The present application is further described below in conjunction with the accompanying drawings and specific embodiments:

[0145] Example 1:

[0146] As shown in the accompanying drawings Figure 2As shown, the embodiment of the present application provides a time delay island micro-grid load frequency control system and method based on an adaptive event triggering mechanism to solve the problem of limited communication bandwidth of the island micro-grid, and the specific implementation steps of the method are as follows:

[0147] Step S1: based on the island micro-grid system parameters, an island micro-grid closed-loop state space model containing a controller is established, and the specific steps are as follows:

[0148] The system measurement output y(t) is obtained by sampling the island micro-grid through a sensor, and then the measurement output y(t) is sent to an event generator and judged by the event generator whether the latest measurement output y(t) meets the triggering condition, if yes, the measurement output y(t) is sent to the controller, if not, the next measurement output y(t) is judged, then the discrete signal is converted into a continuous signal through a zero-order holder, and the control command is executed by an executor to restore the frequency of the system.

[0149] S11: define state variable x(t), measurement output y(t), target vector z(t), system disturbance ω1(t) and measurement deviation ω2(t):

[0150]

[0151] ΔP wind (t), ΔP s (t) and ΔP d (t) respectively represent the wind speed change of the wind turbine, the solar radiation intensity change and the load power change, and Δf represents the system frequency deviation. ΔP DEG , ΔP MTG , ΔP FC , ΔP V , ΔP WTG , ΔP FESS , ΔP BESS respectively represent the power output change of the diesel generator, the fuel cell, the photovoltaic cell, the wind turbine, the flywheel energy storage system and the battery energy storage system. In order to facilitate the representation of the system state, intermediate variables ΔP DEG1 , ΔP MTG1 , ΔP FC1 , ΔP FC2 and ΔP V1 are introduced, Δf(t) is the system frequency deviation, and z(t) is the target vector.

[0152] S12: set the PI controller strategy, and use the system frequency deviation Δf(t) as the input signal of the controller:

[0153] u(t)=-K P Δf(t)-K I ∫Δf(t)dt (1)

[0154] wherein K P and K I are the proportional and integral coefficients of the system, and u(t) is the input signal of the PI controller;

[0155] S13: defining an augmented vector

[0156] S14: establishing a closed-loop state space model of the island micro-grid:

[0157] The dynamic model of the island micro-grid load frequency control system is shown in Figure 2 and the controller (1) can obtain the closed-loop state space model of the island micro-grid containing the controller as: Figure 1

[0158]

[0159] wherein,

[0160]

[0161] wherein H represents the mechanical inertia of the island micro-grid, R1 and R2 are constants, T WTG , T PV represent the dynamic parameters of the wind turbine and the photovoltaic system, T IC , T t , T FC , T IN represent the time constants of the converter, T DEG , T MTG , T FC , T FESS , T BESS are the response times of the diesel generator, the micro-turbine generator, the fuel cell, the flywheel energy storage system, and the battery energy storage system, respectively;

[0162] Step S2: introducing an adaptive event triggering mechanism to establish a time-delay island micro-grid load frequency control model containing a communication scheme and a controller

[0163] S21: defining a delay function τ(t)∈[τ m ,τ M ], wherein: τ=τ M -τ m (τ m ≥0), τ M and τ m represent the upper and lower limits of the communication delay, t k represents the kth triggering time, k represents the kth triggering, and h is defined as the sampling period, t k ​+ih represents the i-th sampling time after the k-th triggering, assuming the triggering time s k = t k + τ(t k ), τ(t k ) ∈ [τ m , τ M ];

[0164] S22: The measurement output y(t) can be represented as:

[0165] y(t) = C1x(t k ) + Dω2(t k ), t ∈ [s k , s k+1 ) (3)

[0166] S23: The error function can be represented as:

[0167] e(t) = y(t k ) - y(t k +ih) = y(t k ) - y(t-τ(t)) (4)

[0168] S24: The control signal of the PI controller is:

[0169] u(t) = u(t k + τ k ) = Ky(t k ), t ∈ [s k , s k+1 ) (5)

[0170] S25: The state space model of the microgrid load frequency control system can be rewritten as:

[0171]

[0172] S26: The event-triggered condition is constructed:

[0173] An adaptive event-triggering mechanism is introduced to reduce unnecessary data transmission. After the sensor samples the controlled device, it determines whether the transmission condition is met. Only when the event-triggered condition is met, the sampled signal is sent to the controller, otherwise, it is not sent and the next sampled signal is determined. The adaptive event-triggered condition is (7):

[0174]

[0175] where the triggering matrix Ω > 0, and the dynamic threshold σ(t) satisfies the differential equation (8):

[0176]

[0177] where μ > 0 and p > 0 are given constants, and 0 < 1 / p < σ(t) < 1.

[0178] Step S3: Based on the Lyapunov functional method, the stability criterion of the time-delay island microgrid is derived, and the Zeno phenomenon is excluded. The specific steps are as follows:

[0179] In this part, the load frequency control system of the time-delay island microgrid is taken as the research object, an augmented Lyapunov-Krasovskii functional is constructed, and the stability criterion of the closed-loop system is derived. If the closed-loop system (6) satisfies the following two conditions under the event-triggered condition (7), the system is asymptotically stable:

[0180] (5) When ω1(t) = 0 and ω2(t) = 0, the system is asymptotically stable;

[0181] (6) For non-zero If there exists a positive constant γ > 0 such that under the zero initial condition, the following condition is satisfied:

[0182]

[0183] The following are two lemmas used in the derivation:

[0184] Lemma 1: For a given positive definite matrix R > 0 and a constant α > 0, for a continuous differential function ω(s) on [a, b], the following inequality holds:

[0185]

[0186] where,

[0187] Lemma 2: For a given positive definite matrix S > 0, τ1 < τ(t) < τ2, there exists a continuous differential function satisfying:

[0188]

[0189] where ψ T (t) = [x T (t-τ1), x T (t-τ(t)), x T (t-τ2)].

[0190] S31: Select the augmented Lyapunov-Krasovskii functional:

[0191] Select the Lyapunov functional as follows, and perform inequality scaling on it;

[0192]

[0193] V1(t) = x T (t)Px(t) (12a)

[0194]

[0195]

[0196]

[0197]

[0198] where P > 0, Q1 > 0, Q2 > 0, Q3 > 0, R > 0 and S > 0 are positive definite matrices with appropriate dimensions, τ = τ M -τ m .

[0199] Taking the derivative of V(t) gives:

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] S32: Solve the system asymptotic stability criterion:

[0207] Based on the closed-loop system (6), the following equations hold:

[0208]

[0209] where M, N ∈ R n×n and ε is a given constant.

[0210] Combining Lemma 1, the integral term of (13c) can be reduced order as:

[0211]

[0212] where, The matrix R > 0.

[0213] Based on Lemma 2, the integral term of (13d) can be simplified as:

[0214]

[0215] Where S>0, ζ T (t)=[x T (t-τ m ),x T (t-τ(t)),x T (t-τ M )).

[0216] When t∈[s] k ,s k+1 From the adaptive event triggering condition (7), we can obtain:

[0217] σ(t)y T (t-τ(t))Ωy(t-τ(t))-e T (t)Ωe(t)≥0,t∈[s k ,s k+1 (17)

[0218] Furthermore, we can obtain:

[0219]

[0220] Suppose there exists a sufficiently small positive number δ such that:

[0221]

[0222] Inequality (19) can be transformed into matrix form:

[0223] η T (t)Ψη(t)≤0 (20)

[0224] when At that time, because It is a continuous function. Integrating both sides of equation (19) from 0 to +∞ simultaneously:

[0225]

[0226] When ω1(t)≡0 and ω2(t)≡0, it can be seen from (19):

[0227]

[0228] Therefore, in order to ensure While maintaining the performance index γ, the closed-loop system (6) is asymptotically stable.

[0229] S33: Criteria for the load frequency control system of islanded microgrids based on linear matrix inequalities (6):

[0230] Based on steps S31-S32, the following stability criterion is obtained:

[0231] For a given sampling period h > 0, a constant ε > 0, 0 < 1 / ρ < σ(t) < 1, μ > 0, The load frequency control system (6) of the islanded microgrid is asymptotically stable if there exist matrices P > 0, Q1 > 0, Q2 > 0, Q3 > 0, R > 0, S > 0, a trigger matrix Ω > 0 and matrices M, N such that the following matrix inequalities hold.

[0232]

[0233] where,

[0234]

[0235]

[0236] Ψ 33 = -Q1 + Q2 + Q3 - S - 4R, Ψ 12 = P - M + εA T N T , τ = τ M - τ m ,

[0237]

[0238] Φ 14 = col{ML, εML, 0, 0, 0}, Φ 15 = col{6R, 0, 6R, 0, 0}, Φ 22 = D T ΩD - γ 2 I,

[0239]

[0240] where I represents the identity matrix, * denotes the transpose item of the matrix opposite position, and all the above matrices have appropriate dimensions.

[0241] The stability criterion of formula (23) is derived on the basis of h > 0, and the following discusses another case;

[0242] S34: Zeno phenomenon analysis:

[0243] When h = 0, the load frequency control system (6) of the islanded microgrid may occur Zeno phenomenon. In order to avoid the islanded microgrid from Zeno phenomenon, it is necessary to ensure that the previous signal is received by the controller before updating the next signal.

[0244] Combined with the adaptive event-triggered criterion (7) and σ(t) > 0, the following can be obtained:

[0245] ||e(sk+1 ||σ(t)||y(t)||,t∈[s k ,s k+1 ) (24)

[0246] When ω2(t)≡0, then the derivative of e(t) at t∈[s k ,s k+1 ) is as follows:

[0247]

[0248] Wherein, p1=||C1BKC1||1||x(t-τ(t))||1+||C1A||1||x(t)||1+||C1A||1||ω1(t)||1, p2=||C1BKC1||1.

[0249] From the definition of e(t), e(s k )=0, combined with (5) and comparison inequality, solving formula (25) can obtain:

[0250]

[0251] Therefore, there is a positive number So that the minimum execution time T satisfies:

[0252]

[0253] This means that while ensuring Performance index γ, the island micro-grid load frequency control system does not exist Zeno phenomenon when h=0, the proof is completed. Based on the continuous event trigger system may exist Zeno behavior, in order to prove that the system does not exist Zeno phenomenon, the invention has carried out the above proof.

[0254] Step S4: solving the trigger matrix Ω and the minimum performance index γ min ;

[0255] S41: solving the feasible solution:

[0256] Using the feasp solver in MATLAB / LMI toolbox to solve a set of feasible solutions of linear matrix inequality (21) as constraint

[0257] S42: solving the minimum performance index γ min :

[0258] When ω1(t)=0, ω2(t)=0, from (20) can obtain that the closed loop system (5) is asymptotically stable, if there is non-zero disturbance The system performance index γ must be satisfied, only then the closed-loop system is asymptotically stable, and the smaller the value of the performance index γ is, the better the system stability is; the least performance index γ is obtained by searching in the interval [γ 1, γ 2] through the least square method min . The precision is set as γ ac , γ 1 and γ 2 are respectively the lower limit and the upper limit of the performance index, and the specific steps of the algorithm are shown in the flow chart. Figure 4

[0259] Embodiment 2

[0260] The system data transmission amount is reduced by the adaptive event-triggered time-delay island micro-grid load frequency control system and method provided in the embodiment.

[0261] For the island micro-grid load frequency control system model, in the embodiment, T DEG = 0.8, T MTG = 0.8, T FC = 0.5, T PV = 1.8, T WTG = 1.5, T FESS = 0.1, T BESS = 0.1, T t = 0.1, T IC = 0.04, T IN = 0.05, R1 = 0.05, R2 = 0.05, H = 5.0, a = 1.0, μ = 0.05, ρ = 20.0 and ε = 0.1.

[0262] The initial value σ (0) = 0.06 of the event-triggered threshold is defined, the sampling period h = 0.5 s, the lower limit of the time delay τ m = 0.5 s, the upper limit of the time delay τ m = 1.0 s, and the controller gain is set as K P1 = 1.2, K I1 = 2.0, K P2 = 2.0 and K I2 = 3.0.

[0263] According to the above given parameters, according to the step S41, the trigger matrix can be obtained by solving the linear matrix inequality (23) by using the MATLAB / LMI toolbox.

[0264]

[0265] According to the above given parameters, according to the step 4.2, the least performance index γ min = 1.0 > 0, which indicates that the system is asymptotically stable. ​

[0266] Finally, the effectiveness of the proposed scheme is verified by simulation in various scenarios. The initial state of the system is set as x(0) = [0.02, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] T , and the rest of the parameters are as described above. The system load changes ΔP d In the case of multi-step changes, as shown in Figure 5

[0267] Scenario 1: Simulate the case where the measurement noise ω2(t) occurs in multiple steps. In this scenario, the external disturbance ω2(t) is not considered, only the measurement noise ω2(t) occurs in multiple steps, where ω a (t) is selected as:

[0268]

[0269] Figure 5 The frequency deviation of the island microgrid using the adaptive event-triggered control (AET-LFC) mechanism of the present application in scenario 1 is shown in

[0270] Scenario 2: Simulate the case where renewable energy disturbance and load occur in multiple steps. In this scenario, the measurement error ω2(t) is not considered, and the external disturbance ω1(t) occurs in multiple steps, as shown in Figure 6 (a). Figure 6 (b) shows the frequency deviation of the island microgrid using the adaptive event-triggered control mechanism, the periodic sampling mechanism, the static event-triggered control mechanism, and the continuous event-triggered control mechanism of the present application in scenario 2, with trigger times of 47, 200, 52, and 211 times, respectively. The results show that the adaptive event-triggered control mechanism of the present application has the smallest overshoot and the fastest recovery speed, and the continuous event-triggered control mechanism has the best frequency response performance. The results show that the adaptive event-triggered control mechanism of the present application has the smallest trigger times, saving network bandwidth resources, and at the same time, the frequency has a faster recovery speed.

[0271] Scenario 3: Simulate the case where renewable energy disturbance and load occur randomly. In this scenario, the measurement error ω2(t) is not considered, and the external disturbance ω1(t) occurs randomly, as shown in Figure 7 (a). Figure 7 ​(b) represents the frequency deviation change of island micro-grid using the adaptive event-triggered control mechanism (AET-LFC), the periodic sampling (PS-LFC) mechanism, the static event-triggered control (SET-LFC) mechanism and the continuous event-triggered control (CET-LFC) mechanism of the present application in scenario 3, and the triggering times are 86 times, 200, 93 times and 389 times respectively. The adaptive event-triggered control mechanism of the present application has the least triggering times and the smallest response overshoot.

[0272] Figures 5-7 The comparison of scenario 1, scenario 2 and scenario 3 under the adaptive event-triggered control mechanism, the static event-triggered control mechanism and the continuous event-triggered control mechanism of the present application shows that the adaptive event-triggered control mechanism of the present application has the least triggering times.

[0273] The embodiment of the present application first considers the communication delay when modeling the island micro-grid load frequency control system, and designs the time-delay island micro-grid load frequency control based on the adaptive event-triggered mechanism, which effectively saves the network bandwidth resources of the system and relieves the burden of the communication system under the premise of not occurring Zeno phenomenon and guaranteeing the frequency control performance of the system.

[0274] The above description is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any changes, modifications, additions or replacements made by using the content of the specification and drawings of the present application are also within the patent protection scope of the present application.

Claims

1. A load frequency control method for a time-delayed islanded microgrid based on an adaptive event-triggered mechanism, characterized in that, It employs a time-delay islanded microgrid load frequency control system based on an adaptive event-triggered mechanism. This system includes sensors, an event generator, a PI controller, a zero-order hold circuit, and actuators. The system's measurement output is obtained by sampling the data through sensors. y ( t Then measure the output. y ( t The latest measurement output is sent to the event generator, which then determines its accuracy. y ( t Check if the triggering condition is met. If it is, then measure the output. y ( t The signal is sent to the PI controller; if the condition is not met, the output is adjusted for the next measurement. y ( t The system makes a judgment, then converts the discrete signal into a continuous signal via a zero-order hold, and the actuator executes the control command to restore the system frequency. The main steps include: S1: Establish a closed-loop state-space model of an islanded microgrid that includes a PI controller; S2: Establish a load frequency control system model for a time-delayed islanded microgrid based on an adaptive event-triggered mechanism; S3: The stability criterion for time-delayed islanded microgrids is derived based on the Lyapunov-Krasovskii functional method; S4: Exclude Zeno's phenomenon; S5: Solve for the trigger matrix using the MATLAB / LMI toolbox. and minimum performance index ; Step S2 establishes a load frequency control system model for a time-delayed islanded microgrid based on an adaptive event-triggered mechanism. The specific steps are as follows: S21: Define a delay function ,in: , and These represent the upper and lower limits of communication latency, respectively. Indicates the first k Next trigger moment k Indicates the first k Second trigger, definition h The sampling period is Indicates the first k After the first trigger, the [number]th i Next sampling time, assuming trigger time ; S22: The measured output y(t) can be expressed as: （3） S23: The error function can be expressed as: （4） S24: The control signal for the PI controller is: （5） S25: The state-space model of the load frequency control system of an islanded microgrid can be rewritten as follows: （6） S26: Construct adaptive event triggering conditions: An adaptive event triggering mechanism is introduced to reduce unnecessary data transmission. After the sensor samples the controlled device, it determines whether the transmission conditions are met. Only when the adaptive event triggering conditions are met will the sampled signal be sent to the PI controller. Otherwise, it will not be sent and the next sampled signal will be determined. The adaptive event triggering condition (7) is as follows: （7） Among them, the trigger matrix Dynamic threshold Satisfying differential equation (8): （8） in, and It is a given constant, and ; If the state-space model (6) of the islanded microgrid load frequency control system satisfies the following two conditions under the adaptive event triggering condition (7), then the system is asymptotically stable: (1) When At that time, the system is asymptotically stable; (2) For non-zero If a positive constant exists , The representative performance metric satisfies the following under zero initial conditions: （9）； Step S3 derives the stability criterion for time-delayed islanded microgrids based on the Lyapunov-Krasovskii functional method. The specific steps are as follows: S31: Select the augmented Lyapunov-Krasovskii functional: Choose the following Lyapunov-Krasovskii functional and perform inequality scaling on it; （10） （10a） （10b） （10c） （10d） （10e） in, , , , , and All are positive definite matrices with appropriate dimensions. ; right V ( t Differentiation yields: （11） （11a） （11b） （11c） （11d） （11e）。 2. The load frequency control method for time-delayed islanded microgrids based on an adaptive event triggering mechanism according to claim 1, characterized in that, The specific process of establishing the closed-loop state-space model of the islanded microgrid including the PI controller in step S1 is as follows: S11: Define state variables x ( t ), measurement output y ( t ), target vector z ( t ), system disturbance and measurement deviation : , , , ， , and These represent changes in wind speed, solar radiation intensity, and load power of the wind turbine, respectively. , , , , , , These represent the power output changes of diesel generators, micro turbine generators, fuel cells, photovoltaic cells, wind turbines, flywheel energy storage systems, and battery energy storage systems, respectively. Intermediate variables are introduced to facilitate the representation of system states. , , , and ; For system frequency deviation, The target vector; S12: Configure the PI controller strategy, using system frequency deviation. As the input signal for the PI controller: （1） in, and These are the proportional and integral coefficients of the system. For the PI controller output signal; S13: Define augmented vectors ; S14: Establish a closed-loop state-space model of an islanded microgrid including a PI controller: The closed-loop state-space model of the islanded microgrid with a PI controller is established as follows: （2） in, , , , , , , , , , , , , ， in, This represents the mechanical inertia of an isolated microgrid. , It is a constant. , These represent the dynamic parameters of the wind turbine and the photovoltaic system, respectively. , , Both represent the time constant of the converter. , , , , These are the response times of diesel generators, micro turbine generators, fuel cells, flywheel energy storage systems, and battery energy storage systems, respectively.

3. The load frequency control method for time-delayed islanded microgrids based on an adaptive event triggering mechanism according to claim 1, characterized in that, Step S4, which eliminates the Zeno phenomenon, involves the following steps: when h When the value is 0, the load frequency control system of the islanded microgrid may experience Zeno's phenomenon. In order to avoid Zeno's phenomenon in the load frequency control system of the islanded microgrid, it is necessary to ensure that the previous signal is received by the PI controller before the next signal is updated. Combined with adaptive event triggering condition (7) and We can get: （22） when At that time, then in hour The derivative is as follows: （23） in, ； Depend on As can be seen from the definition Combining (5) and comparing inequalities, we can solve equation (23) to obtain: （24） Therefore, there exists a positive number. This minimizes the execution time. T satisfy: （25） This means that in ensuring Performance indicators Meanwhile, the islanded microgrid load frequency control system is in h When =0, the Zeno phenomenon does not exist.

4. The load frequency control method for time-delayed islanded microgrids based on an adaptive event triggering mechanism according to claim 1, characterized in that: For nonzero perturbations The microgrid load frequency control system needs to meet certain performance indicators. And under the premise of satisfying system stability, The smaller the better; a binary search algorithm is used to search for the minimum performance index while ensuring system stability. .

5. The load frequency control method for time-delayed islanded microgrids based on an adaptive event triggering mechanism according to claim 1, characterized in that: S3 also includes the following steps: S32: Solving for the asymptotic stability criterion of the system: Based on the load frequency control system of an islanded microgrid, the following equation holds: （12） in, and It is a given constant; The integral term can be reduced to: （13） in, , ,matrix ; The integral term can be simplified to: （14） in, , ; when From the adaptive event triggering condition (7), we can obtain: （15） Furthermore, we can obtain: （16） Suppose there exists a sufficiently small positive number. Make: （17） Inequality (17) can be transformed into matrix form: （18） when At that time, because It is a continuous function, and for equation (17) from 0 to Integrate both sides simultaneously: （19） when and As can be seen from (17): （20） Therefore, in order to ensure Performance indicators Meanwhile, the load frequency control system of the islanded microgrid is asymptotically stable; S33: Criterion for load frequency control systems in islanded microgrids based on linear matrix inequalities: Based on steps S31-S32, the following stability criterion is obtained: For a given sampling period ,constant , , , and control matrix K There exists a matrix , , , , , Trigger matrix and matrix M , N If the following matrix inequality holds, then the load frequency control system of the islanded microgrid is asymptotically stable. （21） In the formula, , , ， , , , , , , , , ， in, I Represents the identity matrix. The transpose of the matrix pair position represents the control matrix K, matrix P, Q1, Q2, Q3, R, S, M, N, and the trigger matrix Ω, all of which have appropriate dimensions. The stability criterion of equation (21) is derived based on h > 0.

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