Power system lfc method based on event triggering and distributed pi control

Abstract

The present application belongs to the technical field of frequency stability control, and relates to load frequency control (LFC) of a power system, and specifically provides a power system LFC method based on event triggering and distributed PI control; firstly, a unified actuator fault model is established, and a distributed fault-tolerant PI control strategy based on the actuator fault model is proposed; then, an event-triggered mechanism (SETS) based on a random sampling data mode is proposed to relieve redundant occupation of a communication channel; finally, the power system LFC method based on event triggering and distributed PI control is obtained, which can effectively avoid periodic interference and has great advantages in saving communication resources.

Description

Technical Field

[0001] This invention belongs to the field of power system load frequency control technology, and relates to load frequency control (LFC) of power systems. Specifically, it provides a power system LFC method based on event triggering and distributed PI control. Background Technology

[0002] A power grid is a typical large-scale networked control system. Each subsystem generates, consumes, and transmits electricity to connected areas in real time, achieving a balance between power supply and demand. To maintain the stable operation of a multi-regional interconnected power system, the frequency deviation of each region and the power flow of the tie lines between interconnected regions should be maintained at their nominal values ​​(e.g., 50Hz or 60Hz). Therefore, minimizing the frequency deviation and tie line power flow from their nominal values ​​under load disturbances is one of the most important control tasks of a power system. Load frequency control (LFC) is an effective method to achieve this goal. Traditionally, frequency stability in each region is achieved through a control center, known as a centralized control architecture. However, traditional centralized control has a significant drawback: the failure of the centralized controller can leave the entire system uncontrolled, particularly detrimental to the frequency stability of large-scale interconnected power systems. Furthermore, the continuous infiltration of numerous uncertain renewable energy sources leads to power mismatch in the power system. In such cases, due to the large inertia of synchronous generators, traditional centralized control may fail to synchronize them.

[0003] To address the practical problem of power system collapse caused by single controller failure, researchers have proposed a distributed power system control architecture and several effective control strategies. For example, an output feedback controller with deceptive attack signals has been designed, but this controller is based on a centralized architecture. Later, distributed proportional-integral (PI) control strategies based on control error signals from local feedback regions were widely adopted. It is worth noting that the proposed PI control strategy only involves a linear combination of local frequency deviation and tie-line power fluctuations, failing to fully utilize control signals from adjacent regions to achieve coordinated control of the interconnected power system. Furthermore, power systems are complex cyber-physical systems composed of numerous electrical and communication devices. In such complex and large-scale systems, actuator failures are unavoidable, making improving the fault tolerance of the controller another challenge.

[0004] Furthermore, in practical applications of power systems, digital devices are widely used for acquiring and transmitting control data. With the development of wide-area measurement technology, sampled data can be transmitted through wireless communication platforms. However, the communication resources of wireless communication networks are limited, and how to avoid redundant occupation of communication channels has become a focus of attention. Event-triggered communication mechanisms are an effective resource-aware method to improve network communication bandwidth utilization. The key technology of event-triggered systems (ETS) is to design appropriate trigger threshold conditions to determine when local control signals are broadcast. In addition, sampled data is only transmitted when a well-defined trigger condition is violated, which achieves an ideal trade-off between frequency stability and resource conservation. Currently, there is research on designing ETSs to achieve effective frequency regulation. The general periodic event-triggered system (PETS) was first proposed for network control systems. Based on this, adaptive ETS based on general PETS, whose event trigger threshold conditions can be adjusted according to system state fluctuations, as well as memory ETS, dynamic ETS, and ETS oriented towards control performance standards, etc., have been proposed. However, most of these are based on periodic sampling data patterns to propose more suitable trigger conditions. This sampling pattern cannot suppress periodic interference and has the problem of redundant occupation of communication resources.

[0005] To address the aforementioned problems, this invention proposes a distributed fault-tolerant proportional-integral (PI) control strategy and an event-triggered mechanism (SETS) based on random sampled data patterns, thereby obtaining a new power system LFC method. Summary of the Invention

[0006] The purpose of this invention is to provide a power system LFC method based on event triggering and distributed PI control. First, a unified actuator fault model is established, and a distributed fault-tolerant PI control strategy based on the actuator fault model is proposed. Then, an event triggering mechanism (SETS) based on random sampled data pattern is proposed to alleviate the redundancy of communication channels. Finally, the power system LFC method based on event triggering and distributed PI control is obtained. This method can effectively avoid periodic interference and has great advantages in saving communication resources.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A power system LFC method based on event triggering and distributed PI control, characterized in that the method specifically comprises:

[0009]

[0010] in, The derivative of x(t);

[0011] x(t) = col(x) i (t)) N Let i = 1, ..., N, where N is the number of control regions.

[0012] Δω i (t) represents the change in frequency deviation from the nominal value. This represents the change in turbomachinery power input. This indicates the change in the governor valve position. ACE represents the change in tie-line power. i (t) represents the area control error signal;

[0013]

[0014] Indicates the amount of load disturbance change;

[0015] The error represents the system state, where h is the sampling period. For set Random numbers selected from

[0016] u(t) = col(u i (t)) N , This represents the input of the m-th actuator in control region i under the fault model;

[0017] It is an increasing sequence;

[0018] A i，j =[v1 0 5×4 ], ν1=col(0,0,0,-2π,0); a ij For the connection weight coefficient of the branch, T ij D is the synchronization coefficient for the tie line. i M i , and R i These are the damping coefficient, governor's moment of inertia, turbine time constant, governor time constant, and frequency droop coefficient, respectively. i This is the frequency offset coefficient;

[0019] B = diag(B) i ) N ,

[0020] Ψ=diag(Ψ i ) N , For unknown fault coefficients, l = 1,...,m, s = 1,...,S, where m represents the total number of actuators and S represents the total number of fault models;

[0021] K = diag(K) i ) N , and These represent the proportional control gain and the integral control gain, respectively.

[0022] C = diag(C i ) N ,

[0023] F = diag(F) i ) N F i =[ν2 0 5×4 ],

[0024]

[0025] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0026] This invention provides an LFC (Low-Fault Tolerance) method for power systems based on event triggering and distributed PI control. First, a unified actuator fault model is established, and a distributed fault-tolerant PI control strategy based on the actuator fault model is proposed. Then, a random event triggering mechanism is proposed to alleviate the redundancy of communication channels. Finally, taking an isolated power system as an example, this invention verifies the effectiveness of the proposed control strategy and the superiority of the SETS (Sequential Event Triggering) control strategy over the periodic event triggering control strategy. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the structure of the two-region interconnected power system in this invention.

[0028] Figure 2 The diagrams show the instantaneous event triggering of the traditional periodic time triggering mechanism and the random time triggering mechanism in this invention, where (a) represents the periodic time triggering mechanism and (b) represents the random time triggering mechanism.

[0029] Figure 3 As shown in the embodiment of the present invention, l max A schematic diagram of dividing the interval Υ under the example of =4.

[0030] Figure 4The fluctuation diagram of the power system under PI control is provided in an embodiment of the present invention.

[0031] Figure 5 This is a diagram showing the trigger moment under PETS and SETS in an embodiment of the present invention.

[0032] Figure 6 As described in the embodiments of the present invention Trend chart. Detailed Implementation

[0033] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0034] This embodiment addresses the redundancy issue of LFC (Low Current Controller) and communication channel occupancy by proposing a power system LFC method based on event triggering and distributed PI control, specifically as follows:

[0035] 1. Establishment of LFC Model for Interconnected Power Systems

[0036] Consider an undirected graph The described power network, in which, Let N be the set of control regions, and N be the number of control regions. This is the set of transmission lines between adjacent regions; branch (i, j) ∈ ε indicates that control region j can receive information from control region i, and for control region i, It represents the set of its neighboring regions, that is like Figure 1 As shown, each control region mainly consists of a control center and an equivalent generator set. The equivalent generator set consists of a governor, a turbine, and a synchronous generator. The control signal for the synchronous generator set is generated by the local control center. The goal of LFC is to minimize the frequency deviation Δω in each control region. i and tie line power variation Maintain at its scheduled value.

[0037] Assume the power grid is lossless, i.e., Y ij =Y ji ≥0, Y ij Let be the susceptance of branch (i,j); the power angle difference between the equivalent generators of any two interconnected regions is less than 90°, and the dynamic model of the i-th region is as follows:

[0038]

[0039] in, ω i (t) and and and These are, respectively, the derivative of the generator rotor's angle relative to the synchronous rotating reference axis, the frequency deviation from the nominal value and its derivative, the turbomachinery power input and its derivative, and the governor valve position and its derivative. For load disturbance, To control the input, D i M i , and R i These are the damping coefficient, the governor's moment of inertia, the turbine time constant, the governor time constant, and the frequency droop coefficient, respectively. The tie-line power is defined as follows:

[0040]

[0041] Among them, V i and V j Let θ be the terminal voltage of the equivalent generator in the i-th and j-th control regions. i (t) represents the angle of the generator rotor relative to the synchronous rotating reference axis; a ij Let a be the connection weight coefficient of branch (i,j), when (i,j)∈ε. ij =1, time a ij =0;

[0042] Assume that model (1) initially operates at an equilibrium point at t = t0. The frequency deviation of the i-th region from the nominal value relative to the equilibrium point. This represents the angle of the i-th region relative to the equilibrium point. This represents the turbine mechanical power input of the i-th region relative to the equilibrium point. This represents the governor valve position of the i-th region relative to the equilibrium point. The reference tie-line power represents the i-th region relative to the equilibrium point. This represents the load disturbance of the i-th region relative to the equilibrium point; the present invention will consider time-varying load disturbances. The frequency control problem described below is:

[0043]

[0044] in, It is a positive scalar. This refers to the change in load disturbance.

[0045] Will Linearization at the equilibrium point yields... in, T ijSynchronization coefficient for tie lines: The power angle difference between the equivalent generators of any two interconnected regions is less than 90°, which means T ij >0, the change in angle Δθ of the generator rotor relative to the synchronous rotating reference axis i (t)=θ i (t)-θ i 0 and tie line power change Let the frequency deviation from the nominal value be the change Turbomechanical power input variation Governor valve position change Load disturbance change Control input change The control input represents the i-th region relative to the equilibrium point; the following linearized model can be obtained from equation (1):

[0046]

[0047] in, They represent Δω i (t), The derivative; defining the area control error signal. β i Let be the frequency offset coefficient;

[0048]

[0049]

[0050]

[0051]

[0052] Model (4) is rewritten as:

[0053]

[0054] in, ν1=col(0,0,0,-2π,0), A i,j =[ν1 0 5×4 ], F i =[ν2 0 5×4 ],

[0055] Thus, the LFC model of the interconnected power system in this invention is obtained.

[0056] 2. Distributed fault-tolerant PI control strategy

[0057] 2.1. Actuator Fault Model

[0058] Based on the single model of actuator failure, this invention further establishes a multi-dimensional model of actuator failure; for the l-th actuator in control region i under failure model s, and Let the input and output be represented respectively, and they satisfy:

[0059]

[0060] Where i = 1,...,N, l = 1,...,m, s = 1,...,S, N represents the total number of control areas, m represents the total number of actuators, and S represents the total number of fault models; For unknown failure coefficients, it satisfies This represents the lower limit of the unknown failure coefficient. The upper limit of the unknown fault coefficient; actuator faults can be summarized into three cases: no fault: Failure / Fault: Power outage fault:

[0061] make The actuator fault model can then be expressed as:

[0062]

[0063] in,

[0064] 2.2. Distributed Fault-Tolerant PI Control Strategy

[0065] In this invention, u i (t) is designed as a distributed PI-type control input as follows:

[0066]

[0067] in, and These represent the proportional control gain and the integral control gain, respectively.

[0068] By considering actuator failure, the distributed PI control strategy is revised as follows:

[0069]

[0070] Substituting equation (9) into the third formula in equation (4), let u(t) = col(u i (t)) N , x(t) = col(x) i (t)) N y(t) = col(y) i (t))N Therefore, the following compact model can be obtained from equation (4):

[0071]

[0072] in, B = diag(B) i ) N Ψ = diag(Ψ) i ) N K = diag(K i ) N , C = diag(C i ) N F = diag(F i ) N ,

[0073] 3. Event triggering mechanism based on random sampling

[0074] PETS has been proposed such as Figure 2 As shown in Figure (a), based on the periodic sampling mode design, the sensor periodically captures the system state. If the latest transmitted state x(t) is... k h) and error If the event trigger threshold condition in the following formula remains unchanged, then the next transmission instant t is determined. k+1 h:

[0075]

[0076] Where h is the sampling period, mh is the sampling time, and t is the sampling period. k h represents the most recent transmission time. Given an increasing sequence, t k ∈N; The parameters for triggering the event. The event trigger weight matrix to be designed;

[0077] Based on this, the present invention proposes an event triggering mechanism (SETS) based on a random sampling pattern, such as... Figure 2 As shown in Figure (b), firstly, a random sampling sequence is defined. Where, h∈N + , m0 = 0 In the set Random selection from Therefore, the moment of transmission is determined by SETS:

[0078]

[0079] Considering the random event triggering mechanism and actuator failure, model (10) is rewritten as follows:

[0080]

[0081] By re-dividing interval Υ in, Due to the time delay in transmission, if but otherwise For transmission delay; such as Figure 3 The image shows l max A schematic diagram illustrating the division of interval Y in the example where = 4;

[0082] right definition Conclusion: and in, η is the upper limit of transmission delay, and η is the lower bound of time-varying delay. This is the upper bound of the time-varying time-delay;

[0083] Based on η(t) and The definition, model (13) is transformed into:

[0084]

[0085] This leads to the model described in the LFC method for power systems based on event triggering and distributed PI control in this invention.

[0086] The following example, an isolated power system, illustrates the effectiveness of this embodiment:

[0087] For isolated power systems, model (5) can be degraded to

[0088]

[0089] in,

[0090]

[0091]

[0092] Where ACE(t) = βΔω(t), β is the frequency bias coefficient; since the power system (15) is isolated, the distributed PI control strategy (9) is downgraded to a general control strategy:

[0093]

[0094] Then, considering the event triggering mechanism, system (15) is rewritten as follows:

[0095]

[0096] Where, K = [K P K I ].

[0097] Table 1 shows the parameters of the isolated power system (17). Other parameters: μ = 0.02, γ = 5. Ψ = 0.5;

[0098] Table 1

[0099]

[0100] Using the LMIs toolbox, the PI control gain matrix K = [0.2722 0.0080] is obtained, and the event triggering matrix is ​​as follows:

[0101]

[0102] Assume the initial state, load disturbance, and time-varying delay are as follows:

[0103] x0=col(5.0, 4.0, -4.5, -2.5 η(t)=0.1sin 2 (t)+0.03

[0104] like Figure 4 The figure shows the fluctuations of the power system under PI control provided in this embodiment. As can be seen from the figure, the trajectory converges to the equilibrium point, thus proving that the PI controller designed in this invention is effective. Assume the sampling interval h = 0.1 and... Randomly selected within the domain (0,10], the triggering instants under PETS(11) and SETS(12) are as follows: Figure 5 As shown, by Figure 5 It can be seen that the triggering instants under PETS(11) are more concentrated than those under SETS(12), indicating that the SETS proposed in this invention has advantages in saving communication resources; the density of PETS(11) is greater than that under SETS(12), indicating that this invention has the advantage of saving communication resources. The changes in MSL are as follows Figure 6 As shown, the value of MSL is in (0,10], which reflects the randomness of SETS(12).

[0105] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A power system LFC method based on event triggering and distributed PI control, characterized in that, The method is specifically as follows: Step 1. Establish an initial LFC model for the interconnected power system; Step 2. Establish a multi-dimensional model of actuator failure, and revise the distributed PI control strategy based on the multi-dimensional model of actuator failure; Step 3. Establish an event triggering mechanism based on a random sampling pattern; Step 4. Rewrite the initial LFC model of the interconnected power system based on the modified distributed PI control strategy and the event triggering mechanism of the random sampling mode to obtain the final LFC model of the interconnected power system, expressed as: ， in, for The derivative; , N is the number of control areas. , This indicates the change in frequency deviation from the nominal value. This represents the change in turbomachinery power input. This indicates the change in the governor valve position. This indicates the change in tie line power. This indicates the area control error signal; ， ； , , Indicates the amount of load disturbance change; The error representing the system state. The sampling period is For set Random numbers selected from ; , It is an increasing sequence; , , , , , ; , For the connection weight coefficient of the branch, For the synchronization coefficient of the tie line, and These are the damping coefficient, the governor's moment of inertia, the turbine time constant, the governor time constant, and the frequency droop coefficient, respectively. This is the frequency offset coefficient; ， ； , , , For unknown failure coefficients, , , Indicates the total number of actuators, This represents the total number of fault models; , , and These represent the proportional control gain and the integral control gain, respectively. ， ； ， ， ； ， 。

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