A load frequency control method, medium, device and product

Abstract

The application discloses a load frequency control method, medium, device and product, relates to the technical field of load frequency control, and the method comprises the steps of establishing a multi-region power system load frequency control model containing a parameter uncertainty term; constructing a full-order terminal sliding mode controller of the load frequency control model, wherein the sliding mode control input is composed of two parts, namely, an equivalent control term and a switching control term; and using the constructed full-order terminal sliding mode controller to perform load frequency control on the multi-region power system. The application enhances the robustness of the system to parameter uncertainty and external disturbance, effectively weakens the inherent chattering phenomenon of the traditional sliding mode, avoids the singularity problem that is prone to occurring in the traditional terminal sliding mode control, and improves the smoothness and engineering realizability of the control input.

Description

Technical Field

[0001] This invention relates to the field of load frequency control technology, and in particular to a load frequency control method, medium, device and product. Background Technology

[0002] As interconnected power systems continue to expand in scale and power exchange between regions becomes increasingly frequent, the impact of load disturbances, parameter perturbations, and external random disturbances on system frequency stability is becoming more and more pronounced. Especially in three-region interconnected power systems, the control areas are coupled together via tie lines. Load fluctuations in one area not only cause frequency deviations within that area but also propagate to other areas through the tie lines, resulting in dynamic fluctuations in the overall system frequency and the power exchanged via the tie lines. Therefore, load frequency control has become a crucial technical means to ensure the safe and stable operation of interconnected power systems. Its core objective is to rapidly restore the frequency deviations of each area and the power deviations of the tie lines to within permissible limits, thereby improving the system's dynamic performance and immunity under complex disturbance conditions.

[0003] Currently, LFC (Limited-Functional Control) commonly employs methods such as PI control, optimal control, adaptive control, and sliding mode control. Among these, sliding mode control exhibits strong robustness, and terminal sliding mode control also boasts advantages such as fast finite-time convergence and small steady-state error. However, existing terminal sliding mode control still suffers from the following shortcomings when applied to high-order complex systems: First, traditional sliding mode control is typically based on reduced-order sliding surface design, making it difficult to consider the overall dynamic coordination between different states in a three-region LFC system; second, terminal sliding mode control is prone to singularity issues, affecting the implementability of the controller; third, switching control is prone to chattering, reducing control smoothness and adversely affecting the stable operation of the actuator and the system, while existing chattering suppression methods often suffer from increased steady-state error or high implementation complexity. Research on full-order terminal sliding mode control shows that it can improve the singularity, chattering, and reduced-order dynamics problems of traditional methods while maintaining finite-time convergence characteristics. Summary of the Invention

[0004] The purpose of this invention is to address the singularity and chattering problems inherent in existing sliding mode control by proposing a load frequency control method, comprising the following steps: S1. Establish a load frequency control model for a multi-regional power system containing parameter uncertainties; S2. Construct a full-order terminal sliding mode controller for the load frequency control model. The sliding mode control input consists of two parts: an equivalent control term and a switching control term. The formula for the switching control term is: , in, This indicates the switching control term, where T = low-pass filter time constant / bandwidth coefficient. This is the upper bound of the derivative of the external disturbance. These are the compensation coefficients for the low-pass filter. Here, s represents the sliding mode control gain, and s represents the sliding surface. S3. Use the constructed full-order terminal sliding mode controller for multi-regional power system load frequency control.

[0005] Furthermore, the mathematical formula for the load frequency control model of a multi-regional power system containing parameter uncertainties is as follows:

[0006]

[0007]

[0008]

[0009]

[0010]

[0011]

[0012] in, For the system matrix, For the input matrix, Let represent the state variable of the i-th region of the system at time t. This represents the input of the i-th region to the controller at time t, where N represents the number of regions. This represents the coefficient matrix of the interconnection terms between the i-th and j-th regions. This represents the state quantity of the j-th region of the system at time t. This represents the total disturbance term in the i-th region at time t. for , Uncertainty in parameters and For the system time constant and gain, The time constant of the turbine. The time constant of the speed controller, and Let be the frequency deviation, governor power deviation, generator mechanical power deviation, tie-line power deviation, and integral control deviation of the i-th region at time t, respectively. Let be the droop coefficient of the i-th region. Let i be the frequency bias factor for the i-th region. express, The coefficient matrix of the disturbance term. This indicates a random perturbation. This is due to load disturbance.

[0013] Furthermore, the sliding surface of the full-order terminal sliding mode controller is:

[0014]

[0015] Where s is the sliding surface. and It is a constant. , This represents the state variable of the i-th region of the system.

[0016] Furthermore, the formula for the equivalent control term is:

[0017] in, Indicates equivalent control items, Represents a smooth nonlinear function. Let t represent an n-dimensional state vector, and t represent time.

[0018] Furthermore, , and The following conditions must be met:

[0019]

[0020] in, This represents the uncertainty function corresponding to the total disturbance term of a multi-regional power system after state transformation. are bounded constants. This is the upper bound of the derivative of the external disturbance. This represents the low-pass filter compensation coefficient, where T = low-pass filter time constant / bandwidth coefficient. express The maximum absolute value, This indicates that the control item is switched at time t.

[0021] The present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described load frequency control method.

[0022] The present invention also proposes an electronic device, including a processor and a memory, wherein the processor and the memory are interconnected, the memory is used to store a computer program, the computer program including computer-readable instructions, and the processor is configured to invoke the computer-readable instructions to execute the above-described load frequency control method.

[0023] The present invention also proposes a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-described load frequency control method.

[0024] The beneficial effects of the technical solution provided by this invention are: This invention proposes a load frequency control method based on full-order terminal sliding mode. First, a load frequency control model for a multi-regional power system with parameter uncertainties is constructed. By constructing a full-order terminal sliding mode surface, the system state is constrained to operate within the sliding mode throughout the entire process. A control law incorporating equivalent control terms and dynamically switching control terms is designed to effectively suppress load disturbances and parameter uncertainties. While retaining the disturbance rejection and finite-time arrival characteristics of sliding mode control, the actual control input is made more continuous and smooth, reducing chattering and avoiding singularity problems easily encountered in traditional terminal sliding mode control. While strictly ensuring system frequency stability, it can significantly improve the dynamic response speed of frequency regulation, enhance the system's robustness to parameter uncertainties and external disturbances, and effectively reduce the chattering phenomenon inherent in traditional sliding mode control, improving the smoothness of control input and engineering feasibility. Attached Figure Description

[0025] Figure 1 This is a flowchart of a load frequency control method according to an example of the present invention; Figure 2 This is an example of the LFC model of a multi-regional power system of the present invention; Figure 3 This is a comparison chart of the frequency deviations of the SMC (sliding mode controller), FOTSMC (the model of this invention), and PI (proportional-integral control) models under step load disturbance, considering parameter uncertainties in any region of this invention. Figure 4 This is a comparison chart of the regional control error ACE of SMC, FOTSMC and PI models under step load disturbance, considering parameter uncertainties in any region of this invention; Figure 5 The frequency deviation IAE performance index of the SMC, FOTSMC and PI models under step load disturbance, considering parameter uncertainties in any region of this invention; Figure 6 The frequency deviation ITAE performance index of the SMC, FOTSMC and PI models under step load disturbance, considering parameter uncertainties in any region of this invention; Figure 7 This is a comparison chart of the frequency deviations of SMC, FOTSMC, and PI in any region of the present invention under random perturbation. Figure 8 This is a comparison chart of the regional control errors (ACE) of SMC, FOTSMC, and PI in any region of the present invention under random disturbance conditions; Figure 9 The frequency deviation IAE performance indicators of SMC, FOTSMC and PI in any region of the present invention under random perturbation. Figure 10 The frequency deviation ITAE performance index of SMC, FOTSMC and PI in any region of the present invention under random perturbation; Figure 11 This is a block diagram of an electronic device according to an exemplary embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0027] A flowchart of a load frequency control method according to an example of the present invention is shown below. Figure 1 Specifically, it includes: S1. Establish a load frequency control model for a multi-regional power system with parameter uncertainties.

[0028] The multi-regional power system LFC model of this invention is as follows: Figure 2 ,according to Figure 2 For a multi-regional power system LFC model, the following state equations are established:

[0029]

[0030]

[0031]

[0032]

[0033] in, and Let be the frequency deviation, governor power deviation, generator mechanical power deviation, tie-line power deviation, and integral control deviation of the i-th region at time t, respectively. and For the system time constant and gain, The time constant of the turbine. The time constant of the speed controller, Indicates load disturbance. This indicates a random perturbation. Let be the droop coefficient of the i-th region. This represents the input of the i-th region to the controller at time t, where N represents the number of regions. This represents the power coefficient of the tie line between the i-th and j-th regions. Let be the frequency deviation of the j-th region at time t. This represents the integral control gain of the i-th region. is the frequency bias factor for the i-th region.

[0034] The above formula can be expressed as the following state model:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] The load in a power system is constantly changing, causing the system's equilibrium operating point to shift, thus introducing uncertainty into the power system parameters. To more accurately describe the power system, the above state model is extended to the following model, which includes parameter uncertainties:

[0041] in, for , Additional terms (parameter uncertainty terms) that are converted into the state equations when parameters deviate from their nominal values ​​refer to the original matrix. Because of the matrix The error term is caused by the uncertainty of parameters. To facilitate the subsequent design of the sliding mode controller, the parameter uncertainty, external load disturbance, and random disturbance are combined into a total disturbance term, resulting in the following equation:

[0042]

[0043] in, For the system matrix, For the input matrix, Let represent the state variable of the i-th region of the system at time t. This represents the input of the i-th region to the controller at time t, where N represents the number of regions. This represents the coefficient matrix of the interconnection terms between the i-th and j-th regions. This represents the state quantity of the j-th region of the system at time t. This represents the total disturbance term in the i-th region at time t. for , Uncertainty in parameters and For the system time constant and gain, The time constant of the turbine. The time constant of the speed controller, and Let be the frequency deviation, governor power deviation, generator mechanical power deviation, tie-line power deviation, and integral control deviation of the i-th region at time t, respectively. Let be the droop coefficient of the i-th region. Let i be the frequency bias factor for the i-th region. express, The coefficient matrix of the disturbance term. This indicates a random perturbation. This is due to load disturbance.

[0044] S2. Construct a full-order terminal sliding mode controller for the load frequency control model. Constructing the sliding mode controller involves two steps: designing the sliding surface and the control law. The core of the control law is to ensure that the system state converges to the preset sliding surface within a finite time and remains within the range of that sliding surface. When the system state reaches the preset sliding surface, it will exhibit ideal characteristics such as stability, tracking accuracy, and disturbance rejection capability. During ideal sliding motion, traditional sliding mode controllers typically behave as reduced-order dynamic systems, which may lead to significant defects such as singularity problems and slow convergence speed. However, by adopting the full-order terminal sliding mode method, the system can maintain ideal full-order dynamic characteristics, effectively alleviate singularity problems, suppress chattering, and significantly improve the convergence speed.

[0045] Based on the state model finally constructed in step S1, during state variable transformation... Under the influence of [various factors], it is transformed into the controllable canonical form. The transformed system matrix can be expressed as [equation]. and The transformed kinetic equation can be expressed as:

[0046] Where n is the system order, Representing an n-dimensional state vector, taking the system model of this invention as an example: express The corresponding state variables after state transformation and These are two smooth nonlinear functions; Indicates control input; known function Represents the total disturbance term The uncertain function after the state transformation is assumed to satisfy the following conditions: ,in It is a bounded constant.

[0047] (1) Sliding surface design For the system state model after S2 transformation, the task of sliding mode control is to design a control strategy that enables it to generate ideal sliding motion on a preset sliding surface and forces the system to converge to the origin along the sliding surface in a finite time.

[0048] Assuming all constants and functions in the system and All coordinates are known and can be measured accurately in real time; the sliding surface of the system can be selected in the following form:

[0049] Where s is the sliding surface. and It is a constant; express The i-th derivative; can be selected Make the polynomial The Hurwitz condition is satisfied, meaning that all eigenvalues ​​of the polynomial lie on the left side of the complex plane. This represents the state variable of the i-th region of the system. It can be determined based on the following conditions:

[0050] in, .

[0051] Once the ideal sliding model is established The system will exhibit the exact same behavioral pattern, namely:

[0052] If the sliding surface is selected using the above formula... and determine the formula To ensure the polynomial If it is of the Hurwitz type, it indicates the ideal sliding mode in the system. The establishment process can start from any initial conditions. Along the sliding surface It converges to its equilibrium point within a finite time. .

[0053] (2) Control Law Design The sliding mode control input consists of two parts: the equivalent control term and the switching control term; that is, the control law can be expressed as: Among them, the equivalent control item It is mainly used to counteract the known dynamic characteristics of the system, as well as the nonlinearity inherent in the sliding surface. Its function is to ensure that the system, after reaching the sliding surface, operates stably according to the designed full-order terminal sliding law, ensuring stable and expected convergence in the ideal sliding phase. Switching control terms. It is mainly used to resist various uncertainties encountered by the system, such as external load fluctuations, parameter changes, and unmodeled dynamic characteristics. It can pull the system state that deviates from the sliding surface back to the sliding surface and always maintain the sliding motion, ensuring the robustness and anti-interference capability of the entire control system.

[0054] Equivalent control It can be designed in the following form:

[0055] in, Indicates equivalent control items, Represents a smooth nonlinear function. Let t represent an n-dimensional state vector, and t represent time.

[0056] Unlike traditional discontinuous switching control, the switching control term in this invention is constructed dynamically, and its switching effect is primarily manifested in the auxiliary input. In the process, the actual control quantity is then generated through a dynamic process. This approach retains the disturbance rejection and finite-time arrival characteristics of sliding mode control while making the actual control input more continuous and smooth, reducing chattering. Furthermore, since the fractional power terms in the sliding surface are not differentiated during the control law derivation, the singularity problem that easily occurs in traditional terminal sliding mode control can also be avoided. (Switching Control) It can be designed in the following form:

[0057]

[0058] in, This represents the switching control term. T = low-pass filter time constant / bandwidth coefficient. Its core function is to smooth the discontinuous switching signal into a continuous control quantity. The larger T is, the higher the bandwidth, the weaker the filtering, and the faster the response. The smaller T is, the stronger the filtering and the better the chatter suppression, but the slower the response. This is the upper bound of the derivative of the external disturbance, representing the severity of the disturbance to the system. These are the compensation coefficients for the low-pass filter, primarily used to compensate for the dynamic errors introduced by the low-pass filter. s is the sliding mode control gain, used to ensure that the system reaches the sliding surface in a finite time. s represents the sliding surface. The physical meaning of s is the error or distance between the current state of the system and the ideal converged state. When s=0, it means that the system has entered a stable convergent state.

[0059] , And T satisfy the following conditions:

[0060]

[0061] in, This represents the uncertainty function corresponding to the total disturbance term of a multi-regional power system after state transformation. are bounded constants. This is the upper bound of the derivative of the external disturbance. This represents the low-pass filter compensation coefficient, where T = low-pass filter time constant / bandwidth coefficient. express The maximum absolute value, This indicates that the control item is switched at time t.

[0062] Based on the multi-region LFC system, this invention adopts a full-order terminal sliding mode design, which enables the system to exhibit the expected full-order dynamics during the sliding mode phase. At the same time, through continuous dynamic switching control, the actual control input is made smoother, effectively reducing chattering and avoiding the singularity problem caused by the differentiation of fractional power terms.

[0063] S3. Use the constructed full-order terminal sliding mode controller for multi-regional power system load frequency control.

[0064] The designed full-order terminal sliding mode controller was applied to a load frequency control model of a three-region interconnected power system, and comparative experiments were conducted on a simulation platform. To verify the control performance of the proposed control method under complex disturbance conditions, random power disturbances were introduced into the system, and the impact of parameter uncertainties on the system's dynamic characteristics was considered. The parameter uncertainties were set to allow the governor, turbine, and system gains to fluctuate around their nominal values ​​with a fluctuation amplitude of 20%, to simulate model mismatch and changes in operating conditions during actual power system operation.

[0065] Under the same operating conditions, a PI controller, a traditional sliding mode controller, and the full-order terminal sliding mode controller proposed in this invention were used to control a three-region LFC system, and the dynamic response processes of each control method were compared and analyzed. Simultaneously, the control effectiveness of each method was evaluated based on the system response's settling time, overshoot, steady-state error, and disturbance rejection recovery capability. Comparison index: Frequency deviation. , area control error The integral absolute error (IAE) and the time-weighted integral absolute error (ITAE) are calculated using the following formulas:

[0066]

[0067] Simulation experiments were conducted according to this invention for step disturbances and random disturbances. The simulation used a MATLAB / Simulink experimental platform. First, a platform was built in Simulink as follows: Figure 2 The three-region LFC model is shown in Table 1. Next, three control methods—full-order terminal sliding mode control, traditional SMC control, and PI control—are built. Simulation experiments are conducted under step disturbance and random disturbance scenarios, and the simulation results are compared and analyzed. The total simulation time is 150 seconds. The PI parameters are selected as: proportional P = 0.3, integral I = 0.5; the traditional SMC switching coefficient gain is: .

[0068] Table 1. Parameter values ​​for the power system model

[0069] For any of the three regions, under nominal parameters, considering parameter uncertainties in the interconnected system under step load disturbances, the frequency deviation comparison chart, regional control error comparison chart, frequency deviation IAE performance index, and frequency deviation ITAE performance index of the three models are as follows: Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown.

[0070] Considering parameter uncertainties and incorporating step disturbances, a three-region load frequency control system was compared and simulated using PI control, traditional sliding mode control (SMC), and the proposed full-order terminal sliding mode controller. The proposed full-order terminal sliding mode controller exhibits the best performance in both frequency deviation and ACE (Accelerated Frequency Acquisition) performance: compared to PI and traditional SMC, the full-order terminal sliding mode controller shows significantly smaller dynamic overshoot, faster frequency recovery speed, and significantly faster ACE convergence speed. It also effectively suppresses the chattering problem of traditional SMC, achieving faster, smoother, and more robust LFC control performance. In terms of performance indicators, the IAE (Independent Isometry) of the full-order terminal sliding mode controller is 0.0843158, a reduction of 28.88% and 38.56% compared to SMC and PI, respectively; the ITAE (Independent Isometry) is 0.104727, a reduction of 77.21% and 62.37% compared to SMC and PI, respectively. This demonstrates that the present invention still exhibits good speed, stability, and robustness under the combined effects of parameter perturbation and step load disturbance, and can effectively improve the dynamic adjustment performance of multi-region load frequency control systems.

[0071] For any of the three regions, with random perturbations added, the frequency deviation comparison chart, the region control error comparison chart, the frequency deviation IAE performance index, and the frequency deviation ITAE performance index of the three models are as follows: Figure 7 , Figure 8 , Figure 9 and Figure 10 As shown in the figure, under the condition of adding random disturbances, the three-region load frequency control system was compared and simulated using PI control, traditional sliding mode control, and the full-order terminal sliding mode proposed in this invention. The results show that under random disturbance conditions, the proposed full-order terminal sliding mode controller has significantly better anti-interference performance than traditional SMC and PI control: its frequency deviation and regional control error fluctuation amplitude are much lower than those of SMC and PI, its dynamic overshoot is smaller and its oscillation is weaker, and it can always keep the system state stable near the rated value, showing stronger robustness and anti-interference ability, effectively ensuring the operational stability of the multi-region LFC system under random disturbances. In terms of performance indicators, the IAE of the full-order terminal sliding mode is 0.260656, which is 77.95% and 90.33% lower than that of SMC and PI, respectively; the ITAE is 9.65943, which is 79.26% and 89.46% lower than that of SMC and PI, respectively. This demonstrates that the present invention still possesses strong anti-disturbance capability, good robustness, and superior dynamic response quality under random disturbances, effectively improving the stable operation performance of the three-zone load frequency control system.

[0072] In one exemplary embodiment, a computer-readable storage medium is included, which stores a computer program that, when executed by a processor, implements the above-described load frequency control method.

[0073] Please see Figure 11 In one exemplary embodiment, the device further includes an electronic device including at least one processor, at least one memory, and at least one communication bus.

[0074] The memory stores a computer program, which includes computer-readable instructions. The processor calls the computer-readable instructions stored in the memory through the communication bus to execute the above-mentioned load frequency control method.

[0075] In one exemplary embodiment, a computer program product is proposed, including a computer program / instructions that, when executed by a processor, implement the steps of the load frequency control method described above.

[0076] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A load frequency control method, characterized in that, Includes the following steps: S1. Establish a load frequency control model for a multi-regional power system with parameter uncertainties; S2. Construct a full-order terminal sliding mode controller for the load frequency control model. The sliding mode control input consists of two parts: an equivalent control term and a switching control term. The formula for the switching control term is: in, This indicates the switching control term, where T = low-pass filter time constant / bandwidth coefficient. This is the upper bound of the derivative of the external disturbance. These are the compensation coefficients for the low-pass filter. Here, s represents the sliding mode control gain, and s represents the sliding surface. S3. Use the constructed full-order terminal sliding mode controller for multi-regional power system load frequency control.

2. The load frequency control method according to claim 1, characterized in that, The mathematical formula for the load frequency control model of a multi-regional power system containing parameter uncertainties is as follows: in, For the system matrix, For the input matrix, Let represent the state variable of the i-th region of the system at time t. This represents the input of the i-th region to the controller at time t, where N represents the number of regions. This represents the coefficient matrix of the interconnection terms between the i-th and j-th regions. This represents the state quantity of the j-th region of the system at time t. This represents the total disturbance term in the i-th region at time t. for , Uncertainty in parameters, and For the system time constant and gain, The time constant of the turbine. The time constant of the speed controller, and Let be the frequency deviation, governor power deviation, generator mechanical power deviation, tie-line power deviation, and integral control deviation of the i-th region at time t, respectively. Let be the droop coefficient of the i-th region. Let i be the frequency bias factor for the i-th region. express, The coefficient matrix of the disturbance term. This indicates a random perturbation. This is due to load disturbance.

3. The load frequency control method according to claim 1, characterized in that, The sliding surface of the full-order terminal sliding mode controller is: Where s is the sliding surface. and It is a constant. , This represents the state variable of the i-th region of the system.

4. The load frequency control method according to claim 3, characterized in that, The formula for the equivalent control term is: in, Indicates equivalent control items, Represents a smooth nonlinear function. Let t represent an n-dimensional state vector, and t represent time.

5. The load frequency control method according to claim 1, characterized in that, , and The following conditions must be met: in, This represents the uncertainty function corresponding to the total disturbance term of a multi-regional power system after state transformation. are bounded constants. This is the upper bound of the derivative of the external disturbance. This represents the low-pass filter compensation coefficient, where T = low-pass filter time constant / bandwidth coefficient. express The maximum absolute value, This indicates that the control item is switched at time t.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.

7. An electronic device, characterized in that, The device includes a processor and a memory, the processor being interconnected with the memory, wherein the memory is used to store a computer program, the computer program including computer-readable instructions, and the processor is configured to invoke the computer-readable instructions to perform the method as described in any one of claims 1 to 5.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1 to 5.

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