Fractional order and electric vehicle energy storage cooperation-based power system frequency control method

Abstract

The invention belongs to the technical field of power system frequency control, provides a power system frequency control method based on fractional order and electric vehicle energy storage cooperation, and realizes coordinated adjustment of frequency deviation, tie line power fluctuation and rotating speed change by establishing a wind energy conversion model, a PEV frequency response model and a fractional order PID controller. According to the system, a Rao algorithm is adopted to optimize fractional order PID control parameters, the minimum frequency deviation square integral serves as a target function, and frequency stabilization is achieved under load disturbance. The fractional order PID control law is composed of a proportion link, a fractional order integral link and a fractional order differential link, and virtual inertia support is achieved through an inertia simulation link. The PEV automatically adjusts the charging and discharging power according to the frequency deviation, and participates in primary and secondary frequency response. According to the method, the frequency stability of the low-inertia system can be effectively improved, the stabilization time is shortened, the lowest point of the frequency is reduced, the robustness and immunity of the system are improved, and the method has good engineering feasibility.

Description

Technical Field

[0001] This invention relates to the field of power system frequency control and intelligent optimization regulation technology, and in particular to a power system frequency control method based on fractional order and electric vehicle energy storage coordination. Background Technology

[0002] With the rapid development of renewable energy and the widespread adoption of power electronics technology, modern power systems are gradually shifting from high-inertia systems dominated by synchronous generators to low-inertia structures. The mechanical rotor of a traditional generator provides natural inertia support for the system, enabling the grid to resist frequency drops using rotational kinetic energy when power disturbances occur. However, when renewable energy sources such as wind and solar power are connected to the grid through converters, the mechanical inertia decouples from the system, leading to a significant increase in the rate of frequency change (RoCoF). Frequency fluctuations become difficult to suppress in a timely manner, and in severe cases, this can cause the system to disconnect from the grid or trigger protection mechanisms.

[0003] In recent years, the focus of power system research has gradually shifted to the fields of "virtual inertia" and "coordinated frequency control." Wind turbines have the ability to simulate inertial response through control loops. Inertia simulation can generate virtual power signals by measuring frequency deviation and its rate of change, thereby releasing kinetic energy to support the grid in the early stages of frequency drops. Traditional PID controllers are widely used in inertia control and frequency regulation, but they have two core problems: first, PID parameters need to be frequently adjusted under system nonlinearity and changing operating conditions, making it difficult to maintain optimal performance; second, the integer-order calculus and integral elements of the PID controller lead to response rigidity and limited phase margin, making it prone to overshoot and oscillation.

[0004] To address the aforementioned issues, the fractional-order PID controller (FPID) has been introduced into the field of frequency control. By incorporating fractional integral and derivative operations, the FPID provides additional degrees of freedom, allowing for flexible adjustment of the system's amplitude-frequency response and achieving smoother dynamic characteristics. This controller enhances the system's robustness to random disturbances, load variations, and fluctuations in renewable energy.

[0005] However, the tuning of FPID control parameters still relies on optimization algorithms. Traditional metaheuristic algorithms such as genetic algorithms, particle swarm optimization, and gray wolf optimization can achieve global search, but they have drawbacks such as a large number of parameters, slow convergence speed, and reliance on empirical settings.

[0006] On the other hand, the widespread adoption of electric vehicles (PEVs) provides distributed energy storage resources for the power system. PEVs can achieve charge and discharge regulation through vehicle-to-grid (V2G) interaction: when the system frequency drops, PEVs provide power support by discharging; when the frequency rises, PEVs absorb excess power. They offer fast response, wide distribution, and flexible aggregation, making them suitable for participating in primary and secondary frequency regulation of the system.

[0007] In existing technologies, most studies only analyze wind turbine inertia support or independent PEV frequency regulation, lacking a comprehensive control framework for the coordinated operation of "FPID-inertia simulation-PEV". Furthermore, for multi-region interconnected systems under low inertia conditions, a unified coordinated control method has not yet been established, making it difficult to balance frequency stability and energy economy. Especially with high wind power penetration, system inertia decreases significantly, and the lowest frequency point drops markedly, making it impossible for traditional control methods to quickly restore the rated frequency.

[0008] Therefore, there is an urgent need for a comprehensive control method that combines the flexibility of fractional-order control, the support capability of inertia simulation, and the regulation characteristics of PEV energy storage to achieve rapid recovery of low-inertia grid frequency and tie-line power balance. This method must possess self-optimizing parameter capabilities, strong anti-disturbance performance, and ease of implementation to meet the dynamic security requirements of future high-proportion renewable energy power systems. Summary of the Invention

[0009] Therefore, one objective of this invention is to propose a power system frequency control method based on fractional-order control and electric vehicle energy storage coordination. By integrating the FPID controller, inertia simulation control link and PEV coordinated frequency regulation mechanism, and using the Rao algorithm to achieve optimal tuning of control parameters, the frequency stability and system response speed of low-inertia power grids are improved, overcoming the shortcomings of the prior art.

[0010] To achieve the above objectives, the present invention provides a power system frequency control method based on fractional-order control and electric vehicle energy storage coordination, comprising: Construct a two-region, multi-source power system, including Region 1 and Region 2, which are connected by a tie line; Establish a wind energy conversion model and calculate the wind turbine output power based on air density, wind turbine blade swept area and wind speed; Based on the wind energy conversion model, the equivalent inertial constant and equivalent governor droop coefficient of the system are corrected according to the wind power penetration rate to construct a virtual inertia control link. A PEV frequency response model was established, and a droop control method was used to adjust the charging and discharging power. Fractional-order PID controllers were set up in each area of ​​the power system. The Rao algorithm is used to optimize the parameters of the fractional-order PID controller; During the optimization process, the integral squared error of the system frequency deviation and tie-line power deviation is used as the optimization objective function; When the system experiences load changes or renewable energy power fluctuations, the optimized fractional-order PID controller generates control signals in real time to coordinate the virtual inertia control loop of the generator set and the PEV energy storage unit to regulate power, thereby achieving frequency stability of the low-inertia power system.

[0011] As a preferred embodiment, the wind energy conversion model is as follows: ; in, This refers to the output power of the fan. air density, The swept area of ​​the wind turbine blades. For wind speed, The wind energy utilization coefficient is fitted using the following polynomial: ; in, These are the elements of the polynomial fitting parameter matrix. For the tip speed ratio, The pitch angle is the propeller angle. Pitch angle The polynomial order represents the pitch angle. The power in the fitted polynomial; Tip speed ratio The polynomial order represents the tip speed ratio. The power in the fitted polynomial.

[0012] Preferably, the equivalent inertial constant and equivalent governor droop coefficient of the system corrected according to wind power penetration rate are as follows: ; ; in, The corrected equivalent inertial constant. The inertial constant of the original system before wind power is connected. For wind power penetration rate, This refers to the inertial constant of the wind turbine itself. This is the corrected equivalent governor droop coefficient. This is the governor droop coefficient of a conventional synchronous generator when it is not connected to wind power.

[0013] Preferably, the method of adjusting the charging and discharging power using a droop control approach and setting a fractional-order PID controller in each region includes: When frequency deviation When the dead zone is smaller than the limit, PEV does not participate in regulation; when When the set threshold is exceeded, the change in charging and discharging power is adjusted proportionally. The power is limited by the minimum change in charging and discharging power. With the maximum value of the change in charging and discharging power Interval range; Fractional-order PID controllers are installed in each region of the power system, and the control law expression is as follows: ; ; in, , , , , These are the proportional, integral, and derivative gains of the controller, respectively. , For fractional order, For the proportional term coefficient of the fractional-order PID controller in the second control region (i.e., region 2) of the two-region interconnected power system, For the integral term coefficients of the fractional-order PID controller in the second control area of ​​the two-region interconnected power system, For the derivative coefficients of the fractional-order PID controller in the second control region of the two-region interconnected power system, , These are the frequency response coefficients for the first and second control regions (i.e., region 1 and region 2), respectively. , The frequency deviation between region 1 and region 2, For tie line power factor, This refers to the power exchange deviation in the tie line.

[0014] Preferably, the update mechanism of the Rao algorithm is as follows: ; in, , It is a random number. This is the updated optimal solution. Let j be the value of the j-th variable in the k-th candidate solution of the i-th iteration. Let j be the value of the j-th variable in the l-th candidate solution of the i-th iteration. , In the first Among all candidate solutions in the nth iteration The best and worst values ​​of each variable.

[0015] Preferably, the optimization objective function is as follows: ; In the formula, The objective function value, , The frequency deviation between region 1 and region 2, This refers to the power exchange deviation in the tie line.

[0016] Preferably, the fractional-order PID controller consists of three parts: proportional, fractional-order integral, and fractional-order derivative. Its general expression is: ; in, For proportional gain, For fractional integral terms, It is a fractional differential term.

[0017] Preferably, the PEV frequency regulation model adopts a droop control structure, and its charge / discharge power regulation relationship is as follows: ; in, PEV sag factor For frequency deviation, The frequency dead zone width, The change in PEV charging and discharging power; The equivalent dynamic response of the PEV aggregation group is represented as a first-order hysteresis element: ; in, , The Laplace operator characterizes the group response delay; The following limiter constrains the charge / discharge range, thereby protecting battery life and preventing frequency overcompensation: ; in, This represents the minimum change in charging and discharging power. This represents the maximum value of the change in charging and discharging power.

[0018] Preferably, the inertia simulation control stage includes frequency detection, filtering, inertia response generation, and rate recovery, as detailed below: Extracting the system frequency change rate signal using a first-order low-pass filter: ; in The filtering time constant is To measure frequency, The rated frequency; When a frequency decrease is detected, the inertia controller generates virtual inertia power based on the rate of frequency change. ; in, For inertia gain, and the virtual inertia of the wind turbine. Proportional; After the frequency is restored, the fan speed is increased by injecting negative power: ; in, The coefficient of recovery, The rated frequency of the fan. This refers to the rated frequency of the power system.

[0019] Preferably, the method further includes: verification via a hardware-in-the-loop platform, including: Input disturbance signal to the load side of area 1 and calculate frequency deviation in real time. With power deviation The fractional-order PID controller outputs a signal that drives the PEV model and wind power inertia module through a digital-to-analog interface. The hardware-in-the-loop platform monitors the frequency response and provides feedback correction.

[0020] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: This invention significantly improves the frequency stability and dynamic performance of low-inertia power systems by coordinating the control of a fractional-order PID controller, Rao algorithm parameter optimization, wind turbine virtual inertia simulation, and plug-in electric vehicle energy storage. The method effectively reduces frequency deviation under load disturbances and shortens the system frequency recovery time; it also significantly enhances system damping, thereby suppressing overshoot and oscillations and making the frequency recovery process smoother. Furthermore, the method effectively suppresses tie-line power fluctuations, improves system robustness and disturbance rejection capabilities, maintains superior performance under different wind power penetration rates, and verifies its engineering feasibility and real-time control effect through hardware-in-the-loop experiments. This provides an effective frequency coordination control solution for power systems with a high proportion of renewable energy integration.

[0021] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of the method steps of the present invention; Figure 2 This is a schematic diagram of a multi-source power system in two regions according to an embodiment of the present invention; Figure 3 This is a comparison chart of the response of a conventional wind power integrated system according to an embodiment of the present invention; Figure 4 This invention provides a performance comparison between the FPID algorithm and traditional algorithms in this embodiment. Figure 5 This is the initial reaction in an embodiment of the present invention; Figure 6 This is a performance comparison of different algorithms in embodiments of the present invention; Figure 7This is a comparison graph of fitness functions in embodiments of the present invention; Figure 8 The response of the FPID controller is shown in the embodiments of the present invention with / without PEV at 25% load. Figure 9 The response of the FPID controller under 40% load conditions with and without PEV in this embodiment of the invention; Figure 10 This describes the response of the present invention under 25% wind speed conditions with and without PEV on the Typhoon HIL platform. Figure 11 This describes the response of the present invention under 40% wind speed conditions with and without PEV on the Typhoon HIL platform. Detailed Implementation

[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0024] like Figure 1 As shown, this invention provides a power system frequency control method based on fractional-order control and electric vehicle energy storage coordination, comprising: Step S1: Construct a two-region multi-source power system, including Region 1 and Region 2, which are connected by a tie line.

[0025] Step S2: Establish a wind energy conversion model and calculate the wind turbine output power based on air density, wind turbine blade swept area, and wind speed; Step S3: Based on the wind energy conversion model, the equivalent inertial constant and equivalent governor droop coefficient of the system are corrected according to the wind power penetration rate to construct a virtual inertia control link; Step S4: Establish a PEV frequency response model, use droop control to adjust the charging and discharging power, and set up fractional-order PID controllers in each area of ​​the power system; Step S5: Optimize the parameters of the fractional-order PID controller using the Rao algorithm; Step S6: During the optimization process, the integral squared error of the system frequency deviation and tie line power deviation is used as the optimization objective function; Step S7: When the system experiences load changes or renewable energy power fluctuations, the optimized fractional-order PID controller generates control signals in real time to coordinate the virtual inertia control loop of the generator set and the PEV energy storage unit to regulate power and achieve frequency stability of the low-inertia power system.

[0026] This invention deeply integrates the flexibility of fractional-order PID control with the dynamic support capability of wind power virtual inertia simulation and the rapid power regulation characteristics of electric vehicle energy storage, and introduces the Rao algorithm to achieve adaptive optimization of controller parameters, forming a multi-level collaborative control architecture. Specifically, the fractional-order PID controller improves the system's phase margin and robustness through its non-integer calculus component; wind power virtual inertia simulation provides dynamic power support in the early stages of frequency disturbances, effectively delaying frequency decline; and the electric vehicle energy storage system, with its rapid response characteristics, works in conjunction with conventional units to achieve timely compensation for power deficits. These control methods, working together, constitute a multi-timescale defense system covering the entire frequency disturbance process, thereby significantly enhancing the frequency stability, dynamic response speed, and anti-interference capability of low-inertia power systems, achieving rapid and smooth recovery of system frequency and effective suppression of tie-line power fluctuations.

[0027] In step S1, this invention takes a two-region low-inertia power system with a high proportion of wind power access as the research object. Addressing issues such as decreased frequency stability, insufficient inertia, and strong randomness of renewable energy, it proposes a coordinated frequency control system based on a fractional-order controller, electric vehicle energy storage, and inertia simulation. The overall structure is shown in the attached figure. Figure 1 As shown, the system consists of Region 1 and Region 2. Region 1 includes thermal power, hydropower, gas turbine units, wind turbine units, and a plug-in electric vehicle energy storage system; Region 2 consists of conventional synchronous generator units. The two regions exchange power through a tie line, and fractional-order PID controllers (FPID1 and FPID2) are configured in each region. The frequency deviation signal is detected and input to the respective fractional-order PID controllers. The control signal is then transmitted to the power generation units and energy storage devices to complete multi-source coordinated automatic load frequency control.

[0028] In step S2, based on air density Wind turbine blade sweep area Wind speed The wind energy conversion model is established and determined by the following formula: ; in, This refers to the output power of the fan. air density, The swept area of ​​the wind turbine blades. For wind speed, The wind energy utilization coefficient depends on the tip speed ratio. and pitch angle Fit according to the following polynomial: ; in, These are the elements of the polynomial fitting parameter matrix obtained through experiments or simulations, used for... Description follows and The changing pattern, For the tip speed ratio, The pitch angle is the propeller angle. Pitch angle The polynomial order represents the pitch angle. The power in the fitted polynomial; Tip speed ratio The polynomial order represents the tip speed ratio. The power in the fitted polynomial.

[0029] This invention uses power modeling of wind energy conversion systems as the basis for control, quantifies wind speed fluctuations into controllable power inputs, and provides model support for inertia simulation and FPID control.

[0030] In step S3, based on the proportion of wind turbine units participating in inertia support... Under these conditions, the equivalent inertial constant and equivalent governor droop parameters of the system are corrected: ; ; in, The corrected equivalent inertial constant. The inertial constant of the original system before wind power is connected. For wind power penetration rate, This refers to the inertial constant of the wind turbine itself. This is the corrected equivalent governor droop coefficient. This is the governor droop coefficient of a conventional synchronous generator when it is not connected to wind power.

[0031] The aforementioned modified inertia is used to construct a virtual inertia control loop, enabling the dynamic release and recovery of wind power. Its corresponding system time constant is: ; in, The rated frequency of the power system. The damping coefficient of the load indicates the degree to which the load changes with frequency.

[0032] This invention proposes and employs an inertia correction strategy based on wind power penetration rate, which adjusts the inertia of wind power penetration rate. The mapping is used to correct the system's equivalent inertia and speed regulation performance, thereby enabling the controller design to adapt to different wind power penetration levels.

[0033] Furthermore, the virtual inertia control stage in step S3 includes four functional modules: frequency detection, filtering, inertia response generation, and rate recovery, as detailed below: Extracting the system frequency change rate signal using a first-order low-pass filter: ; in The filtering time constant is To measure frequency, The rated frequency; When a frequency decrease is detected, the inertia controller generates virtual inertia power based on the rate of frequency change. ; in, For inertia gain, and the virtual inertia of the wind turbine. Proportional; After the frequency is restored, the fan speed is increased by injecting negative power: ; in, The coefficient of recovery, For the rated frequency, This is the system's rated frequency.

[0034] when Exceeding the limit At this time, power limiting is implemented to protect the wind turbine. This inertia simulation mechanism releases kinetic energy during the frequency drop phase and automatically recovers during the frequency rise phase, effectively mitigating system frequency fluctuations caused by insufficient inertia.

[0035] During system operation, this invention first establishes a mathematical model for wind energy conversion to describe the impact of wind speed changes on wind power output. By introducing the parameter of wind power penetration rate, the equivalent inertia and speed regulation performance of the system are corrected, enabling the controller to adapt to inertia changes under different wind power ratios. When the system frequency drops, the inertia simulation module of the wind turbine automatically releases the stored kinetic energy, i.e., virtual inertia power. This creates virtual inertia support, slowing down the frequency decline; when the frequency recovers, the inertia module absorbs power in the reverse direction, which is injected through the recovery channel. This is to restore the fan speed. The entire inertia support process is constrained by filtering and limiting mechanisms to ensure safe fan operation.

[0036] In step S4, the electric vehicle is used as a distributed energy storage unit. A PEV frequency response model is established, and a droop control method is used to realize the frequency-power mapping relationship: when the frequency deviation... When the dead zone is smaller than the regulation zone, PEV does not participate in regulation; when... When the set threshold is exceeded, the charging and discharging power is adjusted proportionally. Power is limited and Scope. Fractional-order PID controllers (FPID) are set up in each interconnected system area, with the control law expression as follows: ; ; in, , , , , These are the proportional, integral, and derivative gains of the controller, respectively. , For fractional order, For the proportional term coefficient of the fractional-order PID controller in the second control area of ​​the two-region interconnected power system, For the integral term coefficients of the fractional-order PID controller in the second control area of ​​the two-region interconnected power system, For the derivative coefficients of the fractional-order PID controller in the second control region of the two-region interconnected power system, , These are the frequency response coefficients for the first and second control regions, respectively. , The frequency deviation between region 1 and region 2, For tie line power factor, This refers to the power exchange deviation in the tie line.

[0037] Furthermore, the fractional-order PID controller (FPID) consists of three parts: proportional, fractional-order integral, and fractional-order derivative. Its general expression is: ; in, This is the proportional gain, used to suppress transient amplitudes caused by frequency deviations. This is a fractional integral term used to eliminate steady-state error; This is a fractional-order differential term, used to advance the phase and improve response speed. Preferably, , At that time, the system damping ratio was at its maximum and the frequency recovery time was at its shortest. Compared with integer-order PID, FPID introduces a non-integer-order phase shift into the phase spectrum of the frequency response, thereby increasing the stability margin and reducing oscillations.

[0038] Furthermore, the PEV frequency regulation model adopts a droop control structure, and its charge / discharge power regulation relationship is as follows: ; in, PEV sag factor For frequency deviation, This is the frequency dead zone width, used to prevent frequent triggering of charging and discharging by small disturbances. The change in PEV charging and discharging power; The equivalent dynamic response of the PEV aggregation group is represented as a first-order hysteresis element: ; in, , The Laplace operator characterizes the group response delay; The following limiter constrains the charge / discharge range, thereby protecting battery life and preventing frequency overcompensation: ; in, This represents the minimum change in charging and discharging power. This represents the maximum value of the change in charging and discharging power.

[0039] The energy storage component of the plug-in electric vehicle (PEV) participates in the primary frequency regulation of the system as a distributed controllable load. Each PEV automatically adjusts its charging and discharging power according to the frequency deviation. When the system frequency is below a set threshold, it enters a discharging state to provide compensation power to the grid; when the frequency is above the threshold, it switches to a charging state to absorb excess power. The response characteristics of the PEV are described using a first-order dynamic process, which can complete power adjustment in tens of milliseconds, thus enabling it to quickly take effect after system disturbances. To prevent overcharging and discharging, this invention incorporates the PEV into the primary frequency response as a distributed energy storage support, including dead zone, droop control, and upper and lower power constraints. A first-order inertial model is used to describe the dynamic response of the aggregated PEV, so that when the frequency deviation exceeds the dead zone, the PEV outputs or absorbs power proportionally to participate in frequency stabilization, thus balancing battery life and system stability.

[0040] This invention employs a fractional-order PID (FPID) control law to regulate ACE within a two-zone AGC framework, and specifies the fractional order of the FPID. , It can be adjusted within (0,1] to balance phase margin and steady-state performance.

[0041] The core of this invention is a fractional-order PID controller. Unlike traditional integer-order PID controllers, fractional-order controllers introduce fractional orders in the integral and derivative parts, allowing for more flexible adjustment of the system's phase characteristics and steady-state performance. The FPID controller of this invention utilizes the area control error formed by frequency deviation and tie-line power deviation as the input signal, and outputs an adjustment quantity to control the power generation output of each region. By introducing fractional orders, the controller maintains a fast response while possessing higher robustness and disturbance rejection capability, adapting to random changes in wind speed and load.

[0042] In step S5, the FPID parameters are optimized using the Rao algorithm. The algorithm update mechanism is as follows: ; in, , It is a random number. This is the updated optimal solution. Let j be the value of the j-th variable in the k-th candidate solution of the i-th iteration. Let j be the value of the j-th variable in the l-th candidate solution of the i-th iteration. , In the first Among all candidate solutions in the nth iteration The best and worst values ​​of each variable.

[0043] Updated solution If its performance indicators If the solution is correct, then the old solution will be replaced. The convergence criterion is: ; in, Preset precision.

[0044] Compared to the PSO or GA algorithms, the Rao algorithm reduces computational complexity by about 40% and shortens convergence time by about 30%.

[0045] This invention employs the Rao algorithm to optimize FPID parameters online or offline, and iteratively updates the formula to realize the control parameter vector. Search and update.

[0046] To ensure optimal control parameters, this invention employs a Rao algorithm that does not require hyperparameters to optimize fractional-order PID parameters. This algorithm iteratively calculates the difference between the optimal and worst solutions, without relying on empirical parameters such as inertia weights and crossover rates, and can quickly converge to the global optimum. The objective function is set as the integral of the square of the system frequency deviation. The algorithm adjusts the control parameters in each iteration to minimize system frequency fluctuations. This optimization method not only improves control accuracy but also simplifies the parameter tuning process, facilitating engineering applications.

[0047] In step S6, the integral squared error is used as the optimization objective: ; In the formula, The objective function value, , The square of the frequency deviation between region 1 and region 2. The square of the tie-line power exchange deviation is minimized. The goal is to achieve minimum frequency deviation and balance the power of the tie line.

[0048] This invention uses integral squared error (ISE) as the optimization objective function and quantifies control performance, serving as a fitness metric for the Rao algorithm, thereby directly incorporating frequency deviation and tie-line power fluctuation into the controller parameter tuning objective.

[0049] In step S7, when the system load changes or the renewable energy power fluctuates, the FPID controller generates a control signal in real time to drive the generator set and PEV to perform power regulation, and finally achieve system frequency stability.

[0050] Furthermore, it also includes: verification on the Typhoon HIL-402 hardware-in-the-loop (HIL) platform, where the control structure is completely equivalent to the MATLAB / Simulink simulation model. The verification steps are as follows: (1) Input disturbance signal To the load side of Zone 1; (2) Real-time calculation of frequency deviation With power deviation ; (3) FPID controller output signal It drives the PEV model and wind power inertia module through the digital-analog interface; (4) HIL monitors frequency response and provides feedback correction.

[0051] The experimental results show that the frequency curves of the simulation and the HIL test deviate by less than 5%; the steady-state recovery time is less than 10s; the system dynamic response is smooth and there is no oscillation phenomenon.

[0052] The control method of this invention demonstrates significant superiority in both simulation and real-time verification. In low-inertia dual-zone power systems, by combining a fractional-order PID controller with Rao algorithm optimization, inertia simulation, and plug-in electric vehicle energy storage, this invention outperforms traditional control methods in terms of frequency dynamic performance, system damping, power balance, and real-time feasibility. Firstly, regarding frequency dynamic characteristics, the method of this invention shows significant improvement under typical operating conditions with a wind power penetration rate of 25%. According to... Figure 3 Compared with the simulation results in Table 1, when the system is subjected to a 1% load disturbance, the lowest frequency point under traditional PID control is 59.9801Hz, while the lowest frequency point of the proposed "FPID+Rao+Inertia Simulation+PEV Cooperative Control" scheme is increased to 59.9876Hz, an increase of approximately 0.0075Hz, indicating a significant reduction in frequency sag. Simultaneously, the system settling time is shortened from approximately 25s for traditional PID control to 12s, improving the response speed by over 50%, and the frequency overshoot decreases from 5.2% to approximately 2.3%. These results demonstrate that the present invention can quickly restore the system frequency after a load disturbance and effectively suppress secondary oscillations.

[0053] Table 1 Performance metrics of different algorithms

[0054] Secondly, regarding system damping and robustness, according to Table 2, the overall damping ratio of the traditional PID controller is approximately 0.248, while the damping ratio of the fractional-order PID controller optimized by the Rao algorithm is increased to 0.496, nearly doubling. This result demonstrates that the control strategy of this invention significantly enhances the dynamic damping performance of the system, resulting in a smooth and oscillating frequency recovery process.

[0055] Meanwhile, this invention maintains system stability under different wind power penetration rates (25%, 40%, 50%). Figure 4-7 As shown, even when wind power accounts for more than 40%, the system can still recover its frequency within 14–16 seconds, with the lowest point maintained in the 59.978–59.975Hz range, demonstrating strong robustness. From the perspective of comprehensive performance indicators, based on the integral squared error (ISE) performance index in Table 3, the ISE value of the traditional PID controller is... The ISE value of the FPID-Rao cooperative control of this invention is only [value missing]. The performance error energy was reduced by approximately 31%. The significant decrease in the ISE value indicates that the overall frequency fluctuation energy of the system was effectively suppressed, and the dynamic deviation was smaller.

[0056] Table 2. Optimal parameters obtained using metaheuristic algorithms

[0057] Table 3 Optimal parameters obtained using the Rao algorithm

[0058] Meanwhile, the system's frequency deviation curve is smoothed, recovery is overshoot-free, and tie-line power fluctuations are significantly reduced. In simulations with PEV support, such as... Figure 8-9 As shown, the peak power oscillation of the tie line decreased by about 20% compared to the case without PEV, and the maximum frequency deviation decreased by about 25%. This indicates that the charging and discharging regulation of plug-in electric vehicles plays a positive role in primary frequency regulation and power balance, further improving the overall stability of the system.

[0059] Furthermore, experimental verification of this invention on the TyphoonHIL-402 real-time hardware-in-the-loop platform shows that, as Figure 10-11As shown, the proposed control strategy has good feasibility. The simulation results are highly consistent with the real-time test results, with frequency settling times of 16.2s and 16.9s, respectively, a deviation of only about 4.3%; steady-state frequency errors of 0.014Hz and 0.015Hz, respectively, an error of 7.1%; and overall response deviation of less than 5%. The measured waveform is smooth without obvious oscillations, proving that the control method can be directly applied to real-time systems and has engineering feasibility.

[0060] In summary, during the simulation phase, this invention was validated under three typical scenarios: wind power penetration rates of 25%, 40%, and 50%. The results show that under a 1% load change, the minimum frequency of the control strategy of this invention is significantly higher than that of traditional PID control, and the system settling time is significantly shortened. When the wind power penetration rate is 25%, the minimum system frequency increases by approximately 0.0075 Hz, the settling time is shortened from 25 seconds to 12 seconds (approximately 50%), the energy deviation integral decreases by approximately 31%, and the system damping increases by approximately 100%. Good stability is maintained even at a 40% wind power penetration rate, indicating strong robustness of the controller. Furthermore, with the addition of inertia simulation and PEV, the system tie-line power oscillation amplitude decreases by approximately 20%, and the peak frequency deviation decreases by approximately 25%, further improving the system's coordination capability.

[0061] In real-time hardware-in-the-loop experiments conducted on the Typhoon HIL-402 platform, the simulation and experimental results showed a high degree of consistency, with only about a 4% deviation in frequency settling time and a steady-state frequency error of approximately 0.015Hz, verifying the real-time feasibility and engineering feasibility of the control strategy. The system exhibited no significant oscillations during disturbance recovery, indicating that the control structure also possesses stable operation capabilities at the hardware execution level. The above values ​​are derived from simulation results of the embodiment.

[0062] This invention achieves rapid frequency recovery, fluctuation suppression, and enhanced system damping by introducing fractional-order PID control, inertia simulation, and a collaborative mechanism between electric vehicle energy storage and low-inertia power systems. This control framework maintains stable performance under varying wind power penetration rates, improves the minimum frequency, shortens recovery time, reduces energy deviation, and significantly enhances overall system stability and disturbance rejection. The method features a clear control structure, simple parameter optimization, and easy integration into existing AGC systems, demonstrating good engineering applicability and promotional value.

[0063] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0064] It will be readily understood by those skilled in the art that this invention includes any combination of the inventive description and specific embodiments outlined in the foregoing specification, as well as the various parts shown in the accompanying drawings. Due to space limitations and for the sake of brevity, not all of these combinations have been described in detail. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

[0065] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination, characterized in that, include: Construct a two-region, multi-source power system, including Region 1 and Region 2, which are connected by a tie line; Establish a wind energy conversion model and calculate the wind turbine output power based on air density, wind turbine blade swept area and wind speed; Based on the wind energy conversion model, the equivalent inertial constant and equivalent governor droop coefficient of the system are corrected according to the wind power penetration rate to construct a virtual inertia control link. A PEV frequency response model was established, and a droop control method was used to adjust the charging and discharging power. Fractional-order PID controllers were set up in each area of ​​the power system. The Rao algorithm is used to optimize the parameters of the fractional-order PID controller; During the optimization process, the integral squared error of the system frequency deviation and tie-line power deviation is used as the optimization objective function; When the system experiences load changes or renewable energy power fluctuations, the optimized fractional-order PID controller generates control signals in real time to coordinate the virtual inertia control loop of the generator set and the PEV energy storage unit to regulate power, thereby achieving frequency stability of the low-inertia power system.

2. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The wind energy conversion model is as follows: ； in, This refers to the output power of the fan. air density, The swept area of ​​the wind turbine blades. For wind speed, The wind energy utilization coefficient is fitted using the following polynomial: ； in, These are the elements of the polynomial fitting parameter matrix. For the tip speed ratio, The pitch angle is the propeller angle. Pitch angle The order of the polynomial, Tip speed ratio The order of the polynomial.

3. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The equivalent inertial constant and equivalent governor droop coefficient of the system corrected according to wind power penetration rate are as follows: ； ； in, The corrected equivalent inertial constant. The inertial constant of the original system before wind power is connected. For wind power penetration rate, This refers to the inertial constant of the wind turbine itself. This is the corrected equivalent governor droop coefficient. This is the governor droop coefficient of a conventional synchronous generator when it is not connected to wind power.

4. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The method of adjusting charging and discharging power using a droop control approach and setting fractional-order PID controllers in each region includes: When frequency deviation When the dead zone is smaller than the limit, PEV does not participate in regulation; when When the set threshold is exceeded, the change in charging and discharging power is adjusted proportionally. The power is limited by the minimum change in charging and discharging power. With the maximum value of the change in charging and discharging power Interval range; Fractional-order PID controllers are installed in each region of the power system, and the control law expression is as follows: ； ； in, , , , , These are the proportional, integral, and derivative gains of the fractional-order PID controller in region 1. , For fractional order, , , These are the proportional, integral, and derivative gains of the fractional-order PID controller in region 2. , These are the frequency response coefficients for region 1 and region 2, respectively. , The frequency deviations for regions 1 and 2 are respectively. For the tie line power factor, This refers to the power exchange deviation in the tie line.

5. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The update mechanism of the Rao algorithm is as follows: ； in, , It is a random number. This is the updated optimal solution. Let j be the value of the j-th variable in the k-th candidate solution of the i-th iteration. Let j be the value of the j-th variable in the l-th candidate solution of the i-th iteration. , In the first Among all candidate solutions in the nth iteration The best and worst values ​​of each variable.

6. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The optimization objective function is as follows: ； in, The objective function value, , The frequency deviations for regions 1 and 2 are respectively. This refers to the power exchange deviation in the tie line.

7. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The fractional-order PID controller consists of three parts: proportional, fractional-order integral, and fractional-order derivative. Its general expression is: ； in, For proportional gain, For fractional integral terms, It is a fractional differential term.

8. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 4, characterized in that, The PEV frequency regulation model adopts a droop control structure, and its charge / discharge power regulation relationship is as follows: ； in, PEV sag factor For frequency deviation, The frequency dead zone width, The change in PEV charging and discharging power; The equivalent dynamic response of the PEV aggregation group is represented as a first-order hysteresis element: ； in, , For the Laplace operator; The following limiter constrains the charge / discharge range, thereby protecting battery life and preventing frequency overcompensation: ； in, This represents the minimum change in charging and discharging power. This represents the maximum value of the change in charging and discharging power.

9. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, The inertia simulation control module includes frequency detection, filtering, inertia response generation, and rate recovery, including: Extracting the system frequency change rate signal using a first-order low-pass filter: ； in, The filtering time constant is To measure frequency, The rated frequency; When a frequency decrease is detected, the inertia controller generates virtual inertia power based on the rate of frequency change. ； in, For inertia gain, and the virtual inertia of the wind turbine. Proportional; After the frequency is restored, the fan speed is increased by injecting negative power: ； in, The coefficient of recovery, The rated frequency of the fan. This refers to the rated frequency of the power system.

10. The frequency coordination control method for low-inertia power systems based on fractional-order control and electric vehicle energy storage coordination as described in claim 1, characterized in that, Also includes: Verification is performed through a hardware-in-the-loop platform, including: Input disturbance signal to the load side of area 1 and calculate frequency deviation in real time. With power deviation The fractional-order PID controller outputs a signal that drives the PEV model and wind power inertia module through a digital-to-analog interface. The hardware-in-the-loop platform monitors the frequency response and provides feedback correction.

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