A sliding mode PI control method for electric vehicle cluster auxiliary power grid frequency modulation

Abstract

The application provides a sliding mode PI control method for frequency regulation of an electric vehicle cluster assisting a power grid, the method adjusts a system frequency deviation by combining SMC control and PI control, and then uses a fuzzy optimization algorithm to generate a variable coefficient for optimizing signals of the sliding mode control and the PI control by taking the frequency deviation and a change rate of the frequency deviation as input signals. The method has dynamic performance and steady-state performance, and can also coordinate output between the EV cluster and a generator, avoid over-regulation or even instability of the system frequency caused by continuous large output of the EV cluster, and reduce economic cost of frequency regulation of the power system. In addition, for the EV cluster, the application considers three types of vehicles, and uses a particle swarm optimization algorithm to optimize input proportion parameters of the three types of EV clusters, so as to obtain optimal input quantity of the electric vehicles.

Description

Technical Field

[0001] This invention relates to a sliding mode PI control method for electric vehicle clusters to assist in power grid frequency regulation, belonging to the field of electric vehicle clusters providing ancillary services to power systems. Background Technology

[0002] As the number of electric vehicles increases, the load of electric vehicles requiring charging also increases, and the grid connection of a large number of electric vehicles will bring many challenges to the stable operation of the power system.

[0003] The integration of a large number of electric vehicles (EVs) into the power grid will inevitably put pressure on the power system, potentially creating new peak loads on top of existing peak periods. This will exacerbate the peak-to-valley load difference, increase the burden on the power grid, and affect its safe and stable operation. This includes impacting voltage quality, causing power system convection pollution, and leading to system frequency instability. Statistics show that most private cars are inactive for an average of 96% of the day, and EVs, being a special type of load that can act as both a load and a power source, offer the possibility for energy interaction between EVs and the power system—V2G (Vehicle-to-Grid). Compared to generators, EVs have the advantage of faster response times, enabling them to output power promptly when generators cannot respond to load disturbances, ensuring the safe and stable operation of the system. Load disturbances in the power system are divided into step disturbances and random load disturbances, requiring EV clusters to ensure the system's disturbance resistance and robustness in both dynamic and static conditions. Furthermore, the continuous high-volume power output of EV clusters not only degrades the cycle life of EV batteries but also causes oscillations or even instability in the system frequency, increasing the cost of system frequency regulation.

[0004] Using EV clusters to regulate the frequency stability of power systems has become one of the main research directions for many scholars, and the literature...

[0005] A tubular model predictive control (MPC) method was proposed, and a disturbance observer was designed to observe the disturbance magnitude. Reference [2] uses the improved sliding mode control (SMC) as the basic controller of the system frequency modulation model. Reference [3] adopts a hierarchical adaptive control strategy to control the system frequency, in which the main controller adopts SMC and the EV cluster adopts an adaptive control method. SMC control has excellent dynamic performance when the system is subjected to large load disturbances, but chattering occurs in steady-state control. References [4-5] use PI control to control the EV cluster when the EV participates in auxiliary frequency modulation. PI control has good static performance when the system is subjected to random load disturbances, but the system will overshoot when subjected to large load fluctuations. Therefore, in order to adapt to the complex load requirements of the system, it is necessary to enable the system to have excellent dynamic and static performance.

[0006] However, frequency regulation of the power system not only requires frequency stability, but also needs to consider the economics of frequency regulation. When EV clusters participate in auxiliary frequency regulation, it helps the system frequency stability, but increases the frequency regulation cost of the system. Considering the fast response characteristics of EVs, the authors of reference [5] allocated the high-frequency signal of frequency deviation to the EV cluster. References [6-9] considered the power battery loss factor in the process of EVs participating in grid frequency regulation. References [10-11] analyzed the economic and environmental benefits of EV clusters participating in auxiliary services. The above references studied the battery loss and V2G economic benefits in the process of EV clusters participating in frequency regulation, but gave less consideration to the coordinated output between generators and EV clusters and the frequency regulation cost, as well as the optimal input ratio of EV clusters in the process of participating in power system frequency regulation. In the process of frequency regulation, the output of EV clusters is related to the number of EVs participating in frequency regulation and the output of a single EV. There are also literatures

[12] that aim to balance the effect and cost of frequency regulation and achieve reasonable charging scheduling for electric vehicles, so that they can meet the travel and charging needs of electric vehicles themselves and better serve the day-ahead economic dispatch and frequency regulation auxiliary services of the power grid. However, literature

[12] considers the interaction between day-ahead dispatch, frequency regulation capacity and frequency regulation power, and achieves the electric vehicle cluster charging optimization method that maximizes the peak regulation and frequency regulation benefits of the power grid through upper and lower level coordination control.

[0007] Literature[1]—OSHNOEI A,KHERADMANDI M,MUYEEN SM,et al.DisturbanceObserver and Tube-Based Model Predictive Controlled Electric Vehicles for Frequency Regulation of an Isolated Power Grid[J].IEEE Transactions on SmartGrid;

[0008] Literature[2]—MU CX, TANG YF, and HE H B.Improved Sliding Mode Design for Load Frequency Control of Power System Integrated an Adaptive LearningStrategy[J].IEEE Transactions on Industrial Informatics;

[0009] Literature [3]—MU CX, LIU WQ, and XU W.Hierarchically Adaptive FrequencyControl for an EV-Integrated Smart Grid With Renewable Energy[J].IEEETransactions on Industrial Informatics;

[0010] Reference [4]—Bao Yan, Jia Limin, Jiang Jiuchun, et al. Research on auxiliary frequency control strategy for mobile energy storage of electric vehicles [J]. Journal of Electrical Engineering Technology;

[0011] Reference [5]—Xiang Leijun, Chen Hao, Guo Xinhua, et al. Secondary frequency control of multi-energy microgrid with electric vehicles based on fuzzy fractional PID [J]. Electric Power Automation Equipment;

[0012] Reference [6]—Li Jiazhuang, Ai Xin, Hu Junjie. Modeling and control strategy for electric vehicles participating in secondary frequency regulation of power grid [J]. Power Grid Technology;

[0013] Reference [6]—Huang Shuaibo, Chen Bei, Gao Jiangyu. Energy management strategy for electric vehicle charging stations based on Markov decision process [J]. Electric Power Automation Equipment;

[0014] Reference [7]—Zhang Qian, Deng Xiaosong, Yue Huanzhan, et al. Collaborative optimization strategy for electric vehicles participating in the energy-frequency modulation market considering battery life loss [J]. Journal of Electrical Engineering;

[0015] Reference [8]—Li Yiran, Zhang Shu, Xiao Xianyong, et al. Electric vehicle charging and discharging scheduling strategy considering supply and demand under V2G mode [J]. Electric Power Automation Equipment;

[0016] Reference [9]—Chen Lijuan, Qin Meng, Gu Shaoping, et al. Optimal scheduling strategy for electric buses participating in V2G considering battery losses [J]. Automation of Electric Power Systems;

[0017] Reference

[10] —Zhou Chunqi, Xiang Yue, Zhang Xin, et al. Analysis of the adjustment potential and economic efficiency of V2G ancillary services: a case study of Shanghai [J]. Electric Power Automation Equipment;

[0018] Reference

[11] —Wang Huaxin, Zhang Gaoli, Liu Jun, et al. Design of differentiated charging packages for electric vehicles based on master-slave game considering user contribution [J]. Electric Power Automation Equipment;

[0019] Reference

[12] —CN112668874A A method for coordinated scheduling of electric vehicle cluster charging in power grid peak regulation and frequency regulation. Summary of the Invention

[0020] The purpose of this invention is to address the shortcomings of existing EV cluster controllers by providing a method for frequency regulation sliding mode PI control and optimization of electric vehicle clusters for grid auxiliary control. The specific solution is as follows:

[0021] The first aspect of this invention provides a sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation, wherein the method regulates the power system load frequency based on a power system load frequency regulation model and an EV cluster model;

[0022] The power system load frequency regulation model includes a main controller model, a speed governor model, a prime mover model, and a load damping model.

[0023] The speed controller model includes a unit regulating power module and a speed controller equivalent model;

[0024] The unit regulating power module takes the power system frequency deviation Δf as input;

[0025] The main controller output signal U p The frequency deviation Δf of the power system after power regulation is summed by the first summing module and then input into the equivalent model of the speed governor to obtain the change in the speed governor position ΔP. v ;

[0026] The prime mover model uses the governor position change ΔP vTo obtain the change in the mechanical power output of the generator, ΔP m ;

[0027] The change in mechanical power output of the generator ΔP m The total output power ΔP of the EV cluster model ev The input terminal ΔP of the system load disturbance load Renewable energy ΔP res After being summed by the second summation module, the result is input into the load damping model to obtain the power system frequency deviation Δf.

[0028] The EV cluster model, based on the EVA controller, is divided into three EV cluster models: private car cluster model, bus cluster model, and taxi cluster model.

[0029] The three EV cluster models use the same model. Each EV cluster model includes a model frequency deviation signal allocation coefficient S, an equivalent model of the EV power battery, an EV output power limiter, and an EV quantity variation module. The equivalent model of the EV power battery uses the frequency deviation signal allocation coefficient and the output signal U of the EVA controller. e The input is used as input, and after calculation, the output is sent to the EV output power limiter to obtain the charging and discharging power of the EV cluster; the EV quantity change module uses the charging and discharging power of the EV cluster as input, and combines it with the number N of EVs participating in frequency modulation to calculate the total output power P of the EV cluster. A ;

[0030] Total output power P of private car cluster A_pri Total output power P of the bus cluster A_bus Total output power P of the taxi cluster A_taxi The total output power ΔP of the EV cluster model is obtained by summing the data using the third summing module. ev ;

[0031] The EVA controller includes a first SMC controller and a first PI controller, and satisfies the following control strategy:

[0032] Both the first SMC controller and the first PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf.

[0033] The adjusted grid frequency deviation Δf is summed to generate the control signal U′. e ;

[0034] Using the power system frequency deviation Δf and the rate of change of the power system frequency deviation Δf as input signals, a fuzzy optimization algorithm is used to generate coefficients U. fuzzy And after passing through a first-order low-pass filter, the variable coefficient β is obtained;

[0035] The variable coefficient β is multiplied by the control signal U′ to obtain the output signal U of the EVA controller. e ;

[0036] The main controller includes a second SMC controller and a second PI controller, satisfying the following control strategy:

[0037] Both the second SMC controller and the second PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf.

[0038] The adjusted grid frequency deviation Δf is summed to generate the output signal U of the main controller. p ;

[0039] Both the first SMC controller and the second SMC controller use the state variable X(t) = [Δf ΔP] m ΔP v ΔP A_pri ΔP A_taxi ΔP A_bus ] T Design the sliding surface S = CX(t); where the vector coefficients C = [c1 c2 c3 c4 c5 c6], c6p 6 +c5p 5 +c4p 4 +c3p 3 +c2p 2 +c1p satisfies the Routh stability criterion.

[0040] Based on the above, both the first SMC controller and the second SMC controller adopt the following constant-rate approach law. Where ε is the reaching law gain coefficient, f sat (S) is a saturation function;

[0041] The control signals of both the first PI controller and the second PI controller satisfy the following relationship:

[0042]

[0043] In the formula, K p_p and K p_i These are the proportional and integral parameters in the PI controller, respectively.

[0044] Based on the above, with the goal of minimizing system frequency regulation cost and frequency deviation, considering generator output, ramp rate and EV cluster input ratio α, a joint optimization model of EV cluster output and frequency regulation is constructed, and the particle swarm optimization algorithm is used for offline solution.

[0045] The proportion α of the EV cluster investment is:

[0046]

[0047] In the formula, N ev_V2G N represents the number of electric vehicles participating in auxiliary frequency modulation within the EV cluster. ev This represents the number of electric vehicles connected to the power grid within the EV cluster.

[0048] Based on the above, the joint optimization model for EV cluster output and frequency regulation is as follows:

[0049] Establish an objective function F, and optimize it with the goal of minimizing F;

[0050] F=k1C+k2Γ

[0051] In the formula, k1 and k2 are weighting coefficients used to reduce the frequency modulation cost and frequency stability index to the same order of magnitude; C is the total cost of auxiliary frequency modulation; Γ is the frequency stability index.

[0052] The total cost C of auxiliary frequency regulation in the power system includes the generator fuel cost C. fuel The compensation cost C for EV users from the power grid V2G The battery degradation cost of electric vehicles, C b That is: C = C fuel +C V2G +C b ;

[0053] To measure the frequency stability of the system, the integral of the absolute value of the system frequency deviation over time at per-unit values ​​is used as the index Γ for measuring the system frequency stability, i.e.:

[0054]

[0055] Based on the above, the proportion α of investment in auxiliary frequency regulation in private car clusters, bus clusters, and taxi clusters is... pri α bus α taxi The generator output and ramp rate must satisfy the following constraints:

[0056]

[0057] -R down ≤(P G，t+1 -P G，t ) / Δt≤R up

[0058]

[0059] In the formula, and These are the minimum and maximum output power of the generator, respectively; P G，t+1 and P G，t The generator output power R at times t+1 and t are respectively. down With R up These are the generator's downward and upward adjustment rate limits, respectively. These are the minimum proportions of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively. These represent the maximum percentage of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively.

[0060] Based on the above, the particle swarm optimization algorithm simulates the predation behavior of bird flocks and solves the optimization model of the objective function.

[0061] A second aspect of the present invention provides a sliding mode PI control device for electric vehicle cluster-assisted grid frequency regulation, comprising a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the sliding mode PI control method for electric vehicle cluster-assisted grid frequency regulation as described above.

[0062] This invention has outstanding substantive features and significant progress compared to the prior art, specifically:

[0063] The sliding mode PI controller provided by this invention combines SMC and PI control, fully utilizing the excellent disturbance rejection performance and robustness of SMC during system transient processes, and the static stability performance of PI control in the face of random load disturbances during system steady-state processes. By integrating SMC and PI control, the system can transition from steady-state operation to transient operation when encountering load disturbances, and finally recover to steady-state operation, ensuring good robustness throughout this process.

[0064] In order to coordinate the power output between the generator and the EV cluster, the method of the present invention uses a fuzzy optimization algorithm to generate variable coefficients to optimize the control signal, thereby avoiding continuous high power output from the EV cluster, reducing the lifespan of the electric vehicle power battery and the economic cost of system frequency regulation.

[0065] The method of this invention aims to minimize frequency regulation cost and frequency deviation. It considers constraints such as generator output, ramp rate, and EV cluster deployment ratio, constructs a joint optimization model of EV cluster output and frequency regulation, and uses particle swarm optimization algorithm for offline solution. This ensures that during the auxiliary frequency regulation process, the optimal number of EV cluster vehicles are deployed to participate in frequency regulation, thereby achieving the best frequency regulation effect, the minimum EV cluster output, and the minimum power battery life loss. Attached Figure Description

[0066] Figure 1 This is a block diagram illustrating the adjustment of power system load frequency based on a power system load frequency adjustment model and an EV cluster model in Embodiment 1 of the present invention.

[0067] Figure 2 This is a block diagram for generating cluster control signals in an embodiment of the present invention.

[0068] Figure 3 This is a flowchart of particle swarm optimization in an embodiment of the present invention.

[0069] Figure 4 This is a graph showing the change in the number of three vehicle models connected to the power grid at different times during system simulation in an embodiment of the present invention.

[0070] Figure 5 The figure shows the system load disturbance change curve in the system simulation of this invention.

[0071] Figure 6 The system frequency fluctuation curve and the power output between the generator and the EV cluster are shown in the system simulation of this embodiment of the invention when the generator capacity is sufficient.

[0072] Figure 7 This is the EV cluster control signal when the generator capacity is insufficient in the system simulation of this embodiment of the invention.

[0073] Figure 8 The output power variation curves of the generator and EV cluster when the generator capacity is insufficient are shown in the system simulation of this embodiment of the invention.

[0074] Figure 9 This is a frequency variation curve when the generator capacity is insufficient in the system simulation of an embodiment of the present invention.

[0075] Figure 10 In the system simulation of this embodiment of the invention, after optimization simulation, the frequency deviation change curve of the system before and after optimization is shown.

[0076] Figure 11 In the system simulation of this invention embodiment, after optimization simulation, the output change curves of the generator and EV cluster before and after optimization are obtained. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely below, but the present invention is not limited to these embodiments:

[0078] Example 1

[0079] like Figure 1As shown, a sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation is proposed. The method is based on a power system load frequency regulation model and an EV cluster model to regulate the power system load frequency.

[0080] EV clusters participate in system frequency modulation model

[0081] The power system load frequency regulation model includes a main controller model, a speed governor model, a prime mover model, and a load damping model.

[0082] The speed controller model includes a unit regulating power module and a speed controller equivalent model;

[0083] The unit regulating power module takes the power system frequency deviation Δf as input;

[0084] The main controller output signal U p The frequency deviation Δf of the power system after power regulation is summed by the first summing module and then input into the equivalent model of the speed governor to obtain the change in the speed governor position ΔP. v ;

[0085] Among them, the frequency deviation of the power system after power regulation is R is the droop coefficient; the equivalent model of the speed governor is... T g The time constant of the speed controller;

[0086] Governor position change ΔP v The following relationship must be satisfied:

[0087]

[0088] The prime mover model uses the governor position change ΔP v To obtain the change in the mechanical power output of the generator, ΔP m The prime mover model is... T t The prime mover time constant;

[0089] Change in generator output mechanical power ΔP m The following relationship must be satisfied:

[0090]

[0091] The change in mechanical power output of the generator ΔP m The total output power ΔP of the EV cluster model ev The input terminal ΔP of the system load disturbance load Renewable energy ΔP resAfter being summed by the second summation module, the result is input into the load damping model to obtain the power system frequency deviation Δf.

[0092] The load damping model is as follows:

[0093] The frequency deviation Δf of the power system satisfies the following relationship:

[0094]

[0095] In the above formula, M is the inertial time constant and D is the load damping constant.

[0096] Currently, electric vehicles have penetrated into various vehicle types. This embodiment considers three types of electric vehicles: private cars, buses, and taxis. Each type forms a cluster to participate in frequency regulation. For modeling the EV cluster, this embodiment assumes that EVs of the same type have the same parameters; for different types of EVs, only the changes in EV time constant, maximum charging and discharging power, and the number connected to the grid are considered.

[0097] The EV cluster model, based on the EVA controller, is divided into three EV cluster models: private car cluster model, bus cluster model, and taxi cluster model.

[0098] The three EV cluster models use the same model. Each EV cluster model includes a model frequency deviation signal allocation coefficient S, an equivalent model of the EV power battery, an EV output power limiter, and an EV quantity variation module. The equivalent model of the EV power battery uses the frequency deviation signal allocation coefficient and the output signal U of the EVA controller. e The input is used as input, and after calculation, the output is sent to the EV output power limiter to obtain the charging and discharging power of the EV cluster; the EV quantity change module uses the charging and discharging power of the EV cluster as input, and combines it with the number N of EVs participating in frequency modulation to calculate the total output power P of the EV cluster. A ;in,

[0099] The equivalent models for the power batteries of private cars, buses, and taxis are as follows:

[0100] The allocation ratio S of FM signals for private cars, buses, and taxis pri S bus S taxi The following relationship must be satisfied:

[0101]

[0102] The following constraints exist:

[0103]

[0104] Total output power P of private car cluster A_pri Total output power P of the bus cluster A_bus Total output power P of the taxi cluster A_taxi The total output power ΔP of the EV cluster model is obtained by summing the data using the third summing module. ev ;

[0105] Total output power P of private car cluster A_pri Total output power P of the bus cluster A_bus Total output power P of the taxi cluster A_taxi The following relationship must be satisfied:

[0106]

[0107] Total output power ΔP ev The following relationship must be satisfied:

[0108]

[0109]

[0110] In the above formula, T pri T bus T taxi N represents the time constants for private cars, buses, and taxis in the cluster, respectively. pri N bus N taxi These represent the number of private cars, buses, and taxis participating in frequency modulation within the cluster; P pri P bus P taxi These represent the charging and discharging power of private cars, buses, and taxis within the cluster; P A_pri P A_bus P A_taxi These represent the total power output from private cars, buses, and taxis, respectively. and They are P pri P bus P taxi The upper and lower limits.

[0111] EV cluster participation in system frequency modulation control strategy

[0112] The large-scale integration of clean energy into the grid and the random fluctuations in load lead to significant uncertainties in grid power generation and consumption. Therefore, smart grids urgently require a robust frequency controller. This embodiment employs a combination of sliding mode control and PI control to generate control signals for the main controller and EVA controller, thereby adjusting the speed governor and prime mover. This allows the power system to possess not only the dynamic performance of SMC (Smooth Mode Control) but also the steady-state performance of PI control, enhancing the power system's disturbance rejection and robustness.

[0113] EVA controller

[0114] like Figure 2 As shown, the EVA controller includes a first SMC controller and a first PI controller, satisfying the following control strategy:

[0115] Both the first SMC controller and the first PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf.

[0116] The adjusted grid frequency deviation Δf is summed to generate the control signal U′. e ;

[0117] Using the power system frequency deviation Δf and the rate of change of the power system frequency deviation Δf as input signals, a fuzzy optimization algorithm is used to generate coefficients U. fuzzy And after passing through a first-order low-pass filter, the variable coefficient β is obtained;

[0118] The variable coefficient β and the control signal U′ e After multiplication, the output signal U of the EVA controller is obtained. e .

[0119] Main controller

[0120] The main controller includes a second SMC controller and a second PI controller, satisfying the following control strategy:

[0121] Both the second SMC controller and the second PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf.

[0122] The adjusted grid frequency deviation Δf is summed to generate the output signal U of the main controller. p .

[0123] Sliding mode control

[0124] Both the first SMC controller and the second SMC controller design the sliding surface S=CX(t) based on the state variable X(t); where,

[0125] X(t)=[Δf ΔP m ΔP v Δ PA_pri Δ PA_taxu ΔP A_bus ] T (7)

[0126] Vector coefficients C = [c1 c2 c3 c4 c5 c6], c6p 6 +c5p 5 +c4p 4 +c3p 3 +c2p 2 +c1p satisfies the Routh stability criterion;

[0127] From equations (1), (2), (3), and (6), we can write the following equation:

[0128]

[0129] ΔP d (t)=ΔP load (t)-ΔP res (t)

[0130] In the above formula, ΔP load ΔP res These are the changes in load disturbance power and the changes in renewable energy power, respectively.

[0131] Both SMC controllers use the following constant-rate reaching law for their sliding mode reaching laws. Where ε is the reaching law gain coefficient, f sat (S) is a saturation function;

[0132] The output signal U of the EVA controller e The following relationship must be satisfied:

[0133] U e (t)=βU′ e (t)=β(U e_SMC(t) +U e_PI(t) (9)

[0134] From the sliding mode approach rate combined with equation (8), we can derive:

[0135] U e_SMC(t) =-(CB) -1 (εf sat (S)+CAX(t)+CB′U p (t)) (10)

[0136] In equation (10),

[0137] The main controller output signal U p The following relationship must be satisfied:

[0138] U p (t)=U p_SMC(t) +U p_PI(t) (11)

[0139] From the sliding mode approach rate combined with equation (8), we can derive:

[0140] U p_SMC(t) =-(CB) -1 (εf sat (S)+CAX(t)+CB′U e (t)) (12)

[0141] In equation (13),

[0142] The values ​​of the reaching law gain coefficients ε of the two SMC controllers need to satisfy the Lyapunov stability theorem; therefore, the Lyapunov function is chosen as L = 0.5S. 2 Differentiating it, we get:

[0143]

[0144] When ε≥|CFΔP d When (t)|, According to Lyapunov's stability theorem, the SMC controller can stabilize the frequency fluctuations of the power system and has strong robustness and anti-interference ability.

[0145] PI control

[0146] The control signals of the first PI controller and the third PI controller satisfy the following relationships:

[0147]

[0148]

[0149] In equations (14) and (15), K e_p and K e_i These are the proportional and integral parameters in the first PI controller, respectively, K. p_p and K p_i These are the proportional and integral parameters in the PI controller, respectively.

[0150] Joint optimization of EV cluster output and frequency regulation

[0151] Under the premise of ensuring system frequency stability, with the goal of minimizing frequency regulation cost and frequency deviation, and considering constraints such as generator output, ramp rate and EV cluster deployment ratio, a joint optimization model of EV cluster output and frequency regulation is constructed and solved offline using particle swarm optimization algorithm.

[0152] The proportion α of the EV cluster investment is:

[0153]

[0154] In equation (16), N ev_V2G N represents the number of electric vehicles participating in auxiliary frequency modulation within the EV cluster. ev This represents the number of electric vehicles connected to the power grid within the EV cluster.

[0155] Optimize objective function

[0156] In the process of EV clusters participating in grid auxiliary frequency regulation, it is necessary not only to exhibit good frequency regulation performance, but also to optimize the economic efficiency of grid frequency regulation. Therefore, the joint optimization model of EV cluster output and frequency regulation is as follows:

[0157] Establish an objective function F, and optimize it with the goal of minimizing F;

[0158] F=k1C+k2Γ (17)

[0159] In equation (17), k1 and k2 are weighting coefficients used to reduce the frequency modulation cost and frequency stability index to the same order of magnitude; C is the total cost of auxiliary frequency modulation; and Γ is the frequency stability index.

[0160] The auxiliary frequency regulation cost mainly includes the fuel cost of generator power generation, the compensation cost of the EV cluster, and the loss cost of the EV battery. The total auxiliary frequency regulation cost C of the power system generated by the EV cluster participating in grid frequency regulation is:

[0161] C = C fuel +C V2G +C b (18)

[0162] In equation (18), C fuel For generator fuel costs, C V2G C is the cost of compensation from the power grid to EV users. b The cost of battery degradation for electric vehicles;

[0163] The fuel cost function for generator power generation is as follows:

[0164] C fuel =aP 2 +bP+c (19)

[0165] In equation (19), a, b, and c are the power generation cost coefficients of the steam turbine unit, and P is the output of the steam turbine unit, where P is:

[0166]

[0167] In equation (20), P N This is the system's base power. During the EV's participation in grid-assisted frequency regulation, the energy of the EV charging and discharging according to grid demand is defined as the EV's frequency regulation output, as shown in equation (19):

[0168]

[0169] In equation (21), ΔP ev This is the per-unit value of the sum of the output power of the three clusters. To incentivize EV users to actively participate in grid frequency regulation, the grid will provide compensation to users based on the EV's output. The compensation cost is:

[0170] C V2G =φE (22)

[0171] In equation (22), φ is the unit price of compensation from the power grid to EV users;

[0172] Battery loss cost is the battery loss rate per unit of electrical energy multiplied by the actual electrical energy contributed by the EV. In this embodiment, the calculation formula for battery loss is as follows:

[0173] C b =k b E (23)

[0174] In equation (23), k b This is the battery loss cost rate converted per unit of electrical energy;

[0175] To measure the frequency stability of a system, the integral of the absolute value of the power system frequency deviation over time at per-unit values ​​is used as the index Γ for measuring system frequency stability, i.e.:

[0176]

[0177] Constraints

[0178] During frequency regulation, the total cost borne by the power grid and the system frequency stability index are used as optimization objectives, and the proportion α of investment in auxiliary frequency regulation among private car clusters, bus clusters, and taxi clusters is considered. pri α bus α taxi As an optimization parameter;

[0179] Among them, the investment ratio α pri α bus α taxiThe generator output and ramp rate must satisfy the following constraints:

[0180]

[0181] -R down ≤(P G，t+1 -P G，t ) / Δt≤R up (26)

[0182]

[0183] In equations (25)-(27), and These are the minimum and maximum output power of the generator, respectively; P G，t+1 and P G，t The generator output power R at times t+1 and t are respectively. down With R up These are the generator's downward and upward adjustment rate limits, respectively. These are the minimum proportions of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively. These represent the maximum percentage of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively.

[0184] Optimize processes

[0185] The Particle Swarm Optimization (PSO) algorithm simulates the foraging behavior of bird flocks and solves the optimization model of the objective function. The specific optimization process is as follows: Figure 3 As shown:

[0186] S1 determines the particle size N and the maximum number of iterations;

[0187] S2, randomly generate N sets of input ratio parameters that satisfy equation (27);

[0188] S3, input the N sets of input scaling parameter values ​​into Simulink for simulation, and obtain C and Γ;

[0189] S4, calculate the objective function value F according to equation (17);

[0190] S5, Obtain the individual optimal value P of the particle. best and the global optimum G of the population best ;

[0191] S6, determine if the required number of iterations is met?

[0192] If not, update the particle's position and velocity, and return to S3; where the number of iterations k it =k it +1;

[0193] If so, output the optimal solution and the optimal input ratio parameter value.

[0194] System Simulation

[0195] This simulation was performed on the MATLAB / Simulink platform, with a simulation step size of 0.01s, and the established microgrid system had a baseline capacity of 300MW; among which, and We take 120MW and 300MW respectively. The battery capacity for private cars and taxis is 40kWh, with a maximum charge / discharge power of 15kW. The battery capacity for buses is 200kWh, with a maximum charge / discharge power of 20kW. The vector coefficients in the SMC controller are C = [2 0.1 0.4 0.01 0.01 0.01], ε in the main controller is 8.1, and K in the second PI controller... p_p and K p_i The values ​​are 0.2 and 15 respectively; ε in the EVA controller is 4, and K... e_p and K e_i The values ​​are 0.02 and 1 respectively. First-order filter parameter T f The value is 5. This simulation references the proportions of private cars, taxis, and buses in Zhengzhou, setting the number of private car, taxi, and bus clusters in the model accordingly. The system parameters are shown in Table 1. For different types of vehicles, besides differences in power and energy, their behavior also varies significantly. Based on the functions and behavioral characteristics of the three types of vehicles, the simulation showed the changes in the number of each type connected to the power grid at different times, such as... Figure 4 As shown;

[0196] Table 1 System Parameters

[0197]

[0198] In the table, P represents the total number of private cars, buses, and taxis in the model. step This represents the magnitude of the step load disturbance in the load disturbance.

[0199] The system load disturbance consists of a step load disturbance, renewable energy generation, and random load disturbances. The random load disturbance is derived from white noise simulation. A step load disturbance is applied at 40 seconds, disappearing at 110 seconds, while the random load disturbance and renewable energy generation remain. The resulting superimposed system load disturbance is as follows: Figure 5 As shown.

[0200] When the generator capacity is sufficient

[0201] With all three EV clusters participating in auxiliary frequency regulation, the load disturbance set in this embodiment was applied, and the system frequency fluctuation curves and the power output between the generator and the EV clusters were compared under PI control, SMC control, MPC control, and sliding mode PI control. For comparative purposes, the parameters for PI control and SMC control were kept consistent with those for sliding mode PI control. Figure 6 As shown in (a), after a 40s step load, the frequency drop amplitudes under PI, SMC, and MPC control reached 0.137Hz, 0.086Hz, and 0.088Hz, respectively, while the frequency drop amplitude under sliding mode PI control reached 0.094Hz. During the period of 40–110s, the sliding mode PI control exhibited smaller frequency fluctuation amplitudes and faster convergence speeds compared to PI and MPC control. The SMC control, however, did not return the frequency fluctuation deviation to near zero when the step load was present. Figure 6 As shown in (b), when a step load occurs, the generator rapidly adjusts its output power, and simultaneously, the EV cluster supplies power to the grid at the instant of the load change, supporting the generator's frequency regulation. To make the EV cluster's participation in grid frequency regulation more economical, once the generator power can meet the load demand, the EV cluster's output gradually decreases to assist in frequency regulation. Figure 6 As shown in (c), the output of the EV cluster under sliding mode PI control is significantly lower than that under PI and SMC individual control. At 110s, compared with MPC control, the output fluctuation amplitude of the EV cluster under sliding mode PI control is smaller, and the output coordination effect with the generator is better, making full use of the output power of both.

[0202] When the generator capacity is sufficient, the proposed sliding mode PI method can not only ensure the stability of the system frequency under step load disturbance and random load disturbance, but also enable better coordination between the output of the EV cluster and the generator, avoid the waste of the output power of the EV cluster, ensure the economy of frequency regulation, and have excellent disturbance resistance and robustness characteristics in the transient and steady state processes of the system.

[0203] When generator capacity is insufficient

[0204] When the system load demand exceeds the generator capacity, and the generator capacity is insufficient to meet the load demand, the load power exceeding the generator capacity limit needs to be handled by the EV cluster. In this embodiment, the maximum generator output power is set to 15MW, and with all three EV clusters participating in auxiliary frequency regulation, the load disturbance specified in this embodiment is applied. For example... Figure 7 As shown, when the step load disturbance appears and disappears at 40s and 110s, the system's frequency deviation and rate of change of frequency deviation fluctuate significantly, such as... Figure 7 As shown in (a), the output signal U after the fuzzy optimization algorithm is...fuzzy with U fuzzy The variable coefficient β increases accordingly after passing through the first-order filter, such as Figure 7 As shown in (b); finally, the variable coefficient β and the control signal U′ e Together, they cause the control signal U of the EV cluster e It has corresponding increases and decreases, such as Figure 7 As shown in (c); during time periods such as 19–27s and 71–84s, the fluctuation amplitudes of frequency deviation and the rate of change of frequency deviation are relatively small, thus the variable coefficient β decreases, and the control signal U of the EV cluster... e This reduces, ultimately decreasing, the output power of the EV cluster. In other words, the output power of the EV cluster is responsive to frequency deviation and the rate of change of frequency deviation.

[0205] like Figure 8 The figure shows the output power variation curves of the generator and EV cluster when the generator capacity is insufficient. As can be seen from the figure, within the timeframes of 0–40s and 110–150s, the generator capacity has not yet exceeded its limit. Therefore, as the load disturbance changes, the generator output power can be adjusted to meet the load demand, while the EV cluster assists in suppressing frequency fluctuations. During the timeframes of 60–65s and 75–85s, due to the increased load demand, the generator output power reaches its limit, and changing the generator output power is no longer sufficient to meet the load demand. Therefore, it is necessary to increase the output power of the EV cluster to meet the load demand and maintain system frequency stability. During the timeframes of 45–53s and 67–79s, the load demand gradually decreases, and the power of the EV cluster also gradually decreases. The system adjusts the generator power to regulate system frequency stability, preventing the EV cluster from continuously and excessively outputting power to the power system.

[0206] For example, the frequency variation curve under insufficient generator capacity Figure 9 As shown, the proposed sliding mode PI method enables EV clusters to not only meet the system's load requirements when generator capacity is insufficient, but also to better coordinate with generators to regulate the system frequency, thereby increasing the system's frequency regulation capacity.

[0207] Joint optimization simulation

[0208] When generator capacity is sufficient, this embodiment uses a particle swarm optimization algorithm to optimize the input ratio parameters of the three EV clusters. All are 0; All parameters are set to 100%; the weights k1 and k2 in the objective function are 0.005 and 5000 respectively; the generation cost coefficient is determined by reference [Gao Hui. Research on the Optimization Problem of Power System Unit Combination Considering New Energy Reserves [D]. Hebei: North China Electric Power University]; the compensation unit price for EVs participating in grid auxiliary frequency regulation is set to 210 yuan / MWh; the battery loss cost rate per unit of electricity is set to 144 yuan / MWh; the input ratio parameters of the three EV clusters before optimization are all set to 100%. After optimization simulation, the frequency deviation curves of the system before and after optimization are shown below. Figure 10 As shown. From Figure 10 It can be seen that the change in system frequency before and after optimization is not much different, that is, the system frequency can be kept stable after optimization.

[0209] By optimizing the allocation parameters for the three EV clusters, the allocation ratios were determined as follows: private car cluster: 62.85%; bus cluster: 68.81%; and taxi cluster: 50.74%. Figure 11 As can be seen, compared with the output before optimization, after a step load disturbance occurs at 40s, the output of the optimized EV cluster is significantly reduced, while the output of the generator is increased. After the step load disturbance disappears at 110s, the system frequency gradually stabilizes, the output of the EV cluster approaches zero, and the system mainly regulates the frequency through the generator output. By optimizing the EV cluster deployment ratio parameters, the system can achieve frequency stability while reducing the number of EV clusters deployed and their output power.

[0210] Based on Table 2 Figure 10 , Figure 11 It can be seen that the system frequency stability index Γ increased by 2.37% after optimization, and the stability did not decrease significantly; the EV cluster output index E decreased by 51.35% after optimization, that is, the EV cluster output decreased significantly; considering fuel cost, compensation cost and loss cost, the total system frequency regulation cost decreased by 11.58% compared with the unoptimized version. In conclusion, reducing the output of the EV cluster can significantly reduce the system frequency regulation cost.

[0211] Table 2 Comparison of indicators before and after optimization

[0212]

[0213] Example 2

[0214] This embodiment provides a sliding mode PI control device for electric vehicle cluster-assisted grid frequency regulation, including a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of the sliding mode PI control method for electric vehicle cluster-assisted grid frequency regulation as described in Embodiment 1.

[0215] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A sliding mode PI control method for electric vehicle clusters to assist in grid frequency regulation, characterized in that: The method described above is to regulate the load frequency of the power system based on a power system load frequency regulation model and an EV cluster model. The power system load frequency regulation model includes a main controller model, a speed governor model, a prime mover model, and a load damping model. The speed controller model includes a unit regulating power module and a speed controller equivalent model; The unit regulating power module takes the power system frequency deviation Δf as input; The main controller output signal U p The frequency deviation Δf of the power system after power regulation is summed by the first summing module and then input into the equivalent model of the speed governor to obtain the change in the speed governor position ΔP. v ; The prime mover model uses the governor position change ΔP v To obtain the change in the mechanical power output of the generator, ΔP m ; The change in mechanical power output of the generator ΔP m The total output power ΔP of the EV cluster model ev The input terminal ΔP of the system load disturbance load Renewable energy ΔP res After being summed by the second summation module, the result is input into the load damping model to obtain the power system frequency deviation Δf. The EV cluster model, based on the EVA controller, is divided into three EV cluster models: private car cluster model, bus cluster model, and taxi cluster model. The three EV cluster models use the same model. Each EV cluster model includes a model frequency deviation signal allocation coefficient S, an equivalent model of the EV power battery, an EV output power limiter, and an EV quantity variation module. The equivalent model of the EV power battery uses the frequency deviation signal allocation coefficient and the output signal U of the EVA controller. e The input is used as input, and after calculation, the output is sent to the EV output power limiter to obtain the charging and discharging power of the EV cluster; the EV quantity change module uses the charging and discharging power of the EV cluster as input, and combines it with the number N of EVs participating in frequency modulation to calculate the total output power P of the EV cluster. A ; Total output power P of private car cluster A_pri Total output power P of the bus cluster A_bus Total output power P of the taxi cluster A_taxi The total output power ΔP of the EV cluster model is obtained by summing the data using the third summing module. ev ; The EVA controller includes a first SMC controller and a first PI controller, and satisfies the following control strategy: Both the first SMC controller and the first PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf. The adjusted grid frequency deviation Δf is summed to generate the control signal U′. e ; Using the power system frequency deviation Δf and the rate of change of the power system frequency deviation Δf as input signals, a fuzzy optimization algorithm is used to generate coefficients U. fuzzy And after passing through a first-order low-pass filter, the variable coefficient β is obtained; The variable coefficient β and the control signal U′ e After multiplication, the output signal U of the EVA controller is obtained. e ; The main controller includes a second SMC controller and a second PI controller, satisfying the following control strategy: Both the second SMC controller and the second PI controller use the power system frequency deviation Δf as input to jointly adjust the power grid frequency deviation Δf. The adjusted grid frequency deviation Δf is summed to generate the output signal U of the main controller. p ; Both the first SMC controller and the second SMC controller use the state variable X(t) = [Δf ΔP] m ΔP v ΔP A_pri ΔP A_taxi ΔP A_bus ] T Design the sliding surface S = CX(t); where the vector coefficients C = [c1 c2 c3 c4 c5 c6], c6p 6 +c5p 5 +c4p 4 +c3p 3 +c2p 2 +c1p satisfies the Routh stability criterion.

2. The sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation according to claim 1, characterized in that: Both the first SMC controller and the second SMC controller employ the following constant-rate approach law. Where ε is the reaching law gain coefficient, f sat (S) is a saturation function; The control signals of both the first PI controller and the second PI controller satisfy the following relationship: In the formula, K p_p and K p_i These are the proportional and integral parameters in the PI controller, respectively.

3. The sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation according to claim 2, characterized in that: With the goal of minimizing system frequency regulation cost and frequency deviation, a joint optimization model of EV cluster output and frequency regulation is constructed, taking into account generator output, ramp rate and EV cluster deployment ratio α, and solved offline using particle swarm optimization algorithm. The proportion α of the EV cluster investment is: In the formula, N ev_V2G N represents the number of electric vehicles participating in auxiliary frequency modulation within the EV cluster. ev This represents the number of electric vehicles connected to the power grid within the EV cluster.

4. The sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation according to claim 3, characterized in that, The joint optimization model for EV cluster output and frequency regulation is as follows: Establish an objective function F, and optimize it with the goal of minimizing F; F=k1C+k2Γ In the formula, k1 and k2 are weighting coefficients used to reduce the frequency modulation cost and frequency stability index to the same order of magnitude; C is the total cost of auxiliary frequency modulation; Γ is the frequency stability index. The total cost C of auxiliary frequency regulation in the power system includes the generator fuel cost C. fuel The compensation cost C for EV users from the power grid V2G The battery degradation cost of electric vehicles, C b That is: C = C fuel +C V2G +C b ; To measure the frequency stability of the system, the integral of the absolute value of the system frequency deviation over time at per-unit values ​​is used as the index Γ for measuring the system frequency stability, i.e.:

5. The sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation according to claim 3, characterized in that, The proportion of investment α in auxiliary frequency regulation among private car clusters, bus clusters, and taxi clusters. pri α bus α taxi The generator output and ramp rate must satisfy the following constraints: -R down ≤(P G,t+1 -P G,t ) / Δt≤R up In the formula, and These are the minimum and maximum output power of the generator, respectively; P G,t+1 and P G,t The generator output power R at times t+1 and t are respectively. down With R up These are the generator's downward and upward adjustment rate limits, respectively. These are the minimum proportions of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively. These represent the maximum percentage of investment in auxiliary frequency regulation for private car clusters, bus clusters, and taxi clusters, respectively.

6. The sliding mode PI control method for electric vehicle cluster-assisted power grid frequency regulation according to claim 3, characterized in that, The particle swarm optimization algorithm simulates the foraging behavior of bird flocks and solves the optimization model of the objective function.

7. A sliding mode PI control device for auxiliary power grid frequency regulation of electric vehicle clusters, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the sliding mode PI control method for electric vehicle cluster-assisted grid frequency regulation as described in any one of claims 1 to 6.

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