CN112186789B - A sliding mode control method for electric vehicles participating in microgrid load frequency regulation - Google Patents

Abstract

A sliding mode control method for electric vehicles participating in microgrid load frequency regulation, belonging to the field of microgrid load frequency regulation, comprising the following steps: step 1: establishing a dynamic model of microgrid load frequency regulation under the participation of electric vehicles; step 2: establishing a sliding mode controller; Step 3: Establish Lyapunov function, analyze the controller and sliding mode surface, and design the sliding mode control based on auxiliary feedback through linear matrix inequality; Step 4: Based on the mathematical process of steps 1, 2, and 3, obtain the corresponding matrix , conduct simulation analysis, and solve linear matrix inequalities. The invention utilizes the equivalent control principle and the sliding mode control principle to design a controller, uses the sliding mode control principle to ensure the stability of the system, improves the control precision of the control system, and enhances the stability of the grid frequency.

Description

A sliding mode control method for electric vehicles participating in microgrid load frequency regulation

Technical Field

The present invention belongs to the field of microgrid load frequency regulation, and in particular relates to a sliding mode control method for electric vehicles to participate in microgrid load frequency regulation.

Background Art

In recent years, with the rapid development of the global economy, environmental pollution and energy shortages have become increasingly serious. Saving resources and protecting the environment have become one of the important themes of the current era. Electric vehicles, which have a series of advantages such as high efficiency, no pollution, and low noise, are considered to be one of the best choices for energy conservation and emission reduction. Surveys and studies have shown that in the near future, electric vehicles will replace traditional cars and become one of the main modes of transportation for people. As more and more renewable energy sources such as wind energy and solar energy are greatly affected by natural conditions, power generation is discontinuous and intermittent. Therefore, in order to ensure the stability of the grid frequency and the quality of power, in 1995, American energy scientists first proposed the technology of electric vehicle access to the grid (V2G), which provided a new idea for maintaining the stability of the power system frequency, thereby improving the quality of power supply. Research shows that electric vehicles in V2G mode have the following advantages: (1) The energy storage function of electric vehicle batteries is used as a grid buffer to provide auxiliary services for the grid, such as peak load regulation and frequency regulation, which can not only increase the stability and reliability of the grid and improve the power supply quality, but also reduce the operating costs of the power system; (2) Electric vehicles in V2G mode can bring additional economic benefits to car owners, reduce the purchase cost of electric vehicles, and are more conducive to the promotion of new energy electric vehicles, and also achieve environmental protection; (3) Electric vehicles in large-scale V2G mode can generate energy storage buffers as a supplement to intermittent renewable energy generation such as wind power and photovoltaic power generation, reduce carbon dioxide emissions, and improve the grid connection capacity of new energy power generation such as wind power and solar power.

At present, the development of electric vehicle access to power system to participate in frequency regulation technology in domestic and foreign scientific research fields mainly involves the construction of frequency regulation models, research on frequency regulation control algorithms, the benefits of electric vehicles providing frequency regulation services, feasibility research on electric vehicles access to microgrid frequency regulation, frequency regulation economy and frequency regulation control strategies.

In the field of the feasibility of electric vehicles accessing the grid system to participate in frequency regulation, the United States has realized the bidirectional flow of electric energy by using power electronic equipment, and has taken the lead in connecting electric vehicles to microgrids, providing theoretical feasibility for electric vehicles to participate in grid frequency regulation; in the field of electric vehicle access to microgrid control, many mathematical methods have been used abroad to improve the control of electric vehicles accessing microgrids, such as: proposing new charging strategies, and evaluating charging strategies through improved particle swarm algorithms; to solve the uncertainty of microgrid systems, fuzzy PI controllers are designed, and the controller parameters are optimized using harmony search algorithms; in response to the problem of frequency fluctuations when electric vehicles are connected to microgrids, a microgrid load frequency regulation model with the participation of electric vehicles is established, and a method based on robust adaptive control strategy is proposed, etc. Compared with foreign countries, the research on electric vehicle participation in microgrid technology started late in China, and related research focuses more on the research of frequency regulation control algorithms, the benefits of electric vehicles providing frequency regulation services, and the feasibility of electric vehicles accessing microgrid frequency regulation.

Frequency is an important indicator of power quality, and maintaining frequency stability is a basic requirement for power system operation. With the introduction of the V2G concept, it has become possible for electric vehicles to be connected to microgrids as micro energy storage units and participate in frequency regulation, but the charging and discharging of electric vehicles also has a huge impact on the stability of grid frequency, thus placing higher requirements on the control method of grid stability.

The research on the connection of electric vehicles to the power system to participate in frequency regulation mainly involves the feasibility study of the connection of electric vehicles to microgrid frequency regulation and the research on grid stability. Based on V2G technology, plug-in electric vehicles are connected to the grid, which can not only charge electric vehicles but also participate in grid frequency regulation as a power source. When a large number of electric vehicles are connected to the grid, the control structure can realize the auxiliary frequency regulation of microgrids by using electric vehicles as a power source while meeting the daily travel needs of car owners.

In view of the situation of electric vehicles connected to the power grid, the current technologies for maintaining the stability of the power grid frequency mainly include traditional PID control technology and model predictive control technology. Traditional PID control technology cannot show good control performance for nonlinear and multi-objective systems, while the existing model predictive control technology has high requirements for the accuracy of the mathematical model of the controlled object, and does not consider the factors that cause the fluctuation of the power grid frequency, and cannot achieve good control performance.

Summary of the invention

In view of the defects of the prior art, the present invention proposes a sliding mode control method for electric vehicles participating in microgrid load frequency modulation, and designs a controller by combining the equivalent control principle and the sliding mode control principle. The sliding mode control principle is used to ensure the stability of the system, improve the control accuracy of the control system, and enhance the stability of the grid frequency.

The technical solution adopted by the present invention is as follows:

A sliding mode control method for electric vehicles participating in microgrid load frequency modulation comprises the following steps:

Step 1: Analyze the working principles of power plant generators and electric vehicles respectively, treat different types of electric vehicles as equivalent, and when electric vehicles are connected to the microgrid, they participate in the process of microgrid load frequency regulation as energy storage elements, and establish a dynamic model of microgrid load frequency regulation with the participation of electric vehicles;

Step 1.1: Considering the characteristics of electric vehicle charging and discharging and their impact on grid frequency, a dynamic model of electric vehicles participating in microgrid load frequency regulation is abstracted. The model includes five parts: power plant, new energy power generation, electric vehicle, microgrid and controller. The dynamic model expression is:

Where: Δf represents the system frequency deviation; M represents the equivalent moment of inertia of the generator set; D represents the load damping coefficient of the power system; ΔP _L represents the external interference input caused by electric vehicles and new energy power generation that affects the frequency stability of the microgrid; R ^f represents the adjustment coefficient; ΔP _v represents the position change of the speed regulator valve of the generator set; _TG represents the speed regulator time constant; T _CH represents the generator time constant; Δu _G represents the terminal voltage of the generator set; ΔP _g represents the power deviation of the generator set; ΔP _EV represents the charging and discharging power of the electric vehicle; Δu _EV represents the terminal voltage of the electric vehicle; _Te represents the time constant of the electric vehicle;

Step 1.2: Take the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv as the system state variable x(t), the generator set terminal voltage _ΔuG as the system control input u(t), and the external interference input _ΔPL caused by electric vehicles and new energy generation that affects the frequency stability of the microgrid as the external interference quantity Φ(x(t),t) to establish the microgrid load frequency regulation dynamic model:

y(t)＝Cx(t)

Among them: x(t)=[Δf,ΔP _g ,ΔP _v ] ^T , u(t)=[Δu _G ], Φ(x(t),t)=[ΔP _L ];

C＝[1 0 0]

都是根据微电网、发电厂实际运行状况选取的实际参数归纳的实常数矩阵；且新能源发电和电动汽车接入微电网产生的频率扰动是有界的，即干扰项|Φ(x(t),t)|≤δ_f；in

They are all real constant matrices summarized from actual parameters selected according to the actual operating conditions of microgrids and power plants; and the frequency disturbances generated by renewable energy generation and electric vehicles connected to microgrids are bounded, that is, the interference term |Φ(x(t),t)|≤δ _f ;

Step 1.3: According to the actual operation data of the microgrid system and the power plant, the initial parameters of the dynamic model are selected as follows:

The power system load damping coefficient D = 2, the equivalent moment of inertia of the generator set M = 3.5, the generator time constant T _CH = 50, the adjustment coefficient R ^f = 1, the generator set speed regulator time constant T _G = 40, and the electric vehicle time constant _Te = 1;

Then the dynamic model parameter matrix of electric vehicles participating in microgrid load frequency regulation is:

Step 2: To ensure the stability of the microgrid frequency, a sliding mode controller is designed for the microgrid frequency. The frequency controller is analyzed by Lyapunov theory to ensure that when the microgrid frequency deviates, the frequency can be restored to its original state at a faster speed and remain stable. The specific method of step 2 is:

Step 2.1: Based on the dynamic mathematical model of electric vehicles participating in the load frequency regulation of the microgrid in step 1, the sliding mode control method is used to express the frequency state of the microgrid as a sliding mode function, and a sliding mode controller is designed;

Based on the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv, the sliding mode function s is defined as:

s＝B ^T Px

且P＝P^T＞0，针对微电网频率设计滑模函数，使微电网频率稳定在50HZ，通过对P的设计实现s＝0；Among them, the frequency controller matrix

And P＝ ^PT ＞0, a sliding mode function is designed for the frequency of the microgrid to stabilize the frequency of the microgrid at 50HZ, and s＝0 is achieved by designing P;

Step 2.2: Design the microgrid frequency controller based on the equivalent control principle;

The frequency controller expression is:

u(t)＝u _eq +u _n

和

得滑模函数的导数为

从而频率控制器的等效控制项u_eq＝-(B^TPB)^{- 1}B^TPAx(t)；According to the equivalent control principle, without considering the external interference caused by renewable energy generation and electric vehicles connected to the microgrid, that is, Φ(x(t), t) = 0, the frequency regulation dynamic model of the microgrid is expressed as

and

The derivative of the sliding mode function is

Therefore ^, the equivalent control term of the frequency controller is u _eq = -( ^BTPB ) ^{- 1BTPAx} (t);

Step 2.3: According to the sliding mode control principle, based on the sliding mode function designed in the above steps, design a robust control term to make the microgrid operation state asymptotically stable;

使系统频率降低，若频率低于50HZ，s＜0，此时须使

使系统频率升高，即保证

取鲁棒控制项为：When the frequency of the microgrid system changes, that is, the operating state of the microgrid system deviates from the sliding surface, if the frequency is higher than 50HZ, s＞0, then

Reduce the system frequency. If the frequency is lower than 50HZ, s＜0, then

Increase the system frequency, that is, ensure

The robust control term is taken as:

u _n =-(δ _f +(B ^T PB) ^-1 ε)sgn(s)

Where ε＞0;

Step 2.4: Select the Lyapunov function, which represents the energy flow of the microgrid system, and prove that its derivative is less than zero, so that the microgrid frequency control system is asymptotically stable;

则

Take the Lyapunov function

but

but

Step 3: Establish the Lyapunov function, analyze the frequency controller and sliding mode function, and design the sliding mode control based on auxiliary feedback through linear matrix inequality. The specific method of step 3 is:

Step 3.1: The frequency controller u(t) is expressed as u(t)=-Kx+v(t), where v(t)=Kx+u _eq + _un , then the original microgrid load frequency regulation dynamic model is expressed as:

in

Step 3.2: Design a Lyapunov function, take the derivative of the Lyapunov function, obtain a linear matrix inequality, and solve the linear matrix inequality to obtain the control rate matrix K and the frequency controller matrix P;

Take the Lyapunov function V = x ^T Px and differentiate it to obtain:

By analyzing the controller expression u(t) = u _eq + u _n , it can be seen that at a certain moment after the frequency conversion, the microgrid frequency will reach a stable state, that is, there exists t ≥ t ₀ so that s = B ^T Px = 0 is established, so s ^T = x ^T PB = 0 is established, then

则

like

but

两边同时乘以Q＝P^-1得：exist

Multiplying both sides by Q=P ^-1 gives:

That is, (A+BK)Q+Q(A+BK) ^T < 0

Let R=KQ, then AQ-BR+QA ^T -R ^T B ^T <0

That is ^, AQ+ ^QAT < BR+ ^RTBT

Step 4: Based on the control process of steps 1, 2, and 3, obtain the corresponding matrix related to the microgrid load frequency regulation system, perform simulation analysis, solve the linear matrix inequality, and obtain the controller matrix P and the control rate matrix K;

R＝[8.9577 22.1605 25.0410],

K = [5.8384 23.412 25.798],

Let the interference term Φ(x(t),t)＝0.1sint, then δ _f ＝0.1, let ε ₀ ＝0.5, and get the simulation diagram of the voltage change at the generator terminal of the power plant and the frequency change of the microgrid. Analyze the image, and control the frequency of the microgrid through the simulation diagram of the control variable and the state variable.

Advantages and effects of the present invention:

The present invention establishes a dynamic load frequency modulation model based on the working characteristics of electric vehicles during charging and discharging and the frequency characteristics of microgrids. The impact of the charging and discharging characteristics of electric vehicles and the intermittent nature of new energy power generation on microgrids is used as interference terms, the terminal voltage of the generator set is used as the control quantity, and the sliding mode function is used to represent the operating state of the microgrid system to achieve control of the microgrid frequency. The main innovation is to design the controller by combining the equivalent control principle with the sliding mode control principle, and to use the sliding mode control principle to ensure the stability of the system, improve the control accuracy of the frequency control system, simplify the linear matrix inequality, and bring great convenience to the design process of the sliding surface. In an era when electric vehicles are gradually increasing, the present invention can enhance the stability of the microgrid frequency, and has guiding significance and promotion value for the operation and control of the microgrid.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of an electric vehicle connected to a microgrid according to the present invention;

FIG2 is a diagram of a power grid frequency control model according to the present invention;

FIG3 is a system simulation diagram of the present invention;

FIG4 is a comparison diagram of microgrid frequency changes obtained by adopting different control strategies of the present invention;

FIG5 is a control variable response diagram in the system dynamic model of the present invention;

FIG. 6 is a sliding mode function response diagram of the present invention.

DETAILED DESCRIPTION

The present invention will be further explained below in conjunction with the accompanying drawings and embodiments.

The present invention is a sliding mode control method for electric vehicles to participate in microgrid load frequency modulation. In view of the situation where electric vehicles are connected to the power grid, the current technologies for maintaining the stability of the power grid frequency mainly include traditional PID control technology and model predictive control technology. Traditional PID control technology cannot show good control performance for nonlinear and multi-objective systems, while the existing model predictive control technology has high requirements for the accuracy of the mathematical model of the controlled object, and does not take into account related factors such as system uncertainty, so the above two control strategies cannot achieve good control performance.

The influence of electric vehicles and intermittent generation of renewable energy on the frequency stability of microgrids is considered, and this is used as an external interference term. The sliding mode control principle is combined with the equivalent control principle to design a microgrid frequency controller to ensure the stability of the microgrid frequency. The main innovation is to use the sliding mode control method to deal with interference terms. The control purpose is to make the voltage change at the generator terminal and the frequency change of the microgrid approach zero; the method of electric vehicles participating in the frequency regulation of microgrid loads is analyzed, including the following steps:

Step 1: Analyze the working principles of power plants and electric vehicles respectively, consider the impact of intermittent and uncertain renewable energy generation on the power grid, and use this as an external interference item to establish a dynamic model of microgrid load frequency regulation with the participation of electric vehicles;

Step 2: Based on the established dynamic model of electric vehicles participating in the load frequency regulation of the microgrid, according to the equivalent control principle, without considering the external interference that affects the frequency of the microgrid, a frequency equivalent controller is established, and a sliding mode controller is designed. In order to ensure that the frequency of the microgrid can be stabilized to the original state at a faster speed after increasing or decreasing, the Lyapunov stability theory is used to ensure the stability of the microgrid frequency;

Step 3: Establish the Lyapunov energy function, analyze the frequency controller, and solve the control rate matrix K and the frequency controller matrix P by solving the linear matrix inequality.

Step 4: According to the above control process, based on the working characteristics of the microgrid and electric vehicles, select the initial parameters of the microgrid load frequency regulation model, obtain the matrix parameters, and perform simulation analysis;

By comparing the simulation diagram with Figure 4, it can be seen that the frequency change curve of the microgrid under the PID control strategy has a large overshoot, which has a great impact on the stable operation of the microgrid; the sliding mode control method provided by the present invention not only takes into account the external interference to the frequency stability of the microgrid due to the intermittent nature of renewable energy generation, but also enables the microgrid frequency to converge to the required range at a faster speed, and has better control performance than the PID control technology.

The equivalent control is combined with the sliding mode control. First, the external interference term that affects the frequency stability of the microgrid is equivalent to zero, and the robust control term of the sliding mode control is designed. The Lyapunov function, that is, the energy function between the microgrid and the electric vehicle, is established. The Lyapunov stability theory is used to ensure the frequency stability of the microgrid. Through the analysis of Figure 4, it can be seen that when the microgrid frequency control system is subject to certain external interference, adjusting the terminal voltage of the generator set can maintain the stability of the microgrid frequency and achieve better control performance.

The frequency controller is analyzed, and a frequency controller based on auxiliary feedback is designed to solve the control rate matrix K. The control rate matrix K can intuitively reflect the control rate of the grid frequency. It also provides more precise conditions for the establishment of linear matrix inequalities to ensure the stability of the microgrid frequency.

The specific steps are as follows:

Step 1: Analyze the working principles of the power plant generator set and electric vehicles respectively. The working principle of the power plant generator set is: use the high-temperature and high-pressure steam generated by the boiler to drive the turbine rotor to rotate, and the turbine rotor drives the generator rotor to rotate to generate electricity. Treat different types of electric vehicles equivalently. When electric vehicles are connected to the microgrid, they can participate in the process of microgrid load frequency regulation as energy storage elements, and establish a dynamic model of microgrid load frequency regulation with the participation of electric vehicles.

Step 1.1: Considering the characteristics of electric vehicle charging and discharging and their impact on grid frequency, a dynamic model of electric vehicles participating in microgrid load frequency regulation is abstracted. The model includes five parts: power plant, new energy power generation, electric vehicle, microgrid and controller. The dynamic model expression is:

Where: Δf represents the system frequency deviation; M represents the equivalent moment of inertia of the generator set; D represents the load damping coefficient of the power system; _ΔPL represents the external interference input caused by electric vehicles and renewable energy power generation that affects the frequency stability of the microgrid; ^Rf represents the adjustment coefficient; _ΔPV represents the position change of the speed regulator valve of the generator set; _TG represents the speed regulator time constant; _TCH represents the generator time constant; _ΔuG represents the terminal voltage of the generator set; _ΔPg represents the power deviation of the generator set; _ΔPEV represents the charging and discharging power of the electric vehicle; _ΔuEV represents the terminal voltage of the electric vehicle; _Te represents the time constant of the electric vehicle.

Step 1.2: Take the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv as the system state variable x(t), the generator set terminal voltage _ΔuG as the system control input u(t), and the external interference input _ΔPL caused by electric vehicles and new energy generation that affects the frequency stability of the microgrid as the external interference quantity Φ(x(t),t) to establish the microgrid load frequency regulation dynamic model:

y(t)＝Cx(t)

Among them: x(t)=[Δf,ΔP _g ,ΔP _v ] ^T , u(t)=[Δu _G ], Φ(x(t),t)=[ΔP _L ];

C＝[1 0 0]

都是根据微电网、发电厂实际运行状况选取的实际参数归纳的实常数矩阵；且新能源发电和电动汽车接入微电网产生的频率扰动是有界的，即干扰项|Φ(x(t),t)|≤δ_f；in

They are all real constant matrices summarized from actual parameters selected according to the actual operating conditions of microgrids and power plants; and the frequency disturbances generated by renewable energy generation and electric vehicles connected to microgrids are bounded, that is, the interference term |Φ(x(t),t)|≤δ _f ;

Step 1.3: According to the actual operation data of the microgrid system and the power plant, the initial parameters of the dynamic model are selected as follows:

The power system load damping coefficient D = 2, the equivalent moment of inertia of the generator set M = 3.5, the generator time constant T _CH = 50, the adjustment coefficient R ^f = 1, the generator set speed regulator time constant T _G = 40, and the electric vehicle time constant _Te = 1;

Then the dynamic model parameter matrix of electric vehicles participating in microgrid load frequency regulation is:

Step 2: To ensure the stability of the microgrid frequency, a sliding mode controller is designed for the microgrid frequency. The frequency controller is analyzed by Lyapunov theory to ensure that when the microgrid frequency deviates, the frequency can be restored to its original state at a faster speed and remain stable. The specific method of step 2 is:

Step 2.1: Based on the dynamic mathematical model of electric vehicles participating in the load frequency regulation of the microgrid in step 1, the sliding mode control method is used to express the frequency state of the microgrid as a sliding mode function, and a sliding mode controller is designed;

Based on the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv, the sliding mode function s is defined as:

s＝B ^T Px

且P＝P^T＞0，针对微电网频率设计滑模函数，该方法最好的控制状态是使微电网频率稳定在50HZ，可通过对P的设计实现s＝0；Among them, the frequency controller matrix

And P＝ ^PT ＞0, a sliding mode function is designed for the frequency of the microgrid. The best control state of this method is to stabilize the frequency of the microgrid at 50HZ, which can be achieved by designing Ps＝0;

Step 2.2: Design the microgrid frequency controller based on the equivalent control principle;

The frequency controller expression is:

u(t)＝u _eq +u _n

和

可得滑模函数的导数为

从而频率控制器的等效控制项u_eq＝-(B^TPB)^{- 1}B^TPAx(t)；According to the equivalent control principle, without considering the external interference caused by renewable energy generation and electric vehicles connected to the microgrid, that is, Φ(x(t), t) = 0, the frequency regulation dynamic model of the microgrid is expressed as

and

The derivative of the sliding mode function is

Therefore ^, the equivalent control term of the frequency controller is u _eq = -( ^BTPB ) ^{- 1BTPAx} (t);

Step 2.3: According to the sliding mode control principle, based on the sliding mode function designed in the above steps, a robust control term is designed to ensure that the operation state of the microgrid is asymptotically stable;

使系统频率降低，若频率低于50HZ，s＜0，此时须使

使系统频率升高，即保证

取鲁棒控制项为：When the frequency of the microgrid system changes, that is, the operating state of the microgrid system deviates from the sliding surface, if the frequency is higher than 50HZ, s＞0, then

Reduce the system frequency. If the frequency is lower than 50HZ, s＜0, then

Increase the system frequency, that is, ensure

The robust control term is taken as:

u _n =-(δ _f +(B ^T PB) ^-1 ε)sgn(s)

Where ε＞0;

Step 2.4: Select the Lyapunov function, which can represent the energy flow of the microgrid system, and prove that its derivative is less than zero to ensure the asymptotic stability of the microgrid frequency control system;

则

Take the Lyapunov function

but

but

Step 3: Establish the Lyapunov function, analyze the frequency controller and sliding mode function, and design the sliding mode control based on auxiliary feedback through linear matrix inequality to ensure the control performance of the microgrid frequency controller. The specific method of step 3 is:

Step 3.1: The frequency controller u(t) is expressed as u(t)=-Kx+v(t), where v(t)=Kx+u _eq + _un , then the original microgrid load frequency regulation dynamic model can be expressed as:

通过对控制率矩阵K的设计，在电动汽车参与微电网负荷调频模型中加入了辅助反馈设计，提高了频率控制器的控制性能，辅助反馈控制方法可保证微电网负荷调频闭环系统是渐进稳定的，微电网频率发生变化时可在较短时间内恢复到原来状态。in

By designing the control rate matrix K, an auxiliary feedback design is added to the microgrid load frequency regulation model in which electric vehicles participate, which improves the control performance of the frequency controller. The auxiliary feedback control method can ensure that the microgrid load frequency regulation closed-loop system is asymptotically stable, and when the microgrid frequency changes, it can return to its original state in a relatively short time.

Step 3.2: Design a Lyapunov function, take the derivative of the Lyapunov function, obtain a linear matrix inequality, and solve the linear matrix inequality to obtain the control rate matrix K and the frequency controller matrix P;

Take the Lyapunov function V = x ^T Px and differentiate it to obtain:

By analyzing the controller expression u(t) = u _eq + u _n , it can be seen that at a certain moment after the frequency conversion, the microgrid frequency will reach a stable state, that is, there exists t ≥ t ₀ so that s = B ^T Px = 0 is established, so s ^T = x ^T PB = 0 is established, then

则

like

but

两边同时乘以Q＝P^-1得：exist

Multiplying both sides by Q=P ^-1 gives:

That is, (A+BK)Q+Q(A+BK) ^T < 0

Let R=KQ, then AQ-BR+QA ^T -R ^T B ^T <0

That is ^, AQ+ ^QAT < BR+ ^RTBT

Step 4: Based on the control process of steps 1, 2, and 3, obtain the corresponding matrix related to the microgrid load frequency regulation system, perform simulation analysis, solve the linear matrix inequality, and obtain the controller matrix P and the control rate matrix K;

R＝[8.9577 22.1605 25.0410],

K = [5.8384 23.412 25.798],

Let the interference term Φ(x(t),t)＝0.1sint, then δ _f ＝0.1, let ε ₀ ＝0.5, then we can get the simulation graph of the voltage change at the generator terminal of the power plant and the frequency change of the microgrid. Analysis of the image shows that the voltage change at the generator terminal of the power plant, the frequency change of the microgrid and the operating status of the microgrid are all stable.

In Figure 4, the dotted line represents the frequency change response curve of the microgrid under the PID control strategy; the solid line represents the frequency change response curve of the microgrid under the sliding mode control strategy; it is easy to see from Figure 4 that under the action of the two control strategies, the microgrid frequency can converge, and the convergence speed is similar, but the maximum overshoot of the microgrid frequency change under the PID control strategy is about 0.2HZ, the overshoot is large, and the normal frequency deviation allowable value of my country's power system is ±0.2HZ, so the traditional PID control strategy cannot achieve good performance for microgrid frequency stability. Under the PID control strategy, the frequency fluctuates slightly, and this small fluctuation may affect the normal use of electrical appliances connected to the microgrid system, and may even affect the normal operation of the generator; it can be seen from Figure 5 that the generator terminal voltage converges faster, which has a good effect on stabilizing the grid frequency and the generator terminal voltage; it can be seen from Figure 6 that the sliding mode control function has a small change amplitude and a fast convergence speed, which can ensure that the microgrid frequency is asymptotically stable in the area near the sliding mode surface.

Through the analysis of state variables, it can be seen that the frequency of the microgrid can reach a stable state relatively quickly, which meets the actual working requirements of the microgrid; through the analysis of control variables, it can be seen that the terminal voltage of the generator set can reach a stable state in a relatively short time and the fluctuation amplitude is very small, which is of great significance for protecting the generator set.

Claims (1)

1. A sliding mode control method for electric vehicles participating in microgrid load frequency modulation, characterized in that it includes the following steps: Step 1: Analyze the working principles of power plant generators and electric vehicles respectively, treat different types of electric vehicles as equivalent, and when electric vehicles are connected to the microgrid, they participate in the process of microgrid load frequency regulation as energy storage elements, and establish a dynamic model of microgrid load frequency regulation with the participation of electric vehicles; Step 1.1: Considering the characteristics of electric vehicle charging and discharging and their impact on grid frequency, a dynamic model of electric vehicles participating in microgrid load frequency regulation is abstracted. The model includes five parts: power plant, new energy power generation, electric vehicle, microgrid and controller. The dynamic model expression is:

Where: Δf represents the system frequency deviation; M represents the equivalent moment of inertia of the generator set; D represents the load damping coefficient of the power system; ΔP _L represents the external interference input caused by electric vehicles and new energy power generation that affects the frequency stability of the microgrid; R ^f represents the adjustment coefficient; ΔP _v represents the position change of the speed regulator valve of the generator set; _TG represents the speed regulator time constant; T _CH represents the generator time constant; Δu _G represents the terminal voltage of the generator set; ΔP _g represents the power deviation of the generator set; ΔP _EV represents the charging and discharging power of the electric vehicle; Δu _EV represents the terminal voltage of the electric vehicle; _Te represents the time constant of the electric vehicle; Step 1.2: Take the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv as the system state variable x(t), the generator set terminal voltage _ΔuG as the system control input u(t), and the external interference input _ΔPL caused by electric vehicles and new energy generation that affects the frequency stability of the microgrid as the external interference quantity Φ(x(t),t) to establish the microgrid load frequency regulation dynamic model:

y(t)＝Cx(t) Among them: x(t)=[Δf,ΔP _g ,ΔP _v ] ^T , u(t)=[Δu _G ], Φ(x(t),t)=[ΔP _L ];

C＝[1 0 0] in

They are all real constant matrices summarized from actual parameters selected according to the actual operating conditions of microgrids and power plants; and the frequency disturbances generated by renewable energy generation and electric vehicles connected to microgrids are bounded, that is, the interference term |Φ(x(t),t)|≤δ _f ; Step 1.3: According to the actual operation data of the microgrid system and the power plant, the initial parameters of the dynamic model are selected as follows: The power system load damping coefficient D = 2, the equivalent moment of inertia of the generator set M = 3.5, the generator time constant T _CH = 50, the adjustment coefficient R ^f = 1, the generator set speed regulator time constant T _G = 40, and the electric vehicle time constant _Te = 1; Then the dynamic model parameter matrix of electric vehicles participating in microgrid load frequency regulation is:

Step 2: To ensure the stability of the microgrid frequency, a sliding mode controller is designed for the microgrid frequency. The frequency controller is analyzed by Lyapunov theory to ensure that when the microgrid frequency deviates, the frequency can be restored to its original state at a faster speed and remain stable. The specific method of step 2 is: Step 2.1: Based on the dynamic mathematical model of electric vehicles participating in the load frequency regulation of the microgrid in step 1, the sliding mode control method is used to express the frequency state of the microgrid as a sliding mode function, and a sliding mode controller is designed; Based on the microgrid system frequency deviation Δf, the generator set power deviation _ΔPg and the generator set governor valve position change _ΔPv, the sliding mode function s is defined as: s＝B ^T Px Among them, the frequency controller matrix

And P＝ ^PT ＞0, a sliding mode function is designed for the frequency of the microgrid to stabilize the frequency of the microgrid at 50HZ, and s＝0 is achieved by designing P; Step 2.2: Design the microgrid frequency controller based on the equivalent control principle; The frequency controller expression is: u(t)＝u _eq +u _n According to the equivalent control principle, without considering the external interference caused by renewable energy generation and electric vehicles connected to the microgrid, that is, Φ(x(t), t) = 0, the frequency regulation dynamic model of the microgrid is expressed as

and

The derivative of the sliding mode function is

Therefore ^, the equivalent control term of the frequency controller is u _eq =-( ^BTPB ) ^-1BTPAx (t); Step 2.3: According to the sliding mode control principle, based on the sliding mode function designed in the above steps, design a robust control term to make the microgrid operation state asymptotically stable; When the frequency of the microgrid system changes, that is, the operating state of the microgrid system deviates from the sliding surface, if the frequency is higher than 50HZ, s＞0, then

Reduce the system frequency. If the frequency is lower than 50HZ, s＜0, then

Increase the system frequency, that is, ensure

The robust control term is taken as: u _n =-(δ _f +(B ^T PB) ^-1 ε)sgn(s) Where ε＞0; Step 2.4: Select the Lyapunov function, which represents the energy flow of the microgrid system, and prove that its derivative is less than zero, so that the microgrid frequency control system is asymptotically stable; Take the Lyapunov function

but

but

Step 3: Establish the Lyapunov function, analyze the frequency controller and sliding mode function, and design the sliding mode control based on auxiliary feedback through linear matrix inequality. The specific method of step 3 is: Step 3.1: The frequency controller u(t) is expressed as u(t)=-Kx+v(t), where v(t)=Kx+u _eq + _un , then the original microgrid load frequency regulation dynamic model is expressed as:

in

Step 3.2: Design a Lyapunov function, take the derivative of the Lyapunov function, obtain a linear matrix inequality, and solve the linear matrix inequality to obtain the control rate matrix K and the frequency controller matrix P; Take the Lyapunov function V = x ^T Px and differentiate it to obtain:

By analyzing the controller expression u(t) = u _eq + u _n , it can be seen that at a certain moment after the frequency conversion, the microgrid frequency will reach a stable state, that is, there exists t ≥ t ₀ so that s = B ^T Px = 0 is established, so s ^T = x ^T PB = 0 is established, then

like

but

exist

Multiplying both sides by Q=P ^-1 gives:

That is, (A+BK)Q+Q(A+BK) ^T < 0 Let R=KQ, then AQ-BR+QA ^T -R ^T B ^T <0 That is ^, AQ+ ^QAT < BR+ ^RTBT Step 4: Based on the control process of steps 1, 2, and 3, obtain the corresponding matrix related to the microgrid load frequency regulation system, perform simulation analysis, solve the linear matrix inequality, and obtain the controller matrix P and the control rate matrix K;

R＝[8.9577 22.1605 25.0410], K = [5.8384 23.412 25.798], Let the interference term Φ(x(t),t)＝0.1sint, then δ _f ＝0.1, let ε ₀ ＝0.5, and get the simulation diagram of the voltage change at the generator terminal of the power plant and the frequency change of the microgrid. Analyze the image, and control the frequency of the microgrid through the simulation diagram of the control variable and the state variable.

Images