CN112186789B - Sliding mode control method for electric automobile to participate in micro-grid load frequency modulation - Google Patents
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- H—ELECTRICITY
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Abstract
A sliding mode control method for an electric automobile to participate in micro-grid load frequency modulation belongs to the field of micro-grid load frequency modulation and comprises the following steps: step 1: establishing a micro-grid load frequency modulation dynamic model under the participation of an electric automobile; step 2: establishing a sliding mode controller; step 3: establishing a Lyapunov function, analyzing a controller and a sliding mode surface, and designing sliding mode control based on auxiliary feedback through a linear matrix inequality; step 4: based on the mathematical procedures of the steps 1, 2 and 3, the corresponding matrix is obtained, simulation analysis is carried out, and the inequality of the linear matrix is solved. The invention combines the equivalent control principle and the sliding mode control principle to design the controller, ensures the stability of the system by utilizing the sliding mode control principle, improves the control precision of the control system and enhances the stability of the frequency of the power grid.
Description
Technical Field
The invention belongs to the field of micro-grid load frequency modulation, and particularly relates to a sliding mode control method for an electric automobile participating in micro-grid load frequency modulation.
Background
In recent years, with the rapid development of global economy, environmental pollution and energy shortage problems are also becoming serious. Saving resources and protecting the environment have been one of the important topics in the current age. The electric automobile with a series of advantages of high efficiency, no pollution, low noise and the like is considered as one of the best choices of energy conservation and emission reduction, and research show that the electric automobile can replace the traditional automobile to become one of the main travel modes of people in the near future. Along with the fact that more and more renewable energy sources such as wind energy, solar energy and the like are greatly influenced by natural condition factors, power generation has discontinuity and intermittence, so that in order to ensure the stability of power grid frequency and the quality of electric energy, in 1995, an American energy source student firstly puts forward an electric automobile access power grid technology (V2G), and a new thought is provided for maintaining the stability of power system frequency, so that the power supply quality is improved. Research shows that the electric automobile in the V2G mode has the following advantages: (1) The energy storage function of the battery of the electric automobile is used as power grid buffer to provide auxiliary services for the power grid, such as peak shaving and frequency modulation, so that the stability and reliability of the power grid can be improved, the power supply quality can be improved, and the operation cost of a power system can be reduced; (2) The electric automobile in the V2G mode can bring extra economic benefits to the automobile owners, reduces the purchase cost of the electric automobile, is more beneficial to popularization of the new energy electric automobile, and also realizes environmental protection; (3) The electric automobile in the large-scale V2G mode can generate energy storage buffer, is used as supplement of intermittent renewable energy power generation such as wind power generation and photovoltaic power generation, reduces carbon dioxide emission, and improves new energy power generation grid-connection capability such as wind energy and solar energy.
At present, the domestic and foreign scientific research field relates to the development of the participation of an electric automobile access power system in the frequency modulation technology, and mainly relates to the establishment of a frequency modulation model, the research of a frequency modulation control algorithm, the aspects of the electric automobile supply of frequency modulation service income, the research of the frequency modulation feasibility of the electric automobile access micro-grid, the frequency modulation economy, the frequency modulation control strategy and the like.
In the field of the feasibility of the electric automobile to participate in frequency modulation, the electric automobile is connected to a power grid system, bidirectional flow of electric energy is realized by utilizing power electronic equipment in the United states, and the electric automobile is firstly connected to a micro-grid, so that theoretical feasibility is provided for the electric automobile to participate in frequency modulation of the power grid; in the field of electric vehicle access micro-grid control, many mathematical methods have been adopted abroad to improve the control of electric vehicle access micro-grid, for example: providing a novel charging strategy, and evaluating the charging strategy through an improved particle swarm algorithm; for solving the uncertainty existing in the micro-grid system, designing a fuzzy PI controller, and optimizing the controller parameters by adopting a harmony search algorithm; aiming at the problem of frequency fluctuation of access of an electric automobile to a micro-grid, a micro-grid load frequency modulation model under the participation of the electric automobile is established, and a method based on a robust self-adaptive control strategy and the like are provided. Compared with foreign countries, the research of participating in the micro-grid technology of the electric automobile in China starts later, and related research is focused on research of frequency modulation control algorithms, and research of frequency modulation feasibility of providing frequency modulation service benefits and accessing the electric automobile into the micro-grid by the electric automobile.
The frequency is an important index of the quality of electric energy, and maintaining the stable frequency is a basic requirement for the operation of the electric power system. Along with the V2G concept, the electric automobile is used as a micro energy storage unit to be connected into a micro power grid and participate in frequency modulation, but the charging and discharging of the electric automobile also have great influence on the frequency stability of the power grid, so that a higher requirement is provided for a control method of the stability of the power grid.
The research of the electric automobile connected with the electric power system to participate in frequency modulation mainly relates to the research of the frequency modulation feasibility of the electric automobile connected with a micro-grid and the research of the stability of the grid, and the electric automobile connected with the grid by plug-in type can be charged and used as a power supply to participate in the frequency modulation of the grid based on the V2G technology. Under the condition that a large number of electric vehicles are connected into a power grid, the control structure can realize auxiliary frequency modulation on the micro-grid by using the electric vehicles as power sources under the condition of meeting the daily traveling condition of a vehicle owner.
Aiming at the condition that an electric automobile is connected with a power grid, the current technology for maintaining the frequency stability of the power grid mainly comprises a traditional PID control technology, a model predictive control technology and the like. The traditional PID control technology cannot show good control performance for a nonlinear and multi-target system, but the existing model predictive control technology has high accuracy requirement for a mathematical model of a controlled object, does not consider factors causing power grid frequency fluctuation, and cannot achieve good control performance.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a sliding mode control method for the electric automobile to participate in the load frequency modulation of the micro-grid, wherein a controller is designed by combining an equivalent control principle and a sliding mode control principle, the stability of a system is ensured by utilizing the sliding mode control principle, the control precision of the control system is improved, and the stability of the frequency of the grid is enhanced.
The invention adopts the following technical scheme:
a sliding mode control method for enabling an electric automobile to participate in micro-grid load frequency modulation comprises the following steps:
step 1: respectively analyzing the working principles of a power plant generator set and electric vehicles, carrying out equivalent treatment on different types of electric vehicles, taking the electric vehicles as energy storage elements to participate in the micro-grid load frequency modulation process when the electric vehicles are connected to the micro-grid, and establishing a micro-grid load frequency modulation dynamic model under the participation of the electric vehicles;
step 1.1: in consideration of the charge and discharge characteristics of the electric automobile and the influence on the frequency of a power grid, the dynamic model of the electric automobile participating in the frequency modulation of the load of the micro-grid is abstracted, the model comprises five parts of a power plant, new energy power generation, the electric automobile, the micro-grid and a controller, and the dynamic model expression is as follows:
wherein: Δf represents the system frequency deviation; m represents the equivalent moment of inertia of the generator set; d represents a load damping coefficient of the power system; ΔP L The method comprises the following steps of representing external interference input which is caused by electric vehicles and new energy power generation and affects the frequency stability of a micro-grid; r is R f Representing a difference adjustment coefficient; ΔP v Representing the position variation of a valve of a speed regulator of the generator set; t (T) G Representing a governor time constant; t (T) CH Representing a generator time constant; deltau G Representing the generator set terminal voltage; ΔP g Representing the power deviation of the generator set; ΔP EV Representing the charge and discharge power of the electric automobile; deltau EV Representing the terminal voltage of the electric automobile; t (T) e Representing the time constant of the electric automobile;
step 1.2: with micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v For the system state variable x (t), the generator set terminal voltage delta u is used G The input u (t) is controlled for the system to input delta P of external disturbance affecting the frequency stability of the micro-grid caused by electric vehicles and new energy power generation L Establishing a micro-grid load frequency modulation dynamic model for an external interference quantity phi (x (t), t):
y(t)＝Cx(t)
wherein: x (t) = [ Δf, Δp g ,ΔP v ] T ，u(t)＝[Δu G ]，Φ(x(t),t)＝[ΔP L ]；
C＝[1 0 0]
Wherein the method comprises the steps of
The real constant matrix is induced by the actual parameters selected according to the actual running conditions of the micro-grid and the power plant; and the frequency disturbance generated by new energy power generation and electric vehicle access to the micro-grid is bounded, namely the interference term |phi (x (t), t) |is less than or equal to delta f ；
Step 1.3: according to actual operation data of a micro-grid system and a power plant, the initial parameters of a dynamic model are selected as follows:
load damping coefficient D=2 of power system, equivalent moment of inertia M=3.5 of generator set and generator time constant T CH =50, difference adjustment coefficient R f Time constant T of generator set speed regulator G =40, electric car time constant T e ＝1；
The dynamic model parameter matrix of the electric automobile participating in the micro-grid load frequency modulation is as follows:
step 2: in order to ensure the stability of the frequency of the micro-grid, a sliding mode controller is designed for the frequency of the micro-grid, and the frequency controller is analyzed through the Lyapunov theory, so that when the frequency of the micro-grid deviates, the frequency can be recovered to the original state at a higher speed and kept stable; the specific method of the step 2 is as follows:
step 2.1: according to the dynamic mathematical model of the electric automobile participating in the micro-grid load frequency modulation in the step 1, a sliding mode control method is utilized, the micro-grid frequency state is expressed as a sliding mode function, and a sliding mode controller is designed;
based on micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v Defining a sliding mode function s as:
s＝B T Px
wherein the frequency controller matrix
And p=p T Designing a sliding mode function aiming at the frequency of the micro-grid to ensure that the frequency of the micro-grid is stabilized at 50HZ, and realizing s=0 through the design of P;
step 2.2: designing a micro-grid frequency controller according to an equivalent control principle;
the frequency controller expression is:
u(t)＝u eq +u n
according to the equivalent control principle, external interference caused by new energy power generation and electric automobile access to a micro-grid is not considered, namely phi (x (t), t) =0, and the micro-grid frequency modulation dynamic model expression is adopted
And->
The derivative of the sliding mode function is +.>
Whereby the equivalent control term u of the frequency controller eq ＝-(B T PB) - 1 B T PAx(t)；
Step 2.3: according to a sliding mode control principle, based on the sliding mode function designed in the steps, a robust control item is designed to enable the running state of the micro-grid to be gradually stable;
when the frequency of the micro-grid system changes, i.e. the running state of the micro-grid system deviates from the sliding mode surface, if the frequency is higher than 50HZ and s is greater than 0, the micro-grid system must be operated
The system frequency is reduced, if the frequency is lower than 50HZ, s < 0, the +.>
Increasing the system frequency, i.e. ensuring +.>
The robust control term is taken as follows:
u n ＝-(δ f +(B T PB) -1 ε)sgn(s)
wherein ε > 0;
step 2.4: selecting a Lyapunov function which represents the energy flow of the micro-grid system and proves that the derivative of the function is smaller than zero, so that the micro-grid frequency control system is gradually stabilized;
taking the Lyapunov function
Then->
Then
Step 3: establishing a Lyapunov function, analyzing a frequency controller and a sliding mode function, designing sliding mode control based on auxiliary feedback through a linear matrix inequality, and specifically, the method in the step 3 is as follows:
step 3.1: the frequency controller u (t) is denoted as u (t) = -kx+v (t), where v (t) = kx+u eq +u n The original micro-grid load frequency modulation dynamic model is expressed as:
wherein the method comprises the steps of
Step 3.2: designing a Lyapunov function, deriving the Lyapunov function to obtain a linear matrix inequality, and solving the linear matrix inequality to obtain a control rate matrix K and a frequency controller matrix P;
taking the lyapunov function v=x T Px, deriving it to obtain:
by expressing u (t) =u to the controller eq +u n The analysis of (a) shows that at a certain moment after the frequency conversion, the micro-grid frequency must reach a stable state, i.e. t is greater than or equal to t 0 So that s=b T Px=0 holds, so s T ＝x T Pb=0 is true, then
If it is
Then->
At the position of
Both sides multiply q=p simultaneously -1 Obtaining: />
Namely (A+BK) Q+Q (A+BK) T ＜0
Let r=kq, then AQ-br+qa T -R T B T ＜0
I.e. AQ+QA T ＜BR+R T B T
Step 4: based on the control process of the steps 1, 2 and 3, solving a relevant corresponding matrix of the micro-grid load frequency modulation system, performing simulation analysis, and solving a linear matrix inequality to obtain a controller matrix P and a control rate matrix K;
R＝[8.9577 22.1605 25.0410]，
K＝[5.8384 23.412 25.798]，
let interference term Φ (x (t), t) =0.1 sint, then δ f Let ε be =0.1 0 And (4) obtaining a simulation diagram of the voltage change of the generator end of the power plant and the frequency change of the micro-grid, analyzing the image, and controlling the frequency of the micro-grid through the simulation diagram of the control variable and the state variable.
The invention has the advantages and effects that:
according to the invention, a dynamic load frequency modulation model is established according to the working characteristics of the electric vehicle during charging and discharging and the frequency characteristics of the micro-grid, the influence of the charging and discharging characteristics of the electric vehicle and the intermittence of new energy power generation on the micro-grid is used as an interference item, the generator set terminal voltage is used as a control quantity, and the running state of the micro-grid system is represented by a sliding mode function, so that the frequency control of the micro-grid is realized. The main innovation point is that the controller is designed by combining an equivalent control principle and a sliding mode control principle, the stability of the system is ensured by utilizing the sliding mode control principle, the control precision of the frequency control system is improved, the inequality of the linear matrix is simplified, and great convenience is brought to the design process of the sliding mode surface. In the era of gradual increase of electric automobiles, the method can enhance the stability of the frequency of the micro-grid, and has guiding significance and popularization value for the operation and control of the micro-grid.
Drawings
FIG. 1 is a schematic view of an electric vehicle connected to a micro-grid;
FIG. 2 is a diagram of a grid frequency control model of the present invention;
FIG. 3 is a system simulation diagram of the present invention;
FIG. 4 is a graph showing the comparison of the frequency variation of the micro-grid obtained by adopting different control strategies;
FIG. 5 is a graph of control variable response in a dynamic model of the system of the present invention;
FIG. 6 is a sliding mode function response chart of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and examples.
The invention discloses a sliding mode control method for electric vehicles to participate in micro-grid load frequency modulation, and aims at the condition that the electric vehicles are connected to a power grid, the current technology for maintaining the stable frequency of the power grid mainly comprises a traditional PID control technology, a model predictive control technology and the like. The traditional PID control technology cannot show good control performance on a nonlinear and multi-target system, the existing model prediction control technology has high requirements on the accuracy of a mathematical model of a controlled object, and meanwhile, related factors such as system uncertainty and the like are not considered, so that the two control strategies cannot achieve good control performance.
The influence of the intermittence of electric automobile and new energy power generation on the frequency stability of the micro-grid is considered, the intermittence is taken as an external interference item, the sliding mode control principle is combined with the equivalent control principle, and the micro-grid frequency controller is designed to ensure the frequency stability of the micro-grid. The main innovation point is that the interference item is processed by a sliding mode control method, and the control aim is to enable the generator terminal voltage variation and the micro-grid frequency variation to approach zero; the method for analyzing the participation of the electric automobile in the micro-grid load frequency modulation comprises the following steps:
step 1: analyzing working principles of a power plant and an electric automobile respectively, taking the influence of the intermittence and uncertainty of new energy power generation on a power grid into consideration, taking the intermittence and uncertainty as external interference items, and establishing a micro-grid load frequency modulation dynamic model under the participation of the electric automobile;
step 2: based on the established electric automobile participation micro-grid load frequency modulation dynamic model, according to an equivalent control principle, firstly, a frequency equivalent controller is established without considering external interference affecting the micro-grid frequency, and a sliding mode controller is designed, so that the micro-grid frequency can be stabilized to an original state at a higher speed after being raised or lowered, and the stability of the micro-grid frequency is ensured by utilizing a Lyapunov stability theory;
step 3: and establishing a Lyapunov energy function, analyzing the frequency controller, and solving a control rate matrix K and a frequency controller matrix P by solving a linear matrix inequality.
Step 4: according to the control process, based on the working characteristics of the micro-grid and the electric automobile, selecting initial parameters of a micro-grid load frequency modulation model, solving matrix parameters, and performing simulation analysis;
as can be seen by comparing the simulation diagram with the diagram of FIG. 4, the micro-grid frequency change curve under the PID control strategy has larger overshoot, which has larger influence on the stable operation of the micro-grid; the sliding mode control method provided by the invention not only considers the external interference to the stability of the micro-grid frequency caused by the intermittence of new energy power generation, but also can enable the micro-grid frequency to be converged into the required range at a higher speed, and has better control performance compared with the PID control technology.
The equivalent control and the sliding mode control are combined, firstly, an external interference item affecting the frequency stability of the micro-grid is equivalent to zero, a robust control item of the sliding mode control is designed, a Lyapunov function, namely an energy function between the micro-grid and an electric automobile is established, and the micro-grid frequency stability is ensured by utilizing the Lyapunov stability theory; as can be seen from the analysis of FIG. 4, when the micro-grid frequency control system is interfered by a certain external environment, the micro-grid frequency can be kept stable by adjusting the generator set terminal voltage, so that better control performance is achieved.
The frequency controller is analyzed, the frequency controller based on auxiliary feedback is designed, the control rate matrix K is solved, the control rate matrix K can intuitively reflect the control rate of the frequency of the power grid, and meanwhile, more accurate conditions are provided for setting up inequality of the linear matrix, so that the stability of the frequency of the micro power grid is ensured.
The method comprises the following specific steps:
step 1: the working principles of a power plant generating set and an electric automobile are analyzed respectively, and the working principles of the power plant generating set are as follows: the high-temperature high-pressure steam generated by the boiler is utilized to push the turbine rotor to rotate, and the turbine rotor drives the generator rotor to rotate, so that electric energy is generated. And carrying out equivalent treatment on different types of electric vehicles, wherein when the electric vehicles are connected into the micro-grid, the electric vehicles can participate in the load frequency modulation process of the micro-grid as energy storage elements, and a dynamic model of the load frequency modulation of the micro-grid under the participation of the electric vehicles is established.
Step 1.1: in consideration of the charge and discharge characteristics of the electric automobile and the influence on the frequency of a power grid, the dynamic model of the electric automobile participating in the frequency modulation of the load of the micro-grid is abstracted, the model comprises five parts of a power plant, new energy power generation, the electric automobile, the micro-grid and a controller, and the dynamic model expression is as follows:
wherein: Δf represents the system frequency deviation; m represents the equivalent moment of inertia of the generator set; d represents a load damping coefficient of the power system; ΔP L The method comprises the following steps of representing external interference input which is caused by electric vehicles and new energy power generation and affects the frequency stability of a micro-grid; r is R f Representing a difference adjustment coefficient; ΔP v Representing the position variation of a valve of a speed regulator of the generator set; t (T) G Representing a governor time constant; t (T) CH Representing a generator time constant; deltau G Representing the generator set terminal voltage; ΔP g Representing the power deviation of the generator set; ΔP EV Representing the charge and discharge power of the electric automobile; deltau EV Representing the terminal voltage of the electric automobile; t (T) e Indicating the time constant of the electric vehicle.
Step 1.2: with micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v For the system state variable x (t), the generator set terminal voltage delta u is used G The input u (t) is controlled for the system to input delta P of external disturbance affecting the frequency stability of the micro-grid caused by electric vehicles and new energy power generation L Establishing a micro-grid load frequency modulation dynamic model for an external interference quantity phi (x (t), t):
y(t)＝Cx(t)
wherein: x (t) = [ Δf, Δp g ,ΔP v ] T ，u(t)＝[Δu G ]，Φ(x(t),t)＝[ΔP L ]；
C＝[1 0 0]
Wherein the method comprises the steps of
The real constant matrix is induced by the actual parameters selected according to the actual running conditions of the micro-grid and the power plant; and the frequency disturbance generated by new energy power generation and electric vehicle access to the micro-grid is bounded, namely the interference term |phi (x (t), t) |is less than or equal to delta f ；
Step 1.3: according to actual operation data of a micro-grid system and a power plant, the initial parameters of a dynamic model are selected as follows:
load damping coefficient D=2 of power system, equivalent moment of inertia M=3.5 of generator set and generator time constant T CH =50, difference adjustment coefficient R f Time constant T of generator set speed regulator G =40, electric car time constant T e ＝1；
The dynamic model parameter matrix of the electric automobile participating in the micro-grid load frequency modulation is as follows:
step 2: in order to ensure the stability of the frequency of the micro-grid, a sliding mode controller is designed for the frequency of the micro-grid, and the frequency controller is analyzed through the Lyapunov theory, so that when the frequency of the micro-grid deviates, the frequency can be recovered to the original state at a higher speed and kept stable; the specific method of the step 2 is as follows:
step 2.1: according to the dynamic mathematical model of the electric automobile participating in the micro-grid load frequency modulation in the step 1, a sliding mode control method is utilized, the micro-grid frequency state is expressed as a sliding mode function, and a sliding mode controller is designed;
based on micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v Defining a sliding mode function s as:
s＝B T Px
wherein the frequency controller matrix
And p=p T The method has the advantages that > 0, a sliding mode function is designed for the frequency of the micro-grid, the best control state of the method is to enable the frequency of the micro-grid to be stabilized at 50HZ, and s=0 can be realized through the design of P;
step 2.2: designing a micro-grid frequency controller according to an equivalent control principle;
the frequency controller expression is:
u(t)＝u eq +u n
according to the equalThe effective control principle is that the external interference caused by new energy power generation and electric automobile access to the micro-grid is not considered, namely phi (x (t), t) =0, and the micro-grid frequency modulation dynamic model expression is adopted
And->
The derivative of the obtainable sliding mode function is +.>
Whereby the equivalent control term u of the frequency controller eq ＝-(B T PB) - 1 B T PAx(t)；
Step 2.3: according to a sliding mode control principle, based on the sliding mode function designed in the steps, a robust control item is designed to ensure that the running state of the micro-grid is gradually stable;
when the frequency of the micro-grid system changes, i.e. the running state of the micro-grid system deviates from the sliding mode surface, if the frequency is higher than 50HZ and s is greater than 0, the micro-grid system must be operated
The system frequency is reduced, if the frequency is lower than 50HZ, s < 0, the +.>
Increasing the system frequency, i.e. ensuring +.>
The robust control term is taken as follows:
u n ＝-(δ f +(B T PB) -1 ε)sgn(s)
wherein ε > 0;
step 2.4: selecting a Lyapunov function, wherein the function can represent energy flow of a micro-grid system, and prove that the derivative of the function is smaller than zero, so that the micro-grid frequency control system is ensured to be gradually stable;
taking the Lyapunov function
Then->
Then
Step 3: establishing a Lyapunov function, analyzing a frequency controller and a sliding mode function, and designing sliding mode control based on auxiliary feedback through a linear matrix inequality in order to ensure the control performance of the micro-grid frequency controller, wherein the specific method of the step 3 is as follows:
step 3.1: the frequency controller u (t) is denoted as u (t) = -kx+v (t), where v (t) = kx+u eq +u n The original micro-grid load frequency modulation dynamic model can be expressed as:
wherein the method comprises the steps of
By designing the control rate matrix K, an auxiliary feedback design is added in the electric automobile participating in the micro-grid load frequency modulation model, so that the control performance of the frequency controller is improved, and the auxiliary feedback control method can ensure that the micro-grid load frequency modulation closed-loop system is gradually stable, and the micro-grid frequency can be restored to the original state in a short time when being changed.
Step 3.2: designing a Lyapunov function, deriving the Lyapunov function to obtain a linear matrix inequality, and solving the linear matrix inequality to obtain a control rate matrix K and a frequency controller matrix P;
taking the lyapunov function v=x T Px, deriving it to obtain:
by expressing u (t) =u to the controller eq +u n The analysis of (a) shows that at a certain moment after the frequency conversion, the micro-grid frequency must reach a stable state, i.e. t is greater than or equal to t 0 So that s=b T Px=0 holds, so s T ＝x T Pb=0 is true, then
If it is
Then->
At the position of
Both sides multiply q=p simultaneously -1 Obtaining:
namely (A+BK) Q+Q (A+BK) T ＜0
Let r=kq, then AQ-br+qa T -R T B T ＜0
I.e. AQ+QA T ＜BR+R T B T
Step 4: based on the control process of the steps 1, 2 and 3, solving a relevant corresponding matrix of the micro-grid load frequency modulation system, performing simulation analysis, and solving a linear matrix inequality to obtain a controller matrix P and a control rate matrix K;
R＝[8.9577 22.1605 25.0410]，
K＝[5.8384 23.412 25.798]，
let interference term Φ (x (t), t) =0.1 sint, then δ f Let ε be =0.1 0 By means of the simulation graph, the voltage change of the generator terminal of the power plant and the frequency change of the micro-grid can be obtained, and the analysis of the graph shows that the voltage change of the generator terminal of the power plant, the frequency change of the micro-grid and the running state of the micro-grid are stable.
In fig. 4, the dashed line represents the microgrid frequency variation response curve under the PID control strategy; the solid line represents the micro-grid frequency variation response curve under the sliding mode control strategy; as can be easily seen from fig. 4, under the action of two control strategies, the frequencies of the micro-grid can be converged, and the convergence speeds are similar, but under the PID control strategy, the maximum overshoot of the frequency change of the micro-grid is about 0.2HZ, the overshoot is larger, and the allowable value of the normal frequency deviation of the power system in China is +/-0.2 HZ, so that the traditional PID control strategy cannot achieve better performance for the frequency stabilization of the micro-grid, and under the PID control strategy, the frequency has small amplitude fluctuation, which can influence the normal use of the electric appliances connected to the micro-grid system, and even can influence the normal operation of the generator; as can be seen from fig. 5, the convergence speed of the generator set terminal voltage is high, and the method has a good effect of stabilizing the frequency of the power grid and stabilizing the generator set terminal voltage; as can be seen from fig. 6, the sliding mode control function has small variation amplitude and high convergence speed, so that the micro-grid frequency can be ensured to be gradually stable in the area near the sliding mode surface.
According to analysis of the state variables, the frequency of the micro-grid can reach a stable state faster, and the actual working requirements of the micro-grid are met; through analysis of control variables, the generator terminal voltage of the generator set can reach a stable state in a short time and the fluctuation range is small, which is significant for protecting the generator set.
Claims (1)
1. A sliding mode control method for electric vehicles to participate in micro-grid load frequency modulation is characterized by comprising the following steps: the method comprises the following steps:
step 1: respectively analyzing the working principles of a power plant generator set and electric vehicles, carrying out equivalent treatment on different types of electric vehicles, taking the electric vehicles as energy storage elements to participate in the micro-grid load frequency modulation process when the electric vehicles are connected to the micro-grid, and establishing a micro-grid load frequency modulation dynamic model under the participation of the electric vehicles;
step 1.1: in consideration of the charge and discharge characteristics of the electric automobile and the influence on the frequency of a power grid, the dynamic model of the electric automobile participating in the frequency modulation of the load of the micro-grid is abstracted, the model comprises five parts of a power plant, new energy power generation, the electric automobile, the micro-grid and a controller, and the dynamic model expression is as follows:
wherein: Δf represents the system frequency deviation; m represents the equivalent moment of inertia of the generator set; d represents a load damping coefficient of the power system; ΔP L The method comprises the following steps of representing external interference input which is caused by electric vehicles and new energy power generation and affects the frequency stability of a micro-grid; r is R f Representing a difference adjustment coefficient; ΔP v Representing the position variation of a valve of a speed regulator of the generator set; t (T) G Representing a governor time constant; t (T) CH Representing a generator time constant; deltau G Representing the generator set terminal voltage; ΔP g Representing the power deviation of the generator set; ΔP EV Representing the charge and discharge power of the electric automobile; deltau EV Representing the terminal voltage of the electric automobile; t (T) e Representing the time constant of the electric automobile;
step 1.2: with micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v For the system state variable x (t), the generator set terminal voltage delta u is used G The input u (t) is controlled for the system to input delta P of external disturbance affecting the frequency stability of the micro-grid caused by electric vehicles and new energy power generation L Establishing a micro-grid load frequency modulation dynamic model for an external interference quantity phi (x (t), t):
y(t)＝Cx(t)
wherein: x (t) = [ Δf, Δp g ,ΔP v ] T ，u(t)＝[Δu G ]，Φ(x(t),t)＝[ΔP L ]；
C＝[1 0 0]
Wherein the method comprises the steps of
The real constant matrix is induced by the actual parameters selected according to the actual running conditions of the micro-grid and the power plant; and the frequency disturbance generated by new energy power generation and electric vehicle access to the micro-grid is bounded, namely the interference term |phi (x (t), t) |is less than or equal to delta f ；/>
Step 1.3: according to actual operation data of a micro-grid system and a power plant, the initial parameters of a dynamic model are selected as follows:
load damping coefficient D=2 of power system, and equivalent moment of inertia M=of generator set3.5 generator time constant T CH =50, difference adjustment coefficient R f Time constant T of generator set speed regulator G =40, electric car time constant T e ＝1；
The dynamic model parameter matrix of the electric automobile participating in the micro-grid load frequency modulation is as follows:
step 2: in order to ensure the stability of the frequency of the micro-grid, a sliding mode controller is designed for the frequency of the micro-grid, and the frequency controller is analyzed through the Lyapunov theory, so that when the frequency of the micro-grid deviates, the frequency can be restored to the original state at a higher speed and kept stable; the specific method of the step 2 is as follows:
step 2.1: according to the dynamic mathematical model of the electric automobile participating in the micro-grid load frequency modulation in the step 1, a sliding mode control method is utilized, the micro-grid frequency state is expressed as a sliding mode function, and a sliding mode controller is designed;
based on micro-grid system frequency deviation delta f and generator set power deviation delta P g And the valve position change delta P of the generator set speed regulator v Defining a sliding mode function s as:
s＝B T Px
wherein the frequency controller matrix
And p=p T Designing a sliding mode function aiming at the frequency of the micro-grid to ensure that the frequency of the micro-grid is stabilized at 50HZ, and realizing s=0 through the design of P;
step 2.2: designing a micro-grid frequency controller according to an equivalent control principle;
the frequency controller expression is:
u(t)＝u eq +u n
according to the equivalent control principle, external interference caused by new energy power generation and electric automobile access to the micro-grid is not considered, namely phi (x (t), t) =0, and the micro-grid is used for generating the electric automobileFrequency modulation dynamic model expression
And->
The derivative of the sliding mode function is +.>
Whereby the equivalent control term u of the frequency controller eq ＝-(B T PB) -1 B T PAx(t)；
Step 2.3: according to a sliding mode control principle, based on the sliding mode function designed in the steps, a robust control item is designed to enable the running state of the micro-grid to be gradually stable;
when the frequency of the micro-grid system changes, i.e. the running state of the micro-grid system deviates from the sliding mode surface, if the frequency is higher than 50HZ and s is greater than 0, the micro-grid system must be operated
The system frequency is reduced, if the frequency is lower than 50HZ, s < 0, the +.>
Increasing the system frequency, i.e. ensuring +.>
The robust control term is taken as follows:
u n ＝-(δ f +(B T PB) -1 ε)sgn(s)
wherein ε > 0;
step 2.4: selecting a Lyapunov function which represents the energy flow of the micro-grid system and proves that the derivative of the function is smaller than zero, so that the micro-grid frequency control system is gradually stabilized;
taking the Lyapunov function
Then->
Then
Step 3: establishing a Lyapunov function, analyzing a frequency controller and a sliding mode function, designing sliding mode control based on auxiliary feedback through a linear matrix inequality, and specifically, the method in the step 3 is as follows:
step 3.1: the frequency controller u (t) is denoted as u (t) = -kx+v (t), where v (t) = kx+u eq +u n The original micro-grid load frequency modulation dynamic model is expressed as:
wherein the method comprises the steps of
Step 3.2: designing a Lyapunov function, deriving the Lyapunov function to obtain a linear matrix inequality, and solving the linear matrix inequality to obtain a control rate matrix K and a frequency controller matrix P;
taking the lyapunov function v=x T Px, deriving it to obtain:
by expressing u (t) =u to the controller eq +u n The analysis of (a) shows that at a certain moment after the frequency conversion, the micro-grid frequency must reach a stable state, i.e. t is greater than or equal to t 0 So that s=b T Px=0 holds, so s T ＝x T Pb=0 is true, then
If it is
Then->
At the position of
Both sides multiply q=p simultaneously -1 Obtaining:
namely (A+BK) Q+Q (A+BK) T ＜0
Let r=kq, then AQ-br+qa T -R T B T ＜0
I.e. AQ+QA T ＜BR+R T B T
Step 4: based on the control process of the steps 1, 2 and 3, solving a relevant corresponding matrix of the micro-grid load frequency modulation system, performing simulation analysis, and solving a linear matrix inequality to obtain a controller matrix P and a control rate matrix K;
R＝[8.9577 22.1605 25.0410]，
K＝[5.8384 23.412 25.798]，
let interference term Φ (x (t), t) =0.1 sint, then δ f Let ε be =0.1 0 And (4) obtaining a simulation diagram of the voltage change of the generator end of the power plant and the frequency change of the micro-grid, analyzing the image, and controlling the frequency of the micro-grid through the simulation diagram of the control variable and the state variable.
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