CN113011104B - Cluster electric vehicle charging load aggregation modeling method for power grid frequency modulation control - Google Patents

Cluster electric vehicle charging load aggregation modeling method for power grid frequency modulation control Download PDF

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CN113011104B
CN113011104B CN202110370045.8A CN202110370045A CN113011104B CN 113011104 B CN113011104 B CN 113011104B CN 202110370045 A CN202110370045 A CN 202110370045A CN 113011104 B CN113011104 B CN 113011104B
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余洋
张瑞丰
王孟云
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North China Electric Power University
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Abstract

The invention discloses a cluster electric vehicle charging load aggregation modeling method for power grid frequency modulation control, which comprises the following steps: firstly, discretizing the SOC of an electric automobile by considering the battery capacity difference, and dividing a probability interval for each SOC interval; then, constructing a transition probability density function and a corresponding probability distribution function related to the SOC according to the battery capacity probability density function, and providing a transition probability calculation formula of two adjacent SOC intervals; and finally, analyzing the dynamic transfer process of the charging load of the electric automobile, providing a controllable aggregation model capable of smoothly adjusting the power of the clustered electric automobile, and performing simulation verification. The method can be used for establishing the cluster electric vehicle charging load aggregation model, and realizes the conversion from a large-scale electric vehicle to a few-dimensional controllable model, so that the time and space pressure calculated by a control algorithm are greatly relieved.

Description

Cluster electric vehicle charging load aggregation modeling method for power grid frequency modulation control
Technical Field
The invention relates to the fields of demand response of an electric power system and interaction of a vehicle network, in particular to an aggregation modeling method of electric vehicles, and particularly relates to a cluster electric vehicle aggregation model oriented to frequency modulation control.
Technical Field
In order to cope with energy crisis and environmental problems, new energy represented by wind power and photovoltaic is accessed into a power grid in a large scale, and higher requirements are put forward on the adjusting capability of the power grid. The conventional manner of increasing the spare capacity on the source side to achieve the supply-demand balance has difficulty in coping with high volatility and randomness of the system load, and the running cost is high. With the improvement of the internet of things and the intelligent power grid technology, the load side demand response technology is developed, and the schedulable load is introduced into the power system regulation, so that the problem of real-time balance of power supply and demand can be more efficiently, rapidly and economically solved.
The electric automobile is a demand response resource with huge schedulable potential and has good battery energy storage characteristics. But large-scale electric automobile access electric wire netting, any unordered charging by it can cause negative effect to the electric wire netting on the contrary. Many researches are carried out at present to achieve the aim of regulating the real-time power of the electric automobiles in clusters by smoothly regulating the charging power of the electric automobiles, but the control algorithm is often limited by the number of the electric automobiles. Therefore, the establishment of the controllable aggregation model which is frequency modulation oriented and is not limited by quantity is one of core technologies for realizing the control of the clustered electric vehicles, and has important guiding significance for realizing the participation demand response of the electric vehicles.
Disclosure of Invention
The invention aims to establish a cluster electric vehicle charging load model oriented to frequency modulation control, and designs a controllable aggregation model for realizing smooth adjustment of power of large-scale electric vehicles. The invention provides an electric vehicle charging load aggregation modeling method based on a Markov chain, wherein charging power is used as a control quantity to construct a controllable model of a cluster electric vehicle, and finally the accuracy and the effectiveness of the model are verified through simulation.
The invention adopts the technical scheme that: a cluster electric automobile charging load model facing power grid frequency modulation control is established, which comprises the following steps:
(1) Taking the battery capacity difference into consideration, discretizing the SOC of the electric automobile, and dividing each SOC section into probability sections;
(2) Constructing a transition probability density function and a corresponding probability distribution function related to the SOC according to the battery capacity probability density function, and providing a transition probability calculation formula of two adjacent SOC intervals;
(3) And analyzing the dynamic transfer process of the charging load of the electric automobile, providing a controllable aggregation model capable of smoothly adjusting the power of the cluster electric automobile, and performing simulation verification.
Specifically, in the step (1), the following is considered to describe the battery capacity of the electric vehicle:
the electric automobile is often affected by the brand of the automobile and the behavior habit of the user, the battery capacity of the electric automobile participating in aggregation needs to be counted, and aggregation modeling is carried out on the basis of the battery capacity. Based on the investigation of the capacity distribution of the main current electric vehicles in China, the capacities of all types of EV batteries in the market in China are mostly between 30 kW.h and 60 kW.h, so that the development theory of the electric vehicles with one capacity distribution is deduced, but the formula has universality for electric vehicles with any capacity distribution, and the electric vehicle cluster charging load model with corresponding capacity distribution can be obtained only by modifying related parameters. Counting battery capacity and adopting a certain probability density distribution function f c (C P ) Representing the difference, wherein C P Representing the battery capacity.
EV charging refers to the dynamic process of battery transition from a low state of charge to a high state of charge. SOC is generally used to represent the remaining power of a battery, and if S is recorded, the recursive formula in discrete time can be expressed as:
wherein: s (k+1) and S (k) represent the states of charge at the k+1 and k times, respectively; p is p ch Is the charging power; η (eta) ch Is the charging efficiency; c (C) P Is the actual capacity of the battery; Δt is the discrete time interval.
As can be seen from equation (1), the battery SOC is a random process with respect to time, and satisfies the following properties: the probability distribution of S (k+1) is independent of the history state of the EV, and depends only on the state of the EV at time k, i.e. markov is satisfied.
Probability density function f for battery capacity c (C P ) Integrating the probability distribution function of the available battery capacity:
wherein: c (C) max And C min Respectively, the most of the battery capacitiesA maximum value and a minimum value; c (C) a Is the battery capacity calculated from the intrinsic charge characteristics:
C a represents a critical capacity, which has the physical meaning: when the charging power, efficiency and time interval are determined, the maximum allowable capacity for shifting from S (k) to S (k+1) in one step can be achieved. This can be achieved by: there is a link between the random variable S (k) and the battery capacity:
P r {S(k+1)|S(k)}＝P r {C min ≤C P ≤C a } (4)
wherein P is r Representing conditional probabilities.
The SOC in the charging process is discretized into N sections, and the maximum value and the minimum value are S respectively max And S is min The transition process between two adjacent intervals i and i+1 is described as follows: s is S down (i+1) and S down (i) The lower limit values of the charge states of the (i+1) th and (i) th intervals are respectively represented; s is S x (i) Represents an arbitrary SOC value within the i-th interval. If the SOC of EV at k-time is S x (i) The SOC at time k+1 is greater than or equal to S down (i+1), then the EV is considered to effect a transition of the adjacent state. And S is x (i) The closer S is down (i+1), the greater the transition probability of the EV, S x (i) The closer S is down (i) The smaller the transition probability. C is C min And C max Bringing the state of charge threshold value of 0 probability and 1 probability into the state of charge threshold value of (3)And->The i-th interval can thus be divided into 3 probability intervals, denoted by letters a, b, c, respectively. Interval->The transition probability in the interval is 0, and the specific gravity in the interval i is m 1 The method comprises the steps of carrying out a first treatment on the surface of the Interval->The transition probability in the interval increases from 0 to 1, and the duty ratio is m 2 . Interval->The transition probability in the interval is 1, and the duty ratio is m 3 The method comprises the steps of carrying out a first treatment on the surface of the If interval b is also defined by a probability value +.>Representing the total probability P of transition of the interval i to the interval i+1, which is obtainable by definition of the desired probability i，i+1 ：
Definition of the definitionThe average probability of interval b, meaning from +.>To->The mean value of the transition probabilities of (a) should be demonstrated at f c (C P ) Known as a constant value.
Specifically, in the step (2), a transition probability density function and a corresponding probability distribution function about the SOC are constructed according to the battery capacity probability density function, and the specific process is as follows:
first, the probability theory theorem is introduced:
let the probability density of the random variable X be f X (x) Wherein α is less than or equal to x is less than or equal to β, and let the function y=g (x), and g (x) is derivable, the probability density of the random variable Y is:
wherein h (y) represents an inverse function of y=g (x); epsilon=min (g (α), g (β)), ω=max (g (α), g (β)).
As can be obtained from the formula (1), the current state of charge S (k) and the battery capacity C during the transition between two adjacent intervals P There is a functional relationship:
transition probability density function with respect to SOC during charging obtainable according to equation (6)
Transition probability distribution function within integral availability interval b
The physical meaning of (2) is: when a certain electric vehicle SOC at time k is S (k), and S (k) belongs to the section b, the electric vehicle can transition to the probability value of the i+1th section after one step Δt.
Assuming that interval b is equally divided into n parts S b (1)，S b (2)，…，S b (n) represents the SOC value of each part respectivelyThe calculation method of (1) is as follows:
when n approaches infinity:
the definition of the integral is as follows:
f c (C P ) Known, thenKnown, and->Is->Double integration of (2), so->Must be constant. Thus, P i，i+1 Can be represented by formula (5).
In the formula (5), m 2 And m 3 The specific gravity of the interval b and the interval c are respectively calculated by the following steps:
in summary, the transition probabilities P of two adjacent intervals i and i+1 i，i+1 The method comprises the following steps:
wherein N, eta ch 、Δt、S max 、S min 、C max 、C min Are all known quantities and average probabilityAt f c (C P ) On the premise of being known as a constant value, the transition probability P i，i+1 Proportional to the actual charging power.
Specifically, in the step (3), the controllable aggregation model establishment process of the clustered electric vehicles is as follows:
the transition probability is proportional to the charging power, and the maximum transition probability is defined asAssuming that the dispatching department can uniformly control the charging power of the electric automobile on line through the excitation signal u (k) generated by the excitation mechanism, the transition probability under the actual charging power is +.>
Electric vehicle charging is a process of dynamic transfer of load from low SOC to high SOC, which can be represented by state space expression (15):
where x (k, i) and x (k+1, i) represent the amounts of loads in the i-th SOC section at the k time and the k+1 time, respectively. When no charging power is applied to the clustered electric vehicles, the load quantity of each SOC interval does not change, the process is described by a transfer matrix A, and the A is an N-dimensional unit matrix. When charging power is applied to the clustered electric vehicles, the load amount of each SOC interval is forcedly transferred, and the process can be described by a forcedly transferring matrix P:
in the method, in the process of the invention,a specific gravity indicating load transfer, a value greater than zero indicating load transfer, and a value less than zero indicating negativeAnd (5) transferring out the load. Specially, the->The specific gravity of the electric vehicle load that is charged at the next time is represented as the total load in the section N.
In addition to the dynamic transfer of charge, it is also considered that a new electric vehicle is added to charge, this part being denoted by ψ (k).The new load amount in the i-th section at the k time is shown.
Thus, a controllable aggregation model of the cluster electric automobile can be obtained:
where x (k) is an N-dimensional column vector, x (k) = [ x (k, 1), …, x (k, N)] T The method comprises the steps of carrying out a first treatment on the surface of the A is an N-dimensional unit array; u (k) is an excitation signal of control quantity and charging power; c is the power output vector; b is a forced transfer matrix; y (k) is the total output power of the electric automobile of the cluster at the moment k.
Wherein the power output vector C is defined by the maximum charging powerThe N-dimensional row vectors that make up are:
the forced transfer matrix B is:
the technical scheme provided by the invention has the beneficial effects that:
the invention discretizes the charge state of the energy storage of the electric automobile based on the difference of battery capacity, deduces a transition probability density function related to the SOC and a transition probability solving formula among all SOC intervals, and finally analyzes the dynamic change process of the charging load to construct a controllable aggregation model of the cluster electric automobile taking the excitation of the charging power as the control quantity. The invention provides a controllable aggregation model for realizing the participation of the clustered electric vehicles in the frequency modulation service by smoothly adjusting the charging power, and the dimension of the model is not limited by the number of the electric vehicles, thereby greatly reducing the control difficulty and relieving the time and space pressure of solving the control algorithm.
Drawings
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of probability transitions for adjacent SOC intervals;
FIG. 3 is a schematic diagram of a dynamic change of a charging process;
fig. 4 is a graph comparing a charge load aggregation model with a monte carlo simulation curve at u=0.4;
fig. 5 is a graph comparing a charge load aggregation model with a monte carlo simulation curve when u=1; fig. 6 is an AGC instruction tracking result.
Detailed description of the preferred embodiments
In order to better understand the objects, technical schemes and technical effects of the present invention, the present invention will be further explained with reference to the accompanying drawings.
The invention provides a cluster electric vehicle charging load model oriented to power grid frequency modulation control, and fig. 1 is a flow chart of the invention, and the implementation process comprises the following detailed steps.
Step 1, discretizing the SOC of the electric automobile by considering the battery capacity difference, and dividing probability intervals for each SOC interval:
the electric automobile is often affected by the brand of the automobile and the behavior habit of the user, the battery capacity of the electric automobile participating in aggregation needs to be counted, and aggregation modeling is carried out on the basis of the battery capacity. Counting battery capacity and adopting a certain probability density distribution function f c (C P ) Representing the difference, wherein C P Representing the battery capacity.
EV charging refers to the dynamic process of battery transition from a low state of charge to a high state of charge. SOC is generally used to represent the remaining power of a battery, and if S is recorded, the recursive formula in discrete time can be expressed as:
wherein: s (k+1) and S (k) represent the states of charge at the k+1 and k times, respectively; p (P) ch Is the charging power; η (eta) ch Is the charging efficiency; c (C) P Is the actual capacity of the battery; Δt is the discrete time interval.
As can be seen from equation (1), the battery SOC is a random process with respect to time, and satisfies the following properties: the probability distribution of S (k+1) is independent of the history state of the EV, and depends only on the state of the EV at time k, i.e. markov is satisfied.
Probability density function f for battery capacity c (C P ) Integrating the probability distribution function of the available battery capacity:
wherein: c (C) max And C min Respectively maximum and minimum values of battery capacity; c (C) a Is the battery capacity calculated from the intrinsic charge characteristics:
C a represents a critical capacity, which has the physical meaning: when the charging power, efficiency and time interval are determined, the maximum allowable capacity for shifting from S (k) to S (k+1) in one step can be achieved. This can be achieved by: there is a link between the random variable S (k) and the battery capacity:
P r {S(k+1)|S(k)}＝P r {C min ≤C P ≤C a } (4)
wherein P is r Representing conditional probabilities.
The SOC in the charging process is discretized into N sections, and the maximum value and the minimum value are S respectively max And S is min The transition process between two adjacent intervals i and i+1 is described as follows: s is S down (i+1) and S down (i) The lower limit values of the charge states of the (i+1) th and (i) th intervals are respectively represented; s is S x (i) Represents an arbitrary SOC value within the i-th interval. If the SOC of EV at k-time is S x (i) The SOC at time k+1 is greater than or equal to S down (i+1), then the EV is considered to effect a transition of the adjacent state. And S is x (i) The closer S is down (i+1), the greater the transition probability of the EV, S x (i) The closer S is down (i) The smaller the transition probability. C is C min And C max Bringing the state of charge threshold value of 0 probability and 1 probability into the state of charge threshold value of (3)And->The ith interval can be divided into 3 probability intervals, which are respectively indicated by letters a, b and c, and the schematic diagram is shown in fig. 2. Interval->The transition probability in the interval is 0, and the specific gravity in the interval i is m 1 The method comprises the steps of carrying out a first treatment on the surface of the Interval->The transition probability in the interval increases from 0 to 1, and the duty ratio is m 2 . Interval ofThe transition probability in the interval is 1, and the duty ratio is m 3 The method comprises the steps of carrying out a first treatment on the surface of the If interval b is also defined by a probability value +.>Representing the total probability P of transition of the interval i to the interval i+1, which is obtainable by definition of the desired probability i，i+1 ：
Definition of the definitionThe average probability of interval b, meaning from +.>To->The mean value of the transition probabilities of (a) should be demonstrated at f c (C P ) Known as a constant value.
Step 2, constructing a transition probability density function and a corresponding probability distribution function related to the SOC according to the battery capacity probability density function, and providing a transition probability calculation formula of two adjacent SOC intervals:
first, the probability theory theorem is introduced:
let the probability density of the random variable X be f X (x) Wherein α is less than or equal to x is less than or equal to β, and let the function y=g (x), and g (x) is derivable, the probability density of the random variable Y is:
wherein h (y) represents an inverse function of y=g (x); epsilon=min (g (α), g (β)), ω=max (g (α), g (β)).
As can be obtained from the formula (1), the current state of charge S (k) and the battery capacity C during the transition between two adjacent intervals P There is a functional relationship:
transition probability density function with respect to SOC during charging obtainable according to equation (6)
Transition probability distribution function within integral availability interval b
The physical meaning of (2) is: when a certain electric vehicle SOC at time k is S (k), and S (k) belongs to the section b, the electric vehicle can transition to the probability value of the i+1th section after one step Δt.
Assuming that interval b is equally divided into n parts S b (1)，S b (2)，…，S b (n) represents the SOC value of each part respectivelyThe calculation method of (1) is as follows:
when n approaches infinity:
the definition of the integral is as follows:
f c (C P ) Known, thenKnown, and->Is->Double integration of (2), so->Must be constant. Thus, P i，i+1 Can be represented by formula (5).
In the formula (5), m 2 And m 3 The specific gravity of the interval b and the interval c are respectively calculated by the following steps:
in summary, the transition probabilities P of two adjacent intervals i and i+1 i，i+1 The method comprises the following steps:
wherein N, eta ch 、Δt、S max 、S min 、C max 、C min Are all known quantities and average probabilityAt f c (C P ) On the premise of being known as a constant value, the transition probability P i，i+1 Proportional to the actual charging power.
And 3, analyzing the dynamic transfer process of the charging load of the electric automobile, providing a controllable aggregation model capable of smoothly adjusting the power of the clustered electric automobile, and performing simulation verification.
The transition probability is proportional to the charging power, and the maximum transition probability is defined asAssuming that the dispatching department can uniformly control the charging power of the electric automobile on line through the excitation signal u (k) generated by the excitation mechanism, the dispatching department can control the charging power of the electric automobile on lineThe transition probability at the actual charging power is +.>
Fig. 3 shows a schematic diagram of an electric vehicle charging process, which is a process of dynamically transferring a load from a low SOC to a high SOC, and the process may be represented by a state space expression (15):
where x (k, i) and x (k+1, i) represent the amounts of loads in the i-th SOC section at the k time and the k+1 time, respectively. When no charging power is applied to the clustered electric vehicles, the load quantity of each SOC interval does not change, the process is described by a transfer matrix A, and the A is an N-dimensional unit matrix. When charging power is applied to the clustered electric vehicles, the load amount of each SOC interval is forcedly transferred, and the process can be described by a forcedly transferring matrix P:
in the method, in the process of the invention,a specific gravity indicating load transfer is greater than zero, and a load transfer is indicated by a value smaller than zero. Specially, the->The specific gravity of the electric vehicle load that is charged at the next time is represented as the total load in the section N.
In addition to the dynamic transfer of charge, it is also considered that a new electric vehicle is added to charge, this part being denoted by ψ (k).The new load amount in the i-th section at the k time is shown.
Thus, a controllable aggregation model of the cluster electric automobile can be obtained:
where x (k) is an N-dimensional column vector, x (k) = [ x (k, 1), …, x (k, N)] T The method comprises the steps of carrying out a first treatment on the surface of the A is an N-dimensional unit array; u (k) is an excitation signal of control quantity and charging power; c is the power output vector; b is a forced transfer matrix; y (k) is the total output power of the electric automobile of the cluster at the moment k.
Wherein the power output vector C is defined by the maximum charging powerThe N-dimensional row vectors that make up are:
the forced transfer matrix B is:
in order to further understand the invention and verify the accuracy and the effectiveness of the electric automobile polymerization model, a Monte Carlo simulation method is adopted for verification. The simulation step length is 4S, the battery capacity is subjected to uniform random distribution, the maximum and minimum battery capacities are 40 kW.h and 30 kW.h, and each electric automobile is started from the initial charge state S start Charging to S max And after the charging state is exited, the specific simulation parameters are shown in table 1.
Table 1 electric vehicle cluster parameter settings
Simulation verification is performed on the charging power excitation signals u (k) =1 and u (k) =0.4, and fig. 4 shows the aggregation model and the monte carlo simulation output power comparison condition under different excitation signals. The invention can be seen that the power obtained by the built charge load aggregation model and the Monte Carlo simulation method is consistent all the time, and the charge load dynamic change process of the clustered electric automobile can be accurately described. And the amplitude and the phase of the total charging power curve of the clustered electric vehicles can be obviously changed by changing the power excitation signal, so that the adjustment of the load curve can be realized by changing the charging power.
And selecting an actual AGC regulating signal of a certain area, and carrying out simulation verification on the aggregation model design controller by adopting a model predictive control algorithm, wherein a tracking result is shown in figure 5. It can be seen that under the action of the corresponding controller, the clustered electric vehicle can quickly and accurately track the AGC command, thereby illustrating the effectiveness of the controllable aggregation model.

Claims (5)

1. The cluster electric automobile charging load model for the power grid frequency modulation control is characterized by comprising the following steps:
(1) Taking the battery capacity difference into consideration, discretizing the SOC of the electric automobile, and dividing each SOC section into probability sections;
(2) Constructing a transition probability density function and a corresponding probability distribution function related to the SOC according to the battery capacity probability density function, and providing a transition probability calculation formula of two adjacent SOC intervals;
(3) Analyzing the dynamic transfer process of the charging load of the electric automobile, providing a controllable aggregation model capable of smoothly adjusting the power of the clustered electric automobile, and performing simulation verification, wherein in the step (1), probability intervals are divided:
dividing the ith interval into 3 probability intervals, respectively denoted by letters a, b and cThe transition probability in the interval is 0, and the specific gravity in the interval i is m 1 The method comprises the steps of carrying out a first treatment on the surface of the Interval->The transition probability in the interval increases from 0 to 1, and the duty ratio is m 2 The method comprises the steps of carrying out a first treatment on the surface of the Interval->The transition probability in the interval is 1, and the duty ratio is m 3 The method comprises the steps of carrying out a first treatment on the surface of the If interval b is also defined by a probability value +.>Representing the total probability P of transition of the interval i to the interval i+1, which is obtainable by definition of the desired probability i,i+1 ：
Wherein,,the average probability of interval b, meaning from +.>To->Is used for the transition probability.
2. The electric power grid frequency modulation control oriented clustered electric vehicle charging load model of claim 1, wherein the transition probability density function with respect to SOC in step (2)Probability distribution function->
Wherein f c (C P ) Is a battery capacity density distribution function; s (k) represents the state of charge at the kth time; p (P) ch Representing the charging power; η (eta) ch Indicating the charging efficiency; Δt is the time interval;a 0 probability critical SOC value; />A 1 probability critical SOC value; s is S down (i+1) represents the lower limit value of each SOC section of the i+1 th.
3. The electric power grid frequency modulation control oriented clustered electric vehicle charging load model of claim 1, wherein in step (2), the average probability is calculatedThe calculation formula is shown as the following formula (4),
4. the electric power grid frequency modulation control oriented clustered electric vehicle charging load model of claim 1, wherein the transition probability P in step (2) is i,i+1 The method comprises the following steps:
wherein N is the number of the large-interval division layers of the SOC of the electric automobile; s is S max And S is min Respectively the maximum value and the minimum value of the battery SOC; c (C) max And C min Respectively, the maximum and minimum values of battery capacity.
5. The electric network frequency modulation control oriented cluster electric vehicle charging load model according to claim 1, wherein the controllable aggregation model in the step (3) is:
where x (k) is an N-dimensional column vector, x (k) = [ x (k, 1), …, x (k, N)] T The method comprises the steps of carrying out a first treatment on the surface of the Psi (k) is an N-dimensional column vector consisting of newly added electric vehicles; a is an N-dimensional unit array; u (k) is an excitation signal of control quantity and charging power; c is the power output vector; b is a forced transfer matrix; y (k) is the total output power of the electric automobile of the cluster at the moment k;
wherein the power output vector C is defined by the maximum charging powerThe N-dimensional row vectors that make up are:
the forced transfer matrix B is:
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