CN113199946B - Electric automobile energy storage aggregation modeling method based on Markov process - Google Patents

Electric automobile energy storage aggregation modeling method based on Markov process Download PDF

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CN113199946B
CN113199946B CN202011480013.5A CN202011480013A CN113199946B CN 113199946 B CN113199946 B CN 113199946B CN 202011480013 A CN202011480013 A CN 202011480013A CN 113199946 B CN113199946 B CN 113199946B
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electric automobile
load
interval
electric vehicle
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CN113199946A (en
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蔡新雷
董锴
崔艳林
孟子杰
邱丹骅
喻振帆
潘远
黎嘉明
王勇超
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Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L53/00—Methods of charging batteries, specially adapted for electric vehicles; Charging stations or on-board charging equipment therefor; Exchange of energy storage elements in electric vehicles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L58/00—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles
    • B60L58/10—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries
    • B60L58/12—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries responding to state of charge [SoC]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J7/00—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
    • H02J7/0047—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries with monitoring or indicating devices or circuits
    • H02J7/0048—Detection of remaining charge capacity or state of charge [SOC]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/70—Energy storage systems for electromobility, e.g. batteries
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/7072—Electromobility specific charging systems or methods for batteries, ultracapacitors, supercapacitors or double-layer capacitors
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02T90/10—Technologies relating to charging of electric vehicles
    • Y02T90/14—Plug-in electric vehicles

Abstract

The invention discloses an electric automobile energy storage aggregation modeling method based on a Markov process. The technical scheme of the invention comprises the following steps: firstly, providing a charge state dividing method of an electric automobile, discretizing the charge state continuously changed in the charging process of the electric automobile, and converting the charge state into a discrete structure with nested double-layer intervals; next, considering probability distribution of battery capacity of the electric automobile, solving one-step transition probability among cells (intervals obtained by dividing the second layer) based on a Markov theory, and further obtaining expected one-step transition probability among large intervals (intervals obtained by dividing the first layer); and finally, deducing a transition probability matrix and a state space expression of the electric automobile cluster according to the dynamic change process of the electric automobile load in the situation discussion interval, namely an electric automobile aggregation model, and verifying the accuracy of the model by using a Monte Carlo simulation method. The invention can be used for establishing a state space model of discretization of the charge state of the large-scale electric automobile, and converting thousands of electric automobiles into linear state space expressions with fewer dimensions, wherein the dimensions of the expressions are irrelevant to the number of the electric automobiles. Therefore, the invention can realize dimension reduction of the electric automobile cluster control variable, so that the time and space pressure calculated by the control algorithm are greatly relieved.

Description

Electric automobile energy storage aggregation modeling method based on Markov process
Technical Field
The invention relates to the field of power system demand response, in particular to an electric vehicle energy storage aggregation modeling method based on a Markov process.
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. Therefore, how to fully utilize the dual characteristics of the charge source and the no-climbing rate of the electric vehicle to serve the power grid is a problem to be solved urgently. The aggregation model research of the clustered electric vehicles is one of core technologies of the auxiliary service of the electric vehicle participation system, and has important guiding significance for realizing the participation demand response of the electric vehicles.
Disclosure of Invention
The invention aims to establish a control-oriented aggregation electric automobile model and solve the dimension disaster problem caused by large-scale electric automobile participation system adjustment under a small time step. The invention provides an aggregation modeling method based on a Markov process, which not only considers uncertainty of user behavior, but also considers inherent characteristics of a battery. And on the basis of the model, a cluster electric automobile energy storage aggregation model is deduced and established, and finally the accuracy of the model is verified through simulation.
The invention adopts the technical scheme that: an electric automobile energy storage aggregation modeling method based on a Markov process comprises the following steps:
(1) The method for dividing the charge states of the electric automobile is provided, and the charge states continuously changed in the charging process of the electric automobile are discretized and converted into a discrete structure with nested double-layer intervals;
(2) Taking probability distribution of battery capacity of the electric automobile into consideration, solving one-step transition probability among cells (intervals obtained by dividing the second layer) based on Markov theory, and further obtaining expected one-step transition probability among large intervals (intervals obtained by dividing the first layer);
(3) And (3) carrying out situation-based discussion on the dynamic change process of the electric vehicle load in the interval to obtain a transition probability matrix and a state space expression of the electric vehicle cluster, namely an electric vehicle aggregation model.
Specifically, in the step (1), the discrete structure of the double-layer interval nesting is described as follows:
considering the safety of electric automobile charging and the limitation of the upper limit and the lower limit of the charge state of the battery in the service life of the battery, the SOC max And SOC (System on chip) min Respectively representing an upper limit and a lower limit of the state of charge; and then equally dividing the continuous charge states between the upper limit and the lower limit into N large sections, which are the first layer division.
Each large section is divided again into n cells, and the i-th and i+1-th large sections are described as an example. Wherein SOC is down (i)、SOC up (i)、SOC down (i+1)、SOC up (i+1) represents the lower and upper bounds of the ith and ith+1th large sections, respectively; SOC (i, j) represents the lower bound of the jth cell segment in the ith large segment; SOC (i+1, j) represents the lower bound of the jth cell segment in the (i+1) th large segment. This is the second layer division.
If the state of charge is currently between the jth cell, the state of charge may be crossed from SOC (i, j) to SOC over a time step down (i+1)(SOC up (i) The electric car between the cells can be considered to complete the process of transferring to the next adjacent large area.
Specifically, in the step (2), considering probability distribution of battery capacity of the electric vehicle, and solving one-step transition probability between cells based on a markov theory, so as to obtain expected one-step transition probability between large cells, wherein the specific process is as follows:
markov can be described in terms of a distribution function:
Figure BSA0000227823370000021
the state space of the random process { X (T), t.epsilon.T } is I. If any n numbers for time t are given under condition X (t i )＝x i ，x i E I, i=1, 2,.. n ) The conditional distribution function is exactly equal to the value under condition X (t n-1 )＝x n-1 Lower X (t) n ) The process satisfies the markov process. I.e. given a known current state, its future conditional probability distribution is no longer dependent on the past state, but only on the current state. The charging process of the electric automobile just meets the requirement, and the state of charge and time are discrete amounts after conversion, so that a one-step Markov chain of the charging process can be obtained:
P ij (1)＝P{X m+1 ＝s j |X m ＝s i } (2)
the meaning of the above formula is: the state of the random variable X at the moment m is s i After a time step, the state is s at the moment m+1 j Probability values of (a) are provided.
Assuming that the battery capacity of the clustered electric vehicle obeys a certain distribution, and the distribution of the battery capacity and the state of charge are related and independent, the probability distribution function is as follows:
Figure BSA0000227823370000022
wherein: c (C) p Battery capacity of electric automobile, C max And C min Maximum and minimum battery capacity for an electric vehicle cluster, f (C p ) Is a probability density function that is amenable to battery capacity. C (C) a Is calculated by the inherent characteristic of battery charging, and the calculation formula is as follows:
Figure BSA0000227823370000031
wherein: p (P) ch Charging power eta of electric automobile ch The charging efficiency of the electric automobile is achieved, and delta t is a time interval; SOC (k) and SOC (k+1) represent states of charge at time k and time k+1.
In connection with the interval division format described in step (1) and the definition of two adjacent large interval transitions, SOC (k+1) is replaced by SOC here down (i+1), and C max And C min Two specific state of charge threshold values SOC (i) can be obtained by respectively carrying in (4) 0 And SOC (i) 1 ：
Figure BSA0000227823370000032
The associated definitions in the association type (3), (4), (5) and step (1), the probability F that the electric automobile in the jth cell in the ith large zone is transferred to the (i+1) th large zone after one time step j (i, i+1) is:
Figure BSA0000227823370000033
the ith large interval contains n cells in total, so the transition probabilities of two neighboring large intervals i and i+1 can be represented by the expected probabilities:
Figure BSA0000227823370000034
wherein: n is more than or equal to 1 0 ≤n 1 ≤n，n 0 Is SOC (i) 0 Corresponding inter-cell sequence number, n 1 Is SOC (i) 1 Corresponding inter-cell sequence numbers.
Specifically, in the step (3), the dynamic change process of the electric vehicle load in the interval is discussed according to the situation, so as to obtain a state transition matrix and a state space expression of the electric vehicle cluster, namely an electric vehicle aggregation model. The specific process is as follows:
the invention aims to solve the problem of equation dimension disaster under a small time step, and an electric automobile is insufficient to realize cross-interval transfer after one time step. Namely, after one time step, the electric automobile only has two states and is still in the original interval or enters the next adjacent interval. The invention equally divides the double layers of the charge states, so that the probability of one-step transition between any two adjacent large intervals is the same. Therefore, only two cases are divided here, i.e., whether the large section is at the head end or not.
Case one: head end region
In the head-end region (near SOC min The first large section) of the electric vehicle, the load change amount of the electric vehicle is only composed of two parts, the load amount transferred to the next section and the load change amount caused by external factors, and the dynamic change process is as follows:
Figure BSA0000227823370000041
wherein: x (k, 1) and x (k+1, 1) respectively represent the electric vehicle load amount in the first interval at the time k and the time k+1; Δx (k, 1) represents the load amount that can enter the next section at the next time; f (1, 2) represents the transition probabilities of the first and second large sections. The above represents a natural transfer process of the load of the electric vehicle, and v (k) represents a load amount change caused by an external factor at time k (the electric vehicle user starts charging or stops charging at this time); p is p 1 A specific gravity of v (k) which is the load in the first section; v (k, 1) represents the load variation in the first section caused by an external factor at time k. The linear difference equation is obtained by arrangement:
Figure BSA0000227823370000042
wherein a is 11 Is a probability transition matrix element.
And a second case: non-head end region
The electric vehicle load variation amount at the non-head end region (all other large regions except the head end region) is composed of three parts: the load amount transferred from the previous section, the load amount transferred from the next section (the load amount considered to be the load amount that has completed charging and exited when the section is the end section), and the load change amount due to external factors. The dynamic change process is as follows:
Figure BSA0000227823370000043
wherein: x (k, i) and x (k+1, i) respectively represent the load quantity of the electric automobile in the ith interval at the moment k and the moment k+1; Δx (k, i) represents the load amount transferred from the i-th section at time k; Δx (k, i-1) represents the load amount at which the i-1 th section shifts to the i-th section at the k time; f (i-1, i) and F (i, i+1) represent transition probabilities of the intervals i-1 to i and the intervals i to i+1, respectively; p is p i The specific gravity of the load in the ith section in v (k); v (k, i) represents the load change amount of the i-th section caused by the external factor at the time k. The linear difference equation is obtained by arrangement:
Figure BSA0000227823370000044
wherein a is i，i-1 、a ii Are transition probability matrix elements.
The state of charge is equally divided into N large intervals, corresponding to N linear equations, and N-dimensional state space expressions are obtained by arrangement:
Figure BSA0000227823370000051
wherein X (k) and X (k+1) are respectively the electric automobile load amounts of N large sections at the moment k and the moment k+1, and are N-dimensional column vectors; v (k) is the load variation caused by external factors at the moment k, and is an N-dimensional column vector; y (k) is the aggregation power of the k moment aggregation model; c is an output matrix, N-dimensional unit row vectors; the A matrix is a transition probability matrix of NxN order:
Figure BSA0000227823370000052
the technical scheme provided by the invention has the beneficial effects that:
the electric automobile aggregation model facing control is designed by introducing a Markov theory to discretize the charge state of energy storage of the electric automobile, converting the charging process under each time step into a Markov chain and simultaneously considering the randomness of the charging behavior of the electric automobile user and the heterogeneity of the battery capacity. In addition, the invention carries out double-layer division on the state of charge and introduces expected transition probability, so that the number of large intervals determines the dimension of the state space expression, the number of small intervals depends on the requirement of time step and precision, decoupling of the dimension and precision of the expression is realized, and the problem of dimension disaster of an equation set for obtaining high precision in a small time step is avoided. In conclusion, thousands of electric vehicles can be converted into the low-dimensional linear state space expression, so that the control difficulty is greatly reduced, and the time and space pressure of solving a control algorithm are relieved.
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 a state of charge double-layer partition structure;
FIG. 3 is a schematic diagram of the load change at the head end region;
FIG. 4 is a schematic diagram of the load change in the non-head end region;
FIG. 5 is a graph comparing an aggregate model to a Monte Carlo simulated power simulation curve.
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 an electric automobile energy storage aggregation modeling method based on a Markov process, and fig. 1 is a flow chart of the invention, and the implementation flow comprises the following detailed steps.
Step 1 provides a method for dividing the state of charge of an electric automobile, which discretizes the state of charge continuously changed in the charging process of the electric automobile and converts the state of charge into a discrete structure with nested double-layer intervals:
as shown in fig. 2, the SOC is limited by the upper and lower limits of the battery state of charge in consideration of the safety of charging the electric vehicle and the battery charging life max And SOC (System on chip) min Respectively representing an upper limit and a lower limit of the state of charge; and then equally dividing the continuous charge states between the upper limit and the lower limit into N large sections, which are the first layer division.
Each large area is divided again into n cells, and the i-th and i+1-th large areas are described as an example according to fig. 2. Wherein SOC is down (i)、SOC up (i)、SOC down (i+1)、SOC up (i+1) represents the lower and upper bounds of the ith and ith+1th large sections, respectively; SOC (i, j) represents the lower bound of the jth cell segment in the ith large segment; SOC (i+1, j) represents the lower bound of the jth cell segment in the (i+1) th large segment. This is the second layer division.
If the state of charge is currently between the jth cell, the state of charge may be crossed from SOC (i, j) to SOC over a time step down (i+1)(SOC up (i) The electric car between the cells can be considered to complete the process of transferring to the next adjacent large area.
Step 2, considering probability distribution of battery capacity of the electric automobile, solving one-step transition probability among cells based on a Markov theory, and further obtaining expected one-step transition probability among large areas:
markov can be described in terms of a distribution function:
Figure BSA0000227823370000061
the state space of the random process { X (T), t.epsilon.T } is I. If any n numbers for time t are given under condition X (t i )＝x i ，x i E I, i=1, 2,.. n ) The conditional distribution function is exactly equal to the value under condition X (t n-1 )＝x n-1 Lower X (t) n ) The process satisfies the markov process. I.e. given a known current state, its future conditional probability distribution is no longer dependent on the past state, but only on the current state. The charging process of the electric automobile just meets the requirement, and the state of charge and time are discrete amounts after conversion, so that a one-step Markov chain of the charging process can be obtained:
P ij (1)＝P{X m+1 ＝s j |X m ＝s i } (2)
the meaning of the above formula is: the state of the random variable X at the moment m is s i After a time step, the state is s at the moment m+1 j Probability values of (a) are provided.
Assuming that the battery capacity of the clustered electric vehicle obeys a certain distribution, and the distribution of the battery capacity and the state of charge are related and independent, the probability distribution function is as follows:
Figure BSA0000227823370000062
wherein: c (C) p Battery capacity of electric automobile, C max And C min Maximum and minimum battery capacity for an electric vehicle cluster, f (C p ) Is a probability density function that is amenable to battery capacity. C (C) a Is calculated by the inherent characteristic of battery charging, and the calculation formula is as follows:
Figure BSA0000227823370000071
wherein: p (P) ch Charging power eta of electric automobile ch The charging efficiency of the electric automobile is achieved, and delta t is a time interval; SOC (k) and SOC (k+1) represent states of charge at time k and time k+1.
In connection with the interval division format described in step (1) and the definition of two adjacent large interval transitions, SOC (k+1) is replaced by SOC here down (i+1), and C max And C min Two specific state of charge threshold values SOC (i) can be obtained by respectively carrying in (4) 0 And SOC (i) 1 ：
Figure BSA0000227823370000072
The associated definitions in the association type (3), (4), (5) and step (1), the probability F that the electric automobile in the jth cell in the ith large area is transferred to the (i+1) th large area after one time step j (i, i+1) is:
Figure BSA0000227823370000073
the ith large interval contains n cells in total, so the transition probabilities of two neighboring large intervals i and i+1 can be represented by the expected probabilities:
Figure BSA0000227823370000074
wherein: n is more than or equal to 1 0 ≤n 1 ≤n，n 0 Is SOC (i) 0 Corresponding inter-cell sequence number, n 1 Is SOC (i) 1 Corresponding inter-cell sequence numbers.
Step 3, discussing the dynamic change process of the electric vehicle load in the interval according to the conditions to obtain a transition probability matrix and a state space expression of the electric vehicle cluster, namely an electric vehicle aggregation model:
the invention aims to solve the problem of equation dimension disaster under a small time step, and an electric automobile is insufficient to realize cross-interval transfer after one time step. Namely, after one time step, the electric automobile only has two states and is still in the original interval or enters the next adjacent interval. The invention equally divides the double layers of the charge states, so that the probability of one-step transition between any two adjacent large intervals is the same. Therefore, only two cases are divided here, i.e., whether the large section is at the head end or not.
Case one: head end region
As shown in fig. 3, in the head-end region (near SOC min The first large section) of the electric vehicle, the load change amount of the electric vehicle is only composed of two parts, the load amount transferred to the next section and the load change amount caused by external factors, and the dynamic change process is as follows:
Figure BSA0000227823370000081
wherein: x (k, 1) and x (k+1, 1) represent electric vehicle load amounts in the 1 st section at the k time and the k+1 time, respectively; Δx (k, 1) represents the load amount that can enter the next section at the next time; f (1, 2) represents transition probabilities between the 1 st and 2 nd regions. The above represents a natural transfer process of the load of the electric vehicle, and v (k) represents a load amount change caused by an external factor at time k (the electric vehicle user starts charging or stops charging at this time); p is p 1 A specific gravity of v (k) which is the load in the first section; v (k, 1) represents the load variation in the first section caused by an external factor at time k. The linear difference equation is obtained by arrangement:
Figure BSA0000227823370000082
wherein a is 11 Is a probability transition matrix element.
And a second case: non-head end region
As shown in fig. 4, the electric vehicle load variation amount at the non-head end region (all other large regions except the head end region) is composed of three parts: the load amount transferred from the previous section, the load amount transferred from the next section (the load amount considered to be the load amount that has completed charging and exited when the section is the end section), and the load change amount due to external factors. The dynamic change process is as follows:
Figure BSA0000227823370000083
wherein: x (k, i) and x (k+1, i) respectively represent the load quantity of the electric automobile in the ith interval at the moment k and the moment k+1; Δx (k, i) represents the load amount transferred from the i-th section at time k; Δx (k, i-1) represents the load amount at which the i-1 th section shifts to the i-th section at the k time; f (i-1, i) and F (i, i+1) represent transition probabilities of the intervals i-1 to i and the intervals i to i+1, respectively; p is p i The specific gravity of the load in the ith section in v (k); v (k, i) represents the load change amount of the i-th section caused by the external factor at the time k. The linear difference equation is obtained by arrangement:
Figure BSA0000227823370000084
wherein a is i，i-1 、a ii Are transition probability matrix elements.
The state of charge is equally divided into N large intervals, corresponding to N linear differential equations, and N-dimensional state space expressions are obtained by arrangement:
Figure BSA0000227823370000091
wherein X (k) and X (k+1) are respectively the electric automobile load amounts of N large sections at the moment k and the moment k+1, and are N-dimensional column vectors; v (k) is the load variation caused by external factors at the moment k, and is an N-dimensional column vector; y (k) is the aggregation power of the k moment aggregation model; c is an output matrix, N-dimensional unit row vectors; the A matrix is a transition probability matrix of NxN order:
Figure BSA0000227823370000092
in order to further understand the invention and verify the accuracy of the electric automobile aggregation model, a Monte Carlo simulation method is adopted for verification. The actual running condition of a cluster of 1000 electric vehicles is simulated by adopting a Monte Carlo method, the simulation step length is 4s, the charging power and the charging efficiency of the 1000 electric vehicles are assumed to be the same, and the battery capacity obeys the sameUniformly and randomly distributed, the maximum and minimum battery capacities are 40 kW.h and 30 kW.h, and each electric automobile is charged from the initial state of charge SOC start Charge to SOC max And after the charging state is exited, the specific simulation parameters are shown in table 1.
Table 1 electric vehicle cluster parameter settings
Figure BSA0000227823370000093
As can be seen from the simulation result of FIG. 5, after the electric automobile cluster is converted into a 28-dimensional state space expression, the aggregate power curve obtained by the electric automobile aggregate model is still highly fitted with the aggregate power curve obtained by the Monte Carlo simulation method, so that the model has higher sensitivity to the electric automobiles newly participating in charging, and the accuracy of the aggregate model is verified.

Claims (7)

1. An electric automobile energy storage aggregation modeling method based on a Markov process is characterized by comprising the following steps:
(1) The method for dividing the charge state of the electric automobile is provided, the charge state continuously changed in the charging process of the electric automobile is discretized and is converted into a discrete structure with nested double-layer intervals, a large interval in the double-layer intervals is a single interval after the charge state of the battery is equally divided, and a small interval is a single interval after the large interval is equally divided;
(2) Considering probability distribution of battery capacity of the electric automobile, and solving one-step transition probability among cells based on a Markov theory, so as to obtain expected one-step transition probability among large areas;
(3) And (3) carrying out situation-based discussion on the dynamic change process of the electric vehicle load in the interval to obtain a transition probability matrix and a state space expression of the electric vehicle cluster, namely an electric vehicle aggregation model.
2. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein the discrete structure of nesting the double-layer intervals in the step (1) is as follows:
first layer state of charge partitioning:
considering the safety of electric automobile charging and the limitation of the upper limit and the lower limit of the charge state of the battery in the service life of the battery, the SOC max And SOC (System on chip) min Respectively representing an upper limit and a lower limit of the state of charge; then equally dividing the continuous charge states between the upper limit and the lower limit into N large sections;
second-layer charge state division:
dividing each large section again into n cells equally, and taking the ith and the (i+1) th large sections as examples for explanation; wherein SOC is down (i)、SOC up (i)、SOC down (i+1)、SOC up (i+1) represents the lower and upper bounds of the ith and ith+1th large sections, respectively; SOC (i, j) represents the lower bound of the jth cell segment in the ith large segment; SOC (i+1, j) represents the lower bound of the jth cell segment in the (i+1) th large segment;
if the state of charge is currently between the jth cell, the state of charge may be crossed from SOC (i, j) to SOC over a time step down (i+1) or SOC up (i) It can be considered that the electric vehicle between the cells completes the process of transferring to the next adjacent large area.
3. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein the probability distribution function of the battery capacity of the electric vehicle in the step (2) is:
Figure FSB0000201224740000011
wherein: c (C) p The battery capacity of the electric automobile; c (C) max And C min The maximum value and the minimum value of the battery capacity of the electric automobile cluster; f (C) p ) Probability density function for battery capacity compliance; c (C) a Is calculated from the inherent characteristics of battery charging:
Figure FSB0000201224740000021
wherein: p (P) ch Charging power for the electric automobile; η (eta) ch The electric automobile is charged with efficiency; Δt is the time interval; SOC (k) and SOC (k+1) represent states of charge at time k and time k+1.
4. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein the step (2) is characterized by a one-step transition probability between cells:
Figure FSB0000201224740000022
wherein: f (F) j (i, i+1) represents a probability that an electric vehicle in a jth cell in an ith large zone is transferred to the (i+1) th large zone after a time step; SOC (i) 0 And SOC (i) 1 Two specific state of charge thresholds:
Figure FSB0000201224740000023
wherein SOC (i) 0 Is 0 probability critical value, when SOC down (i)≤SOC(i，j)＜SOC(i) 0 When the one-step transition probability is 0; SOC (i) 1 Is 1 probability critical value, when SOC (i) 1 ＜SOC(i，j)≤SOC up (i) When the one-step transition probability is 1.
5. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein the expected one-step transition probability between large intervals in the step (2) is:
Figure FSB0000201224740000024
wherein: n is more than or equal to 1 0 ≤n 1 ≤n，n 0 Is SOC (i) 0 Corresponding inter-cell sequence number, n 1 Is SOC (i) 1 Corresponding inter-cell sequence numbers; since the i-th large segment includes n cells, the transition probabilities between the two adjacent large segments i and i+1 can be expressed by the above equation (5).
6. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein the dynamic change process of the load of the electric vehicle in the interval in the step (3) is as follows:
case one: head end region
The load change quantity of the electric automobile in the head end interval is only composed of two parts, the load quantity transferred to the next interval and the load change quantity caused by external factors, and the head end interval is close to the SOC min The dynamic change process of the first large interval of the (a) is as follows:
Figure FSB0000201224740000025
wherein: x (k, 1) and x (k+1, 1) respectively represent the electric vehicle load amount in the first interval at the time k and the time k+1; Δx (k, 1) represents the load amount that can enter the next section at the next time; f (1, 2) represents transition probabilities between the 1 st and 2 nd large areas; the above represents a natural transfer process of the load of the electric vehicle, and v (k) represents a load amount change caused by an external factor at the moment k, and the electric vehicle user starts charging or stops charging at the moment; p is p 1 A specific gravity of v (k) which is the load in the 1 st section; v (k, 1) represents the load variation in the 1 st section caused by an external factor at the time of k; the linear difference equation is obtained by arrangement:
Figure FSB0000201224740000033
wherein a is 11 Is a probability transition matrix element;
and a second case: non-head end region
The load variation of the electric automobile in the non-head end interval consists of three parts: the load quantity transferred from the previous section, the load quantity transferred from the next section and the load change quantity caused by external factors; the non-head end interval is all other large intervals except the head end interval; when the interval is the end interval, the interval is considered as the load amount for completing charging and exiting; the dynamic change process is as follows:
Figure FSB0000201224740000031
wherein: x (k, i) and x (k+1, i) respectively represent the load quantity of the electric automobile in the ith interval at the moment k and the moment k+1; Δx (k, i) represents the load amount transferred from the i-th section at time k; Δx (k, i-1) represents the load amount at which the i-1 th section shifts to the i-th section at the k time; f (i-1, i) and F (i, i+1) represent transition probabilities of the intervals i-1 to i and the intervals i to i+1, respectively; p is p i The specific gravity of the load in the ith section in v (k); v (k, i) represents the load variation in the ith section caused by an external factor at time k; the linear difference equation is obtained by arrangement:
Figure FSB0000201224740000034
wherein a is i，i-1 、a ii Are transition probability matrix elements.
7. The method for modeling energy storage aggregation of an electric vehicle based on a markov process according to claim 1, wherein in the step (3), the electric vehicle aggregation model is as follows:
the state of charge of the electric automobile is equally divided into N large sections, N linear differential equations are corresponding, and an N-dimensional linear state space expression is obtained by arrangement:
Figure FSB0000201224740000032
wherein X (k) and X (k+1) are respectively the electric automobile load amounts of N large sections at the moment k and the moment k+1, and are N-dimensional column vectors; v (k) is the load variation caused by external factors at the moment k, and is an N-dimensional column vector; y (k) is the aggregation power of the k moment aggregation model; c is an output matrix which is an N-dimensional unit row vector; the A matrix is a transition probability matrix of NxN order:
Figure FSB0000201224740000041
and verifying the accuracy of the model by adopting a Monte Carlo simulation method.
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