CN107590580B - Method for evaluating uncertainty of charging load of electric vehicle in residential area under time-of-use electricity price - Google Patents
Method for evaluating uncertainty of charging load of electric vehicle in residential area under time-of-use electricity price Download PDFInfo
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Abstract
The invention discloses an assessment method for uncertainty of charging load of an electric vehicle in a residential area under time-of-use electricity price, which is characterized in that a dynamic probability model of the charging load of the electric vehicle for price elasticity analysis is constructed based on travel statistical characteristics of the electric vehicle, and uncertainty of response relation between a vehicle owner and the time-of-use electricity price is represented by probability characteristics; and measuring the dynamic probability fluctuation of the load through the information entropy and the out-of-limit probability, and further evaluating the uncertainty of the charging load fluctuation degree of the electric automobile in the residential area and the overload risk of the distribution transformer in the residential area.
Description
Technical Field
The invention relates to an evaluation method for uncertainty of charging load of an electric vehicle in a residential area under time-sharing electricity price, and belongs to the field of response of a demand side of the electric vehicle and the field of power system dispatching.
Background
The development of electric automobiles is an important means for reducing the emission of greenhouse gases and reducing the dependence on fossil energy. Therefore, electric vehicles will be a development trend in the automotive field in the future. With the increasing of the access quantity of electric automobiles in a residential area power distribution system, the peak-valley difference of a power grid is increased due to the disordered charging of the electric automobiles, and a distribution transformer is in adverse conditions such as overload operation for a long time. Based on the above, the time-of-use electricity price can guide the electric automobile to be charged in order, so that the hazards of peak-valley difference of a power grid, long-time overload operation of a transformer and the like are effectively reduced, but the charging load of the electric automobile guided by the time-of-use electricity price has certain fluctuation uncertainty, and the responsibility between an automobile owner and the time-of-use electricity price also has certain uncertainty, so that the uncertainty can aggravate the randomness of the fluctuation of the load of a residential area, the overload risk of a distribution transformer of the residential area is increased, and certain hazards are brought to the safe and stable operation of a distribution system.
The method for evaluating the uncertainty of the charging load of the electric automobile in the residential area under the time-of-use electricity price can comprehensively consider the uncertainty of the fluctuation of the charging load of the electric automobile in the residential area, the uncertainty of the response relation between an automobile owner and the time-of-use electricity price and the risk of overload operation of a distribution transformer, construct an electric automobile charging load dynamic probability model for price elasticity analysis based on the trip statistical characteristics of the electric automobile, and represent the uncertainty of the response relation between the automobile owner and the time-of-use electricity price by using the probability characteristics; the load dynamic probability fluctuation is measured through the information entropy and the out-of-limit probability, so that the uncertainty of the charging load fluctuation degree of the electric automobile in a residential area and the overload risk of a distribution transformer in the residential area are evaluated, and an evaluation method considering the uncertainty in a time-of-use electricity price scheme for charging the electric automobile is comprehensively formulated for electric automobile agents.
At present, the influence of uncertainty of charging load fluctuation of an electric vehicle and uncertainty of user response time-of-use electricity price on a scheduling strategy are not comprehensively considered in consideration of uncertainty of charging the electric vehicle when the electric vehicle is accessed into a residential area, and the influence of a pricing strategy on a residential area power distribution system is evaluated without measuring the uncertainty of the system under the guidance of the electricity price.
Disclosure of Invention
The invention aims to provide an assessment method for uncertainty of charging load of an electric vehicle in a residential area under time-of-use electricity price, which is characterized in that a dynamic probability model of the charging load of the electric vehicle for price elasticity analysis is constructed based on travel statistical characteristics of the electric vehicle, and uncertainty of response relation between a vehicle owner and the time-of-use electricity price is represented by probability characteristics; and measuring the dynamic probability fluctuation of the load through the information entropy and the out-of-limit probability, and further evaluating the uncertainty of the charging load fluctuation degree of the electric automobile in the residential area and the overload risk of the distribution transformer in the residential area. Comprises the following steps:
1. a method for evaluating uncertainty of charging load of an electric vehicle in a residential area under time-sharing electricity price mainly comprises the following steps:
A. inputting charging time-of-use electricity price lambda of electric automobile in residential areai(i is 1,2 … 24), start trip time T of electric vehicleSAnd the last trip ending time TEAnd statistical distribution of daily driving mileage l.
B. By electric automobileThe charging time T of the electric automobile is obtained by solving the equation (1)C：
Wherein P is the charging power of the electric automobile, kW, U is the power consumption of hundreds kilometers, kW.h/100 km, η is the charging efficiency,
for rounding up, T is more than or equal to 1C≤24。
C. Through a latin hypercube sampling technology, setting a sampling scale as V, sampling the electric vehicle initial trip time, charging time and final trip end time to obtain a sampling matrix E ═ T [ T ]S,TE,TC]TWherein T isS、TEAnd TCThe starting travel time vector, the last travel end time vector and the charging duration vector are respectively 1 × V-dimensional, and each row of E forms a charging scene of the electric automobile.
D. Calculating the corresponding chargeable time period number d of the single electric automobile in the charging scene vvComprises the following steps:
wherein: t isS,v、TE,v、TC,vAre respectively TS、TE、TCThe v-th column of elements in the vector represents the starting trip time, the last trip end time and the charging time of the electric vehicle in the charging scene v.
E. In charging scenario v, from TS,v、TE,v、TC,vAnd establishing an electric automobile charging load model based on price elasticity analysis.
F. Solving by a semi-invariant method to obtain each order central moment of residential area load power when the electric automobile is considered, solving a probability distribution function of the residential area electric automobile charging load by using a Gram-Charlier infinite series expansion formula, and solving the entropy measure of the residential area electric automobile charging load and the out-of-limit probability of the distribution transformer at each moment, so as to obtain an evaluation model of the uncertainty of the residential area electric automobile charging load fluctuation degree and the distribution transformer overload risk.
Further, in the step E, an electric vehicle charging load model based on price elasticity analysis is established, and the initial travel time T of the electric vehicle in the residential area under the charging scene v is determinedS,vAnd the last trip ending time TE,vCharging duration TC,vThe specific steps of establishing the electric automobile charging load model by the price elasticity coefficient are as follows:
e1, ending time T of last trip of electric automobile under charging scene vE,vThe corresponding initial charging time T of the single electric automobile under the charging scene v can be solvedQ,v：
TQ,v∈(TE,v,TE,v+dv) (3)
Wherein: dvThe solution is obtained by the formula (2).
E2, setting the initial charging time of the single electric automobile to be T under the charging scene vQ,vThe charging scheme is as follows:
wherein: n is a possible initial charging time T in a charging scenario vQ,vThe number of (2);
(N is more than or equal to 1 and less than or equal to N) is the charging power of the electric automobile at the moment j under the charging scene v, and the values are as follows:
e3, first-order central moment (expected) C of charging power corresponding to j time of single electric vehicle in charging scene vvj,1Comprises the following steps:
k (k is more than or equal to 2) order central moment Cvj,k：
Wherein: p is a radical ofvjThe probability that the initial charging time of a single electric vehicle is j time under a charging scene v represents the response relation between the vehicle owner and the charging electricity price of the electric vehicle, and the vehicle owner has lower responsibility in a time period with higher charging cost and higher responsibility in a time period with lower charging cost;
E4、pvjthe uncertainty of the time-of-use electricity price of the electric vehicle owner response is reflected, and the solving formula is as follows:
wherein: is the price elastic coefficient; lambda [ alpha ]rAnd the charging time-of-use electricity price is corresponding to the electric automobile in the residential area at r moment, yuan/kW.h.
Furthermore, in the step F, the entropy measure of the charging load of the electric vehicle in the residential area and the out-of-limit probability of the distribution transformer at each moment are solved, so that an evaluation model of uncertainty of the charging load fluctuation degree of the electric vehicle in the residential area and an evaluation model of overload risk of the distribution transformer in the residential area can be obtained. The method comprises the following specific steps:
f1, setting the reserved quantity of the electric automobiles in the residential area to be M, setting different charging behaviors of the electric automobiles to be independent, and obtaining k-order central moment L of charging power corresponding to a single electric automobile at the moment j by the central limit theoremk,jComprises the following steps:
wherein: cvj,kThe solution is obtained by equation (7).
F2, generally speaking, the total residential area load at each moment can be considered to include the residential area normal load and the electric vehicle charging load, the residential area normal load is set to follow the normal distribution with the expected value of μ, the standard deviation is 0.1 μ, and the third-order and multi-order half-invariants of the residential area normal load are negligible. Therefore, the first and second order semi-invariants of the conventional load of the residential area at time j are:
wherein:
(j is more than or equal to 0 and less than or equal to 24) are respectively the expected value and the variance of the conventional load of the residential area at the time j.
F3, half-invariant D of k (k is 1,2,3 …) order of charging power of single electric vehicle at time j in charging scene vk,jComprises the following steps:
wherein: l isk,jAnd solving a k-order central moment corresponding to the charging power of the electric automobile at the moment j by using an equation (9).
F4, property according to semi-invariant: the k-order semi-invariant of mutually independent random variables satisfies homogeneity and additivity. Therefore, the k-order semi-invariant B of the total load power of the residential area at the time jk,jComprises the following steps:
wherein: m is the holding capacity of electric vehicles in the residential area, Dk,jThe solution is obtained by equation (11).
F5, solving to obtain central moments of the total load power of the residential area at each moment according to the semi-invariants of each order of the total load power at each moment in the residential area, and solving to obtain a probability distribution function F (x) of the total load power of the residential area at each moment and a probability density function F (x) of the charging load of the electric automobile through Gram-Charlier infinite series expansion.
F6, when the overload degree of the distribution transformer in the residential area reaches 60%, the short-time overload allowable time of the transformer is 0.75h, therefore, the evaluation model X of the overload risk of the distribution transformer in the residential area is as follows:
X≤0.75 (14)
wherein: y is the limit value of overload load born by the distribution transformer in the residential area, kW; fj(Y) is a distribution function value of the load power in the residential area at the moment j at the position where the transformer is overloaded by 60%; fj(Y) is obtained by using a semi-invariant and Gram-Charlie infinite series expansion.
F7, F from time jj(x) Information entropy H of charging load of electric vehicle at moment j can be obtained through solvingj(ii) a Information entropy HjThe calculation formula of (2) is as follows:
Hj＝-∫xfj(x)logfj(x)dx (15)
wherein: f. ofj(x) And x is the charging load of the electric automobile in different time periods, kW.
F8, the entropy measure evaluation model of the charging load fluctuation uncertainty of the electric automobile in the residential area is as follows:
wherein: hAnd the standard deviation of the measurement of the charging load entropy when the electric automobile in the residential area is charged disorderly.
Compared with the prior art, the invention has the beneficial effects that:
the method and the device reflect the response relation between the owner of the electric automobile and the charging electricity price by constructing the charging load probability model of the electric automobile based on price elasticity analysis, and the owner has lower responsiveness in a time period with higher charging cost and higher responsiveness in a time period with lower charging cost.
Measuring the dynamic probability fluctuation of the load through the information entropy and the out-of-limit probability, and further evaluating the uncertainty of the charging load fluctuation degree of the electric automobile in the residential area and the overload operation risk of the distribution transformer in the residential area. And the method can also provide a basis for comprehensively evaluating the influence of the charging load uncertainty of the electric automobile on the income of electric automobile dealers and the overload operation risk of distribution transformers in residential areas.
Drawings
FIG. 1 is a table showing a conventional electrical load in a residential area according to an embodiment.
FIG. 2 is a table showing the uncertainty index of the conventional electric vehicle using the random charging and the method of the present invention.
FIG. 3 is a comparison chart of the probability of the load power range of the conventional electric vehicle using the disordered charging method and the load power range of the method of the invention. Wherein, (a) is the situation of disordered charging, and (b) is the situation of charging by adopting the method of the invention.
The specific implementation mode is as follows:
the invention is further described below by means of specific embodiments. The following embodiments are merely examples, and the selection of the parameters is set based on the actual conditions of the existing small residential areas, and the present invention is still applicable to large residential areas or other charging places.
Examples
A. The holding capacity of electric vehicles in residential areas adopted by the invention is 500, 24 hours a day is taken as a time scale, and the starting trip time of the electric vehicles obeys N (8.92, 3.242)2) Is normally distributed and obeys N (17.47, 3.412) at the end time of the last trip2) The daily mileage l in km follows a lognormal distribution, that is: lnl-N (3.46, 1.142)2) The conventional electricity load of the residential area is shown in fig. 1, the hundred-kilometer electricity consumption U of the electric automobile in the residential area is 15.84kWh/100km, the estimated charging efficiency value η of the electric automobile in the residential area is 0.87, the electric automobile is charged by adopting constant power, and the charging power P is 7.3 kW.
The civil electricity price in the residential area is 0.617 yuan/kW.h.
B. Solving the daily driving mileage l of the electric automobile by the formula (1) to obtain the electric automobileCharging time T of automobileC：
Wherein P is the charging power of the electric automobile, kW, U is the power consumption of hundreds kilometers, kW.h/100 km, η is the charging efficiency,
for rounding up, T is more than or equal to 1C≤24。
C. Adopting Latin hypercube sampling for the initial trip time, the final trip ending time and the charging time of the electric automobile, wherein the sampling scale V is 2000, and the charging scene matrix E of the electric automobile is [ T ═ TS,TE,TC]TWherein T isS、TEAnd TCThe starting travel time vector, the last travel end time vector and the charging duration vector are respectively 1 × V-dimensional, and each row of E forms a charging scene of the electric automobile.
D. Calculating the corresponding chargeable time period number d of the single electric automobile in the charging scene vvComprises the following steps:
wherein: t isS,v、TE,v、TC,vAre respectively TS、TE、TCThe v-th column of elements in the vector represents the starting trip time, the last trip end time and the charging time of the electric vehicle in the charging scene v.
E. In charging scenario v, from TS,v、TE,v、TC,vEstablishing an electric automobile charging load model based on price elasticity analysis:
e1, ending time T of last trip of electric automobile under charging scene vE,vThe corresponding initial charging time interval T of the single electric automobile under the charging scene v can be solvedQ,v：
TQ,v∈(TE,v,TE,v+dv) (3)
Wherein: dvThe solution is obtained by the formula (2).
E2, solving the problem that the initial charging time of a single electric automobile under the charging scene v is TQ,vCharging scheme of time:
wherein: n is a possible initial charging period T in a charging scenario vQ,vThe number of (2);
(N is more than or equal to 1 and less than or equal to N) is the charging power of j under the charging scene v, and the values are as follows:
e3, first-order central moment (expected) C of charging power corresponding to j time of single electric vehicle in charging scene vvj,1Comprises the following steps:
k (k is more than or equal to 2) order central moment Cvj,k：
E4, solving for pvj：
Wherein: the value is-1.25 for the price elasticity coefficient; lambda [ alpha ]rThe charging time-of-use electricity price of the electric automobile in the residential area at r moment is Yuan/kW.h.
F. Solving by a semi-invariant method to obtain central moments of each order of residential area loads when the electric automobiles are considered, solving a probability distribution function of the residential area electric automobile charging loads by utilizing a Gram-Charlier infinite series expansion equation, solving to obtain the entropy measure of the residential area electric automobile charging loads and the out-of-limit probability of the distribution transformer at each moment, and further obtaining an evaluation model of the uncertainty of the charging load fluctuation degree of the residential area electric automobiles and an evaluation model of the overload risk of the distribution transformer in the residential area:
f1, setting the reserved quantity of the electric automobiles in the residential area to be M, setting different charging behaviors of the electric automobiles to be independent, and obtaining k-order central moment L of charging power corresponding to a single electric automobile at the moment j by the central limit theoremk,jComprises the following steps:
wherein: cvj,kThe solution is obtained by equation (7).
The first-order and second-order semiinvariant of the conventional load of the residential area at the moment F2 and j (j is more than 0 and less than or equal to 24) are as follows:
wherein:
(j is more than or equal to 0 and less than or equal to 24) are respectively the expected value and the variance of the conventional load of the residential area at the time j.
F3, calculating k (k is 1,2,3 …) order semi-invariant D of charging power of single electric vehicle at j time in charging scene vk,j：
Wherein: l isk,jAnd solving a k-order central moment corresponding to the charging power of the electric automobile at the moment j by using an equation (9).
F4, k-order semi-invariant B of total load power of residential area at j momentk,jComprises the following steps:
wherein: m is the holding capacity of electric vehicles in the residential area, Dk,jThe solution is obtained by equation (11).
F5, solving the central moment of each order of the total load power of the residential area at each moment by using the semi-invariant of each order of the total load power at each moment in the residential area, and solving by using Gram-Charlier infinite series expansion to obtain a probability distribution function F (x) of the total load power of the residential area at each moment and a probability density function F (x) of the charging load of the electric automobile.
F6, when the overload degree of the distribution transformer in the residential area reaches 60%, the short-time overload allowable time of the transformer is 0.75h, therefore, the overload risk X of the distribution transformer in the residential area and the evaluation model thereof can be solved:
X≤0.75 (14)
wherein: the capacity of a distribution transformer in a residential area is 630kVA, and Y is the limit value of overload load borne by the distribution transformer in the residential area, kW; fj(Y) is a distribution function value of the load power in the residential area at the moment j at the position where the transformer is overloaded by 60%; fj(Y) is obtained by using a semi-invariant and Gram-Charlie infinite series expansion.
F7, F at time j due to charging load of electric vehiclej(x) Information entropy H of charging load of electric vehicle at moment j can be obtained through solvingj；
Information entropy HjThe calculation formula of (2) is as follows:
Hj＝-∫xfj(x)logfj(x)dx (15)
wherein: f. ofj(x) And x is the charging load of the electric automobile at different moments, kW.
F8, calculating an entropy measure evaluation model of charging load fluctuation uncertainty of the electric automobile in the residential area:
wherein: hAnd the standard deviation of the measurement of the charging load entropy when the electric automobile in the residential area is charged disorderly.
The effects of the embodiment are shown in fig. 2 and 3.
The conventional load of the residential area is subjected to normal distribution, so that the fluctuation range of the conventional load of the residential area is +/-3, wherein the standard deviation of the load fluctuation of the residential area is generally uncontrollable. It can be observed from fig. 1 that: the fluctuation range W of the resident regular load in the peak period is: 306.48kW, fluctuation range W of residential area load in peak period when electric automobile is charged disorderly1435kW, when the pricing strategy considering the uncertainty evaluation method of the patent guides the charging of the electric automobile, the load fluctuation range W of the cell in the peak time period2365kW, therefore, under the guidance of a pricing strategy of the uncertainty evaluation method, the reduced load fluctuation rate of the electric vehicle during relatively disordered charging is
The data is brought into mu of 45.53%, the load fluctuation is reduced by about half compared with the disordered charging, and the uncertainty of the load fluctuation is obviously reduced.
As can be seen from fig. 2, in contrast to the disordered charging of the electric vehicle:
(1) when the pricing strategy of the uncertainty evaluation method is considered to guide the charging of the electric automobile, the entropy measure of the charging load of the electric automobile is obviously reduced, and the uncertainty of the fluctuation degree of the cell load can be mastered by electric automobile dealers in residential areas, so that the electric automobile dealers in residential areas can purchase electricity to power grid companies in demand, serious surplus and shortage of the electric quantity purchased by the electric automobile dealers to the power grid companies can be avoided, and the electricity purchasing cost of the electric automobile dealers in residential areas can be reduced.
(2) When the pricing strategy of the uncertainty evaluation method is considered to guide the charging of the electric automobile, the overload risk of the distribution transformer in the residential area is obviously reduced, and the expected overload running time of the distribution transformer in the residential area is within the safety limit value, so that the service life of the distribution transformer in the residential area is prolonged, and the stability and the reliability of a power distribution system in the residential area are improved.
Claims (3)
1. An assessment method for uncertainty of charging load of an electric vehicle in a residential area under time-of-use electricity price is characterized in that a dynamic probability model of the charging load of the electric vehicle for price elasticity analysis is constructed based on travel statistical characteristics of the electric vehicle, and uncertainty of response relation between a vehicle owner and the time-of-use electricity price is represented by probability characteristics; the method measures the fluctuation of the load dynamic probability through the information entropy and the out-of-limit probability, further evaluates the uncertainty of the charging load fluctuation degree of the electric automobile in a residential area and the overload risk of a distribution transformer in the residential area, and comprises the following main steps of:
A. inputting charging time-of-use electricity price lambda of electric automobile in residential areai1,2 … 24; starting trip time T of electric automobileSAnd the last trip ending time TEStatistical distribution of daily driving mileage l;
B. solving the charging time T of the electric automobile according to the formula (1) through the daily driving mileage l of the electric automobileC：
Wherein P is the charging power of the electric automobile, kW, U is the power consumption of hundreds kilometers, kW.h/100 km, and η is the charging efficiency;
for rounding up, T is more than or equal to 1C≤24；
C. Through a latin hypercube sampling technology, setting a sampling scale as V, sampling the electric vehicle initial trip time, charging time and final trip end time to obtain a sampling matrix E ═ T [ T ]S,TE,TC]TWherein T isS、TEAnd TCRespectively a 1 × V dimension starting travel time vector, a last travel ending time vector and a charging duration vector in EEach row forms a charging scene of the electric automobile;
D. calculating the corresponding chargeable time period number d of the single electric automobile in the charging scene vvComprises the following steps:
wherein: t isS,v、TE,v、TC,vAre respectively TS、TE、TCThe v-th column of elements in the vector represents the initial trip time, the final trip end time and the charging time of the electric automobile in the charging scene v;
E. in charging scenario v, from TS,v、TE,v、TC,vEstablishing an electric vehicle charging load model based on price elasticity analysis;
F. solving by a semi-invariant method to obtain central moments of each order of residential area loads when the electric vehicles are considered, solving by utilizing a Gram-Charlier infinite series expansion formula to obtain a probability distribution function of the residential area electric vehicle charging loads, solving to obtain the entropy measure of the residential area electric vehicle charging loads and the out-of-limit probability of the distribution transformer at each moment, and further obtaining an evaluation model of the uncertainty of the fluctuation degree of the residential area electric vehicle charging loads and an evaluation model of the overload risk of the distribution transformer in the residential area.
2. The method for assessing uncertainty in charging load of an electric vehicle for a residential area at a time-of-use electricity price according to claim 1, wherein: in the step E, an electric automobile charging load model based on price elasticity analysis is established, and the electric automobile in the residential area starts to travel at the time T under the charging scene vS,vAnd the last trip ending time TE,vCharging duration TC,vThe specific steps of establishing the electric automobile charging load model by the price elasticity coefficient are as follows:
e1, ending time T of last trip of electric automobile under charging scene vE,vThe corresponding initial charging time T of the single electric automobile under the charging scene v can be solvedQ,v：
TQ,v∈(TE,v,TE,v+dv) (3)
Wherein: dvSolving the formula (2) to obtain;
e2, setting the initial charging time of the single electric automobile to be T under the charging scene vQ,vThe charging scheme is as follows:
wherein: n is a possible initial charging time T in a charging scenario vQ,vThe number of (2);
n is more than or equal to 1 and less than or equal to N, and the charging power of the electric automobile in the j time period under the charging scene v is obtained by the following steps:
e3, first-order central moment C of charging power corresponding to j time period of single electric vehicle in charging scene vvj,1Comprises the following steps:
central moment of order k Cvj,k，k≥2；
Wherein: p is a radical ofvjThe probability that the initial charging time of a single electric vehicle is j time under a charging scene v represents the response relation between the vehicle owner and the charging electricity price of the electric vehicle, and the vehicle owner has lower responsibility in a time period with higher charging cost and higher responsibility in a time period with lower charging cost;
E4、pvjthe uncertainty of the time-of-use electricity price of the electric vehicle owner response is reflected, and the solving formula is as follows:
wherein: is the price elastic coefficient; lambda [ alpha ]rAnd the charging time-of-use electricity price is corresponding to the electric automobile in the residential area at r moment, yuan/kW.h.
3. The method for assessing uncertainty in charging load of an electric vehicle for a residential area at a time-of-use electricity price according to claim 1, wherein: in the step F, the entropy measure of the charging load of the electric automobile in the residential area and the out-of-limit probability of the distribution transformer at each moment are solved, and then an evaluation model of uncertainty of the charging load fluctuation degree of the electric automobile in the residential area and an evaluation model of overload risk of the distribution transformer in the residential area can be obtained; the method comprises the following specific steps:
f1, setting the reserved quantity of the electric automobiles in the residential area to be M, setting different charging behaviors of the electric automobiles to be independent, and obtaining k-order central moment L of charging power corresponding to a single electric automobile at the moment j by the central limit theoremk,jComprises the following steps:
wherein: cvj,kSolving the formula (7);
f2, generally considering that the total load of the residential area at each moment comprises the conventional load of the residential area and the charging load of the electric automobile, setting the conventional load of the residential area to be subjected to normal distribution with the expected value of mu, wherein the standard deviation is 0.1 mu, and the third-order and multi-order half-invariant quantities of the conventional load of the residential area are negligible; the first-order and second-order semi-invariants of the conventional load of the residential area at the moment j are as follows:
wherein: mu.sj，
J is more than or equal to 0 and less than or equal to 24; respectively is an expected value and a variance of the conventional load of the residential area at the moment j;
f3, setting k, k to 1,2,3 … of j time period charging power of the single electric vehicle in the charging scene v; semi-invariant of order Dk,jComprises the following steps:
wherein: l isk,jSolving a k-order central moment corresponding to the charging power of the electric automobile at the moment j by using an equation (9);
f4, property according to semi-invariant: the k-order semi-invariant of mutually independent random variables satisfies homogeneity and additivity, and the k-order semi-invariant B of the total load power of the residential area at the moment jk,jComprises the following steps:
wherein: m is the holding capacity of electric vehicles in the residential area, Dk,jSolving the formula (11);
f5, solving to obtain central moments of the total load power of the residential area at each moment according to the semi-invariants of each order of the total load power at each moment in the residential area, and solving to obtain a probability distribution function F (x) of the total load power of the residential area at each moment and a probability density function F (x) of the charging load of the electric automobile through Gram-Charlier infinite series expansion;
f6, when the overload degree of the distribution transformer in the residential area reaches 60%, the short-time overload allowable time of the transformer is 0.75h, therefore, the evaluation model X of the overload risk of the distribution transformer in the residential area is as follows:
X≤0.75 (14)
wherein: y is the limit value of overload load born by the distribution transformer in the residential area, kW; fj(Y) is the load power in the residential area at time jDistribution function values at the position of 60% overload of the transformer; fj(Y) solving by using a semi-invariant and a Gram-Charlie infinite series expansion;
f7, F from time jj(x) Information entropy H of charging load of electric vehicle at moment j can be obtained through solvingj(ii) a Information entropy HjThe calculation formula of (2) is as follows:
Hj＝-∫xfj(x)logfj(x)dx (15)
wherein: f. ofj(x) The probability density function of the charging load of the electric automobile in the residential area at the moment j, wherein x is the charging load of the electric automobile at different moments, kW;
f8, the entropy measure evaluation model of the charging load fluctuation uncertainty of the electric automobile in the residential area is as follows:
wherein: hAnd the standard deviation of the measurement of the charging load entropy when the electric automobile in the residential area is charged disorderly.
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