CN104680255A - Rapid electromobile charge scheme optimization method - Google Patents

Abstract

The invention discloses a rapid electromobile charge scheme optimization method, for optimizing a charge scheme of electromobiles within a whole scheduling period on the basis of machine set combination and economic scheduling by taking margin power generation cost as decision basis, so as to ensure the lowest total charge cost of the electromobiles. The rapid electromobile charge scheme optimization method comprises the following steps: firstly, dividing the whole scheduling period into a plurality of charge zones according to the technical characteristics and the charge modes of the electromobiles, subsequently calculating the average margin power generation cost of different available charge zones; preferentially charging charge zones with the lowest average margin power generation cost of the electromobiles; implementing the steps in an iteration manner until all electromobiles are completely charged. In the iteration process, if all charge zones are not available because of the limit of the startup capacity of a conventional machine set combination scheme, a novel machine set is started up to continue the whole charge scheme optimization process on the basis of the principle of the lowest extra startup cost.

Description

A kind of quick electric vehicle charging scheme optimization method

The application is application number: the divisional application of 201310365531.6, the applying date: 2013-08-20, title " a kind of charging electric vehicle scheme optimization method based on System Margin cost of electricity-generating ".

Technical field

The present invention relates to electric vehicle engineering, be specifically related to a kind of charging electric vehicle scheme optimization method of machine set system marginal generating cost.

Background technology

Fuel-engined vehicle gives off a large amount of greenhouse gases and dusty gas while the most of petroleum resources of consumption, brings huge challenge to environmental protection and sustainable development.Compared with orthodox car, electric automobile has unrivaled advantage in alleviating energy crisis, the harmonious development of promotion people and environment, has become the focus that national governments, energy manufacturer and automobile manufacturing company are paid close attention at present.Along with the continuous progress of battery production, manufacturing technology, increasingly sharpening of environmental pollution and petering out of petroleum resources, the ratio of electric automobile shared by road traffic system will improve day by day.

Under current technical conditions, electric automobile mainly completes charging process by the charging pile be connected with electrical network.Thus, from electrical network angle, networking electric automobile is the newly-increased load of electric system, and it will significantly increase the operating cost of whole electric system.Along with the raising gradually of electric automobile permeability in electrical network, its charging behavior will be day by day remarkable on the impact of cost of electricity-generating, thus be necessary the charging scheme optimizing networking electric automobile, realize charging in order, reduce the total charging cost of electric automobile as far as possible.

For realizing the optimum charging of electric automobile, prior art by introducing the decision variable characterizing charging electric vehicle scheme in Unit Combination model, set up the expansion unit built-up pattern considering that charging electric vehicle is optimized, and utilize optimized algorithm to solve to obtain the optimum charging scheme of electric automobile to this model, thus the charging cost that practices every conceivable frugality.Specific descriptions about this technology can see document one " Intelligent unit commitment with vehicle-to-grid-A cost-emission optimization " (Journal of Power Sources, 195 volumes the 5th phase in 2010 the 898th page to 911 pages) with document two " taking into account the electric system unit optimum combination of the electric automobile that can network " (Automation of Electric Systems, 2011 the 35th volume the 20th phase the 16th page to the 20th page).This technology can optimize the charging scheme of electric automobile, but will there are following 2 weak points.

First, model solution is more difficult.Known from institute, Power System Unit Commitment belongs to containing hybrid variable, multi-period, nonlinear dynamic optimization problem, be difficult to obtain globally optimal solution, this conclusion can see document three " solving the improved mode searching algorithm of Optimization of Unit Commitment By Improved " (Proceedings of the CSEE, 2011 the 31st volume the 28th phase the 33rd page to 41 pages).Obviously, the expansion unit built-up pattern of the consideration charging electric vehicle optimization come from unit model expansion will be difficult to solve more, epimere provides list of references and adopts particle cluster algorithm and MILP (Mixed Integer Linear Programming) method to solve model respectively, solution procedure more complicated, there is certain difficulty in algorithm application when actual scale electric system solves.

Secondly, modeling process have ignored the charge characteristic of electric automobile completely, does not consider that charging electric vehicle process is a continuous process, assuming that its in single scheduling slot (1h or 0.5h) completes charging process.

Summary of the invention

The object of the present invention is to provide a kind of charging electric vehicle scheme optimization method based on System Margin cost of electricity-generating reducing charging electric vehicle cost.

Technical solution of the present invention is:

Based on a charging electric vehicle scheme optimization method for System Margin cost of electricity-generating, it is characterized in that: comprise the following steps:

Step 1: be T-T according to the whole optimization Time segments division that length is T hour by the charge mode of electric automobile _eqbetween+1 charging zone, each interval arranges the electric automobile number of charging to be x _j, 1≤j≤T-T _eq-1; Electric automobile equivalence charge power and duration of charge are respectively P _eqkW and T _eqhour, parameter P _eq, T _eqthe capacity of common decision batteries of electric automobile, its different value corresponds to the different charge modes of electric automobile;

Step 2: judge whether to exist between available charging zone according to the security requirement of system cloud gray model, if exist, performs step 4, if cause between each charging zone all unavailable because of the generation capacity deficiency that existing Unit Combination scheme is corresponding, performs step 3;

Step 3: on the basis of existing Unit Combination scheme, the principle minimum by extra start cost opens new unit, until occur between available charging zone;

Step 4: calculate the average system marginal generating cost E between each available charging zone _j,m, and find j between average system marginal generating cost minimum charging zone _min;

Step 5: according to Optimal Step Size Δ P, unit: MW, increases j between charging zone _minexerting oneself of interior day part t limit unit I (t), that is:

P _I(t),t＝P _I(t),t+ΔP j _min≤t≤j _min+T _eq-1

Increase generated output and be used for charging electric vehicle, obviously, the electric automobile number of the newly-increased charging in this interval is 1000 Δ P/P _eq; Now, the electric automobile number x of charging is arranged in this interval _jmincan by following formula correction:

$x_{j\min }=x_{j\min }+\frac{1000\mathrm{\ΔP}}{P_{\mathrm{eq}}}$

Step 6: judge whether all electric automobiles arrange charging complete, if so, then terminate calculation process and export optimum results; Otherwise, turn to step 2, continue the iterative process of algorithm, until all electric automobiles all arrange charging complete.

Can judge whether to exist between available charging zone according to the security requirement of system cloud gray model described in step 2, specifically in accordance with the following methods:

If each charge period t (j≤t≤j+T in j between charging zone _eq-1) all meet the constraint condition that following formula provides, then illustrate that this interval is between available charging zone;

$P_{l,t}+\frac{P_{\mathrm{eq}}{y}_t}{1000}+R_t\≤\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{i,\max }{U}_{i,t}^{\′}$

In fact, this constraint bar judges whether each charge period t has unnecessary generating capacity to hold charging electric vehicle; In above formula, P _l,tfor the system loading of period t; R _tfor the spinning reserve demand of period t; P _{i, max}for the capacity of unit i; U _i,tfor unit i is in the duty of period t, " 1 " represents start, and " 0 " represents shutdown; y _tfor the electric automobile number charged at period t, it can according to the electric automobile number x having arranged in j between charging zone to charge _jcalculate;

$y_t=\left\{\begin{array}{cc}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{x}_j& 1\≤t{\≤T}_{\mathrm{eq}}\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{t}{\mathrm{\Σ}}}{x}_j& T_{\mathrm{eq}}+1\≤t\≤T-T_{\mathrm{eq}}+1\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{T-T_{\mathrm{eq}}+1}{\mathrm{\Σ}}}{x}_j& T-T_{\mathrm{eq}}+2\≤t\≤T\end{array}\right..$

The concrete grammar of step 3 is:

Step 301: some period cannot hold more charging electric vehicle load because of generation capacity deficiency, namely do not meet constraint condition find these scheduling slots, be denoted by set Φ;

Step 302: the average unit cost C at full capacity of unit of respectively not starting shooting in set of computations Φ _{aFLC, i}.

$C_{\mathrm{AFLC},i}=\frac{a_i}{P_{i,\max }}+b_i+c_i{P}_{i,\max }$

In above formula, a _i, b _iwith c _ifor the fuel cost coefficient of unit i;

Step 303: find day part average unit cost C at full capacity in set Φ _{aFLC, i}minimum unit of not starting shooting, attempts carrying out power-on operation to it, and calculates the newly-increased cost of electricity-generating C that power-on operation may cause _e,t, t ∈ Φ; This newly-increased cost of electricity-generating is made up of two parts: first, average unit cost C at full capacity _{aFLC, i}the start cost of minimum unit itself, is determined by unit parameter; Secondly, new unit start must cause load redistributing between each unit, thus likely causes the increase of fuel cost, and the increase volume of this part cost need obtain according to economic load dispatching result;

Step 304: find newly-increased cost of electricity-generating C _e,tminimum scheduling slot, and to average unit cost C at full capacity in this period _{aFLC, i}minimum unit carries out power-on operation; Whether there is available charge period after judging the start of new unit, if having, then terminate power-on operation; If no, then restart to perform step 301, until there is available charge period.

Average system marginal generating cost E between each available charging zone of the calculating described in step 4 _j,m, specifically in accordance with the following methods:

Step 401: the marginal generating cost M calculating all start units of day part between charging zone according to economic load dispatching result _i,t, its set is designated as Ω _t,

M _i,t＝b _i+2c _iP _i,t

In above formula, b _iwith c _ifor the cost of electricity-generating coefficient of unit i, P _i,tfor unit i exerting oneself at period t;

Step 402: find the unit that period t marginal generating cost is minimum, this unit is the marginal unit of this period, and its call number is designated as I (t); The marginal generating cost of this marginal unit is the System Margin cost of electricity-generating M of this period _t;

M _t＝b _I(t)+2c _I(t)P _I(t),t

＝min{M _i,t} i∈Ω _t

Step 403: each scheduling slot System Margin cost of electricity-generating M in j between available charging zone _tmean value E _j,mjust be the average system marginal generating cost in this interval, namely calculate the average system marginal generating cost E of j between available charging zone according to the following formula _j,m;

$E_{j,m}=\frac{1}{T_{\mathrm{eq}}}\underset{t=j}{\overset{t=j+T_{\mathrm{eq}}-1}{\mathrm{\Σ}}}{M}_t.$

Described in step 6 judge all electric automobiles whether arrange charging complete, specifically in accordance with the following methods:

If the electric automobile number x charged between each charging zone _jsum equals electric automobile sum n to be scheduled ₀, namely then illustrate that all electric automobiles all arrange charging complete.

Beneficial effect: compared with prior art, the advantage that the present invention gives prominence to comprises: the method is on the basis of Unit Combination and economic load dispatching, with the charging scheme of System Margin cost of electricity-generating for decision-making foundation optimization electric automobile, method disclosed by the invention can consider the technical characteristic of electric automobile and electric system, and there is the fast advantage of computing velocity, be applicable to the calculating of actual scale electric system.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is economic load dispatching schematic diagram of the present invention.

Fig. 2 is process flow diagram of the present invention.

Fig. 3 judges whether to there is process flow diagram between available charging zone.

Fig. 4 calculates the average system marginal generating cost process flow diagram between each available charging zone.

Fig. 5 is to be T hour by length according to the charge mode of electric automobile whole optimization Time segments division is T-T _eqschematic diagram between+1 charging zone.

Embodiment

As shown in Figure 1, charging electric vehicle scheme optimization method based on System Margin cost of electricity-generating of the present invention, on the basis of Unit Combination, economic load dispatching, with System Margin cost of electricity-generating for decision-making foundation, the charging behavior of scheduling networking electric automobile, the target of scheduling is that the total charging cost of electric automobile is minimum.

The method is in fact the process of a loop iteration, namely finds average system marginal generating cost E _j,mbetween minimum available charging zone, electric automobile of giving priority in arranging in this interval charging, thus reduces charging cost as far as possible.In iteration, may cause between all charging zones because of the generation capacity deficiency that existing start scheme is corresponding all unavailable, now, according to start cost minimum principle opening section unit, thus whole iterative process should be continued.As shown in Figure 2, step is as follows for idiographic flow of the present invention:

(1) be, T (unit: whole optimization Time segments division h) is T-T according to the charge mode of electric automobile by length _eqbetween+1 charging zone, each interval arranges the electric automobile number of charging to be x _j(1≤j≤T-T _eq-1).Electric automobile equivalence charge power and duration of charge are respectively P _eq(unit: kW) and T _eq(unit: h), parameter P _eq, T _eqthe capacity of common decision batteries of electric automobile, its different value corresponds to the different charge modes of electric automobile.

(2), for ensureing power system security, reliability service, electric system, while guaranteeing to power to the load comprising charging electric vehicle load, also should leave certain spinning reserve.Therefore, the present invention judges whether to exist between available charging zone according to this requirement.If exist, perform step 4, if cause between each charging zone all unavailable because of the generation capacity deficiency that start scheme is corresponding, perform step 3.

Judge whether that the method existed between available charging zone is as follows:

If each charge period t (j≤t≤j+T in j between charging zone _eq-1) all meet the constraint condition that following formula provides, then illustrate that this interval is between available charging zone.

$P_{l,t}+\frac{P_{\mathrm{eq}}{y}_t}{1000}+R_t\≤\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{i,\max }{U}_{i,t}^{\′}$

In fact, this constraint bar judges whether each charge period t has unnecessary generating capacity to hold charging electric vehicle.In above formula, P _l,tfor the system loading of period t; R _tfor the spinning reserve demand of period t; P _{i, max}for the capacity of unit i; U _i,tfor unit i is in the duty of period t, " 1 " represents start, and " 0 " represents shutdown; y _tfor the electric automobile number charged at period t, it can according to the electric automobile number x having arranged in j between charging zone to charge _jcalculate.

$y_t=\left\{\begin{array}{cc}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{x}_j& 1\≤t{\≤T}_{\mathrm{eq}}\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{t}{\mathrm{\Σ}}}{x}_j& T_{\mathrm{eq}}+1\≤t\≤T-T_{\mathrm{eq}}+1\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{T-T_{\mathrm{eq}}+1}{\mathrm{\Σ}}}{x}_j& T-T_{\mathrm{eq}}+2\≤t\≤T\end{array}\right.$

(3), on the basis of existing Unit Combination scheme, the principle minimum by extra start cost opens new unit, until occur between available charging zone, as shown in Figure 3, concrete steps are as follows for its flow process:

1), some period cannot hold more charging electric vehicle load because of generation capacity deficiency, namely do not meet constraint condition find these scheduling slots, be denoted by set Φ.

2), respectively do not start shooting in set of computations Φ the average unit cost C at full capacity of unit _{aFLC, i}.

$C_{\mathrm{AFLC},i}=\frac{a_i}{P_{i,\max }}+b_i+c_i{P}_{i,\max }$

In above formula, a _i, b _iwith c _ifor the fuel cost coefficient of unit i, in general, these three parameters be on the occasion of.

3) day part average unit cost C at full capacity in set Φ, is found _{aFLC, i}minimum unit of not starting shooting, attempts carrying out power-on operation to it, and calculates the newly-increased cost of electricity-generating C that power-on operation may cause _e,t(t ∈ Φ).This newly-increased cost of electricity-generating is made up of two parts: first, average unit cost C at full capacity _{aFLC, i}the start cost (being determined by unit parameter) of minimum unit itself; Secondly, new unit start must cause load redistributing between each unit, thus likely causes the increase of fuel cost, and the increase volume of this part cost need obtain according to economic load dispatching result.

4), newly-increased cost of electricity-generating C is found _e,tminimum scheduling slot, and to average unit cost C at full capacity in this period _{aFLC, i}minimum unit carries out power-on operation.Whether there is available charge period after judging the start of new unit, if having, then terminate power-on operation; If no, then restart to perform step 1), until there is available charge period.

(4), step 4, calculate average system marginal generating cost E between each available charging zone _j,m, and find j between average system marginal generating cost minimum charging zone _min.Calculate the flow process of average system marginal generating cost between available charging zone as shown in Figure 4, concrete steps are as follows:

1) (its set is designated as Ω, to calculate all start units of day part between charging zone according to economic load dispatching result _t) marginal generating cost M _i,t.

M _i,t＝b _i+2c _iP _i,t

In above formula, b _iwith c _ifor the cost of electricity-generating coefficient of unit i, P _i,tfor unit i exerting oneself at period t.

2), find the minimum unit of period t marginal generating cost, this unit is the marginal unit of this period, and its call number is designated as I (t).The marginal generating cost of this marginal unit is the System Margin cost of electricity-generating M of this period _t.

M _t＝b _I(t)+2c _I(t)P _I(t),t

＝min{M _i,t} i∈Ω _t

3), each scheduling slot System Margin cost of electricity-generating M in j between available charging zone _tmean value E _j,mjust be the average system marginal generating cost in this interval, namely calculate the average system marginal generating cost E of j between available charging zone according to the following formula _j,m.

$E_{j,m}=\frac{1}{T_{\mathrm{eq}}}\underset{t=j}{\overset{t=j+T_{\mathrm{eq}}-1}{\mathrm{\Σ}}}{M}_t$

(5), j between charging zone is increased according to Optimal Step Size Δ P (unit: MW) _minexerting oneself of interior day part t limit unit I (t), that is:

P _I(t),t＝P _I(t),t+ΔP j _min≤t≤j _min+T _eq-1

Increase generated output and be used for charging electric vehicle, obviously, the electric automobile number of the newly-increased charging in this interval is 1000 Δ P/P _eq.Now, the electric automobile number x of charging is arranged in this interval _jmincan by following formula correction:

$x_{j\min }=x_{j\min }+\frac{1000\mathrm{\ΔP}}{P_{\mathrm{eq}}}$

(6), judge whether all electric automobiles arrange charging complete.If so, then terminate calculation process and export optimum results; Otherwise, turn to step 2, continue the iterative process of algorithm, until all electric automobiles all arrange charging complete.Judge that electric all electric automobiles complete concrete grammar that whether charges is as follows.

If the electric automobile number x charged between each charging zone _jsum equals electric automobile sum n to be scheduled ₀, namely then illustrate that all electric automobiles all arrange charging complete.

Claims (1)

1. a quick electric vehicle charging scheme optimization method, is characterized in that: comprise the following steps:

Step 1: be T-T according to the whole optimization Time segments division that length is T hour by the charge mode of electric automobile _eqbetween+1 charging zone, each interval arranges the electric automobile number of charging to be x _j, 1≤j≤T-T _eq-1; Electric automobile equivalence charge power and duration of charge are respectively P _eqkW and T _eqhour, parameter P _eq, T _eqthe capacity of common decision batteries of electric automobile, its different value corresponds to the different charge modes of electric automobile;

Step 2: judge whether to exist between available charging zone according to the security requirement of system cloud gray model, if exist, performs step 4, if cause between each charging zone all unavailable because of the generation capacity deficiency that existing Unit Combination scheme is corresponding, performs step 3;

Step 3: on the basis of existing Unit Combination scheme, the principle minimum by extra start cost opens new unit, until occur between available charging zone;

Step 4: calculate the average system marginal generating cost E between each available charging zone _j,m, and find j between average system marginal generating cost minimum charging zone _min;

Step 5: according to Optimal Step Size Δ P, unit: MW, increases j between charging zone _minexerting oneself of interior day part t limit unit I (t), that is:

P _I(t),t＝P _I(t),t+ΔP j _min≤t≤j _min+T _eq-1

Increase generated output and be used for charging electric vehicle, obviously, the electric automobile number of the newly-increased charging in this interval is 1000 Δ P/P _eq; Now, the electric automobile number x of charging is arranged in this interval _jmincan by following formula correction:

$x_{j\min }=x_{j\min }+\frac{1000\mathrm{\ΔP}}{P_{\mathrm{eq}}}$

Step 6: judge whether all electric automobiles arrange charging complete, if so, then terminate calculation process and export optimum results; Otherwise, turn to step 2, continue the iterative process of algorithm, until all electric automobiles all arrange charging complete;

Can judge whether to exist between available charging zone according to the security requirement of system cloud gray model described in step 2, specifically in accordance with the following methods:

If each charge period t (j≤t≤j+T in j between charging zone _eq-1) all meet the constraint condition that following formula provides, then illustrate that this interval is between available charging zone;

$P_{l,t}+\frac{P_{\mathrm{eq}}{y}_t}{1000}+R_t\≤\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_{i,\max }{U}_{i,t}^{\′}$

In fact, this constraint bar judges whether each charge period t has unnecessary generating capacity to hold charging electric vehicle; In above formula, P _l,tfor the system loading of period t; R _tfor the spinning reserve demand of period t; P _{i, max}for the capacity of unit i; U _i,tfor unit i is in the duty of period t, " 1 " represents start, and " 0 " represents shutdown; y _tfor the electric automobile number charged at period t, it can according to the electric automobile number x having arranged in j between charging zone to charge _jcalculate;

$y_t=\left\{\begin{array}{cc}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{x}_j& 1\≤t\≤T_{\mathrm{eq}}\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{t}{\mathrm{\Σ}}}{x}_j& T_{\mathrm{eq}}+1\≤t\≤T-T_{\mathrm{eq}}+1\\ \underset{j=t-T_{\mathrm{eq}}+1}{\overset{T-T_{\mathrm{eq}}+1}{\mathrm{\Σ}}}{x}_j& T-T_{\mathrm{eq}}+2\≤t\≤T\end{array}\right.;$

The concrete grammar of step 3 is:

Step 301: some period cannot hold more charging electric vehicle load because of generation capacity deficiency, namely do not meet constraint condition find these scheduling slots, be denoted by set Φ;

Step 302: the average unit cost C at full capacity of unit of respectively not starting shooting in set of computations Φ _{aFLC, i}.

$C_{\mathrm{AFLC},i}=\frac{a_i}{P_{i,\max }}+b_i+c_i{P}_{i,\max }$

In above formula, a _i, b _iwith c _ifor the fuel cost coefficient of unit i;

Step 303: find day part average unit cost C at full capacity in set Φ _{aFLC, i}minimum unit of not starting shooting, attempts carrying out power-on operation to it, and calculates the newly-increased cost of electricity-generating C that power-on operation may cause _e,t, t ∈ Φ; This newly-increased cost of electricity-generating is made up of two parts: first, average unit cost C at full capacity _{aFLC, i}the start cost of minimum unit itself, is determined by unit parameter; Secondly, new unit start must cause load redistributing between each unit, thus likely causes the increase of fuel cost, and the increase volume of this part cost need obtain according to economic load dispatching result;

Step 304: find newly-increased cost of electricity-generating C _e,tminimum scheduling slot, and to average unit cost C at full capacity in this period _{aFLC, i}minimum unit carries out power-on operation; Whether there is available charge period after judging the start of new unit, if having, then terminate power-on operation; If no, then restart to perform step 301, until there is available charge period;

Average system marginal generating cost E between each available charging zone of the calculating described in step 4 _j,m, specifically in accordance with the following methods:

Step 401: the marginal generating cost M calculating all start units of day part between charging zone according to economic load dispatching result _i,t, its set is designated as Ω _t,

M _i,t＝b _i+2c _iP _i,t

In above formula, b _iwith c _ifor the cost of electricity-generating coefficient of unit i, P _i,tfor unit i exerting oneself at period t;

Step 402: find the unit that period t marginal generating cost is minimum, this unit is the marginal unit of this period, and its call number is designated as I (t); The marginal generating cost of this marginal unit is the System Margin cost of electricity-generating M of this period _t;

M _t＝b _I(t)+2c _I(t)P _I(t),t

＝min{M _i,t} i∈Ω _t

Step 403: each scheduling slot System Margin cost of electricity-generating M in j between available charging zone _tmean value E _j,mjust be the average system marginal generating cost in this interval, namely calculate the average system marginal generating cost E of j between available charging zone according to the following formula _j,m;

$E_{j,m}=\frac{1}{T_{\mathrm{eq}}}\underset{t=j}{\overset{t=j+T_{\mathrm{eq}}-1}{\mathrm{\Σ}}}{M}_t;$

Described in step 6 judge all electric automobiles whether arrange charging complete, specifically in accordance with the following methods:

If the electric automobile number x charged between each charging zone _jsum equals electric automobile to be scheduled

Sum n ₀, namely then illustrate that all electric automobiles all arrange charging complete.