CN104917248A - Coordination charge control method for electric bus quick charge station - Google Patents

Abstract

A coordination charge control method for an electric bus quick charge station includes initiating load information and electric price information of a power distribution grid of a main control computer in future 24 hours; acquiring battery information of an electric bus and a serial number of the electric bus and sending the information and the serial number to the charge station; performing parameter configuration of the main control computer; making a coordination charge control strategy of the electric bus quick charge station; enabling a client to send control signals to different chargers for controlling the switching of the chargers. Therefore, the coordination charge control of all electric buses in the quick charge station is realized and effective allocation of power resource is realized under the premise of satisfying electric energy requirement of the buses.

Description

The coordination charge control method of electric bus quick charge station

Technical field

The present invention relates to a kind of charge control method, be specifically related to the coordination charge control method of electric bus quick charge station.

Background technology

In recent years, along with the trend of energy shortage and climate change increases the weight of, electric automobile, because it is energy-conservation, reduction of discharging, efficiently advantage become increasingly conspicuous, obtains the concern of countries in the world government and supports energetically.Present stage, domestic and international electric vehicle engineering development reaches its maturity, and national governments also in succession put into effect incentive policy and promote the universal of electric automobile.Along with the extensive access electrical network of electric automobile, research shows, its unordered charging brings threat by giving the safe and reliable operation of electrical network.For this reason, China has city, as Shenzhen etc., has designed and has participated in peak load shifting for the tou power price mechanism of electric automobile discharge and recharge to guide electric automobile specially.

In addition, the orderly charging of electric automobile can reduce its operation cost or charging cost to greatest extent.Electric bus is as the important component part of future transportation mode, the planning of its charging strategy will directly have influence on economic benefit own and the operation of electrical network, wherein distribution network line overload is mainly comprised on the impact of electrical network, voltage out-of-limit, the problems such as distribution transformer transships, the aggravation of power distribution network peak load difference.In view of the quick car charging of electric bus completes main in special charging station, it is very necessary for therefore formulating a kind of Based Intelligent Control electric bus being applicable to electric bus quick charge station intelligent charge control method automatically cut-off that charges.The charging station of current domestic construction, electric bus quick charge station does not coordinate the utilization of charge control method.

Summary of the invention

The object of this invention is to provide a kind of coordination charge control method of electric bus quick charge station, realize the cooperation control of electric bus quick charge, effectively avoid peak of power consumption, thus reduce electric bus quick charge to the negative effect of electrical network, save the charging cost of electric bus and charging station operator.

The object of the invention is to adopt following technical proposals to realize:

The coordination charge control method of electric bus quick charge station, described method comprises:

(1) the initialization main control computer power distribution network load information of following 24 hours and electricity price information;

(2) obtain electric bus battery information and bus numbering, be sent to charging station;

(3) parameter configuration is carried out to main control computer;

(4) the coordination charging control strategy of electric bus quick charge station is formulated;

(5) described client transmits control signal to each charger, controls cut-offfing of charger.

Preferably, in described step (1), the distribution network load information of following 24 hours comprises: the charging station power distribution network load information A of following 24 hours _j, represent and carry out the active volume percentage that charges, j=1,2 at a jth time point electric bus ..., 288, the sampling interval is 5 minutes; Described electricity price information is the charging station electric cost c of following 24 hours _j.

Preferably, in described step (2), electric bus battery information and bus numbering comprise, battery charge state SOC liminal value F when Electric Transit pulls in, and this electric bus is numbered m, m=1, and 2 ..., M; Wherein, described F is the liminal value of current power bus battery electric quantity and this electric bus battery capacity; M is the electric bus quantity of charged state.

Preferably, carry out parameter configuration comprise in described step (3) to main control computer, if the charger quantity of charging station is N, the electric bus quantity under charged state is M; The charge power of every platform charger is P; Distribution transformer rated power is S _t; The battery capacity of each electric bus is B _m, m=1,2 ..., M; It is E that each electric bus single stroke consumes power accounts for battery capacity ratio _m, m=1,2 ..., M.

Preferably, the coordination charging control strategy of described step (4) comprises, if detect in the given time, Electric Transit pulls in, then perform following step:

To pull in moment leaving from station adjustment bus timetable according to Electric Transit;

Build charging station charging gating matrix D _{m × J};

Determine target function;

Determine constraints;

Obtain optimum charging station charging gating matrix C _{n × J}.

Further, described electric bus comprises from the moment adjustment bus timetable that enters the station, and compares the whether consistent with bus timetable from the moment of entering the station of all electric bus of charging station; If inconsistent, extracted the liminal value F of the state-of-charge SOC of this charging bus by its numbering, the ratio E of battery total capacity _mwith battery capacity B _m, upgrade described bus timetable.

Further, described structure fills charging station charging gating matrix D _{m × J}, the d wherein comprised _mjbe whether m electric bus is in charged state at current time to the jth period; If d _mj=1, represent that m charging bus is in charged state in the j period, if d _mj=0, be then uncharged state; Wherein, m=1,2 ..., M; M is the electric bus quantity under charged state; J=1,2 ..., J; J=288.

Further, described target function is charging cost minimization, and its expression formula is:

$min\underset{j=1}{\overset{J}{\Σ}}\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}{\mathrm{P\Δtc}}_j---\left(1\right);$

In formula (1), d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, and Δ t is the time interval, c _jfor the charging station electric cost of following 24 hours.

Further, described constraints comprises, at any time section, distribution transformer nonoverload; Namely the available charge capacity of distribution transformer is greater than the electric bus charge power sum of all charged states, and its expression formula is;

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}P\≤A_j{S}_T\mathrm{\λ}---\left(2\right)$

In formula (2), λ is the average power factor of charging load, S _tfor distribution transformer rated power; d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, A _jfor the charging station power distribution network load information of following 24 hours;

Electric bus quantity M under charged state is no more than the charger quantity N of charging station, then

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}\≤N---\left(3\right);$

According to the bus timetable upgraded, determine the time range that electric bus cannot charge; Wherein, the number of times leaving from station that enters the station that each bus is complete in the J=1440 time period in future is a _m, m=1,2 ..., M, at every turn the enter the station leaving from station time corresponding to it is respectively s _miand l _mi, i=1,2 ..., a _m, then

$\∀j\∈\{1,2,...s_{m1}-1\}\∪\{l_{m1},...,s_{m2}-1\}\∪...\∪\{l_{{\mathrm{ma}}_m},...,1440\},m=1,2,...,M---\left(4\right);$

Work as d _mjwhen=0, electric bus is uncharged;

Described electric bus charging interval section is continous way charging, and its constraints is:

$\∀m=1,2,...,M,\∀j\∈\{s_{mi},...,l_{mi}-1\}(i=1,2,...,a_m)---\left(5\right);$

σ≥d _j-d _j-1,σ∈{0,1}

In formula (5), d _jfor the electric bus of jth period charged state;

Electricity after charging is greater than minimum requirements electricity and is less than charger battery capacity; Namely in each docking process, the battery charge state SOC when bus of charging is leaving from station be not less than certain once the average electricity consumed to entering the station next time leaving from station account for the ratio E of total electricity _m, m=1,2 ..., the state-of-charge SOC liminal value F sum of M and charging bus, its expression formula is;

$\begin{array}{c}\∀m\∈\{1,2,\mathrm{...},M\},\∀i\∈\{1,2,\mathrm{...},a_m\};\\ \left(E_m-Y_{m,i,A}+F\right)B_m\≤\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤\left(1-Y_{m,i,A}\right)B_m\\ 1\≤m\≤M,2\≤i\≤a_m\end{array}---\left(6\right)$

In inequality group (6), Y _{m, i, A}be the battery charge state SOC that m charging bus enters the station for i-th time.

Further, E is utilized _mby accumulate mode, formula (6) is changed, obtain about Y _{m, 1, A}inequality group, make i (1≤i≤a before m electric bus _m) secondary charge capacity sum meets minimum requirements electricity respectively and be less than charger battery capacity;

$\begin{array}{c}\∀m\∈\{1,2,\mathrm{...},M\},\∀i\∈\{1,2,\mathrm{...},a_m\}\\ \left({\mathrm{iE}}_m-Y_{m,1,A}+F\right)B_m\≤\underset{j=s_{m1}}{\overset{l_{m1}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t+\mathrm{...}+\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤((i-1)E_m+1-Y_{m,1,A})B_m\end{array}---\left(7\right).$

Further, mixed integer programming approach is adopted to solve formula (1)-Shi (6); If without solution, by each time lengthening 5min leaving from station, and formula (7) is utilized to recalculate, if without solution when reaching the liminal value F of charging bus state-of-charge, under then reducing described minimum restriction F to case of emergency, liminal value solves again, if still without solution, then abandons this time charging; Optimum charging station charging gating matrix C is finally obtained according to above-mentioned calculating _{n × J}.

Compared with the prior art, the beneficial effect that the present invention reaches is:

The input of the information of all electric bus completes at charger and charger client by the present invention, easy and simple to handle.

Client, according to the system mode of input, formulates the optimum charging strategy of all electric bus of charging station, realizes electric bus quick charge station coordination charging and controls.Reduce the negative effect of electric bus quick charge to electrical network, and save the charging cost of electric bus and charging station operator.

This control method is under the prerequisite meeting bus electrical energy demands, and coupling system load condition, avoids peak of power consumption, avoids circuit, transformer overload, realizes the configuration of electric power resource economical and effective.

Accompanying drawing explanation

Fig. 1 is electric bus quick charge station control method for coordinating flow chart.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

As shown in Figure 1, the coordination charge control method of electric bus quick charge station, described method comprises:

(1) the initialization main control computer power distribution network load information of following 24 hours and electricity price information; In described step (1), the distribution network load information of following 24 hours comprises: the charging station power distribution network load information A of following 24 hours _j, represent and carry out the active volume percentage that charges, j=1,2 at a jth time point electric bus ..., 288, the sampling interval is 5 minutes; Described electricity price information is the charging station electric cost c of following 24 hours _j.

(2) obtain electric bus battery information and bus numbering, be sent to charging station; In described step (2), electric bus battery information and bus numbering comprise, battery charge state SOC liminal value F when Electric Transit pulls in, and this electric bus is numbered m, m=1, and 2 ..., M; Wherein, described F is the liminal value of current power bus battery electric quantity and this electric bus battery capacity; M is the electric bus quantity of charged state.

(3) parameter configuration is carried out to main control computer; Carry out parameter configuration to main control computer in described step (3) to comprise, if the charger quantity of charging station is N, the electric bus quantity under charged state is M; The charge power of every platform charger is P; Distribution transformer rated power is S _t; The battery capacity of each electric bus is B _m, m=1,2 ..., M; It is E that each electric bus single stroke consumes power accounts for battery capacity ratio _m, m=1,2 ..., M.

(4) the coordination charging control strategy of electric bus quick charge station is formulated;

The coordination charging control strategy of described step (4) comprises, if detect in the given time, Electric Transit pulls in, then perform following step:

To pull in moment leaving from station adjustment bus timetable according to Electric Transit;

Build charging station charging gating matrix D _{m × J};

Determine target function;

Determine constraints;

Obtain optimum charging station charging gating matrix C _{n × J}.

Described electric bus comprises from the moment adjustment bus timetable that enters the station, and compares the whether consistent with bus timetable from the moment of entering the station of all electric bus of charging station; If inconsistent, extracted the liminal value F of the state-of-charge SOC of this charging bus by its numbering, the ratio E of battery total capacity _mwith battery capacity B _m, upgrade described bus timetable.

Described structure fills charging station charging gating matrix D _{m × J}, the d wherein comprised _mjbe whether m electric bus is in charged state at current time to the jth period; If d _mj=1, represent that m charging bus is in charged state in the j period, if d _mj=0, be then uncharged state; Wherein, m=1,2 ..., M; M is the electric bus quantity under charged state; J=1,2 ..., J; J=288.

Described target function is charging cost minimization, and its expression formula is:

$min\underset{j=1}{\overset{J}{\Σ}}\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}{\mathrm{P\Δtc}}_j---\left(1\right);$

In formula (1), d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, and Δ t is the time interval, c _jfor the charging station electric cost of following 24 hours.

Described constraints comprises, at any time section, distribution transformer nonoverload; Namely the available charge capacity of distribution transformer is greater than the electric bus charge power sum of all charged states, and its expression formula is;

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}P\≤A_j{S}_T\mathrm{\λ}---\left(2\right)$

In formula (2), λ is the average power factor of charging load, S _tfor distribution transformer rated power; d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, A _jfor the charging station power distribution network load information of following 24 hours;

Electric bus quantity M under charged state is no more than the charger quantity N of charging station, then

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}\≤N---\left(3\right);$

According to the bus timetable upgraded, determine the time range that electric bus cannot charge; Wherein, the number of times leaving from station that enters the station that each bus is complete in the J=1440 time period in future is a _m, m=1,2 ..., M, at every turn the enter the station leaving from station time corresponding to it is respectively s _miand l _mi, i=1,2 ..., a _m, then

$\∀j\∈\{1,2,...s_{m1}-1\}\∪\{l_{m1},...,s_{m2}-1\}\∪...\∪\{l_{{\mathrm{ma}}_m},...,288\},m=1,2,...,M---\left(4\right);$

Work as d _mjwhen=0, electric bus is uncharged;

Described electric bus charging interval section is continous way charging, and its constraints is:

$\∀m=1,2,...,M,\∀j\∈\{s_{mi},...,l_{mi}-1\}(i=1,2,...,a_m)---\left(5\right);$

σ≥d _j-d _j-1,σ∈{0,1}

In formula (5), d _jfor the electric bus of jth period charged state;

Electricity after charging is greater than minimum requirements electricity and is less than charger battery capacity; Namely in each docking process, the battery charge state SOC when bus of charging is leaving from station be not less than certain once the average electricity consumed to entering the station next time leaving from station account for the ratio E of total electricity _m, m=1,2 ..., the state-of-charge SOC liminal value F sum of M and charging bus, its expression formula is;

$\begin{array}{c}\∀m\∈\{1,2,\mathrm{...},M\},\∀i\∈\{1,2,\mathrm{...},a_m\};\\ \left(E_m-Y_{m,i,A}+F\right)B_m\≤\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤\left(1-Y_{m,i,A}\right)B_m\\ 1\≤m\≤M,2\≤i\≤a_m\end{array}---\left(6\right)$

In inequality group (6), Y _{m, i, A}be the battery charge state SOC that m charging bus enters the station for i-th time.

Utilize E _mby accumulate mode, formula (6) is changed, obtain about Y _{m, 1, A}inequality group, make i (1≤i≤a before m electric bus _m) secondary charge capacity sum meets minimum requirements electricity respectively and be less than charger battery capacity;

$\begin{array}{c}\∀m\∈\{1,2,\mathrm{...},M\},\∀i\∈\{1,2,\mathrm{...},a_m\}\\ \left({\mathrm{iE}}_m-Y_{m,1,A}+F\right)B_m\≤\underset{j=s_{m1}}{\overset{l_{m1}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t+\mathrm{...}+\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤((i-1)E_m+1-Y_{m,1,A})B_m\end{array}---\left(7\right).$

Mixed integer programming approach is adopted to solve formula (1)-Shi (6); If without solution, by each time lengthening 5min leaving from station, and formula (7) is utilized to recalculate, if without solution when reaching the liminal value F of charging bus state-of-charge, under then reducing described minimum restriction F to case of emergency, liminal value solves again, if still without solution, then abandons this time charging; Optimum charging station charging gating matrix C is finally obtained according to above-mentioned calculating _{n × J}.

(5) described client transmits control signal to each charger, controls cut-offfing of charger.

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit, although with reference to above-described embodiment to invention has been detailed description, those of ordinary skill in the field are to be understood that: still can modify to the specific embodiment of the present invention or equivalent replacement, and not departing from any amendment of spirit and scope of the invention or equivalent replacement, it all should be encompassed in the middle of right of the present invention.

Claims (11)

1. the coordination charge control method of electric bus quick charge station, is characterized in that, described method comprises:

(1) the initialization main control computer power distribution network load information of following 24 hours and the electricity price information in 24 hours futures;

(2) obtain electric bus battery information and bus numbering, be sent to charging station;

(3) parameter configuration is carried out to main control computer;

(4) the coordination charging control strategy of electric bus quick charge station is formulated;

(5) described client transmits control signal to each charger, controls cut-offfing of charger.

2. method according to claim 1, is characterized in that, in described step (1), the distribution network load information of following 24 hours comprises: the charging station power distribution network load information A of following 24 hours _j, represent and carry out the active volume percentage that charges, j=1,2 at a jth time point electric bus ..., 288, the sampling interval is 5 minutes; Described electricity price information is the charging station electric cost c of following 24 hours _j.

3. method according to claim 1, is characterized in that, in described step (2), electric bus battery information and bus numbering comprise, battery charge state SOC liminal value F when Electric Transit pulls in, this electric bus is numbered m, m=1,2 ..., M; Wherein, described F is the liminal value of current power bus battery electric quantity and this electric bus battery capacity; M is the electric bus quantity of charged state.

4. method according to claim 1, is characterized in that, in described step (3), carries out parameter configuration comprise main control computer, if the charger quantity of charging station is N, the electric bus quantity under charged state is M; The charge power of every platform charger is P; Distribution transformer rated power is S _t; The battery capacity of each electric bus is B _m, m=1,2 ..., M; It is E that each electric bus single stroke consumes power accounts for battery capacity ratio _m, m=1,2 ..., M.

5. method according to claim 1, is characterized in that, the coordination charging control strategy of described step (4) comprises, if detect in the given time, Electric Transit pulls in, then perform following step:

To pull in moment leaving from station adjustment bus timetable according to Electric Transit;

Build charging station charging gating matrix D _{m × J};

Determine target function;

Determine constraints;

Obtain optimum charging station charging gating matrix C _{n × J}.

6. method according to claim 5, is characterized in that, described electric bus comprises from the moment adjustment bus timetable that enters the station, and compares the whether consistent with bus timetable from the moment of entering the station of all electric bus of charging station; If inconsistent, extracted the liminal value F of the state-of-charge SOC of this charging bus by its numbering, the ratio E of battery total capacity _mwith battery capacity B _m, upgrade described bus timetable.

7. method according to claim 5, is characterized in that, described structure charging station charging gating matrix D _{m × J}, the d wherein comprised _mjbe whether m electric bus is in charged state at current time to the jth period; If d _mj=1, represent that m charging bus is in charged state in the j period, if d _mj=0, be then uncharged state; Wherein, m=1,2 ..., M; M is the electric bus quantity under charged state; J=1,2 ..., J; J=288.

8. method according to claim 5, is characterized in that, described target function is charging cost minimization, and its expression formula is:

$min\underset{j=1}{\overset{J}{\Σ}}\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}{\mathrm{P\Δtc}}_j---\left(1\right);$

In formula (1), d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, and Δ t is the time interval, c _jfor the charging station electric cost of following 24 hours.

9. method according to claim 5, is characterized in that, described constraints comprises, at any time section, distribution transformer nonoverload; Namely the available charge capacity of distribution transformer is greater than the electric bus charge power sum of all charged states, and its expression formula is;

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}P\≤A_j{S}_T\mathrm{\λ}---\left(2\right)$

In formula (2), λ is the average power factor of charging load, S _tfor distribution transformer rated power; d _mjbe m electric bus at current time to the state of jth period, M is the electric bus quantity under charged state, and P is every platform charger charge power, A _jfor the charging station power distribution network load information of following 24 hours;

Electric bus quantity M under charged state is no more than the charger quantity N of charging station, then

$\∀j\∈\{1,2,...,J\},\underset{m=1}{\overset{M}{\Σ}}{d}_{mj}\≤N---\left(3\right);$

According to the bus timetable upgraded, determine the time range that electric bus cannot charge; Wherein, the number of times leaving from station that enters the station that each bus is complete in the J=1440 time period in future is a _m, m=1,2 ..., M, at every turn the enter the station leaving from station time corresponding to it is respectively s _miand l _mi, i=1,2 ..., a _m, then

$\∀j\∈\{1,2,...s_{m1}-1\}\∪\{l_{m1},...,s_{m2}-1\}\∪...\∪\{l_{{\mathrm{ma}}_m},...,288\},m=1,2,...,M---\left(4\right);$

Work as d _mjwhen=0, electric bus is uncharged;

Described electric bus charging interval section is continous way charging, and its constraints is:

$\∀m=1,2,...,M,\∀j\∈\{s_{mi},...,l_{mi}-1\}(i=1,2,...,a_m)---\left(5\right);$

σ≥d _j-d _j-1,σ∈{0,1}

In formula (5), d _jfor the electric bus of jth period charged state;

Electricity after charging is greater than minimum requirements electricity and is less than charger battery capacity; Namely in each docking process, the battery charge state SOC when bus of charging is leaving from station be not less than certain once the average electricity consumed to entering the station next time leaving from station account for the ratio E of total electricity _m, m=1,2 ..., the state-of-charge SOC liminal value F sum of M and charging bus, its expression formula is;

$\∀m\∈\{1,2,...,M\},\∀i\∈\{1,2,...,a_m\};$

$(E_m-Y_{m,i,A}+F)B_m\≤\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤(1-Y_{m,i,A})B_m$

1≤m≤M,2≤i≤a _m(6)

In inequality group (6), Y _{m, i, A}be the battery charge state SOC that m charging bus enters the station for i-th time.

10. method according to claim 9, is characterized in that, utilizes E _mby accumulate mode, formula (6) is changed, obtain about Y _{m, 1, A}inequality group, make i (1≤i≤a before m electric bus _m) secondary charge capacity sum meets minimum requirements electricity respectively and be less than charger battery capacity;

$\∀m\∈\{1,2,...,M\},\∀i\∈\{1,2,...,a_m\}$

$({\mathrm{iE}}_m-Y_{m,1,A}+F)B_m\≤\underset{j=s_{m1}}{\overset{l_{m1}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t+...+\underset{j=s_{mi}}{\overset{l_{mi}}{\Σ}}{d}_{mj}P\mathrm{\Δ}t\≤\left(\right(i-1)E_m+1-Y_{m,1,A})B_m---\left(7\right).$

11. methods according to claim 5, is characterized in that, described acquisition optimum charging station charging gating matrix C _{n × J}comprise; Mixed integer programming approach is adopted to solve formula (1)-(6); If without solution, by each time lengthening 5min leaving from station, and formula (7) is utilized to recalculate, if without solution when reaching the liminal value F of charging bus state-of-charge, under then reducing described minimum restriction F to case of emergency, liminal value solves again, if still without solution, then abandons this time charging; Optimum charging station charging gating matrix C is finally obtained according to above-mentioned calculating _{n × J}.