Dears

I want to use CVX to solve an optimization problem that consist of nested summations

I wrote a code but the solver says that the solution is infeasible. I want to make sure that I did it right or not. “sorry for not knowing to to make the whole code appear like a code in your website”

My code is

```
% Optimal Price Regulation Based Algorithm for 500 EVs
%% Updating the SOC and CR at every 5 minute and PD set to zero if the SOC
% is greater than the 0.99Mci and running the simulation for the whole 3
% months from 21 July, 2010 to 20 Oct, 2010
%%
clc
clear
%% Initializing Variables
% NEV = 500;
NEV = 10;
Ef = 0.9;
days = 2;
Beta=0.05;
hours = 4;
weeks=3;
years=12;
BatC=200; %200$/KWH so the total cost is MC*Batc
discount_rate=0.05;
Meter_cost=36.1; %29 euro
Comm_cost=88.4; %71 euro
Bidirecional_cost=186.7; %150 euro
weighted_factor=[4 4 4]; %3 months, 4 weeks per month
ExD = zeros(hours,days,weeks);
ExU = zeros(hours,days,weeks);
ExR = zeros(hours,days,weeks); %responsive reserve
Pregup=zeros(days,hours,weeks);
Pregdw=zeros(days,hours,weeks);
Prespres=zeros(days,hours,weeks);
POP = zeros(NEV,hours,days,weeks);
MnAP = zeros(NEV,hours,days,weeks);
MxAP = zeros(NEV,hours,days,weeks);
RsRP = zeros(NEV,hours,days,weeks); %responsive reserve
Deg = zeros(NEV,hours,days,weeks);
% EPD = zeros(NEV,hours,days);
% ReguppD = zeros(hours,days,weeks);
% RegdwpD = zeros(hours,days);
% ResrespD = zeros(hours,days);
PriceD = zeros(hours,days,weeks);
FPriceD = zeros(hours,days,weeks);
DC=zeros(NEV,1);
ReguppW=zeros(hours*days,weeks);
RegdwpW=zeros(hours*days,weeks);
ResrespW=zeros(hours*days,weeks);
ExU_W=zeros(hours*days,weeks);
ExD_W=zeros(hours*days,weeks);
ExR_W=zeros(hours*days,weeks);
PriceD_W=zeros(hours*days,weeks);
FPriceD_W=zeros(hours*days,weeks);
infeasiable_Days=zeros(days,1);
failed_Days=zeros(days,1);
% load Expected_profit;
%% Reading Data from XLS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% LOADING DATA
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
SOCI = [1.187409836
1.484262295
0.593704918
1.042622951
0.890557377
1.088459016
0.692655738
1.385311475
2.374819672
2.374819672
];
% Reading Initial Maximum Power
MP = [3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
];
% Reading Initial Maximum Charge
% Mci = xlsread(EV_Data_100,'MC_100','C1:C100');
Mci = [21.6
21.6
21.6
21.6
21.6
21.6
21.6
21.6
21.6
21.6
];
% Reading Availability of EVs
Av=[1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
];
% % Reading the Morning Trip Time of EVs
Mttrip = [3
2
4
3
4
3
2
4
3
3
];
% % Reading the Evening Trip Time of EVs
Ettrip = [11
11
11
11
11
11
11
13
11
12
];
% % Reading the Trip of EVs of Morning trip (Reduction in SOC)
trip_1 = [2.57536
5.47264
0.035555552
1.93152
0.96576
0.64384
1.28768
2.25344
2.57536
3.54112
];
% % Reading the Trip of EVs of Evening trip (Reduction in SOC)
trip_2= [2.66284221
5.56012221
0.123037762
2.01900221
1.05324221
0.73132221
1.37516221
2.34092221
2.66284221
3.62860221
];
% % Reading the compensation factor of the ith EV to account for unplanned
% departures
total_comp = [1 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1 1 1
1 1 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1 1 1
1 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1.002506266 1 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1 1 1
1 1 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1 1 1
1 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1.002277904 1 1.006289308 1.006289308 1.006289308 1.006289308 1.006289308 1.006289308 1.006289308 1.006289308 1 1 1
1 1 1 1 1.0041841 1.0041841 1.0041841 1.0041841 1.0041841 1.0041841 1 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1 1 1
1 1 1 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1.005586592 1 1 1
1 1 1 1.003584229 1.003584229 1.003584229 1.003584229 1.003584229 1.003584229 1.003584229 1 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1 1 1
1 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1.002785515 1 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1 1 1
1 1 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1.003134796 1 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1.005025126 1 1 1
];
% % Reading the Expected percentage of the EVs remaining to perform V2G at
% hour t
EvPer = [1 0.989671717 0.980991162 0.974294733 0.970128066 0.970128066 0.970128066 0.970128066 0.970128066 0.970128066 0.986546717 0.972727273 0.952777778 0.946527778 0.946527778 0.946527778 0.946527778 0.946527778 0.946527778 0.946527778 0.946527778 1 1 1
];
%% Price Data from XLS
% Reading FORECASTED Energy Price
FPrice = [25.34844871 26.0056763 32.12181122 35.1589504 41.49888019 40.37125422 48.02618913 99.95810515 170.1224283 114.3232142 81.99950949 67.0534449 45.06777494 38.82448189 36.39142323 40.15932157 38.78563793 37.70701738 43.54440679 33.91649244 28.2987497 22.82627733 23.75272459 24.66849407
];
% Reading Regulation Up Price
Regupp = [3.67 4.69 6.03 9.85 9.12 7.03 10 13.67 17.03 20.95 20 20 9.67 10 12 5 7.71 5.67 15 4 3 3 3 3
];
% Reading Regulation Down Price
Regdwp = [4.37 3.81 4.77 4.62 3.81 5.47 6.68 7.07 7.5 10 10 9.38 6.14 4.65 3.49 4.99 6.3 4.27 8 5.03 4 7.03 6.5 5.03
];
% Reading Responsive Reserves Price
Resresp = [4 3.77 5.47 5.48 5 8 10 9.37 15 24.56 25.64 26.47 10.03 9.49 12 5 7.69 5.67 6.32 3.32 2.69 2.69 2.69 2.76
];
%% ExU and ExD Data from XLS
ExUA = [0.015632083 0.045573417 0.056452813 0.114570522 0.31130082 0.032311417 0.186061917 0.241440833 0.294051667 0.378971333 0.014297208 0.164136661 0.452626392 0.26786129 0.0804151 0.042010858 0.065476775 0.002456933 0.045135388 0.35239 0.853553333 0.217934583 0.130421167 0.13385645
];
ExDA = [0.357682712 0.169056759 0.252310833 0.036405331 0.190553 0.229229617 0.236906592 0.168317187 0.310912917 0.20496615 0.3485209 0.337526083 0.009581686 0.192533192 0.400753607 0.430311917 0.36266675 0.434689667 0.223046766 0.03743375 0 0.526098833 0.065650442 0.038289736
];
ExRA = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% LOADING DATA END
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tic
t=hours;
for i=1:NEV
Investment_cost(i)=Meter_cost+Comm_cost+(Bidirecional_cost*MP(i));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
cvx_begin %quiet %quiet for not producing any screen outputs
%in variables we put decision and axuillary variables that are related to
%decision variables
variables POP(NEV,t,days,weeks) MxAP(NEV,t,days,weeks) MnAP(NEV,t,days,weeks) RsRP(NEV,t,days,weeks) Deg(NEV,t,days,weeks)
expressions Inn(t,days,weeks) running_cost(t,days,weeks) Scaled_week_profit(weeks) Yearly_profit(years) Total_profit
for week=1:weeks
week
%loading data for the whole week (the week here is 2 days, each is 4
%hours for simplicity)
ReguppW(:,week) = Regupp((week-1)*days*hours+1:week*days*hours);
RegdwpW(:,week) = Regdwp((week-1)*days*hours+1:week*days*hours);
ResrespW(:,week) = Resresp((week-1)*days*hours+1:week*days*hours);
ExU_W(:,week) = ExUA((week-1)*days*hours+1:week*days*hours);
ExD_W(:,week) = ExDA((week-1)*days*hours+1:week*days*hours);
ExR_W(:,week) = ExRA((week-1)*days*hours+1:week*days*hours);
FPriceD_W(:,week) = FPrice((week-1)*days*hours+1:week*days*hours);
for day = 1:days
day
%loading data for the whole day
Pregup(day,:,week) = ReguppW((day-1)*hours+1 : day*hours,week)'*1e-3;
% RegdwpD(:,day,week) = RegdwpW((day-1)*hours+1 : day*hours,week);
Pregdw(day,:,week) = RegdwpW((day-1)*hours+1 : day*hours,week)'*1e-3;
% ResrespD(:,day,week) = ResrespW((day-1)*hours+1 : day*hours,week);
%Pregup = ReguppD(srt_hrs:end_hrs,day)'*1e-3; % *1e-3 for KW to MW for 9
%hours
Prespres(day,:,week) = ResrespW((day-1)*hours+1 : day*hours,week)'*1e-3; % *1e-3 for KW to MW for 24 hours Responsive reserve price
ExU(:,day,week) = ExU_W((day-1)*hours+1 : day*hours,week); %for the whole day
ExD(:,day,week) = ExD_W((day-1)*hours+1 : day*hours,week);
ExR(:,day,week) = ExR_W((day-1)*hours+1 : day*hours,week);
FPriceD(:,day,week) = FPriceD_W((day-1)*hours+1:day*hours,week)*1e-3; %for the whole day
for i=1:NEV
DC(i,1)=0.042*((BatC*Mci(i))/5000)+ ((1-Ef^2)/Ef)*Beta;
end
% the for loop was done to apply the constraints for each time
for k = 1:t %number of hours
Comp(:,k) = (total_comp(:,k));
k
Inn(k,day,week) == ((Pregup(day,k,week)*(sum(MnAP(:,k,day,week))) + Pregdw(day,k,week)*(sum(MxAP(:,k,day,week))) +Prespres(day,k,week)*(sum(RsRP(:,k,day,week))))*EvPer(k))...
+ Beta*(Av(:,k)'*((MxAP(:,k,day,week)*ExD(k,day,week) + POP(:,k,day,week) - MnAP(:,k,day,week)*ExU(k,day,week) - RsRP(:,k,day,week)*ExR(k,day,week))*EvPer(k)));
running_cost(k,day,week)== (Av(:,k)'*((MxAP(:,k,day,week)*ExD(k,day,week) + POP(:,k,day,week) - MnAP(:,k,day,week)*ExU(k,day,week) - RsRP(:,k,day,week)*ExR(k,day,week))*(FPriceD(k,day,week))...
*EvPer(k)))+ (sum(Deg(:,k,day,week)));
end
end
Scaled_week_profit(week)=weighted_factor(week)*(( sum(sum(Inn(:,:,week)))- sum(sum(running_cost(:,:,week))) ));
end
for year=1:years
Yearly_profit(year)=(1/(1+(discount_rate^year)))*((sum(Scaled_week_profit)));
end
Total_profit=sum(Yearly_profit)-sum(Investment_cost);
maximize Total_profit
subject to
for week=1:weeks
week
for day =1:days
day
for k=1:t
k
for i = 1:NEV
if k<Mttrip(i)
Trip(i)=0;
elseif k>=Mttrip(i) && k<Ettrip(i)
Trip(i)=trip_1(i);
elseif k>=Ettrip(i)
Trip(i)=trip_1(i)+trip_2(i);
end
sum(Av(i,1:k).*(MxAP(i,1:k,day,week).*ExD(1:k,day,week)' + POP(i,1:k,day,week) - MnAP(i,1:k,day,week).*ExU(1:k,day,week)' - RsRP(i,1:k,day,week).*ExR(1:k,day,week)').*Comp(i,1:k) + ...
((Deg(i,1:k,day,week)/DC(i,1))*((1-Ef^2)/Ef)))*Ef + SOCI(i) -Trip(i) <= Mci(i);
sum(Av(i,1:k).*(MxAP(i,1:k,day,week).*ExD(1:k,day,week)' + POP(i,1:k,day,week) - MnAP(i,1:k,day,week).*ExU(1:k,day,week)' - RsRP(i,1:k,day,week).*ExR(1:k,day,week)').*Comp(i,1:k) + ...
((Deg(i,1:k,day,week)/DC(i,1))*((1-Ef^2)/Ef)))*Ef + SOCI(i) -Trip(i) >= 0.1*Mci(i); %avoiding deep discharging
if k==t
sum(Av(i,1:k).*(MxAP(i,1:k,day,week).*ExD(1:k,day,week)' + POP(i,1:k,day,week) - MnAP(i,1:k,day,week).*ExU(1:k,day,week)' - RsRP(i,1:k,day,week).*ExR(1:k,day,week)').*Comp(i,1:k) + ...
((Deg(i,1:k,day,week)/DC(i,1))*((1-Ef^2)/Ef)))*Ef + SOCI(i) -Trip(i)>= 0.99*Mci(i);
sum(Av(i,1:k).*(MxAP(i,1:k,day,week).*ExD(1:k,day,week)' + POP(i,1:k,day,week) - MnAP(i,1:k,day,week).*ExU(1:k,day,week)' - RsRP(i,1:k,day,week).*ExR(1:k,day,week)').*Comp(i,1:k) + ...
((Deg(i,1:k,day,week)/DC(i,1))*((1-Ef^2)/Ef)))*Ef + SOCI(i) -Trip(i)<= Mci(i);
end
(MxAP(i,k,day,week) + POP(i,k,day,week))*Comp(i,k) <= (Av(i,k)*MP(i));
MnAP(i,k,day,week)*Av(i,k) <= POP(i,k,day,week) + MP(i)*Av(i,k);
RsRP(i,k,day,week) <= POP(i,k,day,week) + MP(i)*Av(i,k) - MnAP(i,k,day,week);
MxAP(i,k,day,week) >= 0;
MnAP(i,k,day,week) >= 0;
RsRP(i,k,day,week) >= 0;
POP(i,k,day,week) >= -MP(i)*Av(i,k);
Deg(i,k,day,week)>=0;
Deg(i,k,day,week)>= -(DC(i,1)*min(0,Av(i,k)*(POP(i,k,day,week) - MnAP(i,k,day,week)*ExU(k,day,week)- RsRP(i,k,day,week)*ExR(k,day,week)))*(Comp(i,k)/Ef));
end
end
end
end
cvx_end
```

The output using SDPT3 solver is

## Calling SDPT3 4.0: 3168 variables, 1380 equality constraints

For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 1380

dim. of linear var = 3120

dim. of free var = 48 *** convert ublk to lblk

SDPT3: Infeasible path-following algorithms

## version predcorr gam expon scale_data

NT 1 0.000 1 0

it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

## 0|0.000|0.000|2.6e+003|5.6e+001|1.0e+008| 3.591774e+005 0.000000e+000| 0:0:00| spchol 1 1

1|0.949|0.564|1.3e+002|2.4e+001|5.4e+007| 6.031632e+005 0.000000e+000| 0:0:00| spchol 1 1

2|1.000|0.887|7.9e-004|2.8e+000|6.6e+006| 5.774203e+005 0.000000e+000| 0:0:00| spchol 1 1

3|0.479|0.187|5.9e-004|2.2e+000|7.2e+006| 6.135542e+005 0.000000e+000| 0:0:00| spchol 1 1

4|1.000|0.187|1.9e-004|1.8e+000|9.8e+006| 6.873201e+005 0.000000e+000| 0:0:00| spchol 1 1

5|1.000|0.350|1.5e-005|1.2e+000|1.1e+007| 3.921732e+005 0.000000e+000| 0:0:00| spchol 1 1

6|1.000|0.287|1.8e-005|8.5e-001|1.3e+007|-2.592743e+006 0.000000e+000| 0:0:00| spchol 1 1

7|0.327|0.201|2.9e-005|6.8e-001|1.4e+007|-1.256982e+007 0.000000e+000| 0:0:00| spchol 1 1

8|0.192|0.100|7.7e-005|6.1e-001|2.7e+007|-5.369121e+007 0.000000e+000| 0:0:00| spchol 1 1

9|0.823|0.154|1.5e-005|5.2e-001|1.8e+008|-8.340184e+008 0.000000e+000| 0:0:00| spchol 1 1

10|0.324|0.044|4.2e-005|4.9e-001|2.6e+009|-1.366016e+010 0.000000e+000| 0:0:00| spchol 1 1

11|1.000|0.070|1.1e-004|4.6e-001|1.0e+011|-8.932571e+011 0.000000e+000| 0:0:00| spchol 2 2

12|1.000|0.064|1.2e-002|4.3e-001|8.8e+012|-1.514849e+014 0.000000e+000| 0:0:00| spchol * 3 * 3

stop: primal infeas has deteriorated too much, 2.8e+001

13|1.000|0.025|1.2e-002|4.3e-001|8.8e+012|-1.514849e+014 0.000000e+000| 0:0:00|

prim_inf,dual_inf,relgap = 1.20e-002, 4.31e-001, 5.78e-002

sqlp stop: dual problem is suspected of being infeasible

## number of iterations = 13

residual of dual infeasibility

certificate X = 1.35e-014

reldist to infeas. <= 1.27e-015

Total CPU time (secs) = 0.30

CPU time per iteration = 0.02

termination code = 2

DIMACS: 1.1e-004 0.0e+000 7.4e+000 0.0e+000 -1.0e+000 1.1e-001

Status: Infeasible

Optimal value (cvx_optval): -Inf

## and using sedumi solver

Calling SeDuMi 1.34cvx: 3168 variables, 1380 equality constraints

For improved efficiency, SeDuMi is solving the dual problem.

SeDuMi 1.34cvx by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.

Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500

Split 48 free variables

eqs m = 1380, order n = 3217, dim = 3217, blocks = 1

nnz(A) = 13236 + 0, nnz(ADA) = 55528, nnz(L) = 44786

it : b*y gap delta rate t/tP* t/tD* feas cg cg prec

0 : 3.67E+002 0.000

1 : 0.00E+000 2.33E+002 0.000 0.6357 0.9000 0.9000 7.01 1 1 2.7E+000

2 : 0.00E+000 1.33E+002 0.000 0.5708 0.9000 0.9000 2.02 1 1 1.9E+000

3 : 0.00E+000 5.35E+001 0.000 0.4018 0.9000 0.9000 0.44 1 1 2.2E+000

4 : 0.00E+000 1.42E+001 0.000 0.2660 0.9000 0.9000 -0.51 1 1 4.9E+000

5 : 0.00E+000 9.87E-001 0.000 0.0694 0.9900 0.9900 -0.88 1 1 1.0E+000

6 : 0.00E+000 2.77E-004 0.000 0.0003 0.9999 0.9999 -0.99 1 1

Dual infeasible, primal improving direction found.

iter seconds |Ax| [Ay]_+ |x| |y|

6 0.9 1.3e-009 2.7e-013 3.2e+000 1.1e-012

## Detailed timing (sec)

Pre IPM Post

1.608E+000 2.221E+000 8.500E-002

Max-norms: ||b||=0, ||c|| = 3.451492e+001,

Cholesky |add|=0, |skip| = 0, ||L.L|| = 13.036.

Status: Infeasible

Optimal value (cvx_optval): -Inf