I would like to ask how to insert a script inside cvx for specific variables: For example, in the following program I don’t want charging and discharging happening in the same time. Again buying and selling shouldn’t happen in the same time for one agent

1

function [ B_c_all, B_d_all, M_s_all, M_b_all, G_s_all, G_b_all ] = cvxfunction( L_g, L_c, lambda, p_b, p_s, t,a)

B_c = battery charging
B_d = battery discharging
M_s = selling to the regional market
M_b = buying from the regional market
G_s = selling to the outside grid
G_b = buying from the outside grid

%Initialization for CVX

bc_max=40; bd_max=40; % battery bounds
ms_max=185; mb_max=185; % regional market trading bounds
gb_max=500; % maximum energy to buy from outside grid
S_init=50; S_max=200; % states of the charge of battery
n=0.85; % battery efficiency
gamma=0.95; % transmission efficiency
c=0; % cost for producing energy by microgrid
w=30; v=10; % defining utility function parameters

Cf = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1];

for i=1:t
for j=1:a
if (0<=L_c(i,j)) && (L_c(i,j)<=w/v)
D(i,j)=wL_c(i,j)-0.5vL_c(i,j)^2;
elseif (w/v<L_c(i,j))
D(i,j)=w^2/2v;
else
D(i,j)=0;
end
end
end

for j=1:a
D2=D(:,j);
L_g_a=L_g(:,j);
L_c_a=L_c(:,j);
Lc_min=min(L_c_a);
Lg_max=max(L_g_a);

cvx_begin
variables B_c(t) B_d(t) M_s(t) M_b(t) G_s(t) G_b(t);

for i=1:t
X(i) = D2(i) - cL_g_a(i) + gammap_s(i)G_s(i) - p_b(i)G_b(i) + lambda(i)(gammaM_s(i)-M_b(i));
end
maximize( sum(X) )
subject to
Lc_min-L_c_a<=0;
-L_g_a<=0;
-B_c<=0;
-B_d<=0;
-M_s<=0;
-M_b<=0;
-G_s<=0;
-G_b<=0;
L_g_a-Lg_max<=0;
B_c-bc_max<=0;
B_d-bd_max<=0;
M_s-ms_max<=0;
M_b-mb_max<=0;
G_b-gb_max<=0;
Cf * G_s == 0;

for i=1:t
t_B_c = B_c(1:i);
t_B_d = B_d(1:i);
-S_init-sum(nt_B_c-t_B_d)<=0;
S_init+sum(nt_B_c-t_B_d)-S_max<=0;
end

L_c_a-L_g_a+B_c-B_d+M_s-M_b+G_s-G_b <= 0.0000000001;
L_c_a-L_g_a+B_c-B_d+M_s-M_b+G_s-G_b >= -0.0000000001;

cvx_end

Note: I would like to add inside the cvx code, a script that prevents selling while buying and/or charging while discharging for the same agent

2

I think you should be able to do this using logic modeling with binary variables. You should be able to figure out how to do that after reading http://www.fico.com/en/node/8140?file=5125 .You would need to have a solver installed under CVX which can handle integer variables.

I have not looked at your model carefully enough to determine whether there is a way to do what you want in CVX without using binary of integer variables.

3

This is really a general modeling question, not a CVX-specific one. You should consult more generic optimization help sites, such as Math StackExchange or OR-Exchange.