Solving the Unit Commitment Problem using optimproblem

I am trying to solve the Unit Commitment problem using the optimproblem function. I will explain my problem with an example. Lets say I have three generators which will be operated to meet various loads for a 24 hours period. Now the cost curves for these units are quadratic, so piecewise linearization is required if I am going to use the intlinprog function. I have successfully linearized the system and the problem now involves minimizing:

     Total C(P) = C_1(P_1min)T_1 + s_11*P_11*T_1 + s_12*P_12*T_1 + … + s_1n*P_1n*T_1
            + C_2(P_2min)T_2 + s_21*P_21*T_2 + s_22*P_22*T_2 + … + s_2n*P_2n*T_2
            + C_3(P_3min)T_3 + s_31*P_31*T_3 + s_32*P_32*T_3 + … + s_3n*P_3n*T_3

Where Sik is the slope for each segment of the linearized curve, Pik are the power increments (which I need to determine) for each segment. T_i is a binary variable which keeps track of the state of unit and Ci(Pimin) is the cost at Pimin. Now based on my research, the problem should now be formulated as minimize:

    Total C(P) = C_1(P_1min)T_1 + s_11*Z_11 + s_12*Z_12 + … + s_1n*Z_1n
            + C_2(P_2min)T_2 + s_21*Z_21 + s_22*Z_22 + … + s_2n*Z_2n
            + C_3(P_3min)T_3 + s_31*Z_31 + s_32*Z_32 + … + s_3n*Z_3n

Where Ti = 0 implies that Zik = 0 and Ti = 1 implies that Zik = Pik.

Now I have two optimization variable:

1. Pik
2. Ti

With the optimization problem being made up of two part:

1. Sum of ALL Sik*Pik values
2. Sum of Ci(Pimin)*Ti values.

The following code illustrates this (with the addition of another optimization variable which isn't so important):

 %Amount of power generated in an hour by a plant
power = optimvar('power',nHours,plant,'LowerBound',0,'UpperBound',maxGenConst);
%Indicator if plant is operating during an hour 
isOn = optimvar('isOn',nHours,actual_plant,'Type','integer','LowerBound',0,'UpperBound',1);
%Indicator if plant is starting up during an hour
startup = optimvar('startup',nHours,actual_plant,'Type','integer','LowerBound',0,'UpperBound',1);

    %Costs
powerCost = sum(power*f,1);
isOnCost = sum(isOn*OperatingCost',1);
startupCost = sum(startup*StartupCost',1);

 % set objective
powerprob.Objective = powerCost + isOnCost + startupCost;

   % power generation over all plans meets hourly demand
powerprob.Constraints.isDemandMet = sum(power,2) >= Load;

    % only gen power when plant is on
% if isOn=0 power must be zero, if isOn=1 power must be less than maxGenConst
powerprob.Constraints.powerOnlyWhenOn = power <= maxGenConst.*isOn;   

    % if on, meet MinGenerationLevel
% if isOn=0 power >= 0, if isOn=1 power must be more than minGenConst
powerprob.Constraints.meetMinGenLevel = power >= maxGenConst.*isOn;

My problem lies in this calculation: maxGenConst.*isOn. These have different sizes as maxGenConst is a nHours * (num_of_gen*num_of_segments) whereas isOn is a nHour * num_of_gen. The reason this occurs is because after linearization, the cost equation becomes (num_of_segments + 1) equations. I would appreciate some help in formulating the problem so I can use the optimproblem function. I have attached my full code and data.

[Matt J]

My problem lies in this calculation: maxGenConst.*isOn. These have different sizes as maxGenConst is a nHours * (num_of_gen*num_of_segments) whereas isOn is a nHour * num_of_gen

If they have different sizes, then in what way does it make sense to try multiplying them together?

[Micah Mungal]

I attempted to use another approach to solve the unit commitment problem using the optimproblem function. Did not know this function existed until a couple days ago. But I like that I can just state the constraints using this approach rather than formulating it myself as that way is more prone to humam error.

This multiplication is suppose to be a piecewise multiplication to update the upper limit of maxgenerationlimit based on whether the unit is on or off. But based on the way I formulated my objective function and due to the many segments of the linearized curve, I ended up with the variables being of different size. (A group of segments actually make up the cost function for one generator). So if I have three generator and I used 4 segments to linearize the cost for each generator I end up with 3 x 4 = 12 power segments in total. Whereas the isOn should only be used to keep track of the 3 generators and not all 12 segments.

I attempted to index values in the isOn variable to make it the same size as the maxGenConst variable but ran into alot of problems. I dont think you can access the optimization variable. I would not have run into the problem if I used the quadratic formulation for the cost curve but MATLAB doed not have a MIQP solver so I am stuck with linearizing the cost function. I am just looking for some advice as to what I should do.

[Micah Mungal]

I was able to solve my problem. I made maxGenConst the same size as isOn. Then I did the dot multiplication with isOn and was able to index the optimization expression and reshape into the proper dimensions. I have attached my code with data for a test system for anyone who will need it. This code considers power generation constraints, minimum up and down times, start up costs and the basic load demand constraints. I have included the data for a 6 unit system with the necessary data and the load demand over a 24hr period. This code does not consider losses in the system.

[Sivateja Maturu]

Can you please explain how you have defined the values of a, b, c for the power plants defined in your Gen_Data?

Answer 1

[Micah Mungal]

I was able to solve my problem. I made maxGenConst the same size as isOn. Then I did the dot multiplication with isOn and was able to index the optimization expression and reshape into the proper dimensions. I have attached my code with data for a test system for anyone who will need it. This code considers power generation constraints, minimum up and down times, start up costs and the basic load demand constraints. I have included the data for a 6 unit system with the necessary data and the load demand over a 24hr period. This code does not consider losses in the system.

[MUTHUSELVI G]

In this code Error in UC (line 178) powerprob = optimvar; is coming . what will i do?

[Micah Mungal]

What do you mean by "is coming"?

[ali gh]

An error appears after running the code

Subscripted assignment dimension mismatch.

Error in Untitled2 (line 244) sub_maxGenConst(:, num) = maxGenConst(:, (num * K));

[Kadyrbek]

Hello. Could you please send the code. [e-mail]

Answer 2

[amrit singh]

Undefined function or variable 'optimproblem'.

Error in ELD_LP (line 168)

powerprob = optimproblem;

Answer 3

[Martin Cruz]

tiene errores tu huevada