TomSym compared to the Symbolic Toolbox

A hydroelectric dam.

We look at the optimization problem of maximizing the revenue of a hydroelectric dam. This problem was published by By Seth DeLand of the MathWorks, as an example of how to combine their optimization and symbolic toolboxes. [1] We solve the same probem using tomSym and the TOMLAB solvers, noting a XXX times speed up. The problem can be solved in seconds with TOMLAB, as compared to hours with the MathWork's toolboxes.

The dynamics of the dam is described by the following equations.

Electricity(t) = TurbineFlow(t-1)*[½ k1(Storage(t) + Storage(t-1)) + k2] Storage(t) = Storage(t-1) + ∆t * [inFlow(t-1) - spillFlow(t-1) - turbineFlow(t-1)]

The actual data used by DeLand can be downloaded from Matlab Central.[2] To avoid attaching data files to our example, we will use an approximation to this data, as generated by the following Matlab code:

N = 480;
t = (0:N-1)';
inFlow = reshape(repmat(10*(107+[0 0 0 -3 3 2 2 -8 9 5 0 1 -6 -4 5 0 -6 -6 -17 -7]),24,1),N,1);
price = 46 + t./57 - 3*cos((t+46)/43) - 4*sin(pi/12*(t+4)) - 4*sin(pi/6*(t+1));