Economic Dispatch

ED tries to allocate available generation to meet the current system load at lowest cost. The classic text is Wood & Wollenburg.

The problem

$min\sum _g{C}_g\left(P_g\right)$

$\text{s.t.}{P}_{min\left(g\right)}\le P_g\le P_{max\left(g\right)}\forall \text{generators}\left(g\right)$

$\text{s.t.}\sum _g{P}_g=P_{\text{load}}$

In this mathematical formulation generators are indexed by $g$. $P_g$ is a generator’s power output and $C_g\left(\right)$ is its cost function. The objective is to minimize the total cost. There are two constraints:

• each generator must be within its real power limits and
• total power generated must equal the power consumed by the load.

The basics

Let’s say you have made a folder called mydispatch and put the information about your problem in the folder. Then if you run the script:

from minpower import solve
solve.problem('mydispatch/')

you get a plot:

and a spreadsheet:

generator name, u,     P,     IC
cheap,          True,  65.4,  44.5
expensive,      True,  38.7,  44.5

These outputs show that the problem’s two generators (named cheap and expensive) are being dispatched so that their incremental costs (the vertical axis in the plot and IC in the spreadsheet) are equal. Each generator’s incremental cost curve is shown in the plot, with a dot on its current real power output (P). Because this is a dispatch each generator is on (u=True) unless specified in the input spreadsheet.

These outputs are saved in the mydispatch folder as dispatch.png and dispatch.csv.

What’s actually going on?

It’s easy once you get the hang of it. minpower will:

1. read in your files (see get_data)
2. set up an optimization problem (see solve.create_problem())
3. send it off to a solver (see optimization.solve())
4. show you the results (see results.Solution_ED)

minpower just looks for the files in the mydispatch directory that describe the generators and load.

Tell it the specifics of your problem by editing the generator file (generators.csv):

name,     P max, cost curve equation
cheap,    100,   200 + 5 * P + .3 P^2
expensive,100,   300 + 10 P + .25 P^2 + .005 P^3

and load file (loads.csv):

name,               Pd
Seattle City Light, 50
Tacoma Power,       50 

Note

For more information about what options you can specify in each spreadsheet see: Data Input.