Economic Dispatch

Economic dispatch minimizes total generation cost while meeting load demand and respecting generator limits.

Generator Data Indices

MATPOWER generator array columns (0-indexed):

Index	Field	Description
0	GEN_BUS	Bus number (1-indexed)
8	PMAX	Maximum real power (MW)
9	PMIN	Minimum real power (MW)

# Use bus number mapping (handles non-contiguous bus numbers)
bus_num_to_idx = {int(buses[i, 0]): i for i in range(n_bus)}
gen_bus = [bus_num_to_idx[int(g[0])] for g in gens]

pmax_MW = gen[8]
pmin_MW = gen[9]

Cost Function Format

MATPOWER gencost array (polynomial type 2):

Index	Field	Description
0	MODEL	2 = polynomial
1	STARTUP	Startup cost ($)
2	SHUTDOWN	Shutdown cost ($)
3	NCOST	Number of coefficients
4+	coeffs	Cost coefficients (highest order first)

For quadratic (NCOST=3): coefficients are [c2, c1, c0] at indices 4, 5, 6 For linear (NCOST=2): coefficients are [c1, c0] at indices 4, 5

Cost = c₂·P² + c₁·P + c₀ ($/hr) where P is in MW.

Optimization Formulation

import cvxpy as cp

Pg = cp.Variable(n_gen)  # Generator outputs in per-unit

# Objective: minimize total cost (handles variable NCOST)
cost = 0
for i in range(n_gen):
    ncost = int(gencost[i, 3])
    Pg_MW = Pg[i] * baseMVA

    if ncost >= 3:
        # Quadratic: c2*P^2 + c1*P + c0
        c2, c1, c0 = gencost[i, 4], gencost[i, 5], gencost[i, 6]
        cost += c2 * cp.square(Pg_MW) + c1 * Pg_MW + c0
    elif ncost == 2:
        # Linear: c1*P + c0
        c1, c0 = gencost[i, 4], gencost[i, 5]
        cost += c1 * Pg_MW + c0
    else:
        # Constant cost
        cost += gencost[i, 4] if ncost >= 1 else 0

# Generator limits (convert MW to per-unit)
constraints = []
for i in range(n_gen):
    pmin = gens[i, 9] / baseMVA
    pmax = gens[i, 8] / baseMVA
    constraints.append(Pg[i] >= pmin)
    constraints.append(Pg[i] <= pmax)