Economic Dispatch: Minimizing Grid Energy Cost

Grid Demand

Demand D 650 MW

Dual-ascent step size λ̇ 0.60

Optimizer State

Total cost

$0/h

Iteration

Generation

0 MW

Mismatch

0 MW

System marginal price λ (shadow price of demand)

$0.00 / MWh

Plants

How it works

Each generator i has a quadratic fuel-cost curve C_i(P_i) = a_iP_i² + b_iP_i, with 0 ≤ P_i ≤ P_max,i. The economic dispatch problem is:

minimize  Σ C_i(P_i)
subject to  Σ P_i = D   (must meet demand)
            0 ≤ P_i ≤ P_max,i

This is solved by Lagrangian dual ascent — the classic "equal incremental cost" rule used by real grid operators:

P_i ← clip( (λ − b_i) / (2 a_i),  0,  P_max,i )
λ  ← λ + η · (D − Σ P_i)

λ is the shared marginal price: every unconstrained plant is pushed to the output where its marginal cost dC_i/dP_i = 2a_iP_i+b_i equals λ. Cheap plants (small a_i, b_i) ramp up first; expensive ones only turn on once cheaper capacity is saturated. When Σ P_i = D exactly, λ is the price of the next MWh of demand — the same quantity real electricity markets call the locational marginal price.

Demand slider — how much power the grid must supply right now.
Step size η — how fast λ is adjusted; too high overshoots and oscillates, too low converges slowly.
Run / Step — iterate the dual-ascent update continuously or one update at a time.
Randomize plant costs — draws new (a_i, b_i, P_max,i) so the merit order (which plant is cheapest) changes.

mismatch: 0 MW

Bar height = plant output P_i Blue plane = demand target

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