Economic Dispatch

The core objective is to allocate load so that all dispatched units operate at an equal incremental cost (lambda), satisfying the equal lambda criterion. This ensures no cheaper megawatt can be substituted for a more expensive one. The algorithm solves a constrained optimization problem where the cost function of each generator—typically a quadratic curve representing fuel input versus power output—is minimized subject to the total load demand. Units with lower heat rates are preferentially loaded until their incremental cost rises to match the system marginal price.

Sophisticated dispatch algorithms incorporate loss penalty factors to account for the electrical distance between generation and load centers. A generator located far from demand incurs higher transmission losses, effectively increasing its delivered cost. The B-coefficient loss formula or a full AC optimal power flow model calculates these marginal loss factors. This ensures the dispatch minimizes the total cost of delivered energy, not just generated energy, preventing inefficient remote units from being dispatched over closer, slightly more expensive units.

Dispatch must respect strict physical limits of each committed unit:

• Pmin and Pmax: The minimum stable output and maximum rated capacity.
• Ramp rate limits: The maximum speed at which a unit can increase or decrease output, protecting against thermal stress.
• Prohibited operating zones: Ranges of output where severe turbine vibration or boiler resonance occurs, requiring the dispatch to skip these bands entirely.
• Valve point effects: Non-convex, rippled cost curves in thermal units caused by the sequential opening of steam admission valves, requiring advanced heuristic solvers.

Modern economic dispatch is fundamentally a security-constrained optimization. The algorithm must not only minimize cost but also ensure that no transmission line or transformer exceeds its thermal rating under both normal conditions (N-0) and any single credible contingency (N-1). This transforms the problem from a simple economic calculation into a large-scale, iterative linear or quadratic programming exercise. Shift factors (power transfer distribution factors) map generator outputs to line flows, allowing the dispatch to preemptively curtail units that would cause overloads.

Dispatch algorithms increasingly incorporate non-cost objectives and constraints:

• Emission rate limits: Hard caps on SO2, NOx, or CO2 output that may force the dispatch to bypass a cheaper coal unit for a cleaner gas turbine.
• Fuel supply limitations: Contractual or physical limits on gas pipeline delivery or coal stockpile drawdown rates.
• Must-run status: Units designated as essential for voltage support or local reliability are dispatched regardless of their marginal cost.
• Renewable curtailment minimization: The dispatch may be biased to reduce wind or solar curtailment, treating their fuel cost as zero and their availability as a negative load.

Real-time economic dispatch executes every 5 minutes, adjusting generator setpoints based on current system conditions and the latest load snapshot. In contrast, look-ahead dispatch extends the optimization horizon several hours into the future, incorporating forecasted load ramps and wind variability. This multi-interval optimization pre-positions units to meet upcoming steep ramps without violating rate limits, avoiding costly last-minute scarcity pricing. The look-ahead function bridges the gap between hourly unit commitment and real-time operations.

The forward-looking optimization that determines the on/off schedule for generating units days in advance. Unlike economic dispatch, which assumes a fixed set of committed units, unit commitment solves a mixed-integer problem incorporating start-up costs, minimum up/down times, and ramp constraints. The unit commitment solution defines the feasible set of generators available for the subsequent economic dispatch calculation.

The derivative of a generator's input-output curve, representing the additional fuel energy required (MBtu/h) to produce one additional MW of output at a given operating point. Economic dispatch algorithms rank units by their incremental cost—the product of incremental heat rate and fuel price—to achieve true cost minimization. This curve is inherently non-linear and convex.

Coefficients that adjust a generator's incremental cost to account for marginal transmission losses incurred when delivering power from that specific bus to the system load center. The penalty factor is calculated from the Jacobian of the power flow solution. Without these factors, economic dispatch would systematically under-dispatch electrically remote generators and over-dispatch units closer to load.

The nodal price of energy representing the marginal cost of serving the next increment of load at a specific bus. LMP is the Lagrangian multiplier from the security-constrained economic dispatch optimization and decomposes into three components:

• Energy component: System-wide marginal cost
• Congestion component: Cost of binding transmission constraints
• Loss component: Marginal cost of transmission losses

A unit-specific coefficient within the Automatic Generation Control (AGC) system that determines the proportion of the total required regulation change assigned to each generator. While economic dispatch sets the basepoint, the participation factor governs how real-time deviations from that basepoint are allocated among units on regulation, typically favoring fast-ramping resources with low wear-and-tear costs.

An extension of classical economic dispatch that enforces N-1 contingency constraints alongside the standard generation limits and power balance equation. The optimization ensures that no single transmission line or generator outage will cause thermal overloads or voltage violations. This transforms the problem from a simple lambda-iteration to a large-scale linear or quadratic programming formulation solved every 5 minutes.