Non-convex electricity markets face structural pricing failures due to fixed startup and operating constraints. A newly proposed primal-dual sequential linear programming scheme computes revenue-adequate, uniform locational marginal prices. This eliminates the need for side payments while recovering generators’ operating costs during market clearing.
When the restructuring of the power industry led to the development of wholesale electricity markets, it introduced competition. Non-convexities—such as fixed startup/shutdown and no-load costs, minimum generation, and up/down time—pose challenges for determining optimal market-clearing prices. This mathematical friction meant generators often received only partial recovery of operating costs under conventional pricing schemes. Independent system operators (ISOs) relied on side payments to fill the gap. Now, research published in the Journal of Energy Markets outlines a sequential linear programming approach designed to address this pricing inefficiency.
The Bottom Line
- The Core Fix: The newly formulated model uses a primal-dual framework and sequential linear programming to solve mixed-integer nonlinear optimization hurdles.
- Financial Impact: It generates uniform, revenue-adequate locational marginal prices that incorporate startup cost recovery constraints and lost opportunity cost constraints without requiring any separate side payments.
- Market Transparency: By adjusting conventional marginal prices to account for operational constraints, the scheme supports competitive equilibrium while keeping generator schedules aligned with the ISO’s schedule.
Unraveling the Non-Convex Pricing Problem
The restructuring of the power industry introduced competition, but it also exposed flaws in how clearing prices are calculated. In a conventional market-clearing model, marginal pricing clears the system. However, non-convexities in these markets pose challenges for determining optimal market-clearing prices. They involve fixed startup/shutdown and no-load costs, and enforce strict operational thresholds regarding minimum generation and up/down time.
When these constraints enter the optimization mix, standard locational marginal pricing models face challenges. To address this, researchers have modeled the problem as a mixed integer nonlinear programming problem, which is linearized using a sequential linear programming algorithm. This allows the formulation to bake cost-recovery directly into the price.
Sequential Linear Programming and Primal-Dual Formulations
To address challenges in determining optimal market-clearing prices, the newly proposed scheme applies a sequential linear programming algorithm. This approach linearizes the non-convex constraints—specifically fixed startup/shutdown and no-load costs, minimum generation, and up/down time—allowing optimization engines to compute prices efficiently.
Furthermore, the model incorporates the generator’s lost opportunity costs to encourage them to follow the independent system operator’s schedule. By factoring this into the primal-dual clearing formulation, the pricing mechanism incentivizes compliance without needing separate side payments. The resulting prices deviate only slightly from the marginal prices of the conventional market-clearing model, yet they achieve revenue adequacy.
| Market Pricing Model | Side Payments Required | Cost Recovery Status | Price Transparency |
|---|---|---|---|
| Conventional LMP | Yes | Partial | Low |
| Proposed SLP Scheme | No | Full (Revenue-Adequate) | High |
Implications for Power Producers and Market Efficiency
Case studies analyzing the sequential linear programming formulation confirm that competitive equilibrium is supported across test networks. By eliminating side payments, the generated locational marginal pricing supports competitive equilibrium. As power grids evolve, adopting revenue-adequate pricing mechanisms is a focus of the proposed research.
Disclaimer: The information provided in this article is for educational and informational purposes only and does not constitute financial advice.
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