Publication record · 18.cifr/2020.conejo.market-complementarity

Complementarity, Not Optimization, is the Language of Markets

v1.0.0

Antonio J. Conejo (The Ohio State University), Carlos Ruiz (Universidad Carlos III de Madrid)

RAI18.cifr/2020.conejo.market-complementarity

IEEE Open Access Journal of Power and Energy· 2020· doi:10.1109/OAJPE.2020.3029134

This paper argues that the natural language of electricity markets is complementarity, not optimization. While market clearing is often formulated as a social welfare maximization problem, the underlying equilibrium conditions are complementarity conditions derived from KKT optimality. The paper presents both energy-only and network-constrained market models, derives their KKT/complementarity conditions, and solves them as linear complementarity problems (LCPs) to find market equilibria including locational marginal prices.

electricity marketscomplementarityKKT conditionslocational marginal priceslinear complementarity problemDC optimal power flow

✦ Research context

What this agent contributes to the literature.

Problem solved

Optimization-based market clearing obscures the true equilibrium structure underlying electricity markets.
Power systems researchers and market operators lack a unified complementarity language for energy and network-constrained markets.
KKT conditions are typically treated as a solution tool, not as the primary market model.

Novelty

Reframes electricity market clearing as a Linear Complementarity Problem (LCP) derived from KKT conditions, not optimization.

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Canvas contract1-in / 1-out · unpacked into market, network legacy ports

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4/15/2026

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sha256:9a1b75a942ae13908cc87ff8907b563045d95a587acd4b25bbc841cd6a81279a

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input:application/json

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output:application/json

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Pre-filled with the paper's canonical scenario. Click Invoke agent to reproduce the original result, or edit the JSON below to run a counterfactual.

inputapplication/jsonoptional

Unified canvas input. The executor unpacks this JSON blob into legacy per-port files: market, network

Leave empty to run the paper's canonical scenario.

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        "c1": 15,
        "c2": 0.03,
        "qmax": 150
      },
      {
        "id": "G3",
        "bus": "B3",
        "c1": 20,
        "c2": 0.04,
        "qmax": 100
      }
    ],
    "consumers": [
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        "bus": "B1",
        "u1": 50,
        "u2": 0.05,
        "dmax": 300
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        "bus": "B3",
        "u1": 45,
        "u2": 0.06,
        "dmax": 200
      }
    ]
  },
  "network": {
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        "type": "slack"
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      {
        "id": "B2",
        "type": "PQ"
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        "type": "PQ"
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    "lines": [
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        "from": "B1",
        "to": "B2",
        "reactance": 0.1,
        "fmax": 100
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}