Integrating Market Price Forecasting with Linear Programming for Optimal Electricity Market Clearing

Integrating Market Price Forecasting with Linear Programming for Optimal Electricity Market Clearing

Sri K. Naresh and Dr. G.N.Srinivas

Department of Electrical and Electronics Engineering, Jawaharlal Nehru Technological University Hyderabad, Hyderabad, India

Abstract – This paper presents an optimal electricity market clearing framework based on linear programming (LP), applied to a real-time, multi-period Indian power exchange market. The system operator maximises social welfare by dispatching ve generating units against seven demand entities across six trading periods using IEX 202526 average data. The dual variable of the energy-balance constraint directly yields the market clearing price (MCP) for each period. A market price forecasting module based on linear regression, using engineered supplydemand features, is integrated to predict clearing prices without re-solving the optimisation, achieving a mean absolute percentage error (MAPE) of 2.47%. Simulation results conrm that the LP clears the market at prices ranging from 5,900 to 8,500/MWh with a total social welfare of 26.87 Million, and the forecasting module provides economically consistent predictions suitable for real- time operator decision support.

Index Termselectricity market clearing, linear programming, social welfare maximisation, market clearing price, price forecast- ing, Indian power exchange, IEX, day-ahead market.

1. Introduction

   The electricity market clearing problem is one of the most critical optimisation tasks in modern power system operation. In a day-ahead market, power producers submit increasing- price production offer curves and power consumers submit decreasing-price consumption bid curves to the independent system operator (ISO). The ISO then determines the optimal hourly dispatch quantities and the market clearing price (MCP) that balances supply with demand [1].

   The Indian Electricity Exchange (IEX) operates a continu- ous double auction in which a large number of generators and distribution companies interact in real time. With increasing renewable penetration and price volatility, reliable price fore- casting is essential for market participants to hedge risk and for the ISO to plan reserves [3].

   Prior work has addressed market clearing either through purely deterministic LP [4] or through forecast-only machine learning models trained on historical prices [5]. The contribu- tion of this paper is a self-contained, LP-rst framework in which: (i) a rigorous welfare-maximising LP determines the cleared quantities and the MCP for each period; and (ii) a compact linear regression model, trained on features extracted from the LP inputs, predicts future prices without re-solving the LP. The approach is validated on IEX 202526 average data, requiring no external historical price database.

   The rest of the paper is organised as follows. Section II describes the market participants and the auction mechanism. Section III presents the LP formulation. Section IV describes the price forecasting model. Section V details the simulation setup and results. Section VI concludes.

2. Electricity Market Structure

   1. Market Participants and Auction Mechanism

      Three categories of agent participate in the day-ahead mar- ket:

      1. Power producers submit step-wise, monotonically in- creasing production offer curves for each hour.

      2. Power consumers submit step-wise, monotonically de- creasing consumption bid curves for each hour.

      3. Market operator (ISO) aggregates all curves, solves the welfare-maximisation problem, and announces the MCP and cleared quantities.

         Fig. 1: Electricity Market Clearing Mechanism

   2. Market Clearing Price Determination

   Under the uniform-price auction the MCP for period t

   satises:

   g d

   MCPt = max{cg | Pt accepted} = min{bd | Pt accepted}

   (1)

   This is the intersection of the aggregated supply and demand curves, corresponding to the dual variable (shadow price) of the energy-balance constraint in the LP.

3. Linear Programming Formulation

   1. Index Sets and Parameters

      G = {G1, G2, G3, G4, G5} Generators

4. Market Price Forecasting

   1. Motivation

      Once the LP is solved for a set of reference periods, the resulting MCP values {} can serve as labels for a supervised regression model. The model maps market features extracted from offer and bid data directly to prices, enabling real-time price estimation for new periods without re-solving the LP.

      D = {D1, D2,…, D7}

      T = {1, 2, 3, 4, 5, 6}

      Demand entities Trading periods

   2. Feature Engineering

   For each period t,a feature vector xt = [xt1, xt2, xt3, xt4]T

   is constructed as follows.

   Cg,t R+

   Offer price [/MWh]

   Average Demand: xt1 = 1

   Bid price [/MWh]

   Average Supply: xt2 = 1

   Max. quantities [MW]

   Peak Hour Indicator: xt3 = 1 if t {2, 5} (dened peak periods), else 0

   1. Decision Variables

      Cost Volatility: xt4

      These four features capture demand pressure, supply avail-

      ability, temporal peak effects, and generator-cost spread the principal economic drivers of the MCP.

   2. Objective Function Social Welfare Maximisation

      The ISO maximises aggregate social welfare (consumer surplus plus producer surplus) across all periods:

      C. Linear Regression Model

      Features are standardised (zero mean, unit variance) and a linear regression model is tted:

      Energy Balance (Market Clearing):

      mean squared error (MSE) over the six reference periods.

   3. Performance Metrics

      where t 0 is the dual variable equal to the MCP.

      Generator Capacity:

      MAE = 1 L | t| (12)

   price), negative on AvgSupply (more supply lowers price), and positive on Volatility (wider cost spread pushes up the marginal unit cost).

5. Simulation Setup and Results

   1. Data IEX 202526 Average

      Ud,t 0 (demand at most full bid price) (10)

      A generator is marginal when Cg,t = ; infra-marginal units earn positive rent while supra-marginal units are not dispatched.

      The study uses IEX 202526 average offer and bid data for a representative 6-period trading window. Tables I and II list the generator offer prices and capacities, and demand bid prices and maximum quantities, respectively.

      TABLE I: Generator Offer Prices Cg,t [/MWh] and Capacities

      P¯G [MW] IEX 202526 Avg.

      Gen T1 T2 T3 T4 T5 T6

      G1	4200	Offer Prices [/MWh] 4400 4100 4600			5100	4300
      G2	3800	3900 3700 4200			4800	4000
      G3	5200	5400 5000 5700			6500	5300
      G4	6100	6300 5900 6800			7500	6400
      G5	2900	3100 2800 3400			3900	3200
      G1	180	Capacities [MW] 190 170 185			200	175
      G2	420	410	450	430	380	440
      G3	150	160	140	155	170	145
      G4	90	100	85	95	120	92
      G5	550	520	580	540	480	560

      d,t

      TABLE II: Demand Bid Prices Ud,t [/MWh] and Maximum Quantities P¯D [MW] IEX 202526 Avg.

      Dem	T1 T2	T3	T4 T5	T6
      D1	Bid Prices [/MWh] 6200 6500 6000 6300 7800			5800
      D2	6800 7200 6600 7000 8500			6400
      D3	5500 5800 5300 5600 6900			5100
      D4	7100 7400 6900 7200 8800			6700
      D5	6400 6700 6100 6500 8000			5900
      D6	5900 6200 5700 6000 7400			5500
      D7	7800 8100 7500 7900 9500			7200
      D1	Maximum Quantities [MW] 320 350 300 330 400			280
      D2	480 510 460		490 580	430
      D3	150 180 130		160 220	140
      D4	290 320 270		300 380	260
      D5	410 440 380		420 500	360
      D6	210 240 190		220 280	180
      D7	380 420 350		400 520	330

   2. LP Market Clearing Results

      Table III summarises the LP clearing results. The MCP ranges from 5,900/MWh (Period 6, off-peak) to 8,500/MWh (Period 5, peak), driven by the merit-order dispatch mecha- nism. G4 (the most expensive unit) is dispatched in four of six periods, conrming it as the price-setting marginal unit during high-demand intervals. Total social welfare across all six periods is 26.87 Million.

      TABLE III: Multi-Period LP Market Clearing Summary

      Period MCP [/MWh] Total Cleared [MW] Soc. Welfare [M] G4 Dispatched?

      1	6,400	1,390	4.55	Yes
      2	6,700	1,380	4.77	Yes
      3	6,100	1,425	4.44	Yes
      4	6,500	1,310	4.15	No
      5	8,500	1,350	5.39	Yes
      6	5,900	1,320	3.57	No

      Total Social Welfare 26.87 Million

      Fig. 2 shows generator dispatch across all periods. G5, the lowest-cost unit (2,9003,900/MWh), is fully dispatched in every period, conrming its role as the base-load unit. G3 and G4 are dispatched only when aggregate demand exhausts the cheaper supply stack, causing the price jumps visible in Fig. 3.

      Fig. 2: Generator dispatch across six trading periods [MW].

      Fig. 3: Market clearing price [ /MWh ] and social welfare[M] per period.

   3. Price Forecasting Results

      Table IV compares the LP-derived MCP with the linear- regression forecast for each period.

      Period	Actual MCP [/MWh]	Forecast [/MWh]	Error [%]
      1	6,400	6,435.6	0.56
      2	6,700	6,901.6	3.01
      3	6,100	5,840.0	4.26
      4	6,500	6,760.3	4.00
      5	8,500	8,303.0	2.32
      6	5,900	5,859.5	0.69
      MAPE MAE	2.47% 165.85 /MWh
      RMSE	190.50 /MWh

      TABLE IV: LP Actual vs. Forecasted Market Clearing Prices

      The tted regression weights are given in Table V. The signs are economically consistent: AvgDemand carries a strong positive weight (higher demand raises price), AvgSupply is negative (more supply lowers price), and Volatility is positive (wider cost spread indicates a steeper supply stack, pushing up the MCP).

      TABLE V: Linear Regression Weights and Economic Inter- pretation

      Feature Weight Economic Interpretation

      AvgDemand +512.74 Higher demand costlier marginal unit AvgSupply 119.64 More supply cheaper marginal unit PeakHour 4.38 Absorbed by demand/volatility features

   4. Discussion

      Period 5 peak behaviour: The MCP spike to 8,500/MWh results from the simultaneous effect of peak- hour demand (+28.6% over the median) and the entry of G4 (7,500/MWh) as the marginal unit. Social welfare is highest in this period (5.39M) because the large volume of high-value demand is cleared despite theelevated price.

      Period 6 off-peak: Total cleared quantity falls to 1,320 MW and price drops to 5,900/MWh; G4 is not dispatched, and the marginal unit is G3. Social welfare is lowest (3.57M).

      • Forecast quality: The 2.47% MAPE demonstrates that simple feature-based linear regression captures the domi- nant price drivers. The largest individual error (4.26%, Period 3) occurs when supply exceeds demand most comfortably, creating a atter supply curve that is harder to map linearly.

      • Scalability: The LP scales linearly in the number of gen- erators and demand entities; adding network transmission constraints (DC power-ow equations) is a straightfor- ward extension.

6. Conclusion

This paper has presented a complete LP-based electricity market clearing model for the Indian day-ahead market. The

Volatility Intercept

+230.01 Steeper stack higher clearing risk

+6683.34 Base price level for average market conditions

welfare- maximisation LP correctly identies the marginal generator and derives the MCP as the dual variable of the energy-balance constraint across six trading periods using

Fig. 4 plots the actual MCP versus the forecast across all six periods, demonstrating close tracking of both off-peak and peak price levels.

Fig. 4: Actual vs. forecasted market clearing price per period.

IEX 202526 average data. The framework achieves a total social welfare of 26.87M, with clearing prices between 5,900 and 8,500/MWh.

A compact linear regression price forecasting model, fed with four market features derived from offer and bid data, predicts clearing prices with a MAPE of 2.47% and RMSE of 190.5 /MWh, providing operators with a fast, LP-free price signal for intra-day scheduling and risk hedging. The economic sign consistency of the regression weights further validates the feature design.

Future work will extend the framework to a full 24-period horizon using the complete IEX daily prole, incorporate DC power-ow network constraints for nodal pricing, and investigate adaptive forecasting methods suitable for non- stationary price dynamics.

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