Electricity Markets pp 229-246 | Cite as

# Optimal Power Scheduling of a GenCo Using Two-Point Estimate Method

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## Abstract

Optimal scheduling of a generating company (GenCo) is necessary in the day-ahead electricity market to obtain maximum profit. But, the market price uncertainty may lead to negative effects for GenCo which should be modeled in the uncertain environment. First, a deterministic-based model via Mixed-Integer Quadratic Constrained Program (MIQCP) is formulated in this study to obtain optimal scheduling of GenCo. Then, a two-point estimate method (TPEM) is proposed to model the market price uncertainty in order to obtain uncertainty-based scheduling of GenCo. The proposed approach is investigated on two GenCo comprising 5-unit and 54-unit thermal generation to show the capabilities of the proposed approach in a large test system. Furthermore, the obtained results based on proposed approach are compared with the Monte Carlo Simulation (MCS) and deterministic approach in order to show the efficiency of the proposed approach in the uncertain environment.

## Keywords

Generating company (GenCo) Two-point estimate method (TPEM) Monte Carlo simulation (MCS) Mixed-integer quadratic constrained program (MIQCP)## Nomenclature

## Set

*t*Index of time interval

*i*Index of generation units

*j*Auxiliary index for linear modeling of minimum up-time and minimum down-time constraints

## Known Parameters

*a*_{i},*b*_{i},*c*_{i}Quadratic, linear, and fixed coefficients of operation cost function for generation unit

- SD
_{i},SU_{i} Shut-down and start-up costs of generation unit

- \( {P}_i^{\mathrm{G},\min } \),\( {P}_i^{\mathrm{G},\max } \)
Minimum and maximum powers of generation unit

- UR
_{i},DR_{i} Ramp-up and ramp-down limits of generation unit

- MDT
_{i},MUT_{i} Minimum down/up time limits of generation unit

- Dn
_{i, j},Up_{i, j} Auxiliary parameters for the MDT and MUT constraints

- \( {\lambda}_t^D \)
Electricity price

## Decision Variables

- U
_{i, t} Binary variable {0,1}, It is 1 if generation unit is ON; otherwise, it is 0.

- \( {P}_{i,t}^{\mathrm{G}} \)
Generation power of unit

- Δ
*P*_{i, t} An auxiliary variable for using the power generation of unit

- SDC
_{i, t},SUC_{i, t} Shut-down and start-up costs of generation unit

## Functions

- Cost (
*t*) Total cost of GenCo at each time

*F*(*P*^{G},*λ*^{D})Total profit of GenCo

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