# Generation Scheduling Based on Two-Level Optimization Problem

I. A. Nechaev (Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia) and S.I. Palamarchuk (Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia)
DOI: 10.4018/ijeoe.2014010101

## Abstract

A two-level problem for electricity generation scheduling in the wholesale market environment is proposed. The lower level of the problem corresponds to System Operator's (SO) efforts to schedule generation and calculate local marginal prices (LMPs) on the basis of total production cost minimization. The upper level corresponds to the profit maximization of each Generating Company (GC) with true cost functions and true generation ranges. The lower level of the problem is represented as a Mathematical Program with Equilibrium Constraints (MPEC). The problem is deemed solved, when the Nash equilibrium point is reached among strategic producers. The two-level optimization problem is formulated and the method for its solving is developed. A numerical example of a 15-bus Electric Power System (EPS) with thermal and hydro power plants is used to test the applicability of the approaches. The efficiency of the proposed approach is shown in comparison with traditional methods.
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## Notation

The notation used in the paper is presented below for quick reference. Other symbols are defined as needed throughout the text:

• n – number of buses in EPS;

• In – set of numbers of buses in EPS;

• m – number of ties in EPS;

• g – number of generating buses;

• Ig – set of numbers of generating buses;

• F – amount of GCs;

• f – index number of GC;

• nf – amount of generating buses in the f-th GC;

• If – set of numbers of generating buses in the f-th GC;

• Id – set of numbers of demand buses;

• Ri – set of numbers of buses connected with node i;

• Pgi – power generation at bus i, MW;

• Pdi – power load at bus i, MW;

• pi – electricity market clearing price at bus i, \$/MW;

• Pij – power flow from bus i to bus j, MW;

• Pji – power flow from bus j to bus i, MW;

• Pgimin, Pgimax – minimum and maximum power generation at bus i, MW;

• Pijmax – maximum transfer capabilities of the transmission line between buses i and j, MW;

• ij – power losses in the ties between buses i and j as fractions of power flows Pij or Pji.

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