Toward scalable stochastic unit commitment. Part 1: load scenario generation

Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Tra- ditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load sce- narios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessi- tates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation method- ology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator for New England (ISO- NE). The accuracy of the expected scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit com- mitment solvers, as described in the companion paper. The scenarios generated by our method are available as an online supplement to this paper, as part of a novel, publicly available large-scale stochastic unit commitment benchmark

A new trilevel optimization algorithm for the two-stage robust unit commitment problem

We present a new trilevel optimization algorithm to solve the robust two-stage unit commitment problem. In a robust unit commitment problem, rst stage commitment decisions are made to anticipate the worst case realization of demand uncertainty and minimize operation cost under such scenarios. In our algorithm, we decomposed the trilevel problem into a master problem and a sub-problem. The master problem can be solved as a mixed-integer program and the sub-problem is solved as a linear program with complementary constraints with the big-M method. We then designed numerical experiments to test the performance of our algo- rithm against that of the Benders decomposition algorithm. The experiments shows that our algorithm performs consistently better than the Benders approach

A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty

Accepted versio

Start Me Up: Modeling of Power Plant Start-Up Conditions and their Impact on Prices

In this paper we compare different approaches to account for start-up costs when modeling electricity markets. We restrict the model formulation to either linear or mixed integer problems in order to guarantee a robust solution. The results indicate that the choice of the model has a significant impact on the resulting market prices and company profit. The models either calculate higher peak prices or prices below marginal costs in off-peak periods but not both. Furthermore, the models perform differently when we apply a large sample, the number of equations having an important impact. We conclude that different model formulations respond particularly to specific modeling questions

Start Me Up: Modeling of Power Plant Start-Up Conditions and their Impact on Prices

In this paper we compare different approaches to account for start-up costs when modeling electricity markets. We restrict the model formulation to either linear or mixed integer problems in order to guarantee a robust solution. The results indicate that the choice of the model has a significant impact on the resulting market prices and company profit. The models either calculate higher peak prices or prices below marginal costs in off-peak periods but not both. Furthermore, the models perform differently when we apply a large sample, the number of equations having an important impact. We conclude that different model formulations respond particularly to specific modeling questions

Price Formation and Market Power in the German Wholesale Electricity Market in 2006

From 2002 to 2006, German wholesale electricity prices more than doubled. The purpose of this paper is to estimate the price components in 2006 in order to identify the factors responsible for the increase. We develop a competitive benchmark model, taking into account power plant characteristics, fuel and CO2-allowance prices, wind generation, cross-border flows, unit commitment and start-up conditions, to estimate the difference between generation costs and observed market prices for every hour in 2006. We find that prices at the German wholesale market (EEX) are above competitive levels for a large fraction of the observations. We verify the robustness of the results by carrying out sensitivity analyses. We also address the issue of revenue adequacy

Price Formation and Market Power in the German Wholesale Electricity Market in 2006

From 2002 to 2006, German wholesale electricity prices more than doubled. The purpose of this paper is to estimate the price components in 2006 in order to identify the factors responsible for the increase. We develop a competitive benchmark model, taking into account power plant characteristics, fuel and CO2-allowance prices, wind generation, cross-border flows, unit commitment and start-up conditions, to estimate the difference between generation costs and observed market prices for every hour in 2006. We find that prices at the German wholesale market (EEX) are above competitive levels for a large fraction of the observations. We verify the robustness of the results by carrying out sensitivity analyses. We also address the issue of revenue adequacy

A Stochastic Model for Self-scheduling Problem

The unit commitment (UC) problem is a typical application of optimization techniques in the power generation and operation. Given a planning horizon, the UC problem is to find an optimal schedule of generating units, including on/off status and production level of each generating unit at each time period, in order to minimize operational costs, subject to a series of technical constraints. Because technical constraints depend on the characteristics of energy systems, the formulations of the UC problem vary with energy systems. The self-scheduling problem is a variant of the UC problem for the power generating companies to maximize their profits in a deregulated energy market. The deterministic self-scheduling UC problem is known to be polynomial-time solvable using dynamic programming. In this thesis, a stochastic model for the self-scheduling UC problem is presented and an efficient dynamic programming algorithm for the deterministic model is extended to solve the stochastic model. Solutions are compared to those obtained by traditional mixed integer programming method, in terms of the solution time and solution quality. Computational results show that the extended algorithm can obtain an optimal solution faster than Gurobi mixed-integer quadratic solver when solving a stochastic self-scheduling UC problem with a large number of scenarios. Furthermore, the results of a simulation experiment show that solutions based on a large number of scenarios can generate more average revenue or less average loss