A robust optimization approach to energy and reserve dispatch in electricity markets

Abstract

To a large extent, electricity markets worldwide still rely on deterministic procedures for clearing energy and reserve auctions. However, larger and larger shares of the production mix consist of renewable sources whose nature is stochastic and non-dispatchable, as their output is not known with certainty and cannot be controlled by the operators of the production units. Stochastic programming models for the joint determination of the day-ahead energy and reserve dispatch, necessary for coping with the real-time output deviations from these sources, have been proposed in the literature. In this work, we take an alternative approach and cast the problem as an adaptive robust optimization problem. The day-ahead and reserve schedules determined in this fashion yield the minimum system cost, accounting for the cost of the redispatching decisions at the balancing stage, in the worst-case realization of the stochastic production within a specified uncertainty set. In a case-study based on a 24-node system, we assess the degree of suboptimality of the robust solution with respect to the optimal dispatch obtained with a stochastic programming approach, and compare their worst-case cost. Furthermore, we discuss the robustness of these two alternative approaches with respect to changes in the distribution of the uncertainty, as well as their computational properties. d Demand at each node of the system (considered known with certainty);

Operational strategies for predictive dispatch of control reserves in view of stochastic generation

“…Constraint (4) requires that the remaining imbalance P imb − P M, * will be covered by the automatic response, while constraint (5) ensures that this response respects the operational and reserve limits.…”

“…References [2]- [4] formulate a stochastic programming model for joint optimization of day-ahead and balancing operation minimizing the expected cost of the system, while [5] employs adaptive robust optimization in order to minimize the cost of the worst case scenario. Using wind power probabilistic forecasts, [6] defines multi-criteria decision strategies for setting reserve requirements considering risk and economic aspects.…”

On quantification of flexibility in power systems

“…Considering that the above optimization problem cannot be solved directly given its min − max − min structure, we reformulate the max − min problem according to [7] using the dual of the right-hand side problem which is written as…”

“…To incorporate the interaction between flexibility and uncertainty into the dispatch decision-making of the TSO, we propose a twostage adaptive robust optimization model for the procurement of control reserves. Similar applications of adaptive robust optimization in power systems are presented in [7], which however do not explicitly account for ramping and energy limitations.…”

Spinning Reserve Capacity Optimization of a Power System When Considering Wind Speed Correlation

“…Considering uncertainties in wind power and load forecasts, a multi-objective energy and spinning reserve scheduling method for a wind-thermal power system is investigated in a market environment [8]. Cobos, et al [9] establishes a mathematical optimization model for the minimum cost of conventional generators and spinning reserve, and then adopts a robust linear optimization to get the optimal reserve capacity with the wind uncertainty, so as to guarantee the feasibility of the optional solutions for all the realizations of the uncertain data. In [10], based on a robust optimization approach, an energy and reserve joint dispatch model in the real-time electricity markets is presented, considering wind power generation uncertainties as well as zonal reserve constraints under both normal and N-1 contingency conditions.…”