Chance-constrained Unit Commitment via the Scenario Approach

Abstract

Keeping the balance between supply and demand is a fundamental task in power system operational planning practices. This task becomes particularly challenging due to the deepening penetration of renewable energy resources, which induces a significant amount of uncertainties. In this paper, we propose a chance-constrained Unit Commitment (c-UC) framework to tackle challenges from uncertainties of renewables. The proposed c-UC framework seeks cost-efficient scheduling of generators while ensuring operation constraints with guaranteed probability. We show that the scenario approach can be used to solve c-UC despite of the non-convexity from binary decision variables. We reveal the salient structural properties of c-UC, which could significantly reduce the sample complexity required by the scenario approach and speed up computation. Case studies are performed on a modified 118-bus system. The authors are with the Recently, the growing amount of uncertainties from renewables pose new challenges on the operations of power systems. UC, as a critical part of day-ahead scheduling, needs to be improved to consider the impacts of uncertainties. Broadly speaking, there are two approaches for decision making under uncertainties: stochastic optimization (SO) and robust optimization (RO). SO relies on probabilistic models to explain uncertainties and often optimizes the objective function in the presence of randomness. SO has found many successful applications in power systems. References [1]-[3] formulate and solve the stochastic unit commitment problem, which typically minimizes expected commitment and dispatch costs in the presence of uncertainties. RO takes an alternative approach, in which the uncertainty model is set-based and deterministic. Recently, researchers in [4] formulated and solved the robust unit commitment problem, which minimizes the commitment and dispatch costs for the worst case in a predefined uncertainty set. Both approaches attract a lot of attention and are relatively successful in addressing the challenges related with uncertainties. This paper looks at the UC problem through the lens of chance-constrained optimization (CCO), which is closely related with both stochastic and robust optimization [5]. The main difference of CCO from SO or RO is the chance constraint (i.e. (1b) and (2b)), which explicitly considers the feasibility of solutions under uncertainties.Various formulations of chance-constrained (security-constrained) unit commitment have been proposed, e.g.[6]- [14]. As mentioned in [5], chance-constrained optimization problems can be solved via different methods. We take chance-constrained unit commitment problem as an example. It can be solved using sample average approximation [8]-[10], [12]-[14] or robust optimization based techniques [15]. The scenario approach, which might be the most wellknown method to solve chance-constrained optimization, was not directly applied on the unit commitment. The only related references we found are [16], [17], which are built upon a variation of the scen...

Approximate Chance-Constrained Unit Commitment Under Wind Energy Penetration

“…On the other hand, we know that by Kirchhoff's first law, the supply and demand for energy must be balanced at all time, for the system to be in equilibrium. In (6), the load balance is instead formulated as an inequality, which is usually the case under a chance constraint framework, e.g., [29,28,13,33,34], as the probability of a continuous random variable taking on a single value is virtually zero. But, let us remind ourselves that the primary goal of the UC problem is to find the commitment status of the conventional generators for each time period.…”

Two-stage Robust Energy Storage Planning with Probabilistic Guarantees: A Data-driven Approach

“…Ξ1 := (E n , P n , z n )s that satisfy constraints (18) (19) (25) The feasible region of the second stage Ξ2 (E n , P n ; δ) is Ξ2 (E n , P n ; δ) := (p ch n,t , p dis n,t , p G i,n,t , p shed n,t )s that satisfy constraints (21) (22) (26) .…”

“…This simple construction of uncertainty set is closely related with the scenario approach theory [15,16,17,18]. The scenario approach has been recently introduced to the energy systems problems, e.g., resource adequacy and security assessment [19], economic dispatch [20], demand response scheduling [21], and unit commitment [22,23] .…”

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