Optimisation of power system security with high share of variable renewables Consideration of the primary reserve deployment dynamics on a Frequency Constrained Unit Commitment model

The Unit Commitment problem (UC) is a family of optimisation models for determining the optimal short term generation schedule to supply electric power demand with a defined risk level. The UC objective function is given by the operational costs over the optimisation horizon. The constraints include, among others, technical, operational and security limits. Traditionally, the security constraints are given by the requirement of a certain volume of on line spare capacity, which is called the reserve and is meant to handle uncertainty, while preventing the interruption of power supply. It is commonly specified following a static reliability criterion, such as the N 1 rule.Nevertheless, in small systems the fixed, and a priori defined, reserve constraint could entail a violation of the N 1 criterion, although the reserve constraint was met. More recently, the increasing share of variable generation from renewable sources (V RES) such as wind and solar, may lead to UC solutions that no longer ensure system security. Therefore, different impact mitigation techniques have been proposed in literature, which include the revision of UC models to provide a better representation of the system dynamics. This subfamily of UC models is formally defined in this work as the frequency constrained UC problem (FCUC) and aims to keep the frequency above a certain threshold, following pre defined contingencies, by adding enhanced security constraints. In this work this topic is addressed in four parts.The first part identifies the main challenge of formulating the FCUC problem. Indeed, the frequency minimum, also called the frequency nadir, constraint is strongly non linear on the decision variables of the UC model. Moreover, the behaviour of the frequency nadir regarding the binary decision variables is hard to approximate by analytical functions. Thus, a sequential simulation approach is proposed, based on a classic UC model and a reduced order model of the primary frequency response. The potential benefits of a smarter allocation of the primary reserve is revealed.The second part of this work investigates the impact of V RES sources on the primary frequency response. The underlying processes that lead to the increase of the Under Frequency Load Shedding (UFLS) risk are thoroughly discussed. The need of formulating more accurate FCUC models is highlighted.The third part of this work examines the cost/benefit and limitation of FCUC models based on indirect constraints over certain dynamic parameters of the generating units. A methodology is proposed that assesses the effectiveness and optimality of some existing V RES impact mitigation techniques, such as the increase of the primary reserve requirement, the prescription of an inertia requirement, the authorisation of V RES dispatch down or the consideration of fast non synchronous providers of frequency regulation services. This study showed the need for new methods to properly handle the frequency nadir constraint in order to ensure optimality, without compromising the optimisation problem's tractability.The fourth part of this work offers a new formulation of the FCUC problem following a Bender's decomposition approach. This method is based on the decomposition of an optimisation problem into two stages: the master and the slave problems. Here, the master problem deals with the generating unit states and the slave problem handles the frequency nadir constraints through a cutting plane model. Simulation results showed that the more accurate representation of the frequency nadir in the slave problem reduces the risk of UFLS and the security cost, with respect to other FCUC models, such as those based on inertia constraints. In addition, the optimality of the global solution is guaranteed; although the convergence of the master problem is slow, due to the well known tailing off effect of cutting plane methods.