Stochastic Unit Commitment in Low-Inertia Grids

Abstract

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model and included into a stochastic UC that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. For medium-sized networks, this method is shown to be computationally more efficient than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.

Modeling Frequency Dynamics in Unit Commitment With a High Share of Renewable Energy

“…Though the proposed model may look similar to the work of Paturet [15], the two papers have several significant differences. This paper proposes a novel concept referred as frequency security margin.…”

“…With the assumption that the frequency regulation reserve is delivered linearly in the frequency dynamic process, Teng et al formulated linear frequency security constraints and applied them in a stochastic UC model [14]. Paturet et al proposed a stochastic UC model considering the minimum inertial requirement for low-inertia systems [15]. Sokoler et al proposed an optimal reserve planning model for an isolated power system to guarantee that the system frequency maintains above a pre-defined limit during the contingency [16].…”

PFR ancillary service in low‐inertia power system

“…First , in this paper, the frequency response requirements for different system inertia conditions are derived from the fully network models used in grid operation. Compared to previous works, in which simplified dynamic models [22–26, 29–31, 33–35] are used, our approach accurately captures the interplay among the UC statuses, inertia and PFR. Since the PFR requirement is predetermined, running time‐consuming dynamic simulations is not necessary when solving the UC problem.…”

“…The work in [33] developed a robust UC including frequency stability constraints with a simplified dynamic model representing the frequency response. A similar approach was proposed in [34, 35] to incorporate the analytic frequency deviation into UC while considering a set of scenarios. Using simplified models may reproduce satisfactory frequency responses in a small system, but for a larger, realistic regional grid (e.g.…”

Towards Optimal System Scheduling With Synthetic Inertia Provision From Wind Turbines

“…This has been addressed in [12]- [15] through various forms of linearization of the respective constraint. Additionally, in [15] the state-of-theart converter control schemes of inverter-based generation are included in the system frequency dynamics and virtual inertia units are explicitly considered for inertia provision. [16] and [17] consider the combination of a finite number of frequency response services with different delivery times and a dynamically-reduced largest power in-feed.…”