Continuous-time optimization of power systems operation

dissertationWith the large integration of renewable energy resources in power systems, the system operators face new challenges including resource intermittency and uncertainty, as well as high ramping requirements of the system net-load (electricity load minus renewable power output). Current operation models, which utilize zero-order piece-wise constant functions to model the parameter and decision trajectories of the power systems operation optimization problems, start to fall short to accurately model the actual system net-load process as well as the power and ramping processes of generating units, energy storage (ES) devices, and flexible loads. In this dissertation, a novel approach is developed to model the power systems operation problems as continuous-time variational/optimal control problems. This new modeling approach explicitly defines the ramping trajectories as time-derivatives of power trajectories, leading to more realistic quantification of netload ramping requirement as well as ramping flexibility of the resources. The proposed continuous-time scheduling and pricing models enable defining continuous-time marginal prices of electricity, which embed accurately the impact of ramping limitations, intertemporal effect of ES and flexible loads operation, and the spatial impact of continuous-time power flow limits of transmission lines. A function space-based solution method is also proposed to reduce the decision space dimensionality of continuous-time operation problems, obviating the current discrete-time modeling deficiencies and tapping the operation flexibility of the generating units, ES devices, and flexible loads. The proposed model involves using Bernstein polynomials of desired degrees rather than zero-order piecewise constant functions to model the parameter and decision trajectories, converting the infinite-dimensional continuous-time scheduling and pricing problems respectively to finited-imensional MILP and LP problems. The dissertation follows with developing a continuous-time stochastic Gaussian process (GP) load model, which continuously predicts the mean value and uncertainty envelopes of the power system load, and inherently embeds information on the continuous time variations and ramping requirement of the load process. Further, a new definition of power systems flexibility reserve is proposed that combines the balancing and ramping reserves in a single service. Continuous-time stochastic multi-fidelity optimization models are also developed for co-optimizing the energy and flexibility reserve provided by generating units and ES devices. The multi-fidelity stochastic optimization enables modeling day-ahead and real-time decisions with different fidelities as required to match their slow and fast dynamics. Finally, a thorough comparative analysis is conducted to compare the day-ahead and real-time operation performance of the continuous-time models of different degrees with discrete-time models of different resolutions. The models proposed in this dissertation are implemented on the IEEE reliability test system (RTS) where the simulation results demonstrate more accurate and transparent marginal prices, economic efficiency in terms of day-ahead and real-time operation costs, and fewer flexibility scarcity events