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Reflecting the uncertainty of renewable energy generations and loads, power system AGC signals are essentially random processes. For the sake of the optimal operation and control of the AGC participant, such as energy storage systems (ESSs) in a performance/mileage-based regulation market, taking the uncertain nature, especially the temporal correlation, of the AGC signals into consideration can be beneficial; hence, random process models of the AGC signals are needed. However, a continuous random process model of the AGC signal that jointly considers the probability distribution and the temporal correlation is still lacking. To fill this gap, this paper first presents a systematic methodology for modeling the continuous random processes of AGC signals based on stochastic differential equations (SDEs). It is shown that AGC signals may have a saturated stationary probability density function and a biexponential temporal correlation, which are very different from the renewable generations. To capture these special characteristics, SDEs are then carefully constructed, which are easy to use in optimization and control. Using the PJM traditional and dynamic regulation (RegD and RegA) signals and the signal received from a battery ESS (BESS) plant in Jiangsu, China for example, simulation shows that the SDE is able to simultaneously capture the probability distribution and temporal correlation accurately. [ABSTRACT FROM AUTHOR]

To exploit the massive solar energy available in the region, photovoltaic plants have been built in the mountain areas in Southwest China, coexisting with many small cascaded run-of-the-river hydropower plants, interconnected by short-distance transmission lines. Network constraints inside these systems are often negligible. However, due to the volatile nature of solar power and the weak connection to the external power grid, without proper coordination, solar power curtailment and water spillage are inevitable. To address this issue, this paper proposes an ultra-short-term stochastic generation control method for cascaded hydropower to mitigate solar power volatility. Two technical challenges are specifically addressed: to tackle the time-varying stochastic volatility of solar power, the Itô process model is introduced; to characterize the spatial-temporal hydraulic coupling of the cascaded hydropower plants and river operation constraints, a state-space dynamic river model derived from shallow water equations is included. Followingly, a stochastic control (SC) approach for hydropower generation based on stochastic programming is proposed, where hydropower generation commands are parameterized as affine functions of measured solar power, enabling quick response to solar power volatility. Simulation of a real-life cascaded hydro-solar system and a modified system verifies the proposed control method. [ABSTRACT FROM AUTHOR]

The imbalance of generation and load caused by the increasing integration of volatile generations poses challenges on frequency regulation. AGC is required to respond to the generation fluctuations without violating operational and security constraints. Explicit model predictive control (EMPC) provides an approach to reaching such requirements, which calculates the control laws of MPC in an explicit form, allowing for offline validation of the controller and enabling fast online computation. However, the partition number of EMPC's piecewise affine control laws grows exponentially with the number of constraints and prediction/control horizons, which hinders its application in large systems. In this paper, we propose an alternative explicit control approach for AGC by approximating the control laws of EMPC using Legendre polynomial series expansions, thus entirely eliminating the partition issue. The Galerkin method is applied to the KKT conditions of EMPC's multiparametric quadratic programming (mp-QP) problem to compute the approximation. Case studies in an illustrative system and IEEE 118-Bus System verify the performance and efficiency of the proposed controller. [ABSTRACT FROM AUTHOR]