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The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Dynamic power control of wind farms (WFs) is necessary to provide automatic generation control (AGC) services for the power system. However, cooperative WF control for AGC remains a great challenge because of the nonlinear and high-dimensional nature of the wake flow dynamics. To address this challenge, this article proposes a model predictive control (MPC) framework with deep learning-based reduced-order modeling (ROM). Two novel neural network architectures are designed, which successfully formulate a WF ROM capturing the dominant wake steering dynamics in a computationally efficient manner. Compared to physical models, the data-driven ROM reduces the number of model states by orders of magnitude. Then, a novel WF AGC framework embedding the derived WF ROM is proposed. Thrust coefficient and yaw steering are both employed to optimize WF power tracking performance. Compared to prior WF AGC controllers, the dynamic yaw actuation is first optimized for AGC considering the wake steering dynamics. Case studies validate the effectiveness of the deep learning-based WF ROM at capturing the wake traveling dynamics. The WF controllers were stress-tested under time-varying inflow directions. The proposed MPC can react to different wind directions and generates higher-quality control performance than existing alternatives with extended trackable AGC range and better dynamic power tracking performance. [ABSTRACT FROM AUTHOR]

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]

Parametric problems in the transient analysis refer to the investigations of the relationship between parameters and dynamic behavior. To solve parametric problems, we propose a Galerkin method-based polynomial approximation. The proposed method uses a series of polynomials combined with coefficients to approximately represent state variables with parameters, where the Galerkin method is introduced to determine the coefficients. Thereby, the relationship between parameters and dynamic behavior is established through the polynomial expressions. Because models in power system transient analysis are a set of complicated differential-algebraic equations, practical issues related to the non-polynomial model terms, parameterization of initial operation point are discussed in this paper. The proposed method is tested on a three-machine system and the IEEE 145-bus test system. The case studies show that compared to trajectory sensitivities, the proposed method can maintain high accuracy in cases of large parameter variations and strong non-linearity. We also illustrate that the validity of the proposed method for parametric problems like trajectory approximation, finding the critical parameter values and uncertainty quantification. [ABSTRACT FROM AUTHOR]

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A novel method for globally approximating the static voltage stability region boundaries (SVSRBs) of power systems is proposed by applying parametric polynomial approximation to the criterion equation which defines the SVSRB. Known as the Galerkin method, the implicit function portraying the SVSRB is described as a linear combination of basis polynomial functions, and the coefficients of the basis functions are obtained by projecting the SVSRB criterion onto each basis function. The approximation guarantees high precision globally in the whole domain of the parameter of interest rather than only in the neighborhood of a point, and the error can be controlled by the degree of polynomial basis functions. In the meantime, analytical expression of the left or right eigenvector of the system's Jacobian matrix corresponding to the zero eigenvalue is obtained in the form of polynomial, which provides valuable information for online voltage stability control or monitoring. Case studies in a 10-bus test system and IEEE 118-bus test system verifies the validity, accuracy, and flexibility of the proposed method. [ABSTRACT FROM AUTHOR]