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Register a new userMathematical representation of the WECC composite load model
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The Western Electricity Coordinating Council (WECC) composite load model is a newly developed load model that has drawn great interest from the industry. To analyze its dynamic characteristics with both mathematical and engineering rigor, a detailed mathematical model is needed. Although WECC composite load model is available in commercial software as a module and its detailed block diagrams can be found in several public reports, there is no complete mathematical representation of the full model in literature. This paper addresses a challenging problem of deriving detailed mathematical representation of WECC composite load model from its block diagrams. In particular, for the first time, we have derived the mathematical representation of the new DER_A model. The developed mathematical model is verified using both Matlab and PSS/E to show its effectiveness in representing WECC composite load model. The derived mathematical representation serves as an important foundation for parameter identification, order reduction and other dynamic analysis.
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With the increasing complexity of modern power systems, conventional dynamic load modeling with ZIP and induction motors (ZIP + IM) is no longer adequate to address the current load characteristic transitions. In recent years, the WECC composite load model (WECC CLM) has shown to effectively capture the dynamic load responses over traditional load models in various stability studies and contingency analyses. However, a detailed WECC CLM model typically has a high degree of complexity, with over one hundred parameters, and no systematic approach to identifying and calibrating these parameters. Enabled by the wide deployment of PMUs and advanced deep learning algorithms, proposed here is a double deep Q-learning network (DDQN)-based, two-stage load modeling framework for the WECC CLM. This two-stage method decomposes the complicated WECC CLM for more efficient identification and does not require explicit model details. In the first stage, the DDQN agent determines an accurate load composition. In the second stage, the parameters of the WECC CLM are selected from a group of Monte-Carlo simulations. The set of selected load parameters is expected to best approximate the true transient responses. The proposed framework is verified using an IEEE 39-bus test system on commercial simulation platforms.
Accurate identification of parameters of load models is essential in power system computations, including simulation, prediction, and stability and reliability analysis. Conventional point estimation based composite load modeling approaches suffer from disturbances and noises and provide limited information of the system dynamics. In this work, a statistic (Bayesian Estimation) based distribution estimation approach is proposed for both static (ZIP) and dynamic (Induction Motor) load modeling. When dealing with multiple parameters, Gibbs sampling method is employed. In each iteration, the proposal samples each parameter while keeps others fixed. The proposed method provides a distribution estimation of load models coefficients and is robust to measurement errors.
We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient Method (ACGM), for large-scale problems with composite objective structure. ACGM surpasses the state-of-the-art methods for this problem class in terms of provable convergence rate, both in the strongly and non-strongly convex cases, and is endowed with an efficient step size search procedure. We support the effectiveness of our new method with simulation results.
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium.
A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints. Special emphasis is put on the tensorial aspects of the theory. To start with, the kinematical foundations, culminating in the so called variational equation, are put on geometrical grounds, via the introduction of the concept of infinitesimal control . On the same basis, the usual classification of the extremals of a variational problem into normal and abnormal ones is also rationalized, showing the existence of a purely kinematical algorithm assigning to each admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. The whole machinery is then applied to constrained variational calculus. The argument provides an interesting revisitation of Pontryagin maximum principle and of the Erdmann-Weierstrass corner conditions, as well as a proof of the classical Lagrange multipliers method and a local interpretation of Pontryagins equations as dynamical equations for a free (singular) Hamiltonian system. As a final, highly non-trivial topic, a sufficient condition for the existence of finite deformations with fixed endpoints is explicitly stated and proved.
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