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The synchronization of power generators is an important condition for the proper functioning of a power system, in which the fluctuations in frequency and the phase angle differences between the generators are sufficiently small when subjected to stochastic disturbances. Serious fluctuations can prompt desynchronization, which may lead to widespread power outages. Here, we derive explicit formulas that relate the fluctuations to the disturbances, and we reveal the role of system parameters. In particular, the relationship between synchronization stability and network theory is established, which characterizes the impact of the network topology on the fluctuations. Our analysis provides guidelines for the system parameter assignments and the design of the network topology to suppress the fluctuations and further enhance the synchronization stability of future smart grids integrated with a large amount of renewable energy.
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The large-scale integration of converter-interfaced resources in electrical power systems raises new stability threats which call for a new theoretic framework for modelling and analysis. Here we present the theory of power-communication isomorphism to solve this grand challenge. It is revealed that an intrinsic communication mechanism governs the synchronisation of all apparatus in power systems based on which a unified representation for heterogeneous apparatus and behaviours is established. We develop the mathematics to model the dynamic interaction within a power-communication isomorphic system which yield a simple stability criterion for complex systems that can be intuitively interpreted and thus conveniently applied in practice.
Continuous-time random disturbances from the renewable generation pose a significant impact on power system dynamic behavior. In evaluating this impact, the disturbances must be considered as continuous-time random processes instead of random variables that do not vary with time to ensure accuracy. Monte Carlo simulation (MCs) is a nonintrusive method to evaluate such impact that can be performed on commercial power system simulation software and is easy for power utilities to use, but is computationally cumbersome. Fast samplings methods such as Latin hypercube sampling (LHS) have been introduced to speed up sampling random variables, but yet cannot be applied to sample continuous disturbances. To overcome this limitation, this paper proposes a fast MCs method that enables the LHS to speed up sampling continuous disturbances, which is based on the It^{o} process model of the disturbances and the approximation of the It^{o} process by functions of independent normal random variables. A case study of the IEEE 39-Bus System shows that the proposed method is 47.6 and 6.7 times faster to converge compared to the traditional MCs in evaluating the expectation and variance of the system dynamic response.
Adaptive synchronization protocols for heterogeneous multi-agent network are investigated. The interaction between each of the agents is carried out through a directed graph. We highlight the lack of communication between agents and the presence of uncertainties in each system among the conventional problems that can arise in cooperative networks. Two methodologies are presented to deal with the uncertainties: A strategy based on robust optimal control and a strategy based on neural networks. Likewise, an input estimation methodology is designed to face the disconnection that any agent may present on the network. These control laws can guarantee synchronization between agents even when there are disturbances or no communication from any agent. Stability and boundary analyzes are performed. Cooperative cruise control simulation results are shown to validate the performance of the proposed control methods.
The problem of integrating multiple overlapping models and data is pervasive in engineering, though often implicit. We consider this issue of model management in the context of the electrical power grid as it transitions towards a modern Smart Grid. We present a methodology for specifying, managing, and reasoning within multiple models of distributed energy resources (DERs), entities which produce, consume, or store power, using categorical databases and symmetric monoidal categories. Considering the problem of distributing power on the grid in the presence of DERs, we show how to connect a generic problem specification with implementation-specific numerical solvers using the paradigm of categorical databases.
Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel model for determining the optimal offering strategy in the day-ahead energy-reserve market and the optimal self-scheduling plan. It considers exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind power generation, as well as the endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution method based on strong duality theory, McCormick relaxation, and the Benders decomposition to solve the proposed stochastic adaptive robust optimization with DDUs formulation is developed. Simulation results demonstrate the applicability of the proposed approach.
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