Finding a feasible solution is the primary concern in power system dispatch. This paper studies the feasibility condition of power system dispatch under a multistage robust optimization framework considering the non-anticipativity of dispatch policy, which is difficult to be expressed via explicit constraints. The multistage robust feasible regions (MRFRs) are defined as the sets in the state space containing all points that can maintain the robust feasibility in the next period against renewable and demand uncertainties; we give a polyhedral projection condition to characterize exact MRFRs in a recursive manner, which can be regarded as an analog of Bellman’s optimality condition. However, because the multistage dispatch problem of a bulk power system has a high-dimensional state space, the computation of exact MRFRs suffers from the curse of dimensionality. We propose an inner approximation method that identifies the maximal polyhedra that are embraced by the unknown exact MRFRs; we devise a computationally efficient algorithm to retrieve the hyperplane representation of the inner approximator. Finally, we discuss how MRFRs can be used in combination with existing approaches, such as dynamic programming and rolling horizon optimization. Numerical simulations on a modified IEEE 118-bus system verify the effectiveness and advantages of the proposed methodNote to Practitioners—This paper is motivated by the problem of maintaining the feasibility in power system multistage dispatch under renewable generation uncertainty. The proposed method regards the multistage dispatch as a sequential decision-making process and recursively defines the MRFR using polyhedral projection technique, which contains all the state points in each period that can guarantee the robust feasibility in the next period. To release the curses of dimensionality, the large-scale MRFR is approximated by an inner hyper-rectangle in the state space, which can be decomposed into independent intervals of state variables, such as the generation power range of coal-fired unit and the state-of-charge range of battery storage unit. These decoupled intervals are convenient for practical use and desired in the real-world power system. At the current stage, the calculation of MRFR requires a linear model; in the future research, integers will be addressed so that more facilities such as non-ideal energy storage units and fast-startup generators can be involved.

With the proliferation of distributed generations and energy storage systems, traditional passive consumers in the distribution network have been gradually evolving into “prosumers”, who can both produce and consume energy. To alleviate the energy surplus and shortage problem, energy sharing between prosumers is advocated. This paper investigates an online distributed method to seek the generalized Nash equilibrium (GNE) of the energy sharing market. We first formulate the energy sharing problem as a multi-period generalized Nash game (GNG), which has been proven to have a unique variational GNE (v-GNE) with the same multiplier. Then, the GNG is transformed into an equivalent optimization problem based on the variational inequality, which is further divided into multiple single-period problems under the Lyapunov optimization framework. An online distributed algorithm is introduced to solve the Lyapunov drift problems and consequently seek the v-GNE in a time-varying environment. We prove that the expected performance gap is bounded compared to the deterministic offline v-GNE with perfect uncertainty information, while all the constraints across the entire horizon are maintained. Finally, numerical results with 33 and 123 prosumers validate the performance of the algorithm.

Estimating the stability boundary is a fundamental and challenging problem in transient stability studies. It is known that a proper level set of a Lyapunov function or an energy function can provide an inner approximation of the stability boundary, and the estimation can be expanded by trajectory reversing methods. In this paper, we streamline the theoretical foundation of the expansion methodology, and generalize it by relaxing the request that the initial guess should be a subset of the stability region. We investigate topological characteristics of the expanded boundary, showing how an initial guess can approach the exact stability boundary locally or globally. We apply the theory to power system transient stability assessment, and propose expansion algorithms to improve the well-known Potential Energy Boundary Surface (PEBS) and Boundary of stability region based Controlling Unstable equilibrium point (BCU) methods. Case studies on the IEEE 39-bus system well verify our results and demonstrate that estimations of the stability boundary and the critical clearing time can be significantly improved with modest computational cost. Note to Practitioners—This paper was motivated by the problem of determining whether a power system can retain transient stability subject to large disturbances such as short-circuit fault and generator tripping. The most well-known approaches to such a problem are the direct methods that can avoid time-costly simulations and “directly” determine the transient stability by estimating the stability boundary. Nevertheless, such estimations are generally too conservative. This paper proposes a new expansion method to improve the direct methods, which allows the initial estimation to lie partially outside the real boundary and hence enables applications to both global and local direct methods. Our method can expand the initial estimation towards the real stability boundary, thus reducing the conservativeness and providing a more accurate stability assessment such as the critical clearing time (CCT) of a fault. In this paper, we first mathematically establish the expansion theory and then propose numerical algorithms for power system applications. Simulations on the IEEE 39-bus benchmark verify our approach and show that the conservativeness can be significantly reduced with modest computational cost. Our approach can be further extended to scenarios where a valid Lyapunov (energy) function is unavailable.

In this paper, a hybrid machine learning model is applied to evaluate the relationship between random initial states and the power system’s vulnerability to cascading outages. A cascading outage simulator (CS), which uses off-line AC power flows, is proposed for generating training data. The initial states are randomly selected and the CS model is deployed for each initial state, where power system generation and loads are adjusted dynamically and power flows are redistributed to quantify the vulnerability metric. Furthermore, the proposed hybrid machine learning model deploys a combined Support Vector Machine (SVM) classification and Gradient Boosting Regression (GBR) to improve the learning precision. The classification model is trained by SVM, which divides the data into two categories with and without load shedding. Then, GBR is adopted only for the data with load shedding to determine the relationship between input power outage states and the vulnerability metric. The proposed vulnerability analysis approach is applied to several test systems and the results are analyzed. Note to Practitioners—The power system vulnerability can be quantified by cascading outage simulations. However, there are two challenges: i) there are a huge number of possible initial states and we cannot enumerate all these initial states for the cascading outage simulation. Neither can we precisely quantify the bus vulnerability. ii) The cascading outage simulation may be time-consuming for large-scale power systems, which is challenging for the online application. To address the above challenges, we expect to design a machine learning technique to predict the power system vulnerability, which can train the model in an offline way and then use it for the online application. Firstly, since there is not enough operation data from practical power systems, we develop a cascading outage simulator, using off-line AC power flows, for generating synthetic training data. Secondly, we observe that the training precision by directly applying the regression model may be very poor because the output of the machine learning model may take on an uneven distribution concerning input parameters. Thus, we propose a hybrid machine learning model with a combined classification and regression method, where the classification model is employed to remove the data without the load shedding, and the regression model then determines the relationship between input power outage states and the vulnerability metric. The proposed model and method have been tested on several systems including a practical large-scale Polish power system to show the effectiveness.

Integration of heat and electricity supply improves the overall energy efficiency and system operational flexibility. The renewable powered heat-electricity energy system is a promising way to set up residential energy supply facilities in remote areas beyond the reach of power system infrastructures. However, the volatility of wind and solar energy brings about the risk of supply inadequacy. This article proposes a data-driven robust method to quantify two measures of such a risk in the stand-alone renewable powered heat-electricity energy system. The uncertainty of renewable generation is modeled through a family of ambiguous probability distributions around an empirical one based on the Wasserstein metric; then, the probability of heat and electricity load shedding during a short period and related penalty cost are discussed. Through a polyhedral characterization of renewable power feasible region, the load shedding probability under the Wasserstein ambiguity set comes down to a linear program. With a piecewise linear optimal value function of the penalty cost, its expectation under the worst case distribution in the Wasserstein ambiguity set also gives rise to a linear program. The proposed method requires moderate information on renewable generation and makes full use of available data, whereas sustains computational tractability. The evaluation result is robust against the inaccuracy of renewable power distributions. Case studies demonstrate the effectiveness of the proposed approach.

This paper first presents a comprehensive model of the gas system with detailed formulations on pipelines, short pipes, resistors, valves, compressors, and compressor stations. Furthermore, an optimal energy flow model is proposed for integrated power-gas generation and transmission systems. Specifically, on the generation side, gas-fired units couple the two energy systems as the power generation and gas sink; on the transmission side, gas compressor stations link the two energy systems as the power demand and gas transportation. However, gas flow equations are nonlinear and gas flow directions also need to be optimized. Logical programming and tailored piecewise linearization techniques are performed, leading to a mixed-integer linear program (MILP). Only a logarithmic number of binary variables are introduced to represent the nonlinear quadratic function, and thus, the MILP model can be solved very efficiently. Numerical results on four power-gas test systems demonstrate the effectiveness of the proposed approach.

The development of the cutting-edge technologies in cogeneration and trigeneration has led to a rapid transition toward integrated energy systems and the mushrooming of energy hubs, calling for effective energy management schemes. This paper proposes a distributed algorithm for autonomous energy management (AEM) of a cluster of residential energy hubs. Given the interactive behaviors of energy purchasing at the supply side, we treat each hub as a self-interested agent, and formulate the AEM problem of these hubs as a monotone generalized Nash game (MON-GNG). On one hand, there are global coupling constraints representing the supply limits of the input energy systems, which are imposed by the limited capacities of electrical feeders and natural gas pipelines, thus making it a GNG. On the other hand, the cost function of each hub is merely convex in its actions considering the input-to-output energy transformation inside and the impacts of the energy storage devices, which leads to an MON game. The existence of the generalized Nash equilibria (GNEs) of this MON-GNG can be theoretically guaranteed. Then, by reformulating the MON-GNG as a variational inequality problem with special decomposition structure, an efficient and single-loop distributed algorithm is then proposed for computing a GNE with clear economic interpretation based on an improved Tikhonov regularization technique. Principles of parameter selection that will guarantee convergence are suggested. Numeric simulations validate the convergence performance and effectiveness of the proposed algorithm.