In an integrated energy system (IES), fluctuations in coupled district heating networks and renewable energy sources pose risks to the power system’s operation. To effectively mitigate the risk of rare events, it is crucial to identify the key factors that influence their likelihood. Traditional global sensitivity analysis (GSA) assesses the sensitivity of full probability density functions (PDFs) of the system output to uncertain inputs. However, it fails to evaluate the sensitivity of rare event probabilities, which are at the tail of the PDF. It also neglects the uncertainties of the input PDFs, whose hyperparameters can heavily affect the rare event probabilities. To address these issues, we propose a novel framework calledrare-event-based global sensitivity analysis(REGSA) that prioritizes the input PDF parameters that impact the risks of the operating state. We also improve the computational efficiency of this framework by quantifying rare event probabilities through subset simulation and using sparse polynomial chaos expansion (SPCE) in REGSA (hereafter referred to as SPCE-REGSA). The simulations reveal the excellent performance of the proposed method.

The inherent thermal storage capacity of buildings brings considerable thermal flexibility to the heating/cooling loads, which are promising demand response resources for power systems. It is widely believed that integrating the thermal flexibility of buildings into the distribution system can improve the operating economy and reliability of the system. However, the private information of the buildings needs to be transferred to the distribution system operator (DSO) to achieve a coordinated optimization, bringing serious privacy concerns to users. Given this issue, we propose a novel privacy-preserved optimal dispatch approach for the distribution system incorporating buildings. Using it, the DSO can exploit the thermal flexibility of buildings without accessing their private information, such as model parameters and indoor temperature profiles. Specifically, we first develop an optimal dispatch model for the distribution system integrating buildings, which can be extended to other storage-like flexibility resources. Second, we reveal that the privacy-preserved integration of buildings is a joint privacy preservation problem for both parameters and state variables and then design a privacy-preserved algorithm based on transformation-based encryption, constraint relaxation, and constraint extension techniques. Besides, we implement a detailed privacy analysis for the proposed method, considering both semihonest adversaries and external eavesdroppers. Case studies demonstrate the accuracy, privacy-preserved performance, and computational efficiency of the proposed method.

Dynamic state estimation (DSE) plays a fundamental role in the monitoring and operation of power systems. Although previous work focuses mainly on traditional synchronous generations, with the increasing penetration of renewables, the estimation of photovoltaic (PV) systems is gaining increasing popularity. However, they primarily address static estimation or adopt an oversimplified dynamic model with a deterministic assumption for solar irradiance. Obviously, this cannot hold in practice, which will inevitably lead to biased estimation results. Facing these problems, this article explores DSE for the first time for a detailed two-stage PV system with the PV array, boost converter, inverter, and filter included. Also, to avoid biased estimation results under solar irradiance variations, we further propose to treat the randomness of solar irradiance as the unknown input of a DSE, which is further analytically merged into the unscented Kalman filter (UKF) framework with an unbiased minimum-variance (UMV) manner. Simulations performed on IEEE standard test systems reveal that even under severe variations of solar irradiation that serve as unknown inputs to the system, the proposed method can produce an unbiased estimate of the dynamic states of the PV, which is also verified in a real-world system. This accurate DSE can serve as a reliable prerequisite for the protection and control of PV-penetrated power systems.

Phasor measurement units (PMUs) are increasingly being deployed in power systems due to their high sampling rates and diverse data sampling types. However, this undoubtedly poses significant challenges to data centers in terms of data storage and transmission. This article proposes an adaptive rank-based tensor ring (TR) method for PMU data compression to address these issues. More specifically, we first extend the orders of the PMU measurement data to achieve high-order tensorization. Subsequently, based on using the alternating least-squares method to decompose the high-order data TR, we introduce a rank-increment strategy to obtain adaptive ranks. Using a TR data structure, the proposed method can transform high-order data with exponentially increasing volumes into a polynomial scale. This allows us to achieve cost-effective PMU data compression. The simulation results using real-world PMU measurement data reveal the excellent performance of our proposed method.

Electricity industry marketization and combined heat and power (CHP) systems are actively considered efficacious approaches for balancing supply and demand in future energy systems with high penetration of renewable sources. Relevant research to date has paid little attention to the interaction of economic behaviors with the dynamics of the CHP system, focusing only on optimal bidding at the economic level or stability at the physical level. By leveraging the primal-dual method and the insights from reverse engineering, we propose a unified economic-physical model to investigate how market dynamics interact with its underlying physical CHP systems. The market clearing optimization is redesigned as a controller that restores the nominal frequency while maximizing social welfare. This work steps further toward developing a novel control scheme for frequency regulation in market-oriented power systems with CHP units and renewable sources. As the proposed model can be formulated in port-Hamiltonian form, the stability of the closed-loop system can be assessed using Lyapunov's direct method. The capability and effectiveness of the proposed model are demonstrated through simulations.

A phasor measurement unit (PMU) serves as a superior tool to monitor the dynamics of the power system, but its high cost remains a practical concern that requires the optimal placement of the PMU (OPP). Traditionally, researchers relied on model-based approaches to analyze this problem. However, these methods not only suffer from inevitable parameter uncertainties but can also be computationally expensive for complicated power system dynamic models. Faced with these issues, this article proposes a data-driven OPP approach utilizing an augmented Koopman operator. This operator lifts the original nonlinear state space to a high-dimensional linear Koopman space in a data-driven manner, which fully eliminates the model discrepancy while achieving high computing efficiency. Theoretically, we prove that the observability matrix in the augmented Koopman canonical coordinates preserves the whole dynamic evolution of both the system model and its associated measurement model. Finally, we propose a modified genetic algorithm to solve the established OPP problem, which is enhanced to further accelerate the search speed. The simulation results reveal the excellent performance of our proposed method.

The heat-electric-integrated energy system (HE-IES) represents a prominent approach to achieving low-carbon energy supply, garnering considerable attention from both theoretical and practical perspectives. However, verifying the theoretical analysis of HE-IES is challenging due to the limited availability of operational data for practical heating system (HS). This difficulty, in turn, poses challenges for system monitoring, state estimation, and optimized operation. To tackle these issues, in this article, we establish an HS platform based on a similarity model and conduct a series of HE-IES verification experiments. First, we derive the HS-scale model based on the similarity theory. With this model, the operating condition of practical HS can be reproduced in an experimental platform (EP). Then, we introduce two distinct sets of EP parameter ratio factors and propose an experimental verification framework for evaluating practical HS operation strategies and assessing the accuracy of simulations. With the proposed model and framework, we establish a nine-pipe, 12.5-m HS-EP and conduct two experiments. In the first experiment, we scrutinized the HS operation strategy generated by mainstream HE-IES optimization algorithms. The results unveiled that, during the experiment, the EP exceeded its security limits for 2.87 h—a deviation unanticipated by theoretical analysis. In the second experiment, we meticulously evaluated the accuracy of the HE-IES simulation algorithm. Our findings reveal minimal temperature errors, with an average of 0.1864 and a maximum of 0.622, validating the precision of the simulation algorithm.

As extreme events such as natural disasters and cyberattacks become more frequent, the resilience of energy systems has become increasingly important. However, due to the growing interdependence between natural gas, district heating, and power systems, the resilience of energy systems is becoming more and more complicated. Typical challenges include conflicts in the restoration of heterogeneous energy systems due to infrastructure limitations and multiple uncertainties, such as renewable energy and outdoor temperature, during the system restoration. To address these challenges, we propose a novel combined electrical and heat load restoration (CEHLR) model for the heat and electricity-integrated energy systems. The CEHLR model is formulated as a bi-objective distributionally robust chance-constrained programming, which can coordinate the electrical and heat load recovery process and has strong robustness to uncertainties from renewable energy and outdoor temperature. Then, we convert the CEHLR model into an equivalent bi-objective mixed-integer second-order conic programming problem. Finally, we use a tailored normalized normal constraint method to obtain an evenly distributed Pareto frontier to facilitate the decision selection. Case studies demonstrate the effectiveness of the proposed method, which also reveals the significant impact of the coupling between electricity and heat on the load recovery process.

In this paper, we study a distributed convex optimization problem with inequality constraints. Each agent is associated with its cost function, and can only exchange information with its neighbors. It is assumed that each cost function is convex and the optimization variable is subject to an inequality constraint. The objective is to make all the agents reach consensus, and meanwhile converge to the minimum point of the sum of local cost functions. A distributed protocol is proposed to guarantee that all agents can reach consensus in finite time and converge to the optimal point within the inequality constraints. Based on the ideas of parameter projection, the protocol includes two decent directions. One makes the cost function decrease, and the other makes agents step forward to the constraint set. It is shown that the proposed protocol solves the problem under connected undirected graphs without using a Lagrange multiplier technique. Especially, all of the agents could reach the constraint sets in finite time and stay in there after. The method could also be used in the centralized optimization problems.

The uncertainties of renewable energy, loads, and electricity prices pose significant challenges to the economical and secure energy management of smart grids. In this article, a hybrid stochastic/robust (HSR) optimization method is developed to minimize the overall cost of all units. The proposed approach takes advantage of stochastic programming, robust optimization, and distributed optimization methods while considering various system constraints. First, stochastic electricity price scenarios are selected by the Latin hypercube sampling method. Second, the uncertainties of renewable energy generation and loads are managed by the proposed robust optimization method under each price scenario. Then, an improved distributed optimization method is proposed to solve the formulated HSR optimization problem, which considerably enhances the convergence with the accelerated gradient method. Numerical case studies of both small-scale and large-scale power systems demonstrate the accuracy, effectiveness, and scalability of the proposed distributed HSR approach. Additionally, the optimality and convergence of this proposed distributed algorithm are mathematically proven and analyzed.

Multiuncertainties in community grids bring enormous challenges to system scheduling. To reply to renewable uncertainties on the prosumer side, this article proposes a trilayer stackelberg game (SG) based robust power management method for a typical community grid. Firstly, in the upper-layer, the supplier acts as a leader to determine the trading prices according to prosumers' power demands in the normal scenario. The scheduling of prosumers before and after uncertainties is formulated as an inner-loop SG model in the middle- and lower-layers, and a linear robust counterpart model is developed to address the nonlinearity and nonconvexity of traditional robust models, thereby ensuring the convergence of the robust equilibrium solution. Second, to solve the trilayer SG model effectively, the existence and uniqueness of the equilibrium solution are proved based on a multistep backward induction method. Third, a novel two-stage distributed iterative algorithm is further exploited to avoid the nested iterations in existing solution methods. Furthermore, the possible oscillation in iterative optimization is also prevented to improve the computational efficiency. Case studies illustrate the effectiveness of the proposed trilayer SG model, and the developed distributed algorithm requires fewer iterations and less solution time comparing to other algorithms. Besides, this method shows better scalability and practicality with the expansion of the grid-scale.

A deeper coupling of information and power would make active distribution networks (ADNs) evolve into typical cyber-physical systems (CPSs). The unreliability of cyber systems can affect the security of ADNs. In this article, a methodology based on cyber-power joint analysis is presented to quantitatively evaluate the operational risk of ADNs caused by cyber contingencies. First, a typical CPS structure of ADNs is demonstrated and the influence ways of cyber contingencies are discussed. Then, a CPS modeling framework is proposed to analyze the information flow and cyber contingencies of cyber systems. To determine the best data transmission paths in cyber networks, a routing algorithm based on the link-state protocol is presented. Furthermore, in view of the response of ADNs to physical failures, an optimization model is developed to minimize the load shedding that results from the over-limited voltage. Finally, the expected load curtailment and the expected fault coverage used to quantify potential system losses are calculated using Monte Carlo simulation. The simulation results explain the effectiveness and practicability of the proposed models and methods.

The integrated energy system (IES) has bright prospects in engineering applications for its excellent performance in energy efficiency and renewable energy consumption. In the IES, the thermal comfort is affected by the heating power, buildings parameters, and outdoor temperatures simultaneously. Therefore, the uncertainty of the outdoor temperature will bring some adverse effects on thermal comfort, which need to be considered in the dispatch decision of the IES. In this article, we propose a day-ahead adaptive robust dispatch model (ARDM) for the IES to make a dispatch plan under the uncertainties of the net electrical-load and outdoor temperature, with the aim of guaranteeing the safe operation of IES and the thermal comfort of end-users. The thermal dynamic characteristics of the district heating network and buildings are utilized to provide operational flexibility and improve economic performance. To decrease the conservatism of dispatch results, the multi-interval uncertainty set is introduced to model the uncertainties. The ARDM model is a two-stage robust optimization with a linear recourse problem, and the column-and-constraint generation method is used to solve it. Two cases of different scale are studied to verify the effectiveness and advantages of the proposed method.

This paper proposes an optimal distributed control strategy for the coordination of multiple distributed generators in an islanded microgrid (MG). A finite-time secondary frequency control approach is developed to eliminate the frequency deviation and maintain accurate active power sharing in a finite-time manner. It is demonstrated that the traditional distributed control approach with asymptotical convergence is just a special case of the proposed finite-time control strategy under the specific control parameter settings. Then, a secondary voltage control approach is presented to regulate the average voltage magnitude of all distributed generators to the desired value and achieve accurate reactive power sharing. The implementation of the proposed distributed control strategy only requires information exchange among neighboring local controllers through a sparse communication network. Simulations with an islanded MG testbed built in MATLAB/Simulink are conducted to validate the effectiveness of the proposed distributed control strategy.