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.

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.

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.

Polynomial-chaos-expansion-based surrogate models have recently been advocated in the literature for power system dynamic parameter estimation. Regarding the estimation of the uncertain generator parameters, a Bayesian inference framework has been proposed based on a polynomial-based reduced-order representation of the synchronous machines using assumed parameter values. Then, the non-Gaussian posterior probability distribution functions (pdfs) of these parameters are recovered through the stochastic sampling approach efficiently. However, facing very large parameter errors, the reliability of the surrogate model decreases, yielding biased estimation results. To overcome this problem, this article develops a hierarchical Bayesian inference framework that processes the measurements provided by phasor measurement units, while making use of multifidelity surrogates together with the importance sampling method. The latter allows us to estimate in an efficient manner the posterior pdfs of the uncertain parameters through the normalized weights of the prior samples. To improve the accuracy of the posterior pdfs, an adaptive procedure is further adopted in the importance sampling for the gradual evolution of its proposal functions. The new proposals assist in fine-tuning the sample space and thereby help to construct surrogates with higher fidelity. Through an iterative process, this approach is able to estimate accurately and efficiently non-Gaussian posterior pdfs of the uncertain generator parameters subject to gross errors.

This letter proposes a new polynomial-chaos-based Kalman filter (PCKF) that is able to track the dynamics of nonlinear dynamical systems subject to strong nonlinearities. Specifically, by resorting to the polynomial chaos theory, the uncertainties of the model and the measurements can be effectively propagated through a set of collocation points. However, this polynomial-chaos-based algorithm suffers from the curse of dimensionality. To overcome this weakness, a dimension reduction strategy is proposed based on variance analysis. This allows us to construct more effective collocations points and to significantly improve the computational efficiency of the PCKF without any loss of estimation accuracy. Simulations carried out on various IEEE systems validate the effectiveness of the proposed method.