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The rapid growth of behind-the-meter (BTM) solar power generation systems presents challenges for distribution system planning and scheduling due to invisible solar power generation. To address the data leakage problem of centralized machine-learning methods in BTM solar power generation estimation, the federated learning (FL) method has been investigated for its distributed learning capability. However, the conventional FL method has encountered various challenges, including heterogeneity, communication failures, and malicious privacy attacks. To overcome these challenges, this study proposes a communication-robust and privacy-safe distributed estimation method for heterogeneous community-level BTM solar power generation. Specifically, this study adopts multi-task FL as the main structure and learns the common and unique features of all communities. Simultaneously, it embeds an updated parameters estimation method into the multi-task FL, automatically identifies similarities between any two clients, and estimates the updated parameters for unavailable clients to mitigate the negative effects of communication failures. Finally, this study adopts a differential privacy mechanism under the dynamic privacy budget allocation strategy to combat malicious privacy attacks and improve model training efficiency. Case studies show that in the presence of heterogeneity and communication failures, the proposed method exhibits better estimation accuracy and convergence performance as compared with traditional FL and localized learning methods, while providing stronger privacy protection.

Gas-fired units (GFUs) with rapid regulation capabilities are considered an effective tool to mitigate fluctuations in the generation of renewable energy sources and have coupled electricity power systems (EPSs) and natural gas systems (NGSs) more tightly. However, this tight coupling leads to uncertainty propagation, a challenge for the real-time dispatch of such integrated electric and gas systems (IEGSs). Moreover, pipeline leakage failures in the NGS may threaten the electricity supply reliability of the EPS through GFUs. To address these problems, this paper first establishes an operational model considering gas pipeline dynamic characteristics under uncertain leakage failures for the NGS and then presents a stochastic IEGS real-time economic dispatch (RTED) model considering both uncertainty propagation and pipeline leakage uncertainty. To quickly solve this complicated large-scale stochastic optimization problem, a novel notion of the coupling boundary dynamic adjustment region considering pipeline leakage failure (LCBDAR) is proposed to characterize the dynamic characteristics of the NGS boundary connecting GFUs. Based on the LCBDAR, a noniterative decentralized solution is proposed to decompose the original stochastic RTED model into two subproblems that are solved separately by the EPS and NGS operators, thus preserving their data privacy. In particular, only one-time data interaction from the NGS to the EPS is required. Case studies on several IEGSs at different scales demonstrate the effectiveness of the proposed method.

With the widespread use of power electronic devices, modern distribution networks are turning into flexible distribution networks (FDNs), which have enhanced active and reactive power flexibility at the transmission-distribution-interface (TDI). However, owing to the stochastics and volatility of distributed generation, the flexibility can change in real time and can hardly be accurately captured using conventional discrete-time (DT) assessment methods. This paper first proposes the notion of continuous-time (CT) TDI active and reactive flexibility and establishes its mathematical model. This model comprehensively considers the flexible devices in the FDN and the impact of uncertainty of photovoltaic power generation and load. In particular, a novel direction-factor-based metric is proposed to model CT-TDI PQ flexibility. Moreover, an efficient solution method is designed to address the difficulties in handling the infinite dimension of CT model and the complexity of bi-objectivity from assessing both active and reactive flexibility to be assessed. The solution successfully transforms the infinite dimensional optimization into a finite dimensional problem and effectively explores the PQ plane in a parallel pattern. Case studies show that the method can more effectively assess the real-time TDI flexibility of an FDN relative to conventional DT counterparts, and also reveals the impact of the relevant factors, such as penetrations of flexible devices and levels of uncertainty.

A low-observable distribution system has insufficient measurements for conventional weighted least square state estimators. Matrix completion state estimators have been suggested, but their computational times could be prohibitive. To resolve this problem, a novel and efficient power-flow-embedded projection conic matrix completion method customized for low-observable distribution systems is proposed in this letter. This method can yield more accurate state estimations (2-fold improvement) in a much shorter time (5% or less) than other methods. Case studies on different-scale systems have demonstrated the efficacy of the proposed method when applied to low-observable distribution system state estimation problems.

The common approaches to construct a data-driven linear power flow (DD-LPF) model cannot completely eliminate the adverse impacts of outliers in a training dataset. In this letter, a novel outlier-immune DD-LPF model construction method via mixed-integer programming is presented for automatically and optimally identifying outliers to form a more accurate LPF model. Two acceleration solution strategies are further suggested to reduce the computational time. Case studies demonstrate the superior accuracy and comparable computational time of the proposed method when compared to three common approaches.

Accurately evaluating the real-time flexibility of electric vehicles (EVs) is necessary for EV aggregators to offer ancillary services. However, regulation-caused uncertain state-of-charge and random departure behavior complicate the evaluation and badly impact the evaluation accuracy. To resolve this issue, this letter proposes a distributionally robust real-time flexibility evaluation model that formulates the uncertain departure behavior and state-of-charge of EVs in an online updating pattern. Thanks to dualization, this model can be efficiently solved via off-the-shelf solvers. Case studies validate the superiority of the proposed method and its scalability regarding EV numbers.

When large-scale uncertain centralized and distributed renewable energy sources are connected to a power system, separate dispatching of the transmission power system (TPS) and the active distribution network (ADN) will lower the network security and frequency security of the system. To address these problems, this paper proposes a coordinated frequency-constrained stochastic economic dispatch (CFC-SED) model for an integrated transmission and distribution (ITD) system. In this model, the dynamic frequency security constraints and network security constraints of the ITD system are constructed, and the joint chance constraints are adopted to handle the uncertainty. Then, the control parameters of inverter-based resources, the base point power, and the regulation reserve of all dispatchable resources in the ITD system are jointly optimized for the minimum operating cost. TPS and ADNs can deliver base point power bidirectionally and provide frequency regulation support bidirectionally, which extend the existing reserve assumption in ITD dispatch and enhance the operational security of the ITD system. Moreover, based on the alternating direction of multiplier algorithm, a two-layer distributed optimization framework is proposed to solve the CFC-SED model. Case studies show that the CFC-SED model can fully utilize the potential of multiple regulation resources to improve the security performance of the ITD system, and TPS and ADNs can be coordinated efficiently through the proposed distributed optimization framework.

In an integrated electricity-gas system (IEGS), the tight coupling of power and natural gas systems is embodied by frequent changes in gas withdrawal from gas-fired units to provide regulation services for the power system to handle uncertainty, which may in turn endanger the secure operation of the natural gas system and ultimately affect the safety of the whole IEGS. Hence, it is necessary to accurately and efficiently evaluate the dynamic security region (DSR) of the natural gas system in the IEGS by considering the real-time dynamic characteristics of natural gas systems, which are not satisfactorily handled in state-of-the-art works. To bridge this gap, this paper first conceptionally verifies the necessity of the DSR and establishes its mathematical model. Then, a dimensionality reduction method is proposed for the efficient solution and visualization of the high-dimensional DSR evaluation model. A fast evaluation (FE) algorithm is developed to address the difficulties of the nonconvex dynamic constraints in the reduced DSR model. Finally, the necessity and notable advantages of the proposed DSR model and FE are verified based on small and relatively large test systems in comparison with common security region models and algorithms. To the best of our knowledge, this is the first paper that comprehensively presents models and efficient algorithms regarding the DSR of natural gas systems in an IEGS.

The issues of uncertainty and frequency security could become significantly serious in power systems with the high penetration of volatile inverter-based renewables (IBRs). These issues make it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch (ED) programs. However, existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation (e.g., virtual inertia and droop coefficients) in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliability. This paper first proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control, the system up/down reserves, and base-point power for the minimal total operational cost. In the proposed model, multiple dispatchable resources including thermal units, dispatchable IBRs and energy storage are considered, and the (virtual) inertias, the regulation reserve allocations and the base-point power are coordinated. To ensure the system reliability, the joint chance-constraint formulation is also adopted. Additionally, since the traditional sample average approximation (SAA) method cost much computational burden, a novel mix-SAA (MSAA) method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers. The case studies validated the satisfactory efficacy of the proposed ED model and the efficiency of the MSAA.

To limit the probability of unacceptable worst-case linearization errors that might yield risks for power system operations, this letter proposes a robust data-driven linear power flow (RD-LPF) model. It is applicable to both transmission and distribution systems and can achieve better robustness than the recent data-driven models. The key idea is to probabilistically constrain the worst-case errors through distributionally robust chance-constrained programming. It also allows guaranteeing the linearization accuracy for a chosen operating point. Comparison results with three recent LPF models demonstrate that the worst-case error of the RD-LPF model is significantly reduced over 2- to 70-fold while reducing the average error. A compromise between computational efficiency and accuracy can be achieved through different ambiguity sets and conversion methods.

Distribution power systems (DPSs) are mostly unbalanced, and their loads may have notable static voltage characteristics (ZIP loads). Hence, despite abundant papers on linear single-phase power flow models, it is still necessary to study linear three-phase distribution power flow models. To this end, this paper proposes a physics-based and data-driven linear three-phase power flow model for DPSs. We first formulate how to amalgamate data-driven techniques into a physics-based power flow model to obtain our linear model. This amalgamation makes our linear model independent of the assumptions commonly used in the literature (e.g., nodal voltages are nearly 1.0 p.u.) and thus have a relatively high accuracy generally - even when those assumptions become invalid. We then reveal how to apply our model to the DPSs with ZIP loads. We also show that with the Huber penalty function employed, the adverse impact of bad data on our model's accuracy is significantly reduced, rendering our model robust against poor data quality. Case studies have demonstrated that our model generally has 2 to over 10-fold smaller average errors than other linear power flow models, enjoys a satisfying accuracy against bad data, and facilitates a faster solution to DPS analysis and optimization problems., Comment: 8 pages

Optimally operating an integrated electricity-gas system (IEGS) is significant for the energy sector. However, the IEGS operation model's nonconvexity makes it challenging to solve the optimal dispatch problem in the IEGS. This letter proposes an improved Benders decomposition (IBD) algorithm catering to a commonly used steady-state dispatch model of the IEGS. This IBD algorithm leverages a refined decomposition structure where the subproblems become linear and ready to be solved in parallel. We analytically compare our IBD algorithm with an existing Benders decomposition algorithm and a typical piecewise linearization method. Case studies have substantiated the higher computational efficiency of our IBD algorithm., Comment: 2 tables, 2 figures, 3 pages to be submitted to PEL

This letter proposes an enhanced sufficient battery model (ESBM) as well as a binary search algorithm for a sharp inner-approximation of the aggregate flexibility of thermostatically controlled load (TCL) arrays. Compared with the previous work on generalized battery models, this ESBM preserves the merits of being sufficient and mitigates the conservativity. Moreover, unlike the work ignoring the coupling constraints that may also restrict TCLs' aggregate flexibility, our ESBM can readily handle these constraints. Numerical tests validate the merits of using the ESBM and its significance for power system operations., Comment: 3 pages, 2 figures containing 4 subfigures

This paper suggests leveraging reactive power potential (RPP) embedded in wind farms to improve power system operational safety and optimality. First, three typical RPP provision approaches are analyzed and a two-stage robust linear optimization based RPP evaluation method is proposed. This approach yields an RPP range that ensures the security of wind farm operations under any realization of uncertainty regarding the wind farm. Simplified DistFlow equations are employed here for a compromise between computational accuracy and cost. Next, an uncertain RPP-involved reactive power optimization problem is introduced, through which system operators ensure system-wide security and optimality regarding the base case and against any possible deviation caused by uncertain lumped loads and renewable generation. Steady-state models of automatic generation control and local voltage control are also captured in this uncertain reactive power optimization, which is then transformed through Soyster's method into a deterministic optimization problem that is readily solvable. Case studies have conceptually validated that even with notable uncertainty, wind farms are still a competent reactive power resource providing considerable RPP. Also, simulation confirms positive and notable improvement of leveraging wind-farm RPP on system-wide operational security and optimality, especially for power systems with high wind penetration., Comment: 8 pages, 4 figures, 6 tables

Distribution system state estimation (DSSE), which provides critical information for system monitoring and control, is being challenged by multiple sources of uncertainties such as random meter errors, stochastic power output of distributed generation (DG), and imprecise network parameters. This paper originally proposes a general interval state estimation (ISE) model to simultaneously formulate these uncertainties in unbalanced distribution systems by interval arithmetic. Moreover, this model can accommodate partially available measurements of DG outputs and inaccurate line parameters. Further, a modified Krawczyk-operator (MKO) algorithm is proposed to solve the general ISE model efficiently, and effectively provides the upper and lower bounds of state variables under coordinated impacts of these uncertainties. The proposed algorithm is tested on unbalanced IEEE 13-bus and 123-bus systems. Comparison with various methods including Monte Carlo simulation indicates that the proposed algorithm is many orders of magnitude faster and encloses tighter boundaries of state variables.

Increasing distributed energy resources (DERs) may result in reactive power imbalance in a transmission power system (TPS). An active distribution power system (DPS) having DERs reportedly can work as a reactive power prosumer to help balance the reactive power in the TPS. The reactive power potential (RPP) of a DPS, which is the range between the maximal inductive and capacitive reactive power the DPS can reliably provide, should be accurately estimated. However, an accurate estimation is difficult because of the network constraints, mixed discrete and continuous variables, and the nonnegligible uncertainty in the DPS. To solve this problem, this paper proposes a robust RPP estimation method based on two-stage robust optimization, where the uncertainty in DERs and the boundary-bus voltage is considered. In this two-stage robust model, the RPP is pre-estimated in the first stage and its robust feasibility for any possible instance of the uncertainty is checked via a tractable problem in the second stage. The column-and-constraint generation algorithm is adopted, which solves this model in finite iterations. Case studies show that this robust method excels in yielding a completely reliable RPP, and also that a DPS, even under the uncertainty, is still an effective reactive power prosumer for the TPS., Comment: 8 pages, 2 figures. This paper will be submitted to IEEE Transactions on Power Systems

Transmission-Distribution coordinated energy management (TDCEM) is recognized as a promising solution to the challenge of high DER penetration, but there is a lack of a distributed computation method that universally and effectively works for the TDCEM. To bridge this gap, a generalized mas-ter-slave-splitting (G-MSS) method is presented in this paper. This method is based on a general-purpose transmis-sion-distribution coordination model called G-TDCM, which thus enables the G-MSS to be applicable to most of the central functions of the TDCEM. In this G-MSS method, a basic heter-ogenous decomposition (HGD) algorithm is first derived from the HGD of the coupling constraints in the optimality conditions of the G-TDCM. Its optimality and convergence properties are then proved. Further, inspired by the conditions for conver-gence, a modified HGD algorithm that utilizes the subsystem's response function is developed and thus converges faster. The distributed G-MSS method is then demonstrated to successfully solve a series of central functions, e.g. power flow, contingency analysis, voltage stability assessment, economic dispatch and optimal power flow, of the TDCEM. The severe issues of over-voltage and erroneous assessment of the system security that are caused by DERs are thus resolved by the G-MSS method with modest computation cost., Comment: This paper is to be submitted to IEEE Transactions on Power Systems

With distributed generation highly integrated into the grid, the transmission-distribution-coupled AC OPF (TDOPF) becomes increasingly important. This paper proposes a response-function-based coordination method to solve the TDOPF. Different from typical decomposition methods, this method employs approximate response functions of the power injections with respect to the bus voltage magnitude in the transmission-distribution (T-D) interface to reflect the "reaction" of the distribution to the transmission system control. By using the response functions, only one or two iterations between the transmission system operator (TSO) and the distribution system operator(s) (DSO(s)) are required to attain a nearly optimal TDOPF solution. Numerical tests confirm that, relative to a typical decomposition method, the proposed method does not only enjoy a cheaper computational cost but is workable even when the objectives of the TSO and the DSO(s) are in distinct scales., Comment: This paper will appear at 2018 IEEE PES Transmission and Distribution Conference and Exposition

Currently, most district heating networks are running in a heat-setting mode, limiting the adjustment of the electrical power of combined heat and power (CHP) units. By considering the electrical power system (EPS) and district heating system (DHS) together, the peak regulatory capability of CHP units can be improved and renewable energy accommodation can be promoted. In this paper, a tractable integrated heat and electricity dispatch (IHED) model is described that addresses the thermal dynamic characteristics of pipelines and buildings to increase flexibility. To deal with the complexity of the optimization model, a water mass method (WMM) for pipeline thermal dynamics is proposed. Benefiting from the WMM, the proposed IHED model is an ordinary, non-linear model. An iterative algorithm based on the generalized Benders decomposition, and a sequential approach combined with the iterative algorithm and IPOPT, are proposed to solve the IHED model. Compared with a steady state model without thermal dynamics, considering the thermal dynamic characteristics in the DHS can further expand the peak regulatory capabilities of CHP units. The WMM is tested in the thermal dynamic simulations compared to an existing node method and a commercial simulation software. And the proposed solution strategy is verified in a small-scale system and a practical system. The simulation results of case studies are discussed to demonstrate the feasibility and economy of the dispatch model proposed here.

Storage-concerned economic dispatch (ED) problems with complementarity constraints are strongly non-convex and hard to solve because traditional Karush-Kuhn-Tucker (KKT) conditions do not hold in this condition. In our recent paper, we proposed a new exact relaxation method which directly removes the complementarity constraints from the model to make it convex and easier to solve. This paper further extends our previous study, with more than one group of sufficient conditions that guarantee the exact relaxation presented, proven and discussed. This paper may contribute to wider application of the exact relaxation in storage-concerned ED problems., Comment: 6 pages, 3 figures. Extention work based on the paper that is to appear in IEEE Transactions on Power Systems: Z. Li, Q. Guo, H. Sun, J. Wang, "Sufficient conditions for exact relaxation of complementarity constraints for storage-concerned economic dispatch". The work presented here with possible further improvement and addition is considered to be submitted to the IEEE for possible publication