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Rapid growth of gas-fired generators strengthens the interdependency of electricity and natural gas markets. To meet the uncertainty challenge, a robust day-ahead market clearing framework for the integrated electricity and natural gas system (IEGS) is presented. First, a robust security-constrained unit commitment (SCUC) model is built considering the joint dispatch of ancillary services. Regulation-up/down reserve is scheduled to balance electrical load/wind power uncertainties, spinning reserve is to manage N-1 generator outage, and natural gas reserve is to withstand gas load uncertainty and provide fuel for gas-fired electrical reserve. The SCUC model is a two-stage mixed-integer nonlinear optimization problem so that a sequential linear approximation-based Column & Constraint Generation (SLA-based C&CG) algorithm is proposed. Then, according to SCUC solutions, an economic dispatch model is derived to obtain market clearing and pricing results. Based on locational marginal pricing, novel definitions of electrical energy, natural gas and multiple ancillary service prices are proposed, which can reflect network limits and uncertainty effects. Numerical cases on two test IEGSs and a provincial-level IEGS demonstrate the high accuracy of proposed SLA-based C&CG algorithm and the impact of uncertainties on market clearing.

Currently, the increasing wind power penetration, with consequent randomness and variability, presents great challenges to power system planning and operation. Probabilistic power flow (PPF) has been developed to calculate the power flow under uncertain circumstances. However, the current wind power models are subject to specific probability distributions, limiting their accuracies in wider applications. Additionally, the cumulant method (CM)-based PPF, if nonlinear relationship is considered in, would face an impractically high computational complexity. To address these problems in modeling and cumulant calculation, this article proposes a novel generalized density/distribution fitting method (GDFM) combining with the Copula function to establish a joint probability model for wind power generation. A special impulse- mixed probability density (IMPD) integration method is also introduced to derive the input cumulants from the model. Finally, a fast cumulant method (FCM) is proposed to reduce the computational burden of output cumulant calculation while retaining a high accuracy in a nonlinear context. Case study on the IEEE-118 test system validates the effectiveness of the proposed methods, and a real application to a provincial power grid in China provides some useful power flow risk information for decision making. The whole FCM-based PPF scheme can be helpful for future power flow examination in power system planning and operation.

Resilience is an overarching concept that requires combined efforts from interdependent critical infrastructures to achieve. As the interdependence between the power system and the natural gas system grows, the roles of coordination in post-disaster repair will be unneglectable to improve the resilience of the two systems. In this paper, a combined repair crew dispatch problem for the interdependent power and natural gas systems is proposed. The repair schedule of the two systems is coordinated and co-optimized. Both power system topology reconfiguration and intentional DG islanding are modeled as operational measures to further improve the resilience of the interdependent systems. Case studies validate the effectiveness of the proposed method in reducing load shedding and repair duration, and prove that the interdependence has a significant impact on the repair sequence and crew coordination.

Distribution service restoration (DSR) is critical for improving the resilience and reliability of modern distribution systems by strategically and sequentially energizing the system components and customer loads. Restoring electricity service to affected customers also requires multiple crews with different skill sets to perform multiple tasks that are procedurally interdependent with safety guaranteed. However, in existing DSR practices, switch operations and crew dispatch are scheduled separately, and their interdependence is not fully considered. As advanced technologies are enabling remote communication, control, and dispatch, utilities now desire an integrated DSR framework to achieve seamless coordination among multiple DSR tasks such as switch operation, crew dispatch, and component repair. In this paper, we introduce a synthetic model that integrates the service restoration model and the crew dispatch model based on a universal routing model. The proposed model can provide the estimated time of restoration for each load, the switching sequence for safely operating remotely/manually operated switches, and dispatch solutions for crews with different skill sets. The proposed synthetic model is formulated as a mixed-integer linear programming model, and its effectiveness is evaluated via the IEEE 123 bus test feeder and several large-scale test feeders (EPRI Ckt5, Ckt7, Ckt24, and IEEE 8500 node test feeder.

This paper proposes a reliability-oriented planning method to design reliable topologies for meshed high-voltage direct-current (HVdc) grids. Based on the proposed steady-state model for HVdc grids, a bi-level and multiobjective planning problem is formulated. The optimization model not only regards reliability as an independent objective, but also takes the power flow controllers (PFCs) into account. Compared with conventional methods, it overcomes the curse of dimensionality and solves the optimal allocation of PFCs. Then, the nondominated sorting genetic algorithm II is employed to solve the upper-level problem. For lower-level problems, an algorithm based on minimum spanning trees is proposed to optimally allocate PFCs, and an improved least frequently used cache algorithm and an optimum-test algorithm are developed to promote the computing efficiency of reliability evaluation. The European Supergrid and a Chinese ultra-HVdc system are adopted as test systems to validate the proposed method. Case studies prove that the proposed method provides an effective tool for the planning of HVdc grids. Also, results show that the cache technique and the optimum-test algorithm can reduce more than 70% of the total elapsed time.

As the rapid development of natural-gas fired units (NGUs), power systems begin to rely more on a natural gas system to supply the primary fuel. On the other hand, natural gas system contingency might cause the nonavailability of NGUs and inevitably jeopardize power system security. To address this issue, this paper studies security-constrained joint expansion planning problems for this combined energy system. We develop a computationally efficient mixed-integer linear programming (MILP) approach that simultaneously considers N-1 contingency in both natural gas system and electricity power system. To reduce the combinatorial search space of MILP models, an extension of a reduced disjunctive model is proposed to decrease the numbers of binary and continuous variables as well as constraints. The involving nonlinear terms in N-1 constraints are exactly linearized without sacrificing any optimality. Numerical results on two typical integrated energy systems demonstrate the necessity of extending N-1 criterion to the whole network of a combined energy system. Experimental results also show that compared with the conventional approach, our proposed MILP approach achieves a great computational performance improvement in solving security-constrained co-optimization expansion planning problems.

As the sharp growth of gas-fired power plants and the new emergence of power-to-gas (PtG) technology intensify the interdependence between electricity and natural gas systems, it is imperative to co-optimize the two systems for improving the overall efficiency. This paper presents a long-term robust co-optimization planning model for interdependent systems, for minimizing total investment and operation costs. Beside generators, transmission lines, gas suppliers, and pipelines, PtGs and gas compressor stations are also considered as investment candidates to effectively handle wind power uncertainties in the power system and compensate pressure losses in the gas network. Furthermore, the proposed model includes a joint N-1 and probabilistic reliability criterion to promote economical and reliable planning solutions. The proposed model is solved via a decomposition approach, by iteratively solving a base-case master problem and two operation subproblems to check N-1 and probabilistic reliability criteria. Numerical case studies illustrate the effectiveness of the proposed robust co-optimization planning approach.

A novel multi-stage stochastic programming model is proposed for the expansion coplanning of gas and power networks considering the uncertainties in net load demand. Meanwhile, the nonanticipativity constraints are taken into account to guarantee the decisions should only depend on the information of realized uncertainties up to the present stage. Compared with the traditional two-stage stochastic programming model, the proposed multi-stage stochastic programming model yields sequential investment decisions with the uncertainties revealed gradually over time, such that the investment decisions are capable of keeping future options open and can shift from “never be changed” decisions to a flexible “wait and see” decisions. The test on three systems shows the effectiveness of the proposed multi-stage stochastic programming model.

This paper presents a bilevel optimization model for the risk assessment of transmission systems. Specifically, the lower level model is expected to provide a generation redispatch by minimizing the total load shedding, and the upper-level model is to maximize the severity risk by constructing a binary optimization model to identify the worst N - k contingency. To further reduce the complexity of the proposed model, the logarithmic transformation and linearization techniques are utilized, leading to a general mixed integer linear programming. In addition, a recursive method is proposed for contingency ranking based on the bilevel optimization model. Compared with the benchmark analytic method, the proposed method does not need to enumerate every contingency, reducing the computational burden. In contrast to the traditional Monte Carlo Simulation method, the proposed method can give as precise a risk assessment result as the analytic method and has higher evaluation efficiency. Numerical results on three test systems verify the effectiveness of the proposed method.

Reliability costs are used to evaluate the influence of large-scale wind power integration on security constrained unit commitment (SCUC), but the nonlinear expressions of reliability costs increase the complexity of the SCUC model. To address this issue, this letter presents a novel variant to exactly linearize the nonlinear expressions. Compared with the traditional approach, the proposed variant can reduce the number of binary variables, such that the computational performance of the SCUC model is significantly improved. Numerical results of the IEEE reliability test system verify the effectiveness of the proposed variant.

With the growing trend of extreme weather events in the Northeast U.S., a region of dense vegetation, evaluating hazard effects of wind storms on power distribution systems becomes increasingly important for disaster preparedness and fast responses in utilities. In this paper, probabilistic wind storm models for the study region have been built by mining 160-year storm events recorded in the National Oceanic and Atmospheric Administration's Atlantic basin hurricane database (HURDAT). Further, wind storms are classified into six categories according to NOAA criteria and IEEE standard to facilitate the evaluation of distribution system responses under different levels of hazards. The impacts of wind storms in all categories are accurately evaluated through a Sequential Monte Carlo method enhanced by a temporal wind storm sampling strategy. Extensive studies for the selected typical distribution system indicate that our models and methods effectively reveal the hazardous effects of wind storms in the study region, leading to useful insights towards building better system hardening schemes.

Reliability evaluation of composite systems involves extensive calculations. Current solutions to this computational burden have mainly focused on extracting failure states from the state space. Instead, the evaluation of failure states is accelerated by methods presented in this paper. The scale of optimizations required for generation redispatching and/or load shedding in failure states is reduced by eliminating redundant line flow constraints. First, a sufficient and necessary condition for a line flow constraint to be redundant is established in the form of a linear programming problem, based on the concept of steady-state security region (SSR). Then, two redundancy elimination methods are proposed-a conservative one based on a heuristic, and a radical one based on an analytical condition. Numerical tests are conducted on IEEE-RTS79 and a real-life system. More than half of the line flow constraints are eliminated by the conservative method and nearly 90% by the radical method. The proposed methods can be used in conjunction with most of the existing acceleration techniques to further improve efficiency.

Phase shifting transformers (PSTs) can be regulated to minimize total generation cost in optimal power flow problems. Under the perception that there exists multiple optimal solutions of PST angle adjustment and better economy may be achieved by controlling a small fraction of PSTs, this letter proposes a mixed integer linear programing model to optimally determine the subset of PSTs for angle adjustment. Numerical results on several test systems including large-scale systems show that the proposed model can provide better economic dispatch with regulating a small number of PSTs.

Dynamic economic dispatch (DED) over multiple time periods is a large-scale coupled spatial-temporal optimization problem. Therefore, the Lagrangian relaxation method has been widely used to split the large-scale optimization problem with coupled structure into several small sub-problems. In order to bring robustness for updating the dual multipliers and yielding convergence without strong assumptions, the augmented Lagrangian relaxation method is introduced in this paper. However, the added penalty term in an augmented Lagrangian function is non-separable, which leads to the difficulty in achieving full decomposition for parallel computation. To address this problem, a diagonal quadratic approximation method is employed to yield an approximated block separation of the non-separable penalty term. Furthermore, the ramp rate constraints are relaxed in this paper, so that the DED model is decomposed into several single-period economic dispatch models that can be efficiently handled in parallel, called the parallel augmented Lagrangian relaxation method. Particularly, the proposed relaxation strategy has a high separability feature which theoretically leads to sound convergence property. Numerical results on the IEEE 118-bus and a practical Polish 2383-bus test system over a different number of time periods show the effectiveness of the proposed method. In addition, the proposed method can be extended to other coupled spatial-temporal scheduling problems in power systems, such as energy storage dispatch.

A novel Geometric Programming (GP) is presented in the first time by the optimization model of importance sampling parameters (ISP) in Variance Minimization (VM) for importance sampling (IS) of power system reliability evaluation. The key point of the proposed method is that the equality constraints of VM optimization model can be relaxed into inequalities because of its special structure, thus a new GP-VM convex optimization model can be built exactly to solve the difficulty of obtaining the optimal ISP. Numerical results of two test systems verify the effectiveness of the proposed method.