(1966). Mathematical Theory of Reliability. Journal of the Operational Research Society: Vol. 17, No. 2, pp. 213-215.

https://link.springer.com/content/pdf/10.1057%2Fjors.1966.43.pdf

Mathematical Theory of Reliability

A real-time price (RTP)-based automatic demand response (ADR) strategy for PV-assisted electric vehicle (EV) Charging Station (PVCS) without vehicle to grid is proposed. The charging process is modeled as a dynamic linear program instead of the normal day-ahead and real-time regulation strategy, to capture the advantages of both global and real-time optimization. Different from conventional price forecasting algorithms, a dynamic price vector formation model is proposed based on a clustering algorithm to form an RTP vector for a particular day. A dynamic feasible energy demand region (DFEDR) model considering grid voltage profiles is designed to calculate the lower and upper bounds. A deduction method is proposed to deal with the unknown information of future intervals, such as the actual stochastic arrival and departure times of EVs, which make the DFEDR model suitable for global optimization. Finally, both the comparative cases articulate the advantages of the developed methods and the validity in reducing electricity costs, mitigating peak charging demand, and improving PV self-consumption of the proposed strategy are verified through simulation scenarios.

Dynamic Price Vector Formation Model-Based Automatic Demand Response Strategy for PV-Assisted EV Charging Stations

This article proposes a distributed multi-period multi-energy operational model for the multi-carrier energy system. In this model, energy hubs function as distributed decision-makers and feature the synergistic interactions of generation, delivery, and consumption of coupled electrical, heating, and natural gas energy networks. The multi-period multi-energy scheduling is a challenging optimization problem due to its strong couplings and inherent nonconvexities within the multi-energy networks. The original problem is thus reformulated as a mixed integer second-order cone programming (MISOCP) and subsequently solved with a sequential second-order cone programming (SOCP) approach to guarantee a satisfactory convergence performance. Furthermore, a fully-distributed consensus-based alternating direction method of multipliers (ADMM) approach with only neighboring information exchange required is developed to optimize the multi-energy flows while considering the local energy-autonomy of heterogeneous energy hubs. The proposed methodology is performed and benchmarked on a four-hub urban multi-energy system over a 24 hourly scheduling periods. Simulation results demonstrated the superiority of the proposed scheme in system operational economy and renewable energy utilization, and also verify the effectiveness of the proposed distributed approach.

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Distributed Multi-Energy Operation of Coupled Electricity, Heating, and Natural Gas Networks

A robust security-constrained unit commitment (robust SCUC) model is proposed in this paper to enhance the operational reliability of integrated electricity-natural gas system (IEGS) against possible transmission line outages. In this work, adjustable capability of natural gas contract is considered to avoid dramatic changes in real-time gas demand. Distributed natural gas storage is also included to smooth out power system demand curve and further improve operational efficiency at normal state and during contingencies. Nonlinear and nonconvex natural gas flow functions are relaxed into second-order cone (SOC) constraints, then the SOC-based column and constraint generation method is adopted to solve the proposed two-stage robust convex optimization problem. In this iterative method, the security-check subproblem feeds back worst case constraints to the first-stage master problem, until no violated scenarios can be detected. Simulations tested on 6-bus-6-node and 118-bus-10-node IEGS with natural gas storage show that the proposed storage model is effective in the robust SCUC solution for IEGS considering possible N − k contingencies with limited natural gas adjustments.

Robust Constrained Operation of Integrated Electricity-Natural Gas System Considering Distributed Natural Gas Storage

The frequency of extreme events (e.g., hurricanes, earthquakes, and floods) and man-made attacks (cyber and physical attacks) has increased dramatically in recent years. These events have severely impacted power systems ranging from long outage times to major equipment (e.g., substations, transmission lines, and power plants) destructions. This calls for developing control and operation methods and planning strategies to improve grid resilience against such events. The first step toward this goal is to develop resilience metrics and evaluation methods to compare planning and operation alternatives and to provide techno-economic justifications for resilience enhancement. Although several power system resilience definitions, metrics, and evaluation methods have been proposed in the literature, they have not been universally accepted or standardized. This paper provides a comprehensive and critical review of current practices of power system resilience metrics and evaluation methods and discusses future directions and recommendations to contribute to the development of universally accepted and standardized definitions, metrics, evaluation methods, and enhancement strategies. This paper thoroughly examines the consensus on the power system resilience concept provided by different organizations and scholars and existing and currently practiced resilience enhancement methods. Research gaps, associated challenges, and potential solutions to existing limitations are also provided.

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Power System Resilience: Current Practices, Challenges, and Future Directions

Power systems are exceedingly faced with extreme events such as natural disasters and deliberate attacks. In comparison, the underground natural gas system is considered less vulnerable to such extreme events. We consider that the overhead power grid can be hardened by replacing segments of electric power grid with underground natural gas pipelines as an energy transportation system to countereffect extreme events which can damage interdependent infrastructures severely. In this paper, an integrated electricity and natural gas transportation system planning algorithm is proposed for enhancing the power grid resilience in extreme conditions. A variable uncertainty set is developed to describe the interactions among power grid expansion states and extreme events. The proposed planning problem is formulated as a two-stage robust optimization problem. First, the influence of extreme events representing natural disasters is described by the proposed variable uncertainty set and the proposed robust model for the integrated planning is solved with the grid resilience represented by a set of constraints. Second, the investment decisions are evaluated iteratively using the conditional events. The integrated electricity and natural gas planning options are analyzed using the modified IEEE-RTS 1979 for enhancing the power grid resilience. The numerical results point out that the proposed integrated planning is an effective approach to improving the power grid resilience.

Integrated Planning of Electricity and Natural Gas Transportation Systems for Enhancing the Power Grid Resilience

In this paper, an mixed integer linear programming (MILP) method is proposed for calculating the optimal power flow in a multicarrier energy system. A state variable-based linear energy hub model is developed, which avoids the introduction of dispatch factor variables applied traditionally to the optimal power flow problem. The multidimensional piecewise linear approximation method is proposed for representing nonconvex natural gas transmission constraints in which the approximation error is further analyzed. Accordingly, the optimal power flow is reformulated as an MILP problem. Compared with the nonlinear models, the proposed model can be solved by the existing optimization techniques, which can be easily implemented in the optimal power system planning problem. The proposed method is verified by case studies applied to the modified six-bus and the IEEE-118 systems. The test results show that the proposed method can provide a fast solution for the optimal power flow which can be applied to large scale hub systems with sufficient accuracy. The results also demonstrate that the proposed method outperforms the existing MILP methods in calculation time especially in large scale hub applications.

An MILP-Based Optimal Power Flow in Multicarrier Energy Systems

Power system operation has recently witnessed major challenges, which are often due to large-scale integrations of wind power generation. In this paper, a two-stage robust security-constrained unit commitment (SCUC) model is proposed for managing the wind power uncertainty in the hourly scheduling of power system generation. Different from previous studies on robust SCUC, which considered a predefined uncertainty set, the proposed method applies a flexible uncertainty set for managing the variable wind power generation. The proposed method seeks a feasible and economic dispatch in the flexible uncertainty set, takes into account wind spillage and load curtailment risks, and makes a tradeoff between the optimal wind power absorption and the economic grid operation. Several case studies are applied to the proposed method and the corresponding solutions are analyzed in the paper. The impacts of major factors, including flexible generation resources and power transmission capacity, on the proposed solution are also discussed. The numerical results demonstrate the merits of the proposed method for managing large variations in the hourly wind power generation and lowering the power system operation cost in uncertain conditions.

Security-Constrained Unit Commitment With Flexible Uncertainty Set for Variable Wind Power

Cooperation between the controllable load, such as electrical vehicles (EVs) and the generation, provides the power system new operating strategies. A novel hierarchical charge control framework is proposed based on the Benders decomposition for large populations of EVs. The grid, unit, and accurate EV constraints can be considered. On the upper level, the cooperative dispatch scheme between the generation and the EV aggregators is obtained. On the lower level, the feasibility of the scheme is checked with EV constraints considered. The levels are coordinated by the Benders cuts. In addition, the distributed approximate Benders cuts is also proposed, which helps to protect user privacy and a three-level framework is developed based on the decentralized control. The case studies on IEEE Reliability Test System have verified the proposed framework and method is valid and feasible. The charge control based on it can minimize the grid operation cost and improve the unit operating efficiency.

Hierarchical Charge Control of Large Populations of EVs

The electric vehicles (EVs) can introduce new operation strategies, such as charging management and vehicle-to-grid control, which could provide a considerable level of distributed storage to the power grid. In this paper, a partial decomposition method which is based on the Lagrangian relaxation framework is proposed for the EV charging control in transmission-constrained power systems. The partial decomposition method helps reduce the number of dual multipliers and stabilize the iterative process. The proposed partial decomposition framework is applied to a day-ahead SCUC algorithm which can be easily implemented in the existing hierarchical power system operations. The proposed EV charging control method can not only help reduce the total generation cost of power systems but also alleviate the transmission grid congestion. The feasibility of the proposed method is validated by the case studies applied to the modified IEEE-RTS1979.

Biyang Wang

Papers

Integrated Planning of Electricity and Natural Gas Transportation Systems for Enhancing the Power Grid Resilience

An MILP-Based Optimal Power Flow in Multicarrier Energy Systems

Security-Constrained Unit Commitment With Flexible Uncertainty Set for Variable Wind Power

Hierarchical Charge Control of Large Populations of EVs

Partial Decomposition for Distributed Electric Vehicle Charging Control Considering Electric Power Grid Congestion