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This article presented a convex relaxation approach for the optimal power flow problem. The proposed approach leveraged the second-order cone programming (SOCP) relaxation to tackle the non-convexity within the feasible region of the power flow problem. Recovering an optimal solution that is feasible for the original non-convex problem is challenging for networks with cycles. The main challenge is the lack of convex constraints to present the voltage angles within a cycle. This article aims to fill this gap by presenting a convex constraint enforcing the sum of voltage angles over a cycle to be zero. To this end, the higher-order moment relaxation matrix associated with each maximal clique of the network is formed. The elements of this matrix are utilized to form a convex constraint enforcing the voltage angle summation over each cycle. To keep the computation burden of leveraging the higher-order moment relaxation low, a set of second-order cone constraints are applied to relate the elements of the higher-order moment relaxation matrix. The case study presented the merit of this work by comparing the solution procured by the introduced approach with other relaxation schemes.

Convergence bidding (CB), a.k.a., virtual bidding (VB), is a market mechanism facilitated by Independent System Operators (ISOs) in wholesale electricity markets to help lower the gap between the prices in the day-ahead market (DAM) and prices in the real-time market (RTM). In this paper, we seek to answer two questions: 1) how can a strategic market participant maximize its profit when submitting CBs? 2) how can such strategically placed CBs affect the price gaps? Answering these questions is not straightforward but the results are insightful. The bidding problem in this context is a bi-level optimization, where the upper-level is about maximizing the profit for the convergence bidder and the lower-level is the economic dispatch problem. By solving the formulated bidding problem, we investigate the impact of strategic CBs on the DAM and RTM locational marginal prices (LMPs) under various practical scenarios. We demonstrate the scenarios under which a strategic CB, whether on its own, or when it is submitted jointly with a physical demand or physical supply bid, can or cannot work as intended, and result in decreasing or increasing the price gap in nodal electricity markets. We also examine how the performance of strategic CBs can be affected by uncertainty in demand or generation bids as well as physical contingencies in the power system, such as transmission line tripping. Special cases, such as net-zero convergence bidding are studied. The long-term performance of strategic convergence bidding is investigated. The above and other market implications are discussed in multiple case studies.

This paper presents a framework to determine the strategic bidding of the wireless charging aggregators that operate wireless charging stations to provide in-motion charging services for the electric vehicles. The proposed framework captures the interactions between the electricity and transportation networks through competition among the wireless charging aggregators. Wireless charging aggregators participate in the wholesale electricity market to minimize the cost of gained energy from the bulk electricity network. In the retail wireless charging market, wireless charging aggregators compete to maximize their revenue by offering energy to the electric vehicles that are traveling on the transportation links. The strategic behavior of the wireless charging aggregators highlights the interdependence between the electricity and transportation infrastructure systems. In each system, the strategic behavior of the entities is determined by formulating a bi-level optimization problem which is further transformed into a mathematical problem with equilibrium constraints. The upper-level problem maximizes the profit of the entities while the lower level problem ensures the balance between the demand and supply in each infrastructure system. The demand and supply balance is guaranteed by the optimal power flow in the electricity network and the user equilibrium traffic assignment in the transportation network.

A new solution method is introduced to the problem of optimally deploying manual and automatic switches in distribution systems, where the product of two continuous variables and the inverse of a continuous variable are reformulated as a linear relation. This leads to a (mixed integer linear problem) MILP power flow formulation too. The objective function includes cost and reliability. The cost term itself includes capital investment, installation, and maintenance costs (MC) as well as customer interruption cost (CIC); while the reliability term is represented by system average interruption duration index (SAIDI). The problem is formulated as a MILP, which guarantees a global optimal solution. The effectiveness of the proposed method is validated through various case studies and sensitivity analyses on the RBTS4, followed by a comprehensive discussion and analysis of results. The proposed MILP formulation prescribes fewer switches while achieving lower SAIDI, compared to that of a previous MINLP formulation.

Improving the prediction of the availability of solar energy resources became a necessary component in the operation of utilities with a high penetration level of renewable energy resources. In this article, the solar insolation data in spatial proximity is leveraged to investigate the error in the prediction of solar insolation using multiple learning algorithms. Different error measures are utilized to evaluate the accuracy of the presented linear and nonlinear learning algorithms. Essential data preprocessing steps are conducted on the solar insolation data available from multiple meteorological stations in spatial proximity. The impact of utilizing the spatiotemporal data compared with the temporal data is analyzed. A comprehensive analysis based on multiple error measures is presented to compare the prediction error while employing multiple learning algorithms. It is shown that it is possible to identify the particular station and the particular learning algorithm that contribute the most in improving the solar insolation prediction of a specific location.

Power flow is a fundamental problem for analyzing the power system. It is to solve a set of equations with quadratic terms. Procuring a reliable solution methodology for this problem is challenging as the feasibility region for this problem is nonconvex. Iterative approaches were employed to solve the problem, which may fail to provide a solution under certain circumstances such as bad initial point. In this paper, a solution methodology that is capable of providing a reliable solution to the power flow problem is presented. First, by exploiting sparsity in the power network, a convex relaxation for the problem is presented using the first order of the Lasserre hierarchy of moment relaxations. Then, a distributed approach using Jacobi-proximal alternating directions method of multipliers (JP-ADMM) is implemented to efficiently solve the power flow problem. To solve the sub-problems within JP-ADMM approach, the second order of the Lasserre hierarchy of moment relaxations is employed. To illustrate the effectiveness of the proposed approach, several case studies are presented.

In different areas across the U.S., there are utility poles and other critical infrastructure that are vulnerable to flooding damage. The goal of this multidisciplinary research is to assess and minimize the probability of utility pole failure through conventional hydrological, hydrostatic, and geotechnical calculations embedded to a unique mixed-integer linear programming (MILP) optimization framework. Once the flow rates that cause utility pole overturn are determined, the most cost-efficient subterranean pipe network configuration can be created that will allow for flood waters to be redirected from vulnerable infrastructure elements. The optimization framework was simulated using the Julia scientific programming language, for which the JuMP interface and Gurobi solver package were employed to solve a minimum cost network flow objective function given the numerous decision variables and constraints across the network. We implemented our optimization framework in three different watersheds across the U.S. These watersheds are located near Whittier, NC; Leadville, CO; and London, AR. The implementation of a minimum cost network flow optimization model within these watersheds produced results demonstrating that the necessary amount of flood waters could be conveyed away from utility poles to prevent failure by flooding.

Natural gas-fired generation units can hedge against the volatility in the uncertain renewable generation, which may occur during very short periods. It is crucial to utilize models capable of correctly capturing the natural gas network dynamics induced by the volatile demand of gas-fired units. The Weymouth equation is commonly implemented in literature to avoid dealing with the mathematical complications of solving the original governing differential equations of the natural gas dynamics. However, it is shown in this paper that this approach is not reliable in the short-term operation problem. Here, the merit of the non-convex transient model is compared with the simplified Weymouth equation, and the drawbacks of employing the Weymouth equation are illustrated. The results demonstrate how changes in the natural gas demand are met by adjustment in the pressure within pipelines rather than the output of natural gas suppliers. This work presents a convex relaxation scheme for the original non-linear and non-convex natural gas flow equations with dynamics, utilizing a rank minimization approach to ensure the tightness. The proposed method renders a computationally efficient framework that can accurately solve the non-convex non-linear gas operation problem and accurately capture its dynamics. Also, the results suggest that the proposed model improves the solution optimality and solution time compared to the original non-linear non-convex model. Finally, the scalability of the proposed approach is verified in the case study.

Utilities in California conduct Public Safety Power Shut-offs (PSPSs) to eliminate the elevated chances of wildfire ignitions caused by power lines during extreme weather conditions. We propose Wildfire Risk Aware operation planning Problem (WRAP), which enables system operators to pinpoint the segments of the network that should be de-energized. Sustained wind and wind gust can lead to conductor clashing, which could ignite surrounding vegetation. The 3D non-linear vibration equations of power lines are employed to generate a dataset that considers physical, structural, and meteorological parameters. With the help of machine learning techniques, a surrogate model is obtained which quantifies the risk of wildfire ignition by individual power lines under extreme weather conditions. The cases illustrate the superior performance of WRAP under extreme weather conditions in mitigating wildfire risk and serving customers compared to the naive PSPS approach and another method in the literature. Cases are also designated to sensitivity analysis of WRAP to critical load-serving control parameters in different weather conditions. Finally, a discussion is provided to explore our wildfire risk monetization approach and its implications for WRAP decisions.

Microgrids with AC/DC architecture benefit from advantages of both AC and DC power. In this paper, daily operation problem for a zero-carbon AC/DC microgrid in presence of electric vehicles (EVs) is considered. In this framework, EVs' batteries are mobile energy storage systems, which allow desirable operation of the microgrid during peak demand hours. This study shows in absence of storage system, EVs' batteries can be properly managed to satisfy the system requirements. In the case studies, several sensitivity analyses based on variations in battery degradation costs, solar irradiance, and inverter capacity are investigated., Comment: ITEC 2021

A solution to the power flow problem is imperative for many power system applications and several iterative approaches are employed to achieve this objective. However, the chance of finding a solution is dependent on the choice of the initial point because of the non- convex feasibility region of this problem. In this paper, a non-iterative approach that leverages a convexified relaxed power flow problem is employed to verify the existence of a feasible solution. To ensure the scalability of the proposed convex relaxation, the problem is formulated as a sparse semi-definite programming problem. The variables associated with each maximal clique within the network form several positive semidefinite matrices. Perturbation and network reconfiguration schemes are employed to improve the tightness of the proposed convex relaxation in order to validate the existence of a feasible solution for the original non-convex problem. Multiple case studies including an ill-conditioned power flow problem are examined to show the effectiveness of the proposed approach to find a feasible solution.

This paper presents the expansion planning for data centers and data routes in the data and electricity networks considering the uncertainties in the planning horizon to ensure an acceptable rate of service to the requests received from the end-users in the data network. The objective is to determine the location and capacity of the data centers as well as the required data routes while considering the imposed constraints in the electricity and data networks. The installation cost of data centers and data routes, as well as the expected operation cost of the data centers, are minimized. The proposed problem addressed the uncertainties in the expansion planning of the electricity networks including the availability of renewable generation resources, the variations in electricity demand, the availability of generation and transmission components in the electricity network, and the uncertainties in the number of requests received by the user groups in the data network. The problem is formulated as a mixed integer linear programming problem and Bender decomposition and electricity price signals are used to capture the interaction among the data and electricity networks. The presented case study shows the effectiveness of the proposed approach.

This work aims to minimize the cost of installing renewable energy resources (photovoltaic systems) as well as energy storage systems (batteries), in addition to the cost of operation over a period of 20 years, which will include the cost of operating the power grid and the charging and discharging of the batteries. To this end, we propose a long-term planning optimization and expansion framework for a smart distribution network. A second order cone programming (SOCP) algorithm is utilized in this work to model the power flow equations. The minimization is computed in accordance to the years (y), seasons (s), days of the week (d), time of the day (t), and different scenarios based on the usage of energy and its production (c). An IEEE 33-bus balanced distribution test bench is utilized to evaluate the performance, effectiveness, and reliability of the proposed optimization and forecasting model. The numerical studies are conducted on two of the highest performing batteries in the current market, i.e., Lithium-ion (Li-ion) and redox flow batteries (RFBs). In addition, the pros and cons of distributed Li-ion batteries are compared with centralized RFBs. The results are presented to showcase the economic profits of utilizing these battery technologies.

This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various measures to evaluate the tightness of the solution procured by the convex relaxation approaches. Therefore, three tightness measures are leveraged to illustrate the performance of convex relaxation methods under different demand scenarios. The main issue of convex relaxation methods is recovering an optimal solution which is not necessarily feasible for the original non-convex problem in networks with cycles. Thus, a cycle measure is introduced to evaluate the performance of relaxation schemes. The presented case study investigates the merit of using various tightness measures to evaluate the performance of various relaxation methods under different circumstances., 6 Pages, 16 Figures, This paper is accepted for the 52nd North American Power Symposium

In this paper, the short-term operation problem for a multiple energy carrier hybrid AC/DC microgrid is discussed. The hybrid microgrid consists of AC and DC parts, which are connected by means of inverters as well as natural gas network. The microgrid includes photovoltaic (PV) unit, wind turbine (WT), battery storage unit and gas-fired microturbines. A mixed integer linear programming is formed to minimize the overall cost of the microgrid including cost of natural gas supply, the value of lost load and battery degradation cost. The presented case study explored the importance of inverter characteristics and pipeline capacity.

A total 19% of generation capacity in California is offered by PV units and over some months, more than 10% of this energy is curtailed. In this research, a novel approach to reduce renewable generation curtailments and increasing system flexibility by means of electric vehicles' charging coordination is represented. The presented problem is a sequential decision making process, and is solved by fitted Q-iteration algorithm which unlike other reinforcement learning methods, needs fewer episodes of learning. Three case studies are presented to validate the effectiveness of the proposed approach. These cases include aggregator load following, ramp service and utilization of non-deterministic PV generation. The results suggest that through this framework, EVs successfully learn how to adjust their charging schedule in stochastic scenarios where their trip times, as well as solar power generation are unknown beforehand., This project was initially submitted to CSEE Journal of Power and Energy Systems in August 2020. The current version was submitted in December 2020

The variability in the generation dispatch of the natural gas generation units will lead to fluctuation in natural gas demand profile that could further jeopardize the security of the natural gas network. The coordinated operation of electricity and natural gas infrastructure systems would help to improve the security and reliability measures in both infrastructure systems and mitigate the risk of demand curtailment. The electricity and natural gas network operation problems are non-convex mixed-integer nonlinear programming problems that are hard to solve in polynomial time. The non-convex feasible regions are formed by the Weymouth constraint and the introduced binary commitment decision variables in the natural gas and electricity network operation problems, respectively. This paper utilized a sparse semidefinite programming (SDP) relaxation to procure the optimal solution for the coordinated operation of electricity and natural gas networks. The presented algorithm leverages the sparseness of the natural gas network to construct several small matrices of lifting variables that are used to form a tight and traceable SDP relaxation. A set of valid constraints that tighten the relaxation ensures the exactness of the solution procured from the relaxed problem. The effectiveness of the presented approach is shown in case studies.

This paper presents risk-averse long-term generation maintenance scheduling in the power systems with a considerable installed capacity of microgrids. Microgrid aggregators facilitate the participation of microgrids in the wholesale market. In this paper, the effect of microgrids as controllable demand entities on the generation maintenance scheduling practices in the power system is investigated. The uncertainties in the marginal cost of generation in microgrids, the generation capacity installed within the microgrids, and the system electricity demand are captured using respective nominal values and uncertainty intervals. Moreover, the contingencies in transmission network are addressed by introducing additional variables. A two-stage robust optimization problem is formulated to determine a trade-off among the performance and conservativeness of the procured solution in the long-term operation horizon. The problem is formulated as a mixed integer linear programming problem and column-and-constraint generation procedure is used to solve the problem. The master problem minimizes the maintenance cost of the generation units subjected to generation units’ constraints in the long-term operation horizon and the sub-problems determine the worst realization of the uncertainties and generate additional constraints in the master problem. The proposed methodology is applied to two case studies for a 6-bus and IEEE 118-bus power systems.

Wireless charging station (WCS) enables in-motion charging of the electric vehicles (EVs). This paper presents the short-term operation of WCS by capturing the interdependence among the electricity and transportation networks. In the transportation network, the total travel cost consists of the cost associated with the travel time and the cost of utilized electricity along each path. Each EV takes the path that minimizes its total travel cost. In the electricity network, the changes in WCS demand as a result of changes in the traffic flow pattern impacts the price of electricity. The changes in the price of electricity further affect the charging strategy of the EVs and the associated traffic flow pattern. The coordination between electricity and transportation networks would help mitigate congestion in the electricity network by routing the traffic flow in the transportation network. The presented formulation leverages decentralized optimization to address the economic dispatch in the electricity network as well as the traffic assignment in the transportation network. The presented case studies highlight the merit of the presented model and the developed algorithms for the coordinated operation of WCS in electricity and transportation networks.

This paper presents an approach to determine the vulnerable components in the electricity and natural gas networks of an islanded microgrid that is exposed to deliberate disruptions. The vulnerable components in the microgrid are identified by solving a bi-level optimization problem. The objective of the upper-level problem (the attacker’s objective) is to maximize the expected operation cost of microgrid by capturing the penalties associated with the curtailed electricity and heat demands as a result of the disruption. In the lower-level problem, the adverse effects of disruptions and outages in the electricity and natural gas networks are mitigated by leveraging the available resources in the microgrid (the defender’s objective). The uncertainties in the electricity and heat demand profiles were captured by introducing scenarios with certain probabilities. The formulated bi-level optimization problem provides effective guidelines for the microgrid operator to adopt the reinforcement strategies in the interdependent natural gas and electricity distribution networks and improve the resilience of energy supply. The presented case study shows that as more components are reinforced in the interdependent energy networks, the reinforcement cost is increased and the expected operation cost as a result of disruption is decreased.

The transactive energy framework provides value-driven control schemes that facilitate power delivery with higher efficiency, sustainability and economic soundness while ensuring the reliability and security of the energy infrastructure system. This article addresses the challenges and solution frameworks for the short-term operation of distributed energy resources, controllable demands, and microgrids in a transactive energy architecture, with a focus on the distributed energy management of hybrid AC/DC microgrids.

With the increase in the investment in the gas-fired electricity generation technology, capturing the operation constraints of the natural gas network in the electricity and natural gas operation problems becomes more crucial. The non-convexity in the feasibility region formed by natural gas network constraints will impede achieving the global solution for these problems. This letter proposed an algorithm to procure a tight and tractable convex relaxation for the natural gas network constraints that can be leveraged in the electricity and/or natural gas network operation problems. The merit of the proposed algorithm is illustrated using a case study and the efficiency of the proposed formulation is compared with mixed integer linear and semidefinite programming formulations.

Electricity grid vulnerabilities can lead to outages with prolonged load interruptions. Research activities on the impact of natural disasters on power system are underway to figure out the outage reasons, identify the ways to prepare for preventive actions, and increase the resiliency for the corrective and preventive actions under such scenarios. This paper presented a review of the methods for the electricity grid vulnerability analysis, pre-disaster recovery planning, and post-disaster restoration models.

This paper proposes a novel framework for a distribution level transactive energy system in order to facilitate energy transaction among microgrids while improving efficiency and reliability of distribution system. The proposed market mechanism simultaneously considers competition among participants, distribution network reliability and operation conditions. To improve the reliability of supply, a reputation system is proposed, which ranks energy suppliers according to a reputation index based on their long term energy transaction history. A demand-oriented approach is utilized for extracting local energy prices. The local energy pricing scheme is based on combination of reputation scores, loss reduction indices and demand-side offering prices. A secondary market is proposed to use the capacity of energy suppliers for reliability support service in distribution network. The local pricing scheme for the reliability market is based on outage scenarios and customer interruption penalties. It is shown that the proposed model enforces energy suppliers to honor their generation commitments and prevents them from greedy behavior in the market. The energy market mechanism improves the reliability of supply and intensifies competition among participants. This mechanism directly reduces active power losses in distribution network and indirectly improves nodal voltage and branch loading profile. Moreover, utilizing the capacity of microgrids in improving the reliability of network, postpones network reinforcement investments needed for keeping the service continuity indices in acceptable range.

This paper proposes a methodology to attain the optimal generation scheduling of hybrid AC/DC microgrids. The hybrid microgrid consists of AC and DC networks with respective generation and demand resources that are connected by bi-directional AC/DC converters. The proposed methodology leverages decentralized optimization framework that uses the dispatch of the AC/DC converter to facilitate the coordinated operation of AC and DC networks. The presented framework utilizes an iterative approach to determine the optimal operation schedule for the hybrid AC/DC microgrid using distinct optimization problems. The results illustrate the effectiveness of the presented approach for operation planning of hybrid AC/DC microgrids.

This paper proposed a hierarchical structure for the electricity market to facilitate the coordination of energy markets in distribution and transmission networks. The proposed market structure enables the integration of microgrids, which provide energy and ancillary services in distribution networks. In the proposed hierarchical structure, microgrids participate in the energy market at the distribution networks settled by the distribution network operator (DNO), and load aggregators (LAs) interact with microgrids and generation companies (GENCOs) to import/export energy to/from the distribution network electricity markets from/to the wholesale electricity market. The proposed approach addressed the synergy of energy markets by introducing dynamic game with complete information for GENCOs, microgrids, and LAs. The proposed hierarchical competition is composed of bi-level optimization problems in which the respective upper-level problems maximize the individual market participants’ payoff, and the lower-level problems represent the market settlement accomplished by the DNO or the independent system operator. The bi-level problems are solved by developing sensitivity functions for market participants’ payoff with respect to their bidding strategies. A case study is employed to illustrate the effectiveness of the proposed approach.

This paper presents an approach to transform the active distribution network with distributed energy resources into multiple autonomous microgrids. The distribution network consists of several generation resources and demand entities, that are clustered into autonomous microgrids. The proposed problem is formulated as a bi-level optimization problem that leverages the Eigen decomposition in the graph spectra of the distribution network to determine the boundaries for microgrids and a mixed-integer programming problem that minimizes the expansion cost within microgrids. The presented approach is evaluated in a case study for a distribution network considering the imposed reliability constraints. The outcomes indicate the effectiveness of the proposed algorithm to determine the expansion strategies to form autonomous microgrids in active distribution networks.