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In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment, which aims to satisfy a target power load at minimal cost. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Using Qiskit, we simulate results for sample systems to validate the effectiveness of our approach. We also compare to purely classical methods. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units. However, for larger problem instances, the classical solvers either scale exponentially in runtime or must resort to coarse approximations. Potential quantum advantage would require problem instances at this scale, with several hundred units.

Practical quantum computing applications to power grids are nonexistent at the moment. This paper investigates how a fundamental grid problem, namely DC power flow, can be solved using quantum computing. Power flow is the most widely used power system analysis technique, either as a stand-alone application or embedded in other applications; therefore, its fast and accurate solution is of utmost significance for grid operators. We base our studies on the Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which has a proven theoretical speedup over classical algorithms in solving a system of linear equations. Practical studies on a quantum computer are conducted using the WSCC 9-bus system.

In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm for the solution of a system of linear equations (SLE) offers an exponential speedup over the classical computers. The speedup advantage is more significant when the size and the frequency of solving the power flow problem become more substantial. Verified quantum computing applications to power systems are merely nonexistent at this point. Through this paper, we plan to (1) provide a proof-of-concept that practical power system problems can be solved using quantum technology, (2) build a quantum-grid foundation by solving a fundamental power system problem with applications in many other critical grid problems, and (3) apply HHL to solve an SLE which has broad applications in many power system problems. A small 3-bus system is used for testing and demonstration purposes, considering the limitations of the available quantum computing hardware and software. The proposed method's merits and effectiveness are demonstrated using IBM open-source quantum computer and reported through proof-of-concept experimental demonstration using a 4-qubit quantum information processor., Comment: Journal Paper

Distribution Asset Management is an important task performed by utility companies to prolong the lifetime of the critical distribution assets and to accordingly ensure grid reliability by preventing unplanned outages. This study focuses on microgrid applications for distribution asset management as a viable and less expensive alternative to traditional utility practices in this area. A microgrid is as an emerging distribution technology that encompasses a variety of distribution technologies including distributed generation, demand response, and energy storage. Moreover, the substation transformer, as the most critical component in a distribution grid, is selected as the component of the choice for asset management studies. The resulting model is a microgrid-based distribution transformer asset management model in which microgrid exchanged power with the utility grid is reshaped in such a way that the distribution transformer lifetime is maximised. Numerical simulations on a test utility-owned microgrid demonstrate the effectiveness of the proposed model to reshape the loading of the distribution transformer at the point of interconnection in order to increase its lifetime., Comment: This is an open access article published by the IET under the Creative Commons Attribution -NonCommercial License

In this paper, an artificial intelligence based grid hardening model is proposed with the objective of improving power grid resilience in response to extreme weather events. At first, a machine learning model is proposed to predict the component states (either operational or outage) in response to the extreme event. Then, these predictions are fed into a hardening model, which determines strategic locations for placement of distributed generation (DG) units. In contrast to existing literature in hardening and resilience enhancement, this paper co-optimizes grid economic and resilience objectives by considering the intricate dependencies of the two. The numerical simulations on the standard IEEE 118-bus test system illustrate the merits and applicability of the proposed hardening model. The results indicate that the proposed hardening model through decentralized and distributed local energy resources can produce a more robust solution that can protect the system significantly against multiple component outages due to an extreme event.

Managing the inherent variability of solar generation is a critical challenge for utility grid operators, particularly as the distribution grid-integrated solar generation is making fast inroads in power systems. This paper proposes to leverage Battery Swapping Station (BSS) as an energy storage for mitigating solar photovoltaic (PV) output fluctuations. Using mixed-integer programming, a model for the BSS optimal scheduling is proposed to capture solar generation variability. The proposed model aims at minimizing the BSS total operation cost, which represents the accumulated cost of exchanging power with the utility grid. The model is subject to four sets of constraints associated with the utility grid, the BSS system, individual batteries, and solar variability. Numerical simulations on a test BSS demonstrate the effectiveness of the proposed model and show its viability in helping the utility grids host a higher penetration of solar generation.

A machine learning model is proposed in this paper to help estimate potential nodal load curtailment in response to an extreme event. This is performed through identifying which grid components will fail as a result of an extreme event, and consequently, which parts of the power system will encounter a supply interruption. The proposed model to predict component outages is based on a Support Vector Machine (SVM) model. This model considers the category and the path of historical hurricanes, as the selected extreme event in this paper, and accordingly trains the SVM. Once trained, the model is capable of classifying the grid components into two categories of outage and operational in response to imminent hurricanes. The obtained component outages are then integrated into a load curtailment minimization model to estimate the nodal load curtailments. The merits and the effectiveness of the proposed models are demonstrated using the standard IEEE 30-bus system based on various hurricane path/intensity scenarios.

Predicting power system component outages in response to an imminent hurricane plays a major role in preevent planning and post-event recovery of the power system. An exact prediction of components states, however, is a challenging task and cannot be easily performed. In this paper, a Support Vector Machine (SVM) based method is proposed to help estimate the components states in response to anticipated path and intensity of an imminent hurricane. Components states are categorized into three classes of damaged, operational, and uncertain. The damaged components along with the components in uncertain class are then considered in multiple contingency scenarios of a proposed Event-driven Security-Constrained Unit Commitment (E-SCUC), which considers the simultaneous outage of multiple components under an N-m-u reliability criterion. Experimental results on the IEEE 118-bus test system show the merits and the effectiveness of the proposed SVM classifier and the E-SCUC model in improving power system resilience in response to extreme events.

In this paper, in an attempt to improve power grid resilience, a machine learning model is proposed to predictively estimate the component states in response to extreme events. The proposed model is based on a multi-dimensional Support Vector Machine (SVM) considering the associated resilience index, i.e., the infrastructure quality level and the time duration that each component can withstand the event, as well as predicted path and intensity of the upcoming extreme event. The outcome of the proposed model is the classified component state data to two categories of outage and operational, which can be further used to schedule system resources in a predictive manner with the objective of maximizing its resilience. The proposed model is validated using \"A-fold cross-validation and model benchmarking techniques. The performance of the model is tested through numerical simulations and based on a well-defined and commonly-used performance measure.

This paper proposes a co-optimization generation and distribution planning model in microgrids in which simultaneous investment in generation, i.e., distributed generation (DG) and distributed energy storage (DES), and distribution, i.e., upgrading the existing distribution network, is considered. The objective of the proposed model is to minimize the microgrid total planning cost which comprises the investment cost of installed generation assets and lines, the microgrid operation cost, and the cost of unserved energy. The microgrid planning solution determines the optimal generation size, location, and mix, as well as required network upgrade. To consider line flow and voltage limits, a linearized power flow model is proposed and used, allowing further application of mixed integer linear programming (MILP) in problem modeling. The proposed model is applied to the IEEE 33-bus standard test system to demonstrate the acceptable performance and the effectiveness of the proposed model.

This paper proposes a coordinated optimal scheduling model for hybrid AC/DC microgrids. The objective of the proposed model is to minimize the total microgrid operation cost when considering interactions between AC and DC sub-systems of the microgrid network. Nonlinear power flow equations for AC and DC networks have been linearized through a proposed model to enable formulating the problem by mixed integer linear programming (MILP) which expedites the solution process and ensures better solutions in terms of optimality. The proposed model is tested on the modified IEEE 33-bus test system. Numerical simulations exhibit the merits of the proposed coordinated AC/DC optimal scheduling model and further analyze its sensitivity to various decisive operational parameters., Comment: 2017 North American Power Symposium (NAPS), Morgantown, WV, Sep 2017

The growing proliferation of microgrids and distributed energy resources in distribution networks has resulted in the development of Distribution Market Operator (DMO). This new entity will facilitate the management of the distributed resources and their interactions with upstream network and the wholesale market. At the same time, DMOs can tap into the flexibility potential of these distributed resources to address many of the challenges that system operators are facing. This paper investigates this opportunity and develops a distribution market scheduling model based on upstream network ramping flexibility requirements. That is, the distribution network will play the role of a flexibility resource in the system, with a relatively large size and potential, to help bulk system operators to address emerging ramping concerns. Numerical simulations demonstrate the effectiveness of the proposed model on when tested on a distribution system with several microgrids., Comment: IEEE PES Transmission and Distribution Conference and Exposition (T&D), Denver, CO, 16-19 Apr. 2018

Rapid growth of machine learning methodologies and their applications offer new opportunity for improved transformer asset management. Accordingly, power system operators are currently looking for data-driven methods to make better-informed decisions in terms of network management. In this paper, machine learning and data fusion techniques are integrated to estimate transformer loss of life. Using IEEE Std. C57.91-2011, a data synthesis process is proposed based on hourly transformer loading and ambient temperature values. This synthesized data is employed to estimate transformer loss of life by using Adaptive Network-Based Fuzzy Inference System (ANFIS) and Radial Basis Function (RBF) network, which are further fused together with the objective of improving the estimation accuracy. Among various data fusion techniques, Ordered Weighted Averaging (OWA) and sequential Kalman filter are selected to fuse the output results of the estimated ANFIS and RBF. Simulation results demonstrate the merit and the effectiveness of the proposed method.

The growing proliferation in solar deployment, especially at distribution level, has made the case for power system operators to develop more accurate solar forecasting models. This paper proposes a solar photovoltaic (PV) generation forecasting model based on multi-level solar measurements and utilizing a nonlinear autoregressive with exogenous input (NARX) model to improve the training and achieve better forecasts. The proposed model consists of four stages of data preparation, establishment of fitting model, model training, and forecasting. The model is tested under different weather conditions. Numerical simulations exhibit the acceptable performance of the model when compared to forecasting results obtained from two-level and single-level studies.

Providing adequate charging infrastructure plays a momentous role in rapid proliferation of Electric Vehicles (EVs). Easy access to such infrastructure would remove various obstacles regarding limited EV mobility range. A Battery Swapping Station (BSS) is an effective approach in supplying power to the EVs, while mitigating long waiting times in a Battery Charging Station (BCS). In contrast with the BCS, the BSS charges the batteries in advance and prepares them to be swapped in a considerably short time. Considering that these stations can serve as an intermediate entity between the EV owners and the power system, they can potentially provide unique benefits to the power system. This paper investigates the advantages of building the BSS from various perspectives. Accordingly, a model for the scheduling of battery charging from the station owner perspective is proposed. An illustrative example is provided to show how the proposed model would help BSS owners in managing their assets through scheduling battery charging time.

DC loads (such as computers, data centres, electric vehicle chargers, and LED lamps) and dc distributed energy resources (such as fuel cells, solar photovoltaics, and energy storages) are rapidly growing in electric power systems, so dc systems are being introduced as emerging practical investment solutions compared to traditional ac options. DC microgrids offer several advantages such as the elimination of need for synchronizing generators and easier supply of dc loads. Hybrid microgrids can benefit from the advantages of both ac and dc microgrid types. Moreover, there would be a huge reduction in the number of required power converters which would enhance the microgrid efficiency and reduce investment and operation costs. This paper introduces hybrid ac/dc microgrid as a viable solution compared to individual ac or dc microgrids and focuses on its planning. The objective of the hybrid microgrid planning is to minimize the microgrid total cost, including investment cost of distributed energy resources (DERs) and converters, operation cost of DERs, the cost of energy exchange with the utility grid, and the cost of unserved energy during the planning horizon. The economic viability of the microgrid planning is investigated in this paper and it is shown how the optimal DER generation mix, the type of feeders, as well as the point of connection of DERs to feeders can be determined by updating the traditional ac microgrid planning model. Numerical simulations on a test microgrid exhibit the merits of the proposed model., Comment: 7 pages, 3 figures, conference paper, CIGRE Grid of the Future Symposium, 2016

The growing penetration of renewable generation in distribution networks, primarily deployed by end-use electricity customers, is changing the traditional load profile and inevitably makes supply-load balancing more challenging for grid operators. Leveraging the potential flexibility of existing microgrids, that is to help with supply-load balance locally, is a viable solution to cope with this challenge and mitigate existing net load variability and intermittency in distribution networks. This paper discusses this timely topic and determines the microgrid value of ramping based on its available reserve using a cost-benefit analysis. To this end, a microgrid ramping-oriented optimal scheduling model is developed and tested through numerical simulations to prove the effectiveness and the merits of the proposed approach in microgrid ramping valuation., Comment: 2017 IEEE International Conference on Smart Grid Communications (IEEE SmartGridComm), Dresden, Germany, 23-26 Oct. 2017

Power supply from renewable resources is on a global rise where it is forecasted that renewable generation will surpass other types of generation in a foreseeable future. Increased generation from renewable resources, mainly solar and wind, exposes the power grid to more vulnerabilities, conceivably due to their variable generation, thus highlighting the importance of accurate forecasting methods. This paper proposes a two-stage day-ahead solar forecasting method that breaks down the forecasting into linear and nonlinear parts, determines subsequent forecasts, and accordingly, improves accuracy of the obtained results. To further reduce the error resulted from nonstationarity of the historical solar radiation data, a data processing approach, including pre-process and post-process levels, is integrated with the proposed method. Numerical simulations on three test days with different weather conditions exhibit the effectiveness of the proposed two-stage model.

Transformer lifetime assessments plays a vital role in reliable operation of power systems. In this paper, leveraging sensory data, an approach in estimating transformer lifetime is presented. The winding hottest-spot temperature, which is the pivotal driver that impacts transformer aging, is measured hourly via a temperature sensor, then transformer loss of life is calculated based on the IEEE Std. C57.91-2011. A Cumulative Moving Average (CMA) model is subsequently applied to the data stream of the transformer loss of life to provide hourly estimates until convergence. Numerical examples demonstrate the effectiveness of the proposed approach for the transformer lifetime estimation, and explores its efficiency and practical merits., Comment: 2017 North American Power Symposium (NAPS), Morgantown, WV, 17-19 Sep. 2017

Transformer life assessment and failure diagnostics have always been important problems for electric utility companies. Ambient temperature and load profile are the main factors which affect aging of the transformer insulation, and consequently, the transformer lifetime. The IEEE Std. C57.911995 provides a model for calculating the transformer loss of life based on ambient temperature and transformer's loading. In this paper, this standard is used to develop a data-driven static model for hourly estimation of the transformer loss of life. Among various machine learning methods for developing this static model, the Adaptive Network-Based Fuzzy Inference System (ANFIS) is selected. Numerical simulations demonstrate the effectiveness and the accuracy of the proposed ANFIS method compared with other relevant machine learning based methods to solve this problem., Comment: IEEE Power and Energy Society General Meeting, 2017

The variable nature of the solar generation and the inherent uncertainty in solar generation forecasts are two challenging issues for utility grids, especially as the distribution grid integrated solar generation proliferates. This paper offers to utilize microgrids as local solutions for mitigating these negative drawbacks and helping the utility grid in hosting a higher penetration of solar generation. A microgrid optimal scheduling model based on robust optimization is developed to capture solar generation variability and uncertainty. Numerical simulations on a test feeder indicate the effectiveness of the proposed model., Comment: IEEE Power and Energy Society General Meeting, 2017

Introduction of market mechanisms in distribution systems is currently subject to extensive studies. One of the challenges facing Distribution Market Operators (DMOs) is to implement a fair and economically efficient pricing mechanism that can incentivize consumers to positively contribute to grid operations and to improve economic performance of the distribution system. This paper studies a penalty-based pricing mechanism in distribution markets and further investigates the interrelationship between the locational marginal prices (LMPs) at transmission and distribution levels. As a result, a closed-form relationship between these LMPs is derived. The possibility of zeroing out the settlement profit is further investigated under the proposed pricing mechanism., Comment: Accepted to the IEEE Power and Energy General Meeting 2017

Distributed renewable energy resources have attracted significant attention in recent years due to the falling cost of the renewable energy technology, extensive federal and state incentives, and the application in improving load-point reliability. This growing proliferation, however, is changing the traditional consumption load curves by adding considerable levels of variability and further challenging the electricity supply-demand balance. In this paper, the application of microgrids in effectively capturing the distribution network net load variability, caused primarily by the prosumers, is investigated. Microgrids provide a viable and localized solution to this challenge while removing the need for costly investments by the electric utility on reinforcing the existing electricity infrastructure. A flexibility-oriented microgrid optimal scheduling model is proposed and developed to coordinate the microgrid net load with the aggregated consumers/prosumers net load in the distribution network with a focus on ramping issues. The proposed coordination is performed to capture both inter-hour and intra-hour net load variabilities. Numerical simulations on a test distribution feeder with one microgrid and several consumers and prosumers exhibit the effectiveness of the proposed model., Comment: IEEE Transactions on Power Systems

The levelized cost of energy (LCOE) presents the energy-normalized cost of a generation asset by considering all associated costs (investment and operation) and total generated energy over its life cycle. As LCOE is a levelized value, it provides a quick and easy measure to compare different energy resource technologies with different characteristics. The LCOE calculation for large-scale power plants and distributed generations (DGs) is extensively studied and can be found in the literature. The discussions on the LCOE calculation for energy storage systems, however, is limited. Although still relatively expensive compared to generation technologies, energy storage is gaining significant attention and has been deployed extensively during the past few years, conceivably due to its many benefits such as load shifting, energy arbitrage, and renewable coordination. Therefore, LCOE calculation of energy storage systems plays an important role in economic evaluation of power systems. This paper proposes a method for calculating the LCOE of energy storage, and further provides the sensitivity analysis with respect to changes in capacity, electricity market prices, and efficiency., Comment: CIGRE Grid of the Future Symposium, Oct.30-Nov.1 2016, Philadelphia, PA

Renewable energy has attracted significant attention over the last decade, conceivably due to its environmental benefits and the recent drops in the development and deployment cost of the technology. The increase in renewable generation, however, has resulted in new challenges in supply-load balancing, owing to its intermittent, non-predictable and volatile generation features. Several methods have been introduced to cope with negative impacts of the renewable generation deployment. In this paper, a novel method, i.e., the application of microgrids in capturing the variabilities of distributed renewable generation in distribution networks is proposed and investigated. Utilizing available flexibility of microgrids represents a local and viable solution which leads to lower investments from electric utilities for increasing their flexibility and providing more reserved power. It is investigated that how the system flexibility requirements can be integrated into the microgrid optimal scheduling model to enable microgrids in supporting the grid operators by offering flexibility services. Using the proposed flexibility constraints, intra-hour and inter-hour variabilities at the distribution feeder will be efficiently captured. Numerical simulations on a test distribution feeder, with one microgrid and several renewable-equipped consumers, show the effectiveness of the proposed model., Comment: CIGRE Grid of the Future Symposium, Oct.30-Nov.1 2016, Philadelphia, PA

The arrival of small-scale distributed energy generation in the future smart grid has led to the emergence of so-called prosumers, who can both consume as well as produce energy. By using local generation from renewable energy resources, the stress on power generation and supply system can be significantly reduced during high demand periods. However, this also creates a significant challenge for conventional power plants that suddenly need to ramp up quickly when the renewable energy drops off. In this paper, we propose an energy consumption scheduling problem for prosumers to minimize the peak ramp of the system. The optimal schedule of prosumers can be obtained by solving the centralized optimization problem. However, due to the privacy concerns and the distributed topology of the power system, the centralized design is difficult to implement in practice. Therefore, we propose the distributed algorithms to efficiently solve the centralized problem using the alternating direction method of multiplier (ADMM), in which each prosumer independently schedules its energy consumption profile. The simulation results demonstrate the convergence performance of the proposed algorithms as well as the capability of our model in reducing the peak ramp of the system., Comment: Accepted in IEEE SmartGridComm 2016

In spite of all advantages of solar energy, its deployment will significantly change the typical electric load profile, thus necessitating a change in traditional distribution grid management practices. In particular, the net load ramping, created as a result of simultaneous solar generation drop and load increase at early evening hours, is one of the major operational issues that needs to be carefully addressed. In this paper, microgrids are utilized to offer a viable and localized solution to this challenge while removing the need for costly investments by the electric utility. In this regard, first the microgrid ramping capability is determined via a min-max optimization, and second, the microgrid optimal scheduling model is developed to coordinate the microgrid net load with the distribution grid net load for addressing the ramping issue. Numerical simulations on a test distribution feeder with one microgrid exhibit the effectiveness of the proposed model., Comment: Accepted to 2016 IEEE PES Innovative Smart Grid Technologies (ISGT), 6-9 Sep. 2016

In this paper, a flexibility-oriented microgrid optimal scheduling model is proposed to mitigate distribution network net load variability caused by large penetration distributed solar generation. The distributed solar generation variability, which is caused by increasing adoption of this technology by end-use consumers, is mainly addressed by electric utilities using grid reinforcement. Microgrids, however, provide viable and local solutions to this pressing challenge. The proposed model, which is developed using mixed-integer programming and employs robust optimization, not only can efficiently capture distribution network net load variations, mainly in terms of ramping, but also accounts for possible uncertainties in forecasting. Numerical simulations on a test distribution feeder with one microgrid and several consumers/prosumers indicate the effectiveness of the proposed model., Comment: Accepted to 2016 North American Power Symposium (NAPS), Denver, CO, 18-20 Sep. 2016

Distribution markets are among the prospect being considered for the future of power systems. They would facilitate integration of distributed energy resources (DERs) and microgrids via a market mechanism and enable them to monetize services they can provide. This paper follows the ongoing work in implementing the distribution market operator (DMO) concept, and its clearing and settlement procedures, and focuses on investigating the pricing conducted by the DMO. The distribution locational marginal prices (D-LMPs) and their relationship with the transmission system locational marginal prices (T-LMPs) are subject of this paper. Numerical simulations on a test distribution system exhibit the benefits and drawbacks of the proposed DMO pricing processes., Comment: Accepted to 2016 IEEE PES Innovative Smart Grid Technologies (ISGT)

An optimal scheduling model for a microgrid participating in the electricity distribution market in interaction with a Distribution Market Operator (DMO) is proposed in this paper. The DMO administers the established electricity market in the distribution level, sets electricity prices, determines the amount of the power exchange among market participants, and interacts with the Independent System Operator (ISO). Considering a predetermined main grid power transfer to the microgrid, the microgrid scheduling problem will aim at balancing the power supply and demand while taking financial objectives into account. Numerical simulations exhibit the application and the effectiveness of the proposed market-based microgrid scheduling model and further investigate merits over a price-based scheme., Comment: Accepted to the IEEE Transactions on Smart Grid

There are various undergoing efforts by system operators to set up an electricity market at the distribution level to enable a rapid and widespread deployment of distributed energy resources (DERs) and microgrids. This paper follows the previous work of the authors in implementing the distribution market operator (DMO) concept, and focuses on investigating the clearing and settlement processes performed by the DMO. The DMO clears the market to assign the awarded power from the wholesale market to customers within its service territory based on their associated demand bids. The DMO accordingly settles the market to identify the distribution locational marginal prices (DLMPs) and calculate payments from each customer and the total payment to the system operator. Numerical simulations exhibit the merits and effectiveness of the proposed DMO clearing and settlement processes., Comment: 2016 IEEE Power & Energy Society General Meeting

The increased need for reliable, resilient, and high quality power combined with a falling cost of distributed generation technologies has resulted in a rapid growth of microgrid in power systems. Although providing multitude of benefits, the microgrid power transfer with the main grid, which is commonly obtained using economy and reliability consideration, may result in major operational drawbacks, most notably, a large mismatch between actual and forecasted system loads. This paper investigates the impact of high penetration microgrids on the power system net load, and further proposes three paradigms that can be adopted to address the emerging operational issues. The IEEE 6-bus test system is used for numerical studies and to further support the discussions., Comment: To appear in "IEEE PES Transmission and Distribution Conference, Dallas, TX, 2016."

This paper presents an optimal scheduling model for a microgrid participating in the electricity distribution market in interaction with the Distribution Market Operator (DMO). The DMO is a concept proposed here, which administers the established electricity market in the distribution level, i.e., similar to the role of Independent System Operator (ISO) in the wholesale electricity market, sets electricity prices, determines the amounts of the power exchange between market participators, and interacts with the ISO. Considering a predetermined main grid power transfer to the microgrid, the microgrid scheduling problem will aim at balancing the power supply and demand while taking financial objectives into account. A stochastic programming method is employed to model prevailing uncertainties in the microgrid grid-connected and islanded operations. Numerical simulations exhibit the application and the effectiveness of the proposed market-based microgrid scheduling model., Comment: Appeared in 6th IEEE International Conference on Smart Grid Communications (SmartGridComm 2015)