Zhongjie Guo

In low-carbon power systems, Compressed Air Energy Storage (CAES) system is deployed to compensate for volatile renewable generation, thus fulfilling the desired generation schedule. This requires energy storage subsystem to operated over a wide range to meet regulation commands from the grid operator. However, the surge instability phenomenon of multi-stage compressors poses a threat on secure operation. In current practice, the compression power can only be slightly changed to maintain a stable margin, which greatly limits the operational flexibility of CAES. Accurate characterization of the stability boundary can effectively reduce this conservatism, but the variability of operating points makes it challenging to fit a point-wise boundary from time-domain simulation due to the high-dimensional characteristics. This paper proposes the concept of CAES security region, which shifts the analytical perspective from individual operating points to a system-wide domain. A multi-stage coupled compression-side dynamic model incorporating controller regulation effects is developed. The stability boundary is constructed in the control input space, which holistically assesses system stability across various regulation directions compared to the state space. Simulation results demonstrate that the proposed method comprehensively characterizes the stability boundary under variable operating conditions. After adding a damping ratio of 0.6, the system can withstand a 4% disturbance and remain stable. The introduction of the linear approximation algorithm reduced the security domain calculation time from 7 minutes to 1 s. This approach offers a novel practical and visualization tool for control design and operational assessment of CAES systems.

The increasing penetration of renewable energy sources introduces significant power fluctuations across multiple timescales, from sub-hourly resolution to seasonal resolution. Multiple energy storages are required to mitigate such fluctuations. To size multiple energy storages while adaptively matching up the fluctuating patterns, this paper proposes a time–frequency hybrid method. First, a spectral decomposition of net power is performed to identify dominant frequency components, which are then converted into representative timescales. Then, based on these timescales, a coordinated optimization model is developed to size multiple energy storages; the sizing model varies with the results of spectral decomposition and thus is adapted to renewable power frequencies, where inter-timescale coordinating constraints couple energy storage operation across timescales while retaining flexibility within each timescale. Case studies on modified IEEE 9-bus and 39-bus systems demonstrate the effectiveness of the proposed method. Compared with single frequency- and time-domain methods, the proposed model achieves more economical storage configurations. Sensitivity analysis shows that adopting the adaptive timescale resolution reduces total system cost by 17.97% in the 9-bus system and 21.69% in the 39-bus system.

Although wind energy is volatile, the output of a wind-storage plant is partially dispatchable, making it a promising paradigm on the generation side. A grid-friendly wind-storage plant ought to be able to continuously output the desired power over a certain period of time. This paper proposes a dependable dynamic capacity provision scheme of a wind-storage plant over a daily horizon. It stipulates a minimum number of periods during which the committed capacity must be fulfilled and a maximum mismatch during the remaining periods when the desired power output is not achievable. In the general case, the day-ahead piecewise constant capacity provision results in a two-stage stochastic program formulated as a mixed-integer linear program. Specifically, for constant capacity provision, a decomposition algorithm is developed to determine the global optimal solution, and the complexity grows linearly with the number of scenarios. Given the committed capacity trajectory, the real-time operation problem is modeled as a four-state stochastic dynamic program. The discrete state-action values are derived recursively via the principle of optimality. Real-time dispatch actions are generated by using the action-value tabular leveraging inexact ultra-short-term forecasts. Numerical tests over one year demonstrate that the proposed method successfully fulfills reliable operation on 355 days and achieve an optimality gap of 9.47% compared with the ex-post optimum, which is comparable to model predictive control using exact 2-3-hour-ahead wind power forecasts.

Long-term unit commitment (LTUC) plays an important role in power system planning and production simulation, especially when seasonal volatility of renewable generation and ultra-long-term energy storage are taken into account. Solving LTUC exactly is challenging due to the large number of binary variables. This paper proposes a tractable method to obtain a near-optimal solution to LTUC with a guaranteed bound on its sub-optimality. The proposed method first constructs a lower bound by formulating a relaxed unit commitment (UC) problem in which binary variables are replaced by continuous ones, and a family of valid inequalities is introduced to strengthen the relaxation. A general framework for generating such inequalities is developed by exploiting the specific structural properties of single-unit operational constraints. Subsequently, by fixing the seasonal energy storage levels at the optimal solution of the relaxed UC problem, a feasible LTUC solution is constructed through sequential short-term UC optimization with look-ahead augmentation, which provides an upper bound for the true optimum. The sub-optimality is measured by the gap between the lower and upper bounds. Numerical tests demonstrate that the monthly or annual UC problems of practically-sized power systems can be solved on a laptop in hours with an optimality gap of less than 1.5%.

In active distribution networks, topology change is an important scheme to cope with the rapid fluctuations of distributed renewable generations. This paper studies the real-time distribution network reconfiguration (DNR) problem while ensuring a reliable power supply under set-based uncertainty. Considering the intertemporal constraint on the maximum number of action times for each switchable line, real-time DNR is formulated as a multi-stage robust optimization (MRO) problem. To solve this problem, a customized implicit policy method is proposed. First, the non-anticipative constraints of each switchable line are specifically devised to generate the upper and lower bounds for line status, ensuring that the intertemporal constraint is always satisfied as long as the bounds are met. Second, by augmenting the stage to optimize the above bounds, the original MRO problem is reformulated as a two-stage robust optimization problem with mixed-integer recource by relaxing the intertemporal constraints and aggregating stages, thereby suggesting an OPF-based real-time DNR policy that is robustly feasible and parameterized in the bounds of line status. Finally, these bounds are obtained by solving the two-stage robust optimization problem through the nested column-and-constraint generation algorithm. Tests on IEEE 33-, 69-, and 123-bus distribution systems comprehensively verify the effectiveness of the proposed method, as well as its advantages in scalability and optimality over state-of-the-art methods.

Reactive power regulation is crucial for active distribution networks (ADNs). This paper studies the multi-stage reactive power optimization in ADNs with renewables considering intertemporal constraints imposed on total action times of discrete regulation facilities. First, we regard reactive power regulation as a sequential decision-making process and formulate it as a multi-stage robust optimization problem with hybrid continuous and discrete recourses. Then, we propose a customized implicit policy method to solve this problem, devising bounding variables and non-anticipative constraints of shunt capacitor bank (SCB) and on-load tap changer (OLTC). Next, the bounding variables are optimized prior to dispatch subject to non-anticipative constraints; with their help, intertemporal couplings are broken and the multi-stage robust optimization problem shrinks to a two-stage robust one, which can be solved by decomposition algorithms. Finally, we use the bounding variables to build a non-anticipative and robustly feasible policy based on time-decoupled optimal power flow (OPF) where intertemporal constraints are relaxed but satisfied at the optimums. Case studies on the modified IEEE 33-bus, 69-bus, and 123-bus systems verify the advantages of the proposed method.

This paper studies the problem of multi-stage robust unit commitment with discrete load shedding. In the day-ahead phase, the on-off status of thermal units is scheduled. During each period of real-time dispatch, the output of thermal units and the action of load shedding are determined, and the discrete choice of load shedding corresponds to the practice of tripping substation outlets. The entire decision-making process is formulated as a multi-stage adaptive robust optimization problem with mixed-integer recourse, whose solution takes three steps. First, we propose and apply partially affine policy, which is optimized ahead of the day and restricts intertemporal dispatch variables as affine functions of previous uncertainty realizations, leaving remaining continuous and binary dispatch variables to be optimized in real time. Second, we demonstrate that the resulting model with partially affine policy can be reformulated as a two-stage robust optimization problem with mixed-integer recourse. Third, we modify the standard nested column-and-constraint generation algorithm to accelerate the inner loops by warm start. The modified algorithm solves the two-stage problem more efficiently. Case studies on the IEEE 118-bus system verify that the proposed partially affine policy outperforms conventional affine policy in terms of optimality and robustness; the modified nested column-and-constraint generation algorithm significantly reduces the total computation time; and the proposed method balances well optimality and efficiency compared with state-of-the-art methods.

Multistage robust unit commitment (MRUC) is an important decision-making problem in power system operations. The affine policy facilitates problem-solving, but it compromises flexibility. This letter proposes a partially affine policy for MRU C problem with fast-ramping units; this policy imposes affine relations to coupling variables only and leaves the remaining variables to be optimized in the real-time dispatch. As a result, the real-time flexibility of fast-ramping units is retained. By adopting this approach, MRU C with a partially affine policy becomes a special two-stage adaptive robust optimization problem. Numerical tests verify that the proposed partially affine policy significantly reduces the conservativeness compared with affine policy, improving the dispatch economy and flexibility.

Finding a feasible solution is the primary concern in power system dispatch. This paper studies the feasibility condition of power system dispatch under a multistage robust optimization framework considering the non-anticipativity of dispatch policy, which is difficult to be expressed via explicit constraints. The multistage robust feasible regions (MRFRs) are defined as the sets in the state space containing all points that can maintain the robust feasibility in the next period against renewable and demand uncertainties; we give a polyhedral projection condition to characterize exact MRFRs in a recursive manner, which can be regarded as an analog of Bellman’s optimality condition. However, because the multistage dispatch problem of a bulk power system has a high-dimensional state space, the computation of exact MRFRs suffers from the curse of dimensionality. We propose an inner approximation method that identifies the maximal polyhedra that are embraced by the unknown exact MRFRs; we devise a computationally efficient algorithm to retrieve the hyperplane representation of the inner approximator. Finally, we discuss how MRFRs can be used in combination with existing approaches, such as dynamic programming and rolling horizon optimization. Numerical simulations on a modified IEEE 118-bus system verify the effectiveness and advantages of the proposed method.

With the progress of decarbonization, renewable-powered microgrids are attracting wide attention. To cope with the fluctuation of renewable power at different timescales, both long-term and short-term energy storage devices are required. This paper studies the operation of renewable-dominated isolated microgrids integrated with hybrid seasonal-battery storage. A data-driven scheduling-correction framework is proposed. By leveraging the historical data of renewable power and load, the scheduling module generates ex-post optimal state-of-charge (SoC) sequences of the seasonal energy storage ahead of the operating year. In each period of real-time operation, the correction module performs two steps: the first step is to update the reference SoC for the seasonal storage based on the ex-post optimal SoC sequences and the newly observed data; the second step is to solve a bi-objective rolling-horizon optimization problem which minimizes the instant operating cost while steering the SoC of seasonal storage to its reference value. An appealing feature of the proposed method is that the long-term renewable power forecasts are not required. A microgrid system is devised to verify the proposed framework. Numerical tests show that the scheduling-correction framework outperforms existing rolling horizon approaches in compromising economy, power supply reliability, and renewable energy utilization.

Renewable energy is a promising solution to address the energy crisis and environmental issues, but it comes with challenges due to its inherent volatility and limited dispatchability. Advanced adiabatic compressed air energy storage (AA-CAES) is a favorable partner for centralized renewable integration, due to its numerous benefits, such as large capacity, long lifetime, fast response capability, and zero carbon emissions. For the economic management of a wind-AACAES system, a battery-like AA-CAES dispatch model is proposed, where the chargingdischarging efficiencies and capacities are dependent on the operating power and state-of-charge (SoC) to capture the part-load characteristics. A hybrid control strategy is proposed to enhance the flexibility and efficiency of the compression side under off-design conditions caused by simultaneous changes in back pressure and load. To provide dispatch and control strategies of AA-CAES, a multi-timescale optimization problem is established. The slow timescale determines the baseline output scheduling on an hourly basis to maximize total revenue, while the fast timescale updates the real-time adjustment every five minutes to minimize the penalty of tracking error. A bi-level stochastic dynamic programming (SDP) framework is formulated to incorporate the wind uncertainties and multi timescale coordination, where terminal SoCs and value functions are essential to integrate decisions across slow and fast timescales. A non-iterative parametric programming-based method is proposed to solve the slow-timescale SDP, and a simulation-based rollout algorithm is applied to extract the fast-timescale actions, which yields evident improvement over any heuristic base policy that is sequentially consistent. The numerical results demonstrate that the proposed method has a performance gap of approximately 7.1%, which outperforms the rule-based method by 32.6%. The installation of AA-CAES improves the total revenue by 11.9%. Additionally, the hybrid control strategy enhances the charging flexibility and efficiency by 30.7% and 4.3%, respectively, resulting in a 3.9% reduction in tracking deviation penalty.

The integration of volatile renewable resources and energy storage entails making dispatch decisions for conventional coal-fired units and fast-response devices in different timescales. This paper studies intraday dynamic energy-reserve dispatch following a two-timescale setting. The coarse timescale determines the hourly reference output and reserve allocation, which offers a sufficient backup for the fine-timescale operation; the fine timescale determines the adjustment of gas-fired units and energy storage system every 15 minutes in response to the actual wind power. A stochastic dynamic programming method is proposed to make decisions at the coarse timescale while guaranteeing the robust feasibility of the fast process via vertex scenarios of uncertainty set and bounding the state-of-charge intervals for energy storage; the fast-response actions at the fine timescale are updated using a truncated rolling-horizon optimization, which incorporates the cost-to-go functions calculated at the coarse timescale to prevent the fast decisions from being myopic. Case studies on the modified IEEE 5-bus system and 118-bus system validate the proposed framework.

The weather-dependent renewable energy sources(RESs) and voltage stability performance associated with reactive power balance pose immense challenges to power systems' operation. Salt cavern advanced adiabatic compressed air energy storage(S-CAES) is one of the most promising options to cope with the emerging issues. Though S-CAES has been extensively studied, limited attention focuses on the value of its reactive power ancillary service. This paper presents a novel S-CAES condenser operation mode that consumes little compressed air and less heat for synchronization and warm-keeping while releasing reactive power by the turbine-generator unit's excitation system for voltage regulation. The merits of condenser mode are highlighted, and the accurate thermodynamic model of S-CAES with multi-parameter coupled charging/discharging power functions is developed. Then, an optimal dispatch model linking the part-load characteristics and multiple service requirements is proposed and further formulated as a mixed-integer linear programming(MILP) problem. Numerical simulation results indicate that S-CAES operating in condenser mode contributes its application in ancillary services markets, and neglecting the part-load characteristics will lead to overly optimistic or even infeasible dispatch results. The breakeven point of the peak-valley ratio is 1.725, below which S-CAES will not participate in the energy market. Besides, sensitivity analysis provides a primary reference for S-CAES's heat supplement optimization and the design of condenser compensation mechanisms in the power system with a high proportion of RESs.

Renewable energy integration is an effective measure to resolve environmental problems and implement sustainable development, yet the volatility of wind and solar generation has a profound impact on power system operation, calling for sufficient backup capacity. Energy storage can shift demand over time and mitigate real-time power mismatch and thus help integrate renewable energy resources into power grids. However, the unit capacity price of energy storage is still relatively high, and the capacity of energy storage is usually limited. Given the prominent uncertainty and finite capacity of energy storage, it is crucially important to take full advantage of energy storage units by strategic dispatch and control. From the mathematical point of view, energy storage dispatch and control give rise to a sequential decision-making process involving uncertain parameters and inter-temporal constraints. Multitudinous optimisation methods have been developed for such a problem while they differ in two aspects: the modelling of uncertainty and the mechanism to handle uncertainty. This review aims to draw a methodological picture of historical developments and state-of-the-art advances in this research field. These methods are subsumed into three major categories: multistage optimisation, online optimisation, and multi-timescale optimisation. In addition to introducing the advancements and applications, the authors also explain the motivations and theoretical foundations of these methodologies. The authors hope interested readers can attain a holistic outlook of these sophisticated approaches and choose the most appropriate one for their specific applications.

The output of renewable generation depends on the real-time weather conditions and changes rapidly; so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters; then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance; this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method; by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively.

Distribution systems are operated with an increasing level of uncertainty. Energy storage is playing an important role in shaving the peak load and mitigating uncertainty. This paper proposes a multistage robust optimization model for distribution system operation with energy storage under uncertainty. Unlike the conventional robust optimization paradigm which minimizes the worst-case cost, the proposed formulation optimizes the cost in the nominal scenario. In analogy to dynamic programming, we define dynamic robust feasible regions in a recursive manner. In each period, the dynamic robust feasible region is shown to be polyhedral, and a linear programming based projection algorithm is developed to compute such regions offline. In the online stage, the method is executed following a rolling horizon manner: renewable output is observed at the beginning of each period, and the cost of remaining periods in the forecast scenario is to be minimized subject to operation constraints and dynamic robust feasible regions, giving rise to a linear program. In this way, the dispatch strategy ensures multistage operation security regardless of future realizations of renewable power. In numeric tests on a modified IEEE 33-bus distribution system, the dynamic robust feasible regions are visualized and analyzed, and the proposed method is compared with two prevailing robust optimization methods, verifying its advantages in terms of optimality and robustness.

This paper investigates real-time self-dispatch of a remote wind-storage integrated power plant connecting to the main grid via a transmission line with a limited capacity. Because prediction is a complicated task and inevitably incurs errors, it is a better choice to make real-time decisions based on the information observed in the current time slot without predictions on the uncertain electricity price and wind generation in the future. To this end, the operation problem is formulated under the Lyapunov optimization framework to maximize the long-term time-average revenue of the wind-storage plant. Inter-temporal storage dynamics are represented by a virtual queue which is mean rate stable. An online method for real-time dispatch is proposed based on Lyapunov drift algorithm via a drift-minus-revenue function. The upper bound of such a function, which does not depend on future uncertainty, is minimized in each time slot. Explicit dispatch policies are obtained through multi-parametric programming technique so that no optimization problem is solved online. It is proved that the online algorithm can maintain all the constraints across the entire horizon and the expected optimality gap compared to the deterministic offline optimum with perfect uncertainty information is inversely proportional to the weight coefficient in the drift-minus-revenue function. Numerical tests using real wind and electricity price data validate the effectiveness and performance of the proposed method.

Energy storage unit (ESU) is playing an increasingly important role in load shifting and uncertainty mitigation. This paper aims to quantify the value of ESU in the unit commitment (UC) with renewable generation. By treating the power and energy capacities of ESU as continuous parameters, the stochastic UC problem is cast as a multi-parametric mixed-integer linear program (mp-MILP), whose optimal value function (OVF) gives the relation between storage capacity and the daily UC cost in an analytical manner. It encompasses abundant sensitivity information, and its surface can be easily visualized. The reduced cost compared with the benchmark case without storage can be regarded as the value of ESU. As a potential application, the OVF is used to formulated an optimal storage sizing problem that maximizes the ratio between the reduced operation cost and the investment cost, ensuring the minimum time of cost recovery. The solution consists of two steps: the first step constructs the OVF parameterized in storage capacity; the second step reformulates the fractional storage sizing program into an MILP, leveraging the expression of the OVF and variable transformations. Case studies conducted on the IEEE 9-bus system and IEEE 118-bus system illustrate how the OVF offers useful reference for power system operation and planning. The proposed optimal sizing model shows advantages in efficient utilization of investment in terms of payback time and rate of return.

Hydrogen is a promising form of secondary energy in the future. This paper studies the equilibrium state of supply-demand flow in a regional hydrogen market. We consider peer-to-peer transactions between renewable energy-based suppliers, profit-driven retailers, and transportation costs. A game model is proposed to characterize the market equilibrium taking into account the strategic behaviors of individual participants. The uncertainty of available renewable energy is described by an inexact probability distribution, and suppliers’ problems give rise to distributionally robust optimization. The market clearing price is endogenously determined from the supply and demand, precipitating an equilibrium in the market. Based on Karush-Kuhn-Tucker optimality conditions and linearization techniques, a mixed-integer linear program is developed to compute the market equilibrium. Case studies and numerical analysis conducted on a testing system demonstrate that the proposed method can provide useful insights on hydrogen market design and analysis.

Prosumers are agents that both consume and produce energy. This article studies the optimal energy management of a residential prosumer which consists of a renewable power plant and an energy storage unit. Energy could stream among power grid, renewable plant, storage unit, and demand, providing a highly flexible energy supply and the opportunity of arbitrage. To capture the uncertainty of renewable generation and electricity price, as well as the rolling horizon feature of the multiperiod energy management, the problem is formulated as a robust data-driven dynamic programming (RDDP). Kernel regression is utilized to build the empirical conditional distribution in a data-driven manner, and all candidates that reside in a Wasserstein metric-based ambiguity set are taken into account to tackle the inexactness of the empirical distribution. The RDDP can be transformed into a series of convex optimization problems with cost-to-go functions in their constraints. The piecewise linear expression of the cost-to-go function is retrieved from dual linear programs. Through such an analytical expression of cost-to-go functions, the RDDP can be solved via backward induction, unlike the popular stochastic dual dynamic programming technique that incorporates forward and backward passes. Case studies validate the performance and advantage of the proposed RDDP approach.

The limited reserve of fossil fuels and public awareness of environmental issues prompt the rapid development of renewable energy generation. However, the centralised utilisation of renewable energy in bulk power systems is impeded mainly by its volatile nature and transmission congestion, leading to the spillage of renewable power. The energy storage unit is expected to be a promising measure to smooth the output of renewable plants and reduce the curtailment rate. This study addresses the energy storage sizing problem in bulk power systems. To capture the operating status of the power system more accurately, the authors use a dedicated power flow model which involves voltage and reactive power. The uncertainty of renewable generation is described via inexact probability distributions encapsulated in a data-driven Wasserstein-metric based ambiguity set, based on which the renewable energy curtailment rate is formulated as a distributionally robust chance constraint. The objective is to minimise the total investment cost, and the optimal sizing problem gives rise to a distributionally robust chance-constrained program, and is reformulated as a tractable linear program via conservative approximation. Case studies conducted on the modified IEEE 30-bus and 118-bus systems demonstrate the effectiveness and performance of the proposed approach.

The high penetration of volatile renewable energy challenges power system operation. Energy storage units (ESUs) can shift the demand over time and compensate real-time discrepancy between generation and demand, and thus improve system operation flexibility and reduce renewable energy curtailment. This paper proposes two parametric optimization models to quantify how the power (MW) and energy (MWh) capacity of ESU would impact renewable energy utilization from two aspects: renewable energy curtailment and system flexibility for uncertainty mitigation. The two indicators are characterized as multivariate functions in the capacity parameters of ESUs. A severity ranking algorithm is suggested to pick up critical scenarios of fluctuation patterns from the uncertainty set; consequently, the proposed models come down to multi-parametric mixed-integer linear programs (mp-MILPs) which can be solved by a decomposition algorithm. The proposed method provides analytical expressions of the two indicators as functions in MW and MWh capacity. Such a characterization delivers abundant sensitivity information on the impact of ESU capacity parameters, and provides a powerful tool for visualization and useful reference for storage sizing. Case studies verify the effectiveness of the proposed method and demonstrate how to use the geometric information.

Line contingency-constrained dispatch (LCCD) problems are challenging to solve due to the large number of transmission constraints in pre- and post-contingency scenarios, yet the majority of them are never active. This letter proposes a fast method to remove redundant constraints in LCCD problems. The linear programming problems solved in the proposed method are significantly smaller than those in the known approach.

Energy storage is playing an increasingly important role in power system operation due to its ability to shave the peak and fill the valley. Advanced adiabatic compressed-air energy storage (AA-CAES) is a clean and scalable energy storage technology and has attracted wide attention recently. This paper proposes a multi-state operation model of AA-CAES capturing the dynamic change of internal physical status. A stand-by state is introduced, at which AA-CAES works like a condenser that produces only reactive power. It brings two benefits. First, the facility is started up and shut down less frequently, which helps extend its service time. Second, it can provide continuous reactive power support all day long, unlike on-load tap changers or shunt capacitors whose voltage regulation strategy is discrete and suffers from a very low switching frequency. Taking AA-CAES into account, the optimal operation of a distribution network is formulated as a bi-objective dynamic optimal power flow problem. Nash bargaining is employed to extract a single Pareto optimal solution that fairly compromises two objectives. To solve the operation problem in a tractable manner, the bargaining objective and power flow constraints are convexified, giving rise to a mixed-integer second-order cone program. A feasibility recovery algorithm is developed to find a physically meaningful solution whenever the convex relaxation on power flow is inexact. Case studies on the IEEE 33-bus system demonstrate the effectiveness and advantages of the proposed method.