Mixed-integer Second-order Cone Programming Research Articles

Strategic active and reactive power scheduling of integrated community energy systems in day-ahead distribution electricity market

The increasing penetration of distributed energy resources (DERs) enable integrated community energy systems (ICESs) as emerging techno-economic energy entities at the end-user side. In the deregulated electricity market, the ICESs can actively participate in the distribution electricity market (DEM) to provide active and reactive power dispatched by ICES operator (ICESO). In this context, a strategic active and reactive power scheduling model for ICESs in the day-ahead DEM is proposed in this paper. A novel trading mechanism designed for ICESO and distribution system operator (DSO)’s interaction toward both active and reactive power is represented in the day-ahead DEM, where distribution locational marginal prices (DLMPs) for both active and reactive power are introduced as the market settlements. Then, the trading process is formulated as a bi-level programming problem. The upper level describes the combined cooling, heating, and power (CCHP)-dominated ICESO’s strategic active and reactive power dispatch, in which the DLMPs for active and reactive power, internal flexibility services, and optimal dispatch for inverter-based distributed generators are considered. The lower level performs a DEM clearing for both active and reactive power. Further, Karush–Kuhn–Tucker (KKT) conditions, Big-M approach, and duality theory are used to convert the bi-level model from a Mathematical Programing with Equilibrium Constraints (MPEC) model to a single-level mixed-integer second-order cone programming (MISOCP) model for efficient calculation. Finally, case studies on modified IEEE 33-node and IEEE 123-node distribution systems are adopted to evaluate the performance of the proposed scheduling method. The results show that the proposed scheduling approach can contribute to the renewable energy share and energy efficiency, reduce CCHP-dominated ICESs’ operation costs by 38.13% and 13.21% compared to the case where ICESO only acts as a price-taking consumer, and 6.64% and 3.44% compared to the case where ICESO does not consider reactive power bids/offers, respectively.

A novel robust Volt/Var optimization method based on worst‐case scenarios for distribution network operation

AbstractThe Volt/Var optimization (VVO) problem is used for scheduling the voltage regulation and reactive power compensation equipment in distribution networks to minimize power loss and voltage violation. In order to solve the VVO problem for a forthcoming time horizon, it is necessary to predict some parameters such as load demand and renewable energy production. The prediction of these parameters is always accompanied by uncertainty that robust optimization can be used to solve this concern. This paper presents a scenario‐based robust Volt/Var optimization (RVO) method that significantly reduces the number of scenarios required for the worst‐case approach. Solving the VVO problem with the worst‐case scenarios reduces the computational burden and maintains the voltage security of the distribution network against the severe events. The proposed RVO is formulated based on a mixed‐integer second‐order cone programming (MISOCP) model in which Volt/Var control (VVC) equipment is scheduled over a two‐stage strategy. The proposed method is validated using modified 33‐bus and 69‐bus IEEE test systems. The results demonstrate that the proposed RVO method maintains the network's voltage profile within the acceptable range against uncertainties.

Optimal voyage scheduling of all-electric ships considering underwater radiated noise

Underwater radiated noise (URN) emanating from ships can adversely impact the life functions of certain marine mammals that rely on sound to navigate, communicate, and locate prey. This paper formulates an optimal voyage scheduling problem to mitigate the impact of URN on sensitive marine species by choosing amongst different possible paths and specifying the cruising speed along the selected path. We focus on all-electric ships (AESs) owing to their greater flexibility for speed regulation by coordinating an integrated power system. The proposed optimization model schedules generators and energy storage devices toward minimizing the operation cost while satisfying constraints pertinent to URN levels and atmospheric greenhouse gas (GHG) emissions, the electric power network and operational limits, and expected voyage timelines, culminating in a mixed-integer nonlinear programming problem. To promote computational tractability, we approximate the nonlinear relationships for URN, propulsion load, and fuel consumption with piecewise linear functions. This leads to a mixed-integer second-order cone programming problem, which enables convergence to the global optimum and computationally efficient solutions. We illustrate the effectiveness of the proposed model in curbing URN levels and GHG emissions with numerical case studies involving an 18-node ship test system.

Mixed-Integer Conic Formulation of Unit Commitment with Stochastic Wind Power

Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained programming (CCP) method is used to study the UC problem with uncertainty wind power generation, and chance constraints such as power balance and spinning reserve are satisfied with a predetermined probability. In order to effectively solve the CCP problem, first, we used the sample average approximation (SAA) method to transform the chance constraints into deterministic constraints and to obtain a mixed-integer quadratic programming (MIQP) model. Then, the quadratic terms were incorporated into the constraints by introducing some auxiliary variables, and some second-order cone constraints were formed by combining them with the output characteristics of thermal unit; therefore, a tighter mixed-integer second-order cone programming (MISOCP) formulation was obtained. Finally, we applied this method to some systems including 10 to 100 thermal units and 1 to 2 wind units, and we invoked MOSEK in MATLAB to solve the MISOCP formulation. The numerical results obtained within 24 h confirm that not only is the MISOCP formulation a successful reformulation that can achieve better suboptimal solutions, but it is also a suitable method for solving the large-scale uncertain UC problem. In addition, for systems of up to 40 units within 24 h that do not consider wind power and pollution emissions, the numerical results were compared with those of previously published methods, showing that the MISOCP formulation is very promising, given its excellent performance.

A Coordinated Restoration Method of Hybrid AC/DC Distribution Network for Resilience Enhancement

In recent years, the frequent occurrence of extreme natural disasters has caused huge economic losses, which makes it extremely important to improve the resilience of distribution networks. With the increasing penetration of DC sources and loads, the urban distribution network is transitioning from AC to hybrid AC/DC configuration that can operate in a ring structure. The features of flexible interconnections and low network losses of DC lines can break the bottleneck of traditional restoration methods for AC distribution networks under extreme disasters, thereby further enhancing the resilience of distribution networks. Based on the interconnection feature of DC lines, this paper proposes a topology search strategy with DC lines as the core to realize the joint recovery of multiple power sources and multiple critical loads. With the obtained interconnection topology after topology search, a fault restoration model for maximizing the resilience index is established. To ensure the generality of the proposed model and explore the advantages of flexible DC power control, this paper transforms the objective function from the complex model into a mixed integer second-order cone programming (MISOCP) that can be solved directly. The optimal restoration strategy for resilience enhancement of AC/DC hybrid distribution networks can be obtained by solving the proposed MISOCP model. The numerical results in case study validate the effectiveness and superiority of the proposed method.

Soft Open Points-Assisted Resilience Enhancement of Power Distribution Networks Against Cyber Risks

Cyberattacks are increasingly threatening the normal operation of electric power grids. The purpose of this study is to develop an optimization model for planning and operation of distribution systems to enhance the resilience to cyberattacks. A new distribution system planning method is presented utilizing a Defender-Attacker-Defender (DAD) tri-level model to improve the system resilience to withstand potential disruptions from cyberattacks. In the first level of the model, the system planner optimizes the Soft Open Points (SOPs) installation in the planning stage. The attacker’s objective in the second level of the model is to change the status of the network circuit breakers and jam the communication maximizing disruption of the system. The optimization of Distribution Generators’ (DGs’) outputs, SOPs’ power flow, and topology reconfiguration are comprehensively considered in the third level. The novel model presented in this paper considers hardening measures of the SOPs in response to the attacks on distribution systems. The Column and Constraint Generation (C&CG) algorithm is utilized to solve the proposed DAD model. A procedure is devised to solve the two-layer subproblem (the Attacker-Defender model), with the bottom layer being a Mixed Integer Second Order Cone Programming (MISOCP) problem. Finally, the proposed models are validated in 33-bus and 135-bus test systems. The results show that the installation of SOPs significantly improves the service restoration under cyberattacks. Both the number and location of SOPs influence the extent of restored service, and differing SOP allocation schemes may lead to similar restoration outcomes. The proposed models and techniques could also be extended to deal with other similar problems in industrial cyber-physical systems.

Identifying Differential Scheduling Plans for Microgrid Operations Under Diverse Uncertainties

To satisfy the differential operation requirements of microgrids under the nominal and uncertain scenarios, a novel three-stage close-looped robust optimization (TSCL-RO) method is proposed to obtain more practical scheduling plans. In the first stage, the fixed startup and shutdown plans are identified considering both the cutting planes from the nominal and uncertain scenarios. According to the startup/shutdown schemes, the decision-making of the basic flexible plans under the nominal scenario is performed to minimize the operation cost in the second stage considering the second-order cone relaxed distflow model. To confront the disturbances from the power and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> uncertainties, the basic flexible variables are revised to capture the worst-case scenario via a max-min bi-level optimization in the third stage, and the derived results are returned as feasibility cuts to preserve the robustness of the fixed plans. To solve this intractable TSCL-RO model proficiently, a tailored bi-layer chaining decomposition algorithm is further devised to handle the resulting multi-level mixed-integer second-order cone programming (MISOCP) via alternate iterations. Finally, numerical simulations verify the applicability and superiority of the investigated TSCL-RO model and the decomposition algorithm.

Short-circuit constrained distribution network reconfiguration considering closed-loop operation

This paper presents a novel scenario-based stochastic mixed-integer second-order cone programming model to solve the problem of optimal reconfiguration of distribution systems with renewable energy sources considering short-circuit constraints. The proposed formulation minimizes technical losses by modifying the statuses of sectionalizing and tie switches, allowing the operation of distribution networks with radial and closed-loop topologies. Since the formation of loops could impact fault current levels, short-circuit constraints are considered in the problem formulation. Numerical experiments are carried out using an 84-node system and the results demonstrate the effectiveness of the proposed formulation to reduce technical losses notably when a closed-loop operation is allowed. Additionally, it is verified that short-circuit constraints prevent the adoption of network configurations with high short-circuit values.

Reliability-Oriented Reconfiguration of Power Distribution Systems Considering Load and RES Production Scenarios

The ever-increasing integration of non-dispatchable distributed generation, i.e., renewable energy sources (RES), arises new challenges in the field of power system's reliability. Distribution network reconfiguration (DNR) is a cost-effective approach for the distribution system operator (DSO) that wishes to enhance system's reliability without infrastructure upgrades. This paper introduces a novel path-based mixed-integer second-order cone programming model to optimally solve the reliability-oriented DNR problem. The DSO's objectives that are optimized are: a) improvement of distribution system's reliability indices and b) minimization of power losses. The proposed model is enriched with a scenario-based stochastic programming formulation that considers multiple levels of load and RES production. The standard 33-nodes distribution system and a real-world 83-nodes distribution system are employed to prove the efficiency and applicability of the model. Firstly, the multi-objective nature of the reliability-oriented DNR problem is investigated by conducting a sensitivity analysis, which reveals a trade-off region between reliability indices and power losses. Moreover, the obtained results show different global optimal solutions when the variability of load and RES production is considered. This highlights the importance of considering a scenario-based approach for load and RES production when solving the reliability-oriented DNR problem.

An Enhanced Second-Order Cone Programming-Based Evaluation Method on Maximum Hosting Capacity of Solar Energy in Distribution Systems with Integrated Energy

In order to adjust to the change of the large-scale deployment of photovoltaic (PV) power generation and fully exploit the potentialities of an integrated energy distribution system (IEDS) in solar energy accommodation, an evaluation method on maximum hosting capacity of solar energy in IEDS based on convex relaxation optimization algorithm is proposed in this paper. Firstly, an evaluation model of maximum hosting capacity of solar energy for IEDS considering the electrical-thermal comprehensive utilization of solar energy is proposed, in which the maximization of PV capacity and solar collector (SC) capacity are fully considered. Secondly, IEDS’s potential in electricity, heat, and gas energy coordinated optimization is fully exploited to enhance the hosting capacity of solar energy in which the electric distribution network, heating network, and natural gas network constraints are fully modeled. Then, an enhanced second-order cone programming (SOCP)-based method is employed to solve the proposed maximum hosting capacity model. Through SOCP relaxation and linearization, the original nonconvex nonlinear programming model is converted into the mixed-integer second-order cone programming model. Meanwhile, to ensure the exactness of SOCP relaxation and improve the computation efficiency, increasingly tight linear cuts of distribution system and natural gas system are added to the SOCP relaxation. Finally, an example is given to verify the effectiveness of the proposed method. The analysis results show that the maximum hosting capacity of solar energy can be improved significantly by realizing the coordination of an integrated multi-energy system and the optimal utilization of electricity, heat, and gas energy. By applying SOCP relaxation, linearization, and adding increasingly tight linear cuts of distribution system and natural gas system to the SOCP relaxation, the proposed model can be solved accurately and efficiently.

Economic-environmental energy supply of mobile base stations in isolated nanogrids with smart plug-in electric vehicles and hydrogen energy storage system

The mobile base stations (MBS) are fundamental communication devices that ensure the constant stream of interconnectivity. However, they are mostly installed in off-grid regions. This study investigates the economic-environmental energy supply of a MBS in an isolated nanogrid (ING) that also includes a hydrogen energy storage system (HES), photovoltaic (PV) system, controllable plug-in electric vehicles (PEV) and a diesel generator (DG). A novel mixed-integer second-order cone programming (MISOCP) formulation is proposed to capture the nonlinearities of the various components through a convex optimization model. The study included different uncertainties including the traffic rate of the MBS, driving schedule of the PEVs, and PV generation via a hybrid stochastic programming (SP) and robust optimization (RO) methods. The influence of the coordinated PEV charging strategy, risk-averse RO and multi-objective optimization was studied through various case studies. The outcomes show that coordinated PEV-charging can have a significant contribution in reducing the risks and curtailing both cost and emission objective functions, while using economic-environmental operation model can cut the emissions by 17.70%.

Closed-loop robust steady-state target calculation for model predictive control

Industrial model predictive control (MPC) typically includes a steady-state target calculation (SSTC) layer that provides targets for the dynamic MPC controller to track. This paper develops the first closed-loop robust SSTC method, which explicitly addresses the closed-loop uncertainty, for stable linear systems with time-invariant parametric uncertainty. The problem is initially formulated as a stochastic bi-level optimization problem, where the lower-level optimization problem describes the nominal MPC law. The problem is then transformed into a deterministic mixed-integer second-order cone program for ellipsoidal uncertainty. Case study results show that the proposed method is more robust than the classical nominal SSTC in that it helps reduce cycling of the steady-state targets. In addition, the proposed method is less conservative than a typical open-loop robust SSTC method, in that it drives the system to the steady state more quickly and can push the steady state closer to the operating boundary when desired.

Two stage affinely adjustable robust optimal scheduling for AC/DC hybrid distribution network based on source–grid–load–storage coordination

Aiming at the uncertain optimization problem of AC/DC hybrid distribution network under the coordination of source, grid load and storage, an AC/DC hybrid distribution network operation scheme based on two stage affinely adjustable robust optimization was proposed in this paper. Firstly, the controllable model of distribution generation (DG), the battery energy storage model with cycle life degradation and the ZIP load model were considered, and the optimization model of AC/DC hybrid distribution network economic operation was constructed. Then the ellipsoid set was used to describe the uncertainty of DG output, and the linear decision-making mechanism of decision variables and uncertainty variables of DG output in the optimization model was formed by combining linear affine strategy, Finally, the robust optimization model of AC/DC hybrid distribution network was transformed into a deterministic mixed integer second-order cone programming model by dual transformation. The effectiveness and advantages of the affinely adjustable robust optimization method proposed in this paper were compared and verified in the two modified IEEE bus system.

Active-reactive power collaborative optimization model of electrical interconnection system based on deep learning under the goal of “carbon neutrality”

With the goal of carbon neutralization put forward, new energy units have gradually become the main power supply, and its volatility has brought great challenges to the control and optimization of the system, especially the distribution network. In order to solve the reactive power problem caused by the high proportion of renewable energy connected to the distribution network, a source network load storage centralized optimal dispatching model considering reactive power optimization and multi energy collaborative interaction is proposed. The model aims at the optimal operation cost, minimum network loss and minimum carbon emission of the multi energy system, and considers reactive power compensation, energy storage regulation and energy conversion, so as to realize the safe and low-carbon economic dispatching of the electrical interconnection system. The switching capacity of the discrete reactive power compensation device is linearized, and the model is transformed into a mixed integer second-order cone programming problem for solution. The simulation results show that the proposed method can effectively compensate the reactive power required by the wind turbine parallel network, coordinate the energy interaction between electricity and gas, and improve the stability and flexibility of the distribution network after large-scale renewable energy access, According to the charging and discharging power and charge state, and the automatic adjustment of the gears of on load voltage regulating transformer and compensation capacitor bank, this paper shows that the system has safe and stable operation performance.

Multi-Agent Deep Reinforcement Learning for Voltage Control With Coordinated Active and Reactive Power Optimization

The increasing penetration of distributed renewable energy resources causes voltage fluctuations in distribution networks. The controllable active and reactive power resources such as energy storage (ES) systems and electric vehicles (EVs) in active distribution networks play an important role in mitigating the voltage excursions. This paper proposes a two-timescale hybrid voltage control strategy based on a mixed-integer optimization method and multi-agent reinforcement learning (MARL) to reduce power loss and mitigate voltage violations. In the slow-timescale, the active and reactive power optimization problem involving capacitor banks (CBs), on-load tap changers (OLTC), and ES systems is formulated as a mixed-integer second-order cone programming problem. In the fast-timescale, the reactive power of smart inverters connected to solar photovoltaic systems and active power of EVs are adjusted to mitigate short-term voltage fluctuations with a MARL algorithm. Specifically, we propose an experience augmented multi-agent actor-critic (EA-MAAC) algorithm with an attention mechanism to learn high-quality control policies. The control policies are executed online in a decentralized manner. The proposed hybrid voltage control strategy is validated on an IEEE testing distribution feeder. The numerical results show that our proposed control strategy is not only sample-efficient and robust but also effective in mitigating voltage fluctuations.

Maximum Hosting Capacity of Photovoltaic Generation in SOP-Based Power Distribution Network Integrated With Electric Vehicles

Photovoltaic generation is playing a significant role in realizing the target of carbon neutralization. This article proposes a two-stage robust optimization model to assess the maximum hosting capacity of photovoltaic generation in power distribution network (PDN) considering the integration of soft open point (SOP) and electric vehicles (EVs). Convex relaxation method is applied to convert the two-stage robust optimization model to the form of mixed-integer second-order cone programming. A solving strategy based on the column-and-constraint generation algorithm is developed to solve the model, in which linearized difference-of-convex strategy is proposed to deal with the relaxation gap. Case studies are carried out on the modified IEEE 33-bus PDN integrated with SOP and EVs, and the results show the advantages of the proposed model and solving strategy.

Optimal operation strategies of pumped storage hydropower plant considering the integrated AC grids and new energy utilization

The large-scale development and utilization of new energy resource extremely promotes the construction and application of the flexible DC power grid especially in China. This paper focuses on the operation stability and new energy transmission of an actual regional power grid in North China, including new energy plants, the flexible DC power grid, a pumped storage hydropower plant (PSHP) with variable speed pumped storage unit (VSPSU) and regional AC power grids. According to the operation rules and goals, the economic operation model of the flexible DC-PSHP system is established by the mixed-integer second-order cone programming. Considering the transmission and consumption of the new energy generation, two operation strategies and three simulation scenarios are proposed. The day-ahead optimal operation schemes of PSHP in different scenarios are given by the case simulation. The results show that the proposed strategies can satisfy the operation demands of the regional power grid both in new energy generation transmission and operation economic benefits.

Exploring Potential Gains of Mobile Sector-Coupling Energy Systems in Heavily Constrained Networks

The coincidence of high levels of variable, non-dispatchable generation from renewable energy sources (RESs) and congested electricity networks imposes significant constraint payments (CP) on electricity system operators (ESOs) which ultimately is charged to the customers. This paper is inspired by this challenge and proposes an integrated electricity, gas, and transportation energy system taking advantage of power-to-gas (P2G) facilities and electricity/gas storage devices to enhance operational efficiency. It proposes mobile gas storage systems (MGSs) that can store and carry liquid hydrogen or liquefied natural gas (LNG) to the load points or remote locations without access to the gas network. So, the green energy of RESs in the form of gases can be injected, transported, and reutilized in the natural gas network or stored in MGS facilities. Besides, the mobile electricity storage system (MES) can directly store the redundant electricity produced by RESs, and the railway transportation system carries both the MESs and MGSs to the load point of electrical and gas systems. The proposed model reflects CP to wind in the marketing phase and considers incentives for the hydrogen-burning generators. Also, a stochastic platform is employed to capture the inherent uncertainties in the predicted values of the load and RESs’ generation. The model is formulated as a mixed-integer second-order cone programming problem and tested on an IEEE 118-bus system integrated with a 14-node gas network and a railway system. The result shows that employing the multi-vector energy system (MVES) elements reduces the total operational cost by 47%, and the CP to wind is reduced by 99.8% by absorbing almost the whole green energy of wind farms while relieving congestion in the electrical grid.

Robust location and sizing of electric vehicle battery swapping stations considering users’ choice behaviors

Battery swapping electric vehicle (EV) is an effective way to achieve vehicle electrification due to its advantage in reducing the waiting time and the upfront purchase cost, and alleviating users’ range anxiety. This paper proposes a robust battery swapping stations location and sizing model for the EV battery swapping service network design problem considering the users’ choice behaviors. Specifically, this paper develops a multinomial logit model to characterize the interaction between the service provider’s decisions and the EV users’ choice, and derives closed-form results for the sizing decisions to satisfy the pre-specified service level criteria by utilizing the distributionally robust chance constraint method and GI∖G∖m queueing model. This paper develops an equivalent mixed integer second-order cone programming (SOCP) reformulation and a generalized Benders decomposition algorithm with speedup strategies to solve the non-convex robust model efficiently. We extend the proposed model to consider the power network constraints, and propose a data-driven algorithm to estimate EV users’ swapping demands from traffic network data. Experimental results show that the proposed algorithm outperforms the state-of-the-art Gurobi solver in terms of run time and solution quality. This paper conducts a case study using real-world data to examine the influence of EV users’ choice behavior, service levels, charging rate, and battery swapping service rate on the optimal decisions and the expected profit, and presents useful managerial implications for practitioners.

A bidding mechanism for maintenance of generation units considering inter-ISO power exchange

To ensure the reliability of power systems, the independent system operator (ISO) manages the planning process of the maintenance of generation units for generation companies (GENCOs). This paper focuses on a widely studied two-layer long-term predictive maintenance decision making framework in a deregulated environment. In the first layer the ISO-wide maintenance schedule is optimized for the GENCOs, targeting minimal total maintenance cost and degradation statuses. In the second layer, a bidding mechanism is designed for GENCOs who are not satisfied with the time slots scheduled by the first layer, so that they can bid for their preferred time slots. A novel bidding mechanism for the host ISO (i.e., the ISO that manages the maintenance planning process) is proposed, called interchangeable bidding mechanism for maintenance (IBMM). In this mechanism, the GENCOs of the host ISO can use their bid price to purchase the supportive energy from the GENCOs of the neighbor ISOs. Furthermore, they also can pay a penalty fee for reducing the amount of energy transmitted from the host ISO to the neighbor ISO with respect to what has been stipulated in the long-term inter-ISO power exchange contract. IBMM provides more opportunities for GENCOs of the host ISO to obtain their preferred maintenance time slots. Additionally, the power system reliability can be ensured. IBMM is formulated as a mixed-integer non-linear bidding programming problem. Then, the bidding programming problem is recast into a mixed-integer second-order cone programming (MISOCP) problem that can be solved using Gurobi. In the case study, the IEEE 118-bus network is studied to illustrate the performance of the proposed bidding strategy.