Mixed-integer Second-order Cone Programming Problem Research Articles

Stochastic model for active distribution networks planning: An analysis of the combination of active network management schemes

The widespread adoption of distributed generation (DG) is changing the operation of distribution networks. To increase the control of power flows and avoid the detriments of DG intermittency, active distribution networks (ADN) emerge as a feasible solution. In this paper, we propose a convex model for ADN expansion planning. Four active network management (ANM) schemes are considered: DG active power curtailment, DG reactive power control, on-load tap changer (OLTC) tap adjustment, and shunt compensation device control. The problem is formulated as a mixed integer second-order cone programming problem (MISOCP) using the distflow equations and second-order cone relaxations (SOCR). By scenario analysis, we address the uncertainty associated with power demand, renewable generation, and electricity prices. The proposed model is used to study the benefits of different combinations of ANM schemes to a modified IEEE 33-bus system and compare them with the individual benefits of each scheme. The results indicate that ANM schemes can reduce total network costs, reduce losses, delay network reinforcement, and improve the voltage profile. In addition, some combinations of schemes develop synergies in which the combined economic benefits are greater than the sum of the individual benefits.

Distributionally Robust Unit Commitment Considering Unimodality-Skewness Information of Wind Power Uncertainty

The deepening penetration of renewable energy sources (RESs) into power grids imposes remarkable challenges that merit special attention. In this paper, we work out a distributionally robust chance-constrained (DRCC) day-ahead unit commitment problem while the stochasticity and variability arising from RESs are taken into consideration. The developed framework optimizes the expected objective function and stipulates that the DRCCs will hold within a moment-based ambiguity set, which additionally incorporates the unimodality information and mode skewness. The employed ambiguity set can not only account for the wind power uncertainty but also expressly alleviate the conservatism compared with the single moment metric. By deriving efficient mathematical reformulations to tackle the expected objective function and DRCCs, the proposed model is reduced to an exact mixed-integer second-order cone programming problem that can readily be implemented. Numerical experiments are carried out on two representative test systems to demonstrate the effectiveness and efficiency of the suggested methodology.

Network-Constrained Transactive Control for Multi-Microgrids-Based Distribution Networks With Soft Open Points

Different from most transactive control studies only focusing on economic aspect, this paper develops a novel network-constrained transactive control (NTC) framework that can address both economic and secure issues for a multi-microgrids-based distribution network considering uncertainties. In particular, we innovatively integrate a transactive energy market with the novel power-electronics device (i.e., soft open point) based AC power flow regulation technique to improve economic benefits for each individual microgrid and meanwhile ensure the voltage security of the entire distribution network. In this framework, a dynamic two-timescale NTC model consisting of slow-timescale pre-scheduling and real-time corrective scheduling stages is formulated to work against multiple system uncertainties. Moreover, the original bilevel game problems are transformed into a single-level mixed-integer second-order cone programming problem through KKT conditions, duality, linearization and relaxation techniques to avoid iterations of transitional methods, so as to improve the solving efficiency. Finally, numerical simulations on modified 33-bus and 123-bus test systems with multi-microgrids verify the effectiveness of the proposed framework.

部材の密集度を考慮した骨組構造物の大域的トポロジー最適化

It is known that the topology optimization (TopOpt) problem of frame structures can be formulated as a mixed-integer second-order cone programming problem (MISOCP), when the compliance is minimized and the cross-section of each member is selected from a set of predetermined candidates. However, when considering the constructability of real-world building structures, it is insufficient to only minimize compliance. In this paper, in order to control the density of members, the constraints of the number of members connected to each node are additionally considered into TopOpt by MISOCP treated in the previous study.

Probabilistic wind power expansion planning of bundled wind-thermal generation system with retrofitted coal-fired plants using load transfer optimization

The bundled wind-thermal generation system (BWTGS) is an attractive option to integrate wind energy to actively participate in power systems. With the greatly enhanced penetration of wind energy in BWTGS, wind curtailment against sharp wind power fluctuations is inevitable. Thus, our study is stimulated by whether and to what extent we can maximize wind power penetration with proper provision of dispatchable loads against wind curtailment, and this is exactly the problem we aim to solve in this paper. Here, we initially focus on the flexible characteristics of retrofitted coal-fired units in BWTGS and the load transfer optimization (LTO) for high voltage distribution networks (HVDNs). Then, an appropriate probabilistic wind power capacity expansion planning method for BWTGS with retrofitted coal-fired units using LTO can be reformulated as a mixed-integer second-order cone programming problem. Moreover, since load and wind power data have inherited uncertainty, we extend this proposed model to be a probabilistic expanding model. This contributes to better decision-making for the short-term wind capacity expansion under quantified uncertainty. Numerical results of the practical HVDNs demonstrate the effectiveness of the proposed method.

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.

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.

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.

Cost-based site and capacity optimization of multi-energy storage system in the regional integrated energy networks

The unbalance between the renewable energy sources and user loads reduces the performance improvement of regional integrated energy systems (RIES), in which the multi-energy storage system with battery and heat tank is necessarily integrated. This paper aims to optimize the sites and capacities of multi-energy storage systems in the RIES. A RIES model including renewable wind power, power distribution network, district heating network, multi-energy storage system, and heat pump to convert electricity to heat is constructed. An optimization method combining a mixed-integer nonlinear programming optimization model is proposed to minimize the comprehensive cost of RIES. The second-order cone relaxation method performs convex relaxation of the power flow constraints, and the district heat network is operated under a constant-flow-variable-temperature strategy. The original optimization model is transformed into a mixed-integer second-order cone programming problem to solve. Three solution methods, including enumeration method, improved enumeration method and genetic algorithm, are employed to determine the optimum installation locations, and they are compared in computation time and efficiency. The results demonstrate that the distributed hybrid integration of electricity and thermal energy storages improves the RIES economy by collaborating the power and heat balances and reducing the purchased electricity from the grid. By integrating the hybrid storage system, the curtailed wind is reduced by 53.9%, and the economy is improved by 13.4%.

Revealing a New Vulnerability of Distributed State Estimation: A Data Integrity Attack and an Unsupervised Detection Algorithm

This article proposes a distributed false data injection attack (FDIA) by attacking to the boundary buses in an interconnected power system. The proposed attack utilizes the measurements corresponding to a set of boundary buses in each neighboring areas to inject arbitrary errors to the estimated states of those buses. It is demonstrated that the attack not only gets through the robust distributed estimators but also bypasses the convergence-based detection methods. Furthermore, in an illustrative example, the differences in the attack with the conventional FDIA are briefly explained. Then, finding the optimal attack vector to minimize the maximum difference between the per area errors by considering the attacker’s limitations is formulated as a mixed-integer second-order cone programming problem. Finally, an unsupervised machine learning-based detection method is proposed utilizing a kernel density estimation technique along with statistical measures. This follows an outlier detection to filter out attacks. To show the performance of the detector, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n-1$</tex-math></inline-formula> contingency, which changes the probability distribution of data is analyzed. The proposed attack and detector are tested on various IEEE systems such as IEEE 14-bus and IEEE 118-bus test systems and the results are discussed.

Data-adaptive robust coordinated optimization of dynamic active and reactive power flow in active distribution networks

The uncertainty of wind power brings security and economic issues in active distribution networks. As an effective solution to these problems, the active/reactive optimization aims at minimizing the total operation cost and network loss by controlling multiple resources. This paper proposes a two-stage data-adaptive robust optimization model for the dynamic active-reactive power flow. The dynamic correlation between the uncertainties of active and reactive power is analyzed at two kinds of power factor modes of wind turbines and then is described by a linear affine decision rule. To characterize these uncertainties, a data-adaptive multi-band uncertainty set is constructed based on historical data, which allows the number of bands and the corresponding weight coefficients to be adjusted under different confidence levels. Subsequently, the conic relaxation and linearization techniques are performed to reformulate the robust optimization model as a mixed-integer second-order cone programming problem. A two-level solution framework, consisting of a column-and-constraint generation algorithm and an outer approximation algorithm, is employed to solve this problem. Simulation results on a modified IEEE 33-bus system indicate that the variable power factor mode is more suitable for describing the dynamic correlation than the constant power factor mode. Besides, the proposed model and method also show better practicality and solution efficiency than the existing ones.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources, which have become a new operation mode with substantial advantages such as high flexibility, adaptability, and economy. This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources. The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments. In this regard, the faults of stochastic optimization and traditional robust optimization can be overcome. Firstly, a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed, and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets. Then, an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem, which improves the computational efficiency of the model. Finally, the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy. They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.

Distribution System Resilience in Ice Storms by Optimal Routing of Mobile Devices on Congested Roads

This article proposes a robust resilience enhancement method for a power distribution network in ice storms by the optimal routing of mobile de-icing devices (MDIDs) on congested transportation roads. We consider MDIDs as emergency vehicles, as other vehicles yield the right-of-way to MDIDs, and propose a de-icing schedule (DIS) to illustrate how MDIDs are routed on congested transportation roads. We further coordinate the DIS and MDID routing, which mitigate transportation routing congestions, with power distribution system operation, which considers distribution network reconfiguration and distributed energy resource dispatch. A two-stage robust model is proposed to manage the effects of ice storms forecast errors on both power distribution and urban transportation networks. The proposed model is reformulated as a mixed-integer second-order cone programming problem. The Benders decomposition and column-and-constraint generation algorithms are further utilized to solve the proposed MISOCP. Numerical results for the modified IEEE 33-bus 12-node, IEEE 123-bus 25-node, and 252-bus 80-node electricity-transportation systems show the effectiveness of the proposed model and solution technique for enhancing the power system resilience.

A probabilistic method to quantify the capacity value of load transfer

When a primary substation reaches its capacity limit reinforcement is required, usually via additional circuits. Load transfer constitutes an alternative solution to this problem, as it can provide substantial capacity support at little, or even zero, capital expenditure. This paper provides a probabilistic method which quantifies the capacity value of load transfer using the Effective Load Carrying Capability methodology within a Sequential Monte Carlo Simulation framework. Load transfer is mathematically formulated as a mixed-integer second-order cone programming problem, which can be efficiently solved using commercial solvers. The proposed methodology is applied to a realistically sized distribution network considering three different redundancy levels, namely N-1, N-0.75, and N-0.5. The results show a maximum capacity value of 25% and 37% of the base case demand for manual and remote control load transfer, respectively, for the N-0.5 case with 4.21 MWh/year. The results also show that the capacity value of load transfer is significantly higher if the initial level of reliability of the network is lower, indicating that the network operator is prepared to accept a higher level of risk.

A multi-period scheduling strategy for ADN considering the reactive power adjustment ability of DES

Nowadays, the active distribution network (ADN) is facing great challenges on safe operation and coordinated scheduling. To resolve these issues, a novel multi-period active-reactive coordination scheduling strategy efficient solution method is proposed in this paper after addressing the uncertainty of DG and load by probabilistic scenario method. Firstly, based on the second-order cone relaxation (SOCR), the power flow equations are convexized and relaxed to transform the original model into mixed integer second-order cone programming (MISOCP). Then, the controllable resources such as on-load tap changer (OLTC), capacitor banks (CB) and ESS are accurately linearized, so the model is converted to 0–1 MISOCP problem. Finally, compared with the existing strategies, numerical tests on the modified IEEE 33-bus test system demonstrate that on the premise of realizing the maximum utilization of DG, the proposed strategy can also achieve the purposes of energy-saving, loss reduction and improvement in voltage level and the utilization of ESS. Meanwhile, the accuracy and efficiency of the 0–1 MISOCP model are verified through four operating schemes. In addition, the sensitivity analysis of adjustment step and action time of the discrete adjustment devices on optimization results is carried out in detail.

Data‐driven distributionally robust joint planning of distributed energy resources in active distribution network

With the increasing penetration of distributed energy resources (DERs) in the active distribution network (ADN), how to enable joint planning of DERs under the uncertainty of distributed generations (DGs) has become a challenging problem. This study establishes a two-stage joint planning model considering doubly-fed induction generator, photovoltaics (PVs) with the ancillary services of PV inverter, distributed energy storage systems and different types of controllable loads in the ADN. To address the uncertainties of DGs, a two-stage data-driven distributionally robust planning model is constructed. The proposed model is solved in a `master and sub-problem' framework by column-and-constraint generation algorithm, where the master problem is to minimise the total cost and find the optimal planning decision under the worst probability distributions, and the sub-problem is to find the worst probability distribution of given uncertain scenarios. Besides, the original mixed-integer non-linear planning problem is converted into a mixed-integer second-order cone programming problem through second-order cone relaxation, Big-M and piecewise linearisation method. The numerical results based on 33-bus system verify the effectiveness of the proposed model.

Optimal generation scheduling in microgrids using mixed-integer second-order cone programming

In this article, a new model is proposed for the operation of microgrids (MGs) using optimal distribution feeder reconfiguration (DFR) and optimal generation scheduling (OGS). The distributed generation units, electric vehicles and demand response (DR) are modelled in the presented model. The DR programs consider load shifting, load curtailing and time-of-use programs. The proposed model is formulated as a mixed-integer second-order cone programming problem and solved by the GAMS software package. The total operating cost is taken into account as the objective function and several operational constraints are used in the optimization problem. The simulation results of the 33-bus MG are shown, where considering OGS along with DFR leads to a lower operating cost. In addition, the load shifting of a DR program can reduce the total operating cost by smoothing the load profile and reducing the cost of power purchases from the main grid.

A novel management scheme to reduce emission produced by power plants and plug-in hybrid electric vehicles in a smart microgrid

Recently, with the growth and development of distributed generation (DGs) and energy storage systems (ESSs), as well as smart control equipment, microgrids (MGs) have been developed. Microgrids are comprised of a limited number of constitutive parts, including loads, DGs, ESSs, and electric vehicles (EVs). This paper presents a novel scheme to manage active and reactive powers, based on DGs, ESSs, and EVs to reduce the total operation cost including power generation and emission costs. Simultaneous management of active and reactive power makes it possible to consider grid operation constraints together. In the proposed schedule, the vehicles are assumed to be plug-in hybrid electric vehicles. They are able to run both on gasoline and electricity. The proposed schedule incorporates the cost of the consumed fuel and generated pollution into the function of the MG. It is programmed using GAMS software as a mixed-integer second-order cone programming problem and is implemented on a test MG. Simultaneous management of active and reactive power sources can result in lower cost compared to separated scheduling.

Interactive Equilibrium of Electricity-Gas Energy Distribution System and Integrated Load Aggregators Considering Energy Pricings: A Master-Slave Approach

Integration of electricity and gas distribution networks improves energy utilization and alleviates environmental pollution. In order to obtain a reasonable energy prices and optimize the day-ahead scheduling scheme under the premise of considering the interests of both supply and demand, an interactive equilibrium model considering electricity-gas energy distribution system and integrated load aggregators is established in this paper. In the upper level, the integrated energy distribution network (IEDN) maximizes the profit via solving the day-ahead optimal energy flow considering energy prices changing in the next day. In the lower level, integrated load aggregators (ILA) minimize charging costs, thus optimizing energy distribution based on integrated demand responses. By using the Karush-Kuhn-Tucker (KKT) optimality conditions and the duality theorem of linear programming, the master-slave game model is transformed into a single layer optimization problem. To solve this problem, second-order cone programming (SOCP) and penalty convex-concave procedure (PCCP) are used to deal with the non-convex functions of electricity-gas distribution system. Therefore, the proposed model is approximated by a mixed-integer second-order cone programming problem. Finally, case studies verify the effectiveness of the proposed model and method.

Privacy-Preserving Collaborative Operation of Networked Microgrids With the Local Utility Grid Based on Enhanced Benders Decomposition

In this paper, a privacy-preserving decision-making framework is developed for a collaborative operation of networked microgrids and the local utility grid, where the distribution system operator (DSO) interacts with microgrid master controllers (MCs) in a leader-followers fashion. First, the paper models the decision-making in the collaborative operation presented as an integrated mixed-integer second-order cone programming problem which satisfies various technical and operational requirements in a look-ahead manner. Then, the integrated optimization problem is decomposed into a master problem and a set of subproblems in order to decentralize the decision-making process of DSO and MCs. The master problem is solved by DSO for optimizing the local utility grid operation, and the subproblems are solved independently by MCs for optimizing the operation of individual microgrids. We propose an enhanced Benders decomposition algorithm to guide the iterations between the master problem and subproblems. In particular, an enhanced approach is introduced in the Benders decomposition algorithm for generating valid cutting planes from mixed-integer linear programming subproblems. Mathematically, the proposed algorithm can find the globally optimal solution after a finite number of iterations. Accordingly, DSO and MCs manage to collaborate on making operational decisions that would maximize the social welfare without compromising independent decision-making and privacy provisions. Numerical experiments are conducted on a simplified two-bus system and a modified IEEE 123-bus system. The results validate the efficiency, the robustness, and the scalability of the proposed collaborative decision-making framework in power systems.