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.

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.

Resilience‐oriented service restoration modelling interdependent critical loads in distribution systems with integrated distributed generators

The exponential increase in the frequency and intensity of high impact low probability weather-related events have pivoted the paradigm of research pertaining to power systems towards resilience. Power system is considered as a critical infrastructure, directly linked to the nation's economy, security and health. Therefore, recent researchers have proposed several techniques to enhance the resilience of power systems. In those techniques, critical loads have been considered independent in nature and different metrics have been proposed to evaluate the resilience of the network. To enhance the resiliency, this paper incorporated distributed generators in the distribution network and critical loads are modelled interdependently. Furthermore, a novel resilience metric is proposed in this paper to evaluate the resilience of a distribution system. The proposed model is formulated as a mixed integer second-order cone programming problem and the efficacy of the proposed model is evaluated on IEEE 33- and 69-bus systems. The competence of the proposed resilience metric is evaluated after comparison with existing resilience metrics.

Two-stage stochastic scheduling approach for AC/DC hybrid distribution system with renewable energy integration

This paper proposes a stochastic scheduling approach for AC/DC hybrid distribution system considering the output uncertainty of wind and photovoltaic. The energy coordination problem has been formulated as a two-stage resource scheduling problem. The first-stage decision produces an hourly day-ahead pre-scheduling plan for the dispatchable distributed generators. For a set of possible scenarios over the next 24 h, the second stage determines the appropriate corrective decisions to handle the output uncertainty. Besides, the scheduling model for AC/DC hybrid system belongs to the non-convex optimization problem, which is transformed into a mixed integer second-order cone programming problem by second-order cone relaxation and linearization techniques. In this way, the optimization problem can be solved effectively. The proposed model has been tested on a modified IEEE 33 bus AC/DC hybrid system. Simulation results demonstrate that the proposed two-stage stochastic scheduling model can better cope with the renewable energy uncertainty and the active and reactive power coordination scheduling can ensure the safe operation of the entire system.

Resilient co‐expansion planning between gas and electric distribution networks against natural disasters

Resiliently designed and constructed integrated gas-electric distribution networks (GEDNs) against natural disasters are crucial to social welfare. In this study, a two-stage robust optimisation-based co-expansion planning model is proposed to attain an integrated GEDN with a given resilience level, by optimising the investment strategies of hardening and selective expansion of power distribution feeders and natural gas pipelines, as well as the location and capacity of natural-gas-fired distributed generation. In the first stage, the overall annual investment and operation cost is minimised under normal operation conditions while in the second stage, the feasibility of the investment decisions under the identified worst-case natural disaster scenario is checked with an adjustable load shedding cost criterion. The proposed model is formulated as a mixed integer second-order cone programming problem with the column and constraint generation algorithm employed to seek the optimal solution. Case studies on two integrated GEDNs demonstrate the performance of the proposed methodology.

Data-driven stochastic service restoration in unbalanced active distribution networks with multi-terminal soft open points

Service restoration is critical in ensuring the reliability of distribution networks after the isolation of faults. Multi-terminal soft open points (MTSOPs) can realize power flow among multiple feeders and provide voltage support for power outage areas. This mechanism can help improve the restoration ability of distribution systems. A distribution network is typically unbalanced when the load, distributed generation, and line parameters are unbalanced. This study proposes accordingly a service restoration model for unbalanced active distribution networks (UADNs) with MTSOP. The power control principles of MTSOP in the fault condition and a service restoration strategy in MTSOP-based UADN are first analyzed. Then, a deterministic service restoration model is established. The maximized weighting restored load and the minimized voltage unbalance are used as the objective functions. The original optimization model is converted into a mixed integer second-order cone programming problem by linearizing the three-phase power flow equation, the big-M method, and the second-order cone relaxation, which can be solved by commercial solvers. A two-stage data-driven stochastic optimization model for service restoration in UADN is established by considering the uncertainty of load demand and the generation of renewable energy. The IEEE 33-node, Taiwan Power Company, and modified IEEE 123-node systems are used to verify the proposed model.

Multi-energy-storage energy management with the robust method for distribution networks

The randomness, volatility and anti-peaking characteristic from distributed renewable energy generation rise great challenges for the safe and economic operation of the distribution networks (DNs). To address this problem, this paper proposes a novel multi-energy-storage energy management system (EMS) to co-optimize the electricity-driven mobile energy storage (MES) and inverter air-conditioning (AC)-based thermal energy storage (TES). To facilitate the energy management of the DN, the MES that considers the delay factors and the TES that regulates reactive power have been developed into a unified analytic model capable of charging and discharging. In addition, considering the impact of the forecasting uncertainties and the risk-aversion of the dispatcher, a novel robust optimization method is proposed to obtain more accurate “worst scenario”. The dispatching model is then converted into a mixed integer second-order cone programming problem (MI-SOCP) and a mixed integer linear programming problem (MILP), and linearized techniques and an iteration method are used to efficiently solve these problems. Simulation studies on a 41-node DN in Ontario indicate that the operational cost and power loss of the DN can be reduced by no less than 1% and 8% using the proposed EMS, respectively, while a safer voltage level with a voltage deviation of 5% can be obtained. The results confirm the effectiveness of the MES and TES for peak shaving, valley filling and voltage supporting.

Coordinated Planning of Converter-Based DG Units and Soft Open Points Incorporating Active Management in Unbalanced Distribution Networks

Soft open points (SOPs) can transfer active power between feeders and compensate reactive power. These features help increase the integration capacity of distributed generation (DG), but the installation location and capacity of SOPs will affect DG planning. In addition, the distribution networks are usually unbalanced due to asymmetric line parameters, unbalanced loads, and DG. Converter-based DG units and SOPs have individual phase active and reactive power regulating ability and provide unbalance compensation. The objective of this paper is to develop a coordinated planning model of converter-based DG units and SOPs in an unbalanced distribution network (UDN) to incorporate their individual phase power control abilities. The individual phase power control characteristics of DG converters and SOPs are first analyzed. A bi-level optimization model of converter-based DG units and SOP planning is then established, in which the upper-level problem minimizes the total cost of the UDN and the lower-level problem minimizes the power loss and voltage unbalance. The bi-level model is transformed into a single-level mixed integer second-order cone programming problem that can be efficiently solved by widely used commercial solvers. Finally, the proposed model is verified on IEEE 33-node and Taiwan Power Company systems.

Chance-constrained optimal dispatch of integrated electricity and natural gas systems considering medium and long-term electricity transactions

A novel stochastic optimal dispatch model is proposed considering medium and long-term electricity transactions for a wind power integrated energy system using chance constrained programming. The electricity contract decomposition problem is introduced into the day-ahead optimal dispatch plan formulation progress. Considering the case that decomposition results may be not executable in the dispatch plan, a coordinated optimization strategy based on the Lagrange multiplier is proposed to eliminate the non-executable electric quantity. At the same time, the uncertainties and correlation of wind power are considered in the dispatch model, and the original stochastic dispatch problem is transformed into a mixed integer second-order cone programming problem using second-order cone relaxation and sample average approximation approach. Case study results demonstrate the validity of the proposed method.

Integrated Day-Ahead Scheduling Considering Active Management in Future Smart Distribution System

Day-ahead scheduling has played a significant role in the operation of distribution systems, aiming at minimizing the total operation cost. With the excessive integration of information and communication technologies and intelligent electronic devices, distribution system operators may seek to optimally control the active management elements to increase the economic and technical performance of future smart distribution systems. This paper focuses on an integrated day-ahead scheduling scheme that is formulated as a mixed integer second-order cone programming problem to obtain the optimal solution by means of the relaxed power flow model (RPFM). The detailed technical constraints for all the elements are accommodated based on the RPFM-based optimization method. Meanwhile, active management cost and punishment cost of wind power curtailed and customer energy not supplied are also considered in the design objectives of this paper. In order to address the uncertainties, a stochastic robust optimization method is first introduced to decide the active management elements (including capacitor bank, electrical storage system, controllable load, and switch) as the robust decision scheme. Afterwards, the column-and-constraint generation algorithm is applied to solve the proposed stochastic robust two-stage optimization model. Numerical results based on the IEEE 33-bus, PG&E 69-bus, and practical 152-bus systems are obtained to verify the effectiveness of the proposed method.

Distributionally robust single machine scheduling with the total tardiness criterion

This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of each job is assumed to be an unknown random variable within a given distributional set, which is described by mean and variance information. The proposed DRO model aims to find an optimal sequence that minimizes the expected worst-case total tardiness. To the best of our knowledge, it is the first time in the relevant literature that a DRO approach is adopted to minimize the total tardiness criterion for machine scheduling. An explicit expression is derived as an upper bound approximation for the robust objective, and then we transform the DRO problem into a mixed integer second-order cone programming problem. To solve this problem, a branch-and-bound algorithm with several novel bounding procedures and dominance rules is designed. Computational experiments confirm that the bounding procedures and dominance rules contribute significantly to the algorithm’s efficiency, and problem instances with up to 30 jobs can be optimally solved within 40 s. To tackle large-scale problem instances, we further design a beam search algorithm with filtering and recovering phases. Additional experiments with instances beyond 30 jobs confirm the efficacy of this beam search algorithm. To test the effectiveness of the proposed DRO model, we compare the robust sequences to nominal sequences under different processing time distributions. Experimental results show that the robust sequences perform better than nominal sequences, especially when the due dates are relatively loose.

Value of Distribution Network Reconfiguration in Presence of Renewable Energy Resources

Proliferation of renewable energy resources in distribution networks has captured distribution companies' attention towards more active management tools. Thanks to the smart grid paradigm, hourly network reconfiguration, which is still among immature ideas, can bring the activeness required to handle fluctuating output of renewable resources. The aim of this study is to analyze the worthiness of the hourly reconfiguration in the presence of renewable energy resources. For doing so, a mathematical model is devised to minimize daily network losses via applying hourly reconfigurations. The model is a mixed integer second-order cone programming problem and is solved via MOSEK solver. The electrical demand variations as well as renewable power generation fluctuations during a day are taken into account. The proposed method is applied to the Baran 33-bus system and the results including a great deal of sensitivity analyses on key parameters are presented and discussed.

A New Mathematical Model for the Restoration Problem in Balanced Radial Distribution Systems

This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions.

A minisum location problem with regional demand considering farthest Euclidean distances

We consider a continuous multi-facility location-allocation problem that aims to minimize the sum of weighted farthest Euclidean distances between (closed convex) polygonal and/or circular demand regions, and facilities they are assigned to. We show that the single facility version of the problem has a straightforward second-order cone programming formulation and can therefore be efficiently solved to optimality. To solve large size instances, we adapt a multi-dimensional direct search descent algorithm to our problem which is not guaranteed to find the optimal solution. In a special case with circular and rectangular demand regions, this algorithm, if converges, finds the optimal solution. We also apply a simple subgradient method to the problem. Furthermore, we review the algorithms proposed for the problem in the literature and compare all these algorithms in terms of both solution quality and time. Finally, we consider the multi-facility version of the problem and model it as a mixed integer second-order cone programming problem. As this formulation is weak, we use the alternate location-allocation heuristic to solve large size instances.

Optimal Allocation of Dispersed Energy Storage Systems in Active Distribution Networks for Energy Balance and Grid Support

Dispersed storage systems (DSSs) can represent an important near-term solution for supporting the operation and control of active distribution networks (ADNs). Indeed, they have the capability to support ADNs by providing ancillary services in addition to energy balance capabilities. Within this context, this paper focuses on the optimal allocation of DSSs in ADNs by defining a multi-objective optimization problem aiming at finding the optimal trade-off between technical and economical goals. In particular, the proposed procedure accounts for: network voltage deviations; feeders/lines congestions; network losses; cost of supplying loads (from external grid or local producers) together with the cost of DSS investment/maintenance; load curtailment; and stochasticity of loads and renewables productions. The DSSs are suitably modeled to consider their ability to support the network by both active and reactive powers. A convex formulation of ac optimal power flow problem is used to define a mixed integer second-order cone programming problem to optimally site and size the DSSs in the network. A test case referring to IEEE 34 bus distribution test feeder is used to demonstrate and discuss the effectiveness of the proposed methodology.