Power Flow Constraints Research Articles

An Iterative Two-Layer Optimization Charging and Discharging Trading Scheme for Electric Vehicle Using Consortium Blockchain

This paper introduces the concept of hierarchical and zonal scheduling and proposes an iterative two-layer model to optimize the charging and discharging trading of electric vehicles (EVs), so as to minimize the overall load variance of the distribution network under the constraints of power flow and vehicle travel demand. In order to solve the mixed-integer programming (MIP) problem that exists in this model, an improved heuristic algorithm, the adaptive inertia weight krill herd (KH) algorithm is proposed. In addition, we design a decentralized trading architecture and related electricity trading process based on the consortium blockchain to ensure the security and privacy of two-way electricity trading between EVs and the smart grid. The IEEE nodes based simulation experiment shows that our scheme can effectively smooth power load fluctuations, and the improved KH algorithm can effectively improve the efficiency of model solving. Security analysis qualitatively proves that our scheme can ensure the security and privacy-preserving of electricity trading. Finally, our scheme is implemented in the Hyperledger Fabric to evaluate the feasibility and effectiveness.

Matrix Completion for Low-Observability Voltage Estimation

With the rising penetration of distributed energy resources, distribution system control and enabling techniques such as state estimation have become essential to distribution system operation. However, traditional state estimation techniques have difficulty coping with the low-observability conditions often present on the distribution system due to the paucity of sensors and heterogeneity of measurements. To address these limitations, we propose a distribution system state estimation algorithm that employs matrix completion (a tool for estimating missing values in low-rank matrices) augmented with noise-resilient power flow constraints. This method operates under low-observability conditions where standard least-squares-based methods cannot operate, and flexibly incorporates any network quantities measured in the field. We empirically evaluate our method on the IEEE 33- and 123-bus test systems, and find that it provides near-perfect state estimation performance (within 1% mean absolute percent error) across many low-observability data availability regimes.

Energy Market Management for Distribution Network with a Multi-Microgrid System: A Dynamic Game Approach

This paper proposes an energy market management framework to address the day-ahead optimization of a distribution network (DN) with a multi-microgrid (MMG). In this framework, an economic optimization based on a dynamic game is designed to ensure the reliability and stability of the DN operation while setting the internal transaction price to minimize the operation cost of the distribution network operator (DNO). The DNO, as a leader, sets the power flow constraints and microgrid operators (MGOs), as followers, respond to the internal transaction price and in turn affect the DNO’s price decision. The price incentive mechanism of the DNO is to encourage MGs to participate in energy market management, to promote joint operation of MGs and to reduce the operation cost of MGOs. The differential evolution algorithm and mixed integer programming method are applied to find the equilibrium solution to the dynamic game. Numerical simulations of a modified IEEE 33-bus system show the effectiveness of the proposed energy market management framework.

Flexible operation of grid‐connected microgrid using ES

This study presents a new solution to cope with the intermittent nature of renewable generations (RGs) and facilitate the integration of RGs in the smart active distribution network. Electric spring (ES) as one of the most influential solutions in demand-side management is proposed as a flexible resource for flexible operation of grid-connected microgrid against other sources of uncertainty such as forecasted load demand and energy price as well as the RGs output. This innovative approach has been considered in the context of a stochastic problem by presenting the static model of ES for the first time. The modelling of uncertainties is done by the roulette wheel mechanism as a scenario generation process and backward method for reducing the number of scenarios. In the proposed optimisation problem, the objective function is minimising the operating cost and voltage deviation as well as maximising system flexibility, subject to the AC power flow, ES and RGs constraints and technical system limitations. Finally, the proposed solution is tested on 33-bus IEEE test system by the general algebraic modelling system software. The case studies demonstrate the efficiency of the proposed ES model in different simulation and experimental cases in providing flexi-renewable microgrid.

An efficient technique‐based distributed energy management for hybrid MG system: A hybrid QOCSOS‐RF technique

AbstractThis paper proposes an efficient hybrid approach–based energy management strategy (EMS) for grid‐connected microgrid (MG) system. The primary objective of the proposed technique is to reduce the operational electricity cost and enhanced power flow between the source side and load side subject to power flow constraints. The proposed control scheme is a consolidated execution of both the random forest (RF) and quasi‐oppositional‐chaotic symbiotic organisms search algorithm (QOCSOS), and it is named as QOCSOS‐RF. Here, the QOCSOS can have the capacity to enhance the underlying irregular arrangements and joining to a superior point in the pursuit space. Likewise, the QOCSOS has prevalence in nonlinear frameworks due over the way that can insert and extrapolate the arbitrary information with high exactness. Here, the required load demand of the grid‐connected MG system is continuously tracked by the RF technique. The QOCSOS optimized the perfect combination of the MG with the consideration of the predicted load demand. Furthermore, in order to reduce the influence of renewable energy forecasting errors, a two‐strategy for energy management of the MG is employed. At that point, proposed model is executed in MATLAB/Simulink working platform, and the execution is assessed with the existing techniques.

Voltage Security-Constrained Optimal Generation Rescheduling for Available Transfer Capacity Enhancement in Deregulated Electricity Markets

Modern utilities are forced to operate very close to their loadable limits (maximum capacity) due to geographical, economical and some technical reasons. The deregulation of the power industry, the competitive nature of modern electricity markets and the continuous quest for modernization of cities and hamlets all over the world has also led to fast increase in the load demand. The stability of power systems all over the world are threatened with recurrent occurrences of voltage stability issues. Hence, Inter-zonal energy transactions between willing supplier and buyers need to be done with adequate consideration for power system security. In this work, a voltage security-constrained optimal generator active and reactive power rescheduling is carried out using the IEEE 30 and IEEE 57 bus systems. The simultaneous maximization of available transfer capacity (ATC) and voltage stability margin (VSM), using the weighted sum approach, is the objective function. Credible optimal power flow and power system security constraints are considered. Three variants of particle swarm optimization in MATLAB® are used in this work for analyzing the results for objectivity. The technical and economic benefits of the optimal generator rescheduling on the system’s ATC, VSM, line losses, line flow and voltage profile are adequately analyzed.

Reduced and aggregated distribution grid representations approximated by polyhedral sets

In this paper we present a novel tractable method to compute reduced and aggregated distribution grid representations that provide an interface in the form of active and reactive power (PQ) capability areas for improving transmission service operator – distribution service operator (TSO–DSO) interactions. Based on a lossless linear power flow approximation we derive polyhedral sets to determine a reduced PQ operating region capturing all voltage magnitude and branch power flow constraints of the entire distribution grid. To demonstrate the usefulness of our method, we compare the capability area obtained from the polyhedral approximation with an area generated by multiple optimal power flow (OPF) solutions for different distribution grids. While the approximation errors are reasonable, especially for low voltage (LV) grids, the computational complexity to compute the PQ capability area can be significantly reduced with our proposed method.

A Robust Optimal Coordinated Droop Control Method for Multiple VSCs in AC–DC Distribution Network

AC–DC hybrid distribution network is viewed as a featured system to efficiently connect to all kinds of power sources and loads. In order to improve the system robustness, adapting to random fluctuations of renewable energy sources, this paper proposed a robust optimal coordinated control method for multiple voltage source converters (VSCs) in AC–DC distribution network. A robust optimization model was established to co-optimize the slopes of active and reactive power droop control of VSCs with the aim to minimize the total network loss, while ensuring the system security. VSC capacity coupling and power flow constraints were both considered. Then, to enhance the computational tractability of the problem, based on the column-and-constraint generation algorithm, ${V^2} - P$ and ${V^2} - Q$ were implemented in the droop control schemes holding the linear feedback characteristic so that the non-convex max–min sub-problem can be transformed into a mixed integer second-order cone (SOC) programming problem. Furthermore, to increase the accuracy of SOC relaxation in the sub-problem, a current limit strategy was designed where the maximum possible network loss was pre-identified to restrain the feasible range of branch current. Numerical experiments suggest that the proposed coordinated control method can improve the system security with little extra economic cost, and the reliability of the results is enhanced by the proposed current limit strategy.

Closure on “Piecewise Linearization of Quadratic Branch Flow Limits by Irregular Polygon”

This paper focusses on the linearization of apparent power flow constraint (APFC) and the polyhedral approximations of second-order cone. The analysis presented in the paper is based on theoretical error (α=e r /S) and not on the absolute error tolerance (e r ) where S is apparent power limit. α is not a great measure to work with. The IEEE-39 bus system has transmission lines capacity ranging from 480 MVA to 1800 MVA. The difference in the objective value is negligible when the irregular polygon method (IPM) is used in comparison to regular polygon method when compared with e r = 0.01 MVA for IEEE-30 bus and IEEE-118 bus systems. The linear optimal power flow (OPF) is very useful in solving transmission expansion planning (TEP) problems. This work can be improved via inclusion of reactive power and voltage using linear OPF with 1PM in deterministic TEP problems.

Grasshopper Optimization Algorithm on Combined Economic Emission Dispatch Problem Involving Cubic Functions

In this paper, grasshopper optimization algorithm is presented to resolve the combined economic emission dispatch (CEED) problem involving cubic functions considering power flow constraints. Electric power system wants to satisfy its customers load demand with minimum fuel cost and emission. Fuel cost and emission has instantly association with energy cost. In CEED problem, the price penalty factor occupies a cardinal role to fetch the optimal results. The various types of price penalty factor available in the literature are analyzed to determine the optimal one for the test cases considered. The test systems used in this CEED problem are 3 unit system considering transmission loss and 13 unit system considering valve point effects. The leading requirement in both the test cases is to optimize the total cost, fuel cost and emission. The numerical and statistical results affirm the high degree of the solution founded by GOA and its superiority is compared with already existing algorithms employed in solving CEED problems.

Research on Double-Layer Optimized Configuration of Multi-Energy Storage in Regional Integrated Energy System with Connected Distributed Wind Power

With the wide application of multi-energy storage technology in the regional integrated energy system, the configuration of multi-energy storage devices is expected to enhance the economic benefits of regional integrated energy systems. To start with, in this paper, the basic framework of the regional integrated energy system is constructed, and a mathematical model of micro-gas turbine, gas boiler, distributed wind power and multi-energy storage device is established. Then, the multi-energy storage and double-layer planning configuration model with multi-energy complementation is established. The upper level of the model aims to minimize the comprehensive investment cost of multi-energy storage, while the lower level of the model aims to minimize the comprehensive systematic operating cost, in which the net losses cost is also included and the required multi-energy storage capacity from the upper level is set as its constraint. During the programming and problem solving, the second-order conic relaxation technology is introduced to realize the convex relaxation for power flow constraint. At the same time, the piecewise linearization method is adopted to deal with the natural gas pipeline flow constraint, which can convert the original model into a mixed integer programming problem. In the end, the example analysis is carried out in the IEEE 33-bus system and the improved 6-node natural gas system. The results show that the multi-energy storage technology can improve the economics of the regionally integrated energy system to a certain extent, and have verified the validity of the model.

Mixed‐integer second‐order cone programming framework for optimal scheduling of microgrids considering power flow constraints

Microgrids have been recognised as one of the most promising but challenging research topics over the last decade. The optimal energy scheduling problem is regarded as the most essential aspect in the tertiary level control in microgrids. However, most existing centralised or distributed scheduling models only focus on the logical and dynamical feature of microgrids’ operation or the non-linear power flow constraint, which would overact the system performance without considering appropriate unit commitment requirements. Moreover, applying decomposition and iteration technics to complex scheduling problems would encounter convergence issues. To address this concern, this study presents a mixed integer linear reformulation to characterise the operation of different controllable devices and convex relaxation techniques to cope with non-linear power flow constraints, leading to a mixed integer second-order cone programming framework in a concordant yet computationally efficient pattern, capturing non-linear, logical and dynamical properties of the optimal energy scheduling problem in microgrids. The effectiveness of the proposed framework is validated on the IEEE 33-bus distribution network with both grid-connected and islanded modes.

Hour-Ahead Energy Trading Management with Demand Forecasting in Microgrid Considering Power Flow Constraints

Multiple small-scale low-voltage distribution networks with distributed generators can be connected in a radial pattern to form a multi-bus medium voltage microgrid. Additionally, each bus has an independent operator that can manage its power supply and demand. Since the microgrid operates in the market-oriented mode, the bus operators aim to maximize their own benefits and expect to protect their privacy. Accordingly, in this paper, a distributed hour-ahead energy trading management is proposed. First, the benefit optimization problem of the microgrid is solved, which is decomposed into the local benefit optimization sub problems of buses. Then, the local sub problems can be solved by the negotiation of operators with their neighbors. Additionally, the reference demand before negotiation is forecasted by the neural network rather than given in advance. Furthermore, the power flow constraints are considered to guarantee the operational stability. Meanwhile, the power loss minimization is considered in the objective function. Finally, the demonstration and simulation cases are given to validate the effectiveness of the proposed hour-ahead energy trading management.

Towards Resilient Operation of Multimicrogrids: An MISOCP-Based Frequency-Constrained Approach

High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in microgrids is one of the main challenges in this context. To address this challenge, this paper proposes a comprehensive optimization and real-time control framework for maintaining frequency stability of multi-microgrid networks under an islanding event and for achieving optimal load shedding and network topology control with AC power flow constraints. The paper also develops a strong mixed-integer second-order cone programming (MISOCP)-based reformulation and a cutting plane algorithm for scalable computation. We believe this is the first time in the literature that such a framework for multi-microgrid network control is proposed, and its effectiveness is demonstrated with extensive numerical experiments.

Flexibility Planning of Distributed Battery Energy Storage Systems in Smart Distribution Networks

The deployment of batteries in the distribution networks can provide an array of flexibility services to integrate renewable energy sources (RES) and improve grid operation in general. Hence, this paper presents the problem of optimal placement and sizing of distributed battery energy storage systems (DBESSs) from the viewpoint of distribution system operator to increase the network flexibility. The problem is formulated as an optimization framework wherein the objective function is to minimize the annualized sum of investment costs and operational costs of DBESSs while it is constrained to power flow, DBESS and RES constraints as well as distribution network operation limits. In addition, while the problem model is as nonlinear programming, this paper suggests an equivalent linear programming model for all constraints and quadratic formulation for the objective function to reach the global optimal solution with low error calculation. In the next step, the Benders decomposition approach is deployed to acquire better calculation speed. Finally, the proposed problem is applied to 19-bus LV CIGRE benchmark grid by GAMS software to investigate the capability of the model.

Solving constrained optimal power flow with renewables using hybrid modified imperialist competitive algorithm and sequential quadratic programming

The objective of this paper was to develop and solve different constrained optimal power flow (OPF) problems for hybrid power systems containing renewable energy sources like wind energy and solar power. OPF seeks to optimize the transmission of electric power by finding a steady state operating point that minimizes gas emission and cost of generated electric power without disturbing network power flow, operating limits and system constraints. The OPF problem was solved using a hybrid modified imperialist competitive algorithm and sequential quadratic programming, (HMICA-SQP). Efficacy of the modified imperialist competitive algorithm (MICA) is further enhanced by the process of hybridization with the sequential quadratic programming (SQP) for rapid local refinement and improved precision of the solution. The potential and effectiveness of the proposed metaheuristic were presented and assessed using three benchmark test systems IEEE 30, IEEE 57 and IEEE 118-bus power systems that incorporates several solar and wind energy sources. Comparison of simulation results with recently published optimization approaches solutions showed that the suggested paradigm is more efficient, robust and provides the lowest cost of generated electric power while keeping low emissions.

Deliverable Energy Flexibility Scheduling for Active Distribution Networks

This paper proposes a fundamental model for defining and optimizing distributed energy flexibility in distribution buses, as well as deliverable energy flexibility as the aggregate distributed flexibility that is available for offering to the day-ahead energy market by distribution system operators (DSOs), without jeopardizing the operational constraints of the distribution network. The distributed energy flexibility is provided by flexible loads in distribution buses, which are modeled by clustered queuing systems representing the aggregation of large population of flexible loads with different energy and service quality requirements. Further, controllable inverters interfacing distributed solar generation provide reactive power flexibility in distribution buses. The deliverable energy flexibility is optimized by the proposed model that coordinates the energy flexibility of queued flexible loads and controllable inverters to maximize DSO’s profit of participating in the day-ahead energy market, while satisfying the service quality constraints of flexible loads, the operational limits of controllable inverters, and power flow constraints of distribution network that are formulated using the branch flow model. Moreover, an index is proposed to calculate the contribution of each distribution bus in providing the deliverable energy flexibility. The proposed model is implemented on the IEEE 33-bus distribution network. The numerical results exhibit profit opportunities for DSOs from providing the deliverable energy flexibility in the day-ahead energy market.

The Optimal Power Flow Operator: Theory and Computation

Optimal power flow (OPF) problems are mathematical programs to determine how to distribute power over networks subject to power flow and operational constraints. In this article, we treat an OPF problem as an operator that maps user demand to generated power, and allow the problem parameters to take values in some admissible set. We formalize this operator theoretic approach, define and characterize restricted parameter sets under which the mapping has a singleton output, independent binding constraints, and is differentiable. We show that for any power network, these analytical properties hold under almost all operating conditions and can thus be relied upon in applications. We further provide a closed-form expression for the Jacobian matrix of the OPF operator and describe how various derivatives can be computed using a recently proposed scheme based on homogenous self-dual embedding. In contrast to related work in the optimization literature, our results have a clear physical interpretation.

Dynamic Energy Management of a Microgrid Using Approximate Dynamic Programming and Deep Recurrent Neural Network Learning

This paper focuses on economical operation of a microgrid (MG) in real-time. A novel dynamic energy management system is developed to incorporate efficient management of energy storage system into MG real-time dispatch while considering power flow constraints and uncertainties in load, renewable generation and real-time electricity price. The developed dynamic energy management mechanism does not require long-term forecast and optimization or distribution knowledge of the uncertainty, but can still optimize the long-term operational costs of MGs. First, the real-time scheduling problem is modeled as a finite-horizon Markov decision process over a day. Then, approximate dynamic programming and deep recurrent neural network learning are employed to derive a near optimal real-time scheduling policy. Last, using real power grid data from California independent system operator, a detailed simulation study is carried out to validate the effectiveness of the proposed method.

Multi-time Scale Scheduling Strategy for Power System with Large-scale Intermittent Energy

Large-scale integration of intermittent energy has brought many problems to active power dispatching of the power grid, which will not only increase the operation cost, but also increase the operation risk. This paper developed a multi-time scale scheduling strategy, integrated day-ahead scheduling, intra-day dispatching and automatic generation control (AGC) system, in order to ensure the safe and stable operation of power grid. The strategy aims to minimize the sum of operating costs of power system, and sets six constraints such as power flow constraint, to analyse and optimize the dispatching process of power systems. After simulation and analysis by Particle Swarm Optimization (PSO) algorithm, the results show that the strategy has a significant optimization on the power system with intermittent energy.