Power Flow In Distribution Networks Research Articles

On the Solution of the Optimal Power Flow for Three-Phase Radial Distribution Networks With Energy Storage

We study a multiperiod optimal power flow (OPF) problem in unbalanced three-phase radial distribution networks with batteries. To address this problem, we first take the resistance-line battery model that treats lossy batteries by adding resistive lines and virtual buses. Then, we derive a linearization for the power flow equations, called generalized three-phase simplified DistFlow, which accounts for shunt elements. Also, it is exact at a freely chosen point while having globally good performance. Using it, we extend the heuristic iterative OPF algorithm, CoDistFlow, to unbalanced three-phase networks. At convergence, three-phase CoDistFlow gives a solution that satisfies the exact nonlinear power-flow equations and the exact security constraints. To theoretically guarantee the convergence of three-phase CoDistFlow, we develop the forced convergent three-phase CoDistFlow. Moreover, we show how to adapt the three-phase CoDistFlow to solve a scenario-based OPF in the presence of uncertainties, whereas other existing OPF solution methods may not offer this possibility. Finally, we perform evaluations on the IEEE 123-bus test feeder and comparisons with Ipopt.

Surrogate-Assisted Multi-Objective Probabilistic Optimal Power Flow for Distribution Network With Photovoltaic Generation and Electric Vehicles

The uncertainties of solar photovoltaics generation, electric vehicle charging demand, and home appliances load are the major challenge of energy management planning in the residential areas. Optimal allocation of battery energy storage systems for distribution networks based on probabilistic power flow (PPF) is an effective solution to deal with these uncertainties. However, the high computational burden is the main obstacle of this method. Therefore, this paper proposes a surrogate-assisted multi-objective probabilistic optimal power flow (POPF) to reduce the expensive computational time. The surrogate model is developed by using a machine learning method namely deep learning which is used for bypassing the deterministic load flow calculation. Zhao’s point estimation method combined with Nataf transformation is selected to handle the PPF analysis considering correlated uncertain input variables. The multi-objective POPF problem is solved using the multi-objective differential evolution. The historical data including solar irradiation, ambient temperature, residential load, and electric vehicle (EV) travel distance is calculated in the low voltage distribution system to demonstrate the potential advantages of the proposed method. Numerical results show that the proposed surrogate assisted multi-objective POPF method provides the optimal solution for operating cost, helps to prolong transformer life and reducing environmental impact. Moreover, the results show that the proposed surrogate-assisted optimization framework gives a better solution when comparing with the conventional surrogate-assisted method.

The Impact of Uncertainty and Time Structure on Optimal Flexibility Scheduling in Active Distribution Networks

The authors focus on a model for system operators that uses centralized scheduling of multiple flexibility assets and services to minimize the cost of managing problems with grid congestion, voltages, and losses. The model schedules flexibility assets using stochastic optimization for AC optimal power flow in an active distribution network. The novelty of the contribution lies in its focus on how the dynamic capabilities of the flexibility resources are defined with regard to how uncertainty is resolved in the model. The impact of uncertainty is studied by using well-known quality measures from stochastic programming, such as the value of the stochastic solution. Moreover, the authors introduce a new measure related to the impact of representing uncertainty and flexibility when considering reactive power. By changing the time attributes of flexibility assets, the authors show the impact of uncertainty and time structure on a scheduling problem. The uncertainties considered are price and load levels. The findings reveal that the quality of the scheduling of each flexibility resource depends on using a stochastic model with a rigorous consideration of time and uncertainty.

Power Flow Calculation of Distribution Network With Multiple Energy Routers

Energy router is an emerging device based on power electronic technology, which can realize the flexible distribution of electric energy in the power system. Therefore, the use of energy routers to improve the operating conditions of the power system not only has broad development prospects, but also brings economic benefits. In this regard, this paper proposes a steady-state model of a single energy router and considers the loss of the DC/DC transformer, establishes a power flow equation with multiple energy routers, and proposes a distribution network power flow alternate iteration that takes into account multiple energy routers Calculation method. A case study of an improved IEEE-33 system with multiple energy routers under different working conditions is carried out. The calculation results show that the alternate iterative power flow calculation method used in this paper is effective and feasible, and it reasonably reflects that the network analysis model with multiple energy routers can achieve stable operation, and it can improve the node voltage and reduce the active power loss of the grid. It makes the operation of the distribution network more flexible.

A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.

Optimal power flow in distribution networks under stochastic [formula omitted] disruptions

It is important to include contingencies in operations and have a post-contingency recovery plan for distribution systems, akin to transmission systems. We consider a multi-period optimal power flow (OPF) problem in distribution systems subject to stochastic N−1 contingency (disruption) in a distribution line or a distributed energy resource. The disruption is stochastic in nature, a type of infrequent event with random magnitude and timing, and that every disruption typically has an associated recovery time. We formulate a multi-stage stochastic convex program, considering modeling features like linearized AC power flow physics, engineering limits and battery devices with efficiencies curves, and develop an efficient decomposition algorithm. We demonstrate the computational effectiveness of our algorithm over the extensive formulation and show that the stochastic-disruption-aware operating costs can be 60% cheaper than the deterministic counterparts.

OPEN: An open-source platform for developing smart local energy system applications

This paper presents OPEN, an open-source software platform for integrated modelling, control and simulation of smart local energy systems. Electric power systems are undergoing a fundamental transition towards a significant proportion of generation and flexibility being provided by distributed energy resources. The concept of ‘smart local energy systems’ brings together related strategies for localised management of distributed energy resources, including active distribution networks, microgrids, energy communities, multi-energy hubs, peer-to-peer trading platforms and virtual power plants. OPEN provides an extensible platform for developing and testing new smart local energy system management applications, helping to bridge the gap between academic research and industry translation. OPEN combines features for managing smart local energy systems which are not provided together by existing energy management tools, including multi-phase distribution network power flow, energy market modelling, nonlinear energy storage modelling and receding horizon optimisation. The platform is implemented in Python with an object-oriented structure, providing modularity and allowing it to be easily integrated with third-party packages. Case studies are presented, demonstrating how OPEN can be used for a range of smart local energy system applications due to its support of multiple model fidelities for simulation and control.

Analysis of the Influence of Electric Vehicle Access on the Power Flow and Voltage of Distribution Network

Due to the load characteristics of electric vehicles (EVs), a large number of charging and replacing power stations connecting to the power grid will have certain influence on the power grid. Therefore, it is necessary to study the impact of EV access on the distribution network power flow and voltage. This paper analyzes the charging and discharging behavior characteristics of electric private cars and the influence factors of vehicle charging load, and proposes a charging method modeling method for EVs considering different charging and discharging behaviors. This method can simulate the charging behavior habits of EV users. According to the data of private car travel in a city in 2018, taking the IEEE33 node system as an example, the distribution network model of EV access was established by using MATLAB software. This paper analyzes the influence of EV access on the distribution network under two charging modes, including transformer load, line current and node voltage, which provides references for the development planning of EV and the coping strategy of the power grid.

Open Capacity Enhancement Model of Medium Voltage Distribution Network With Mobile Energy Storage System

In order to meet the demand of prosumer for power quality and new load in distribution network, an open capacity expansion model of distribution network with mobile energy storage system (MESS) is proposed in this paper. The model gives priority to the problem of voltage violation of prosumer group on feeders. Combined with the mobile energy storage path model, the open capacity of distribution network is calculated. Firstly, the actual distribution network geographic information and traffic routes are combined to establish the distribution network model based on mesh generation. Secondly, the traffic route model of the mobile energy storage system is established on the distribution network model based on mesh generation. Then, the optimal power flow of distribution network is calculated with the optimal network loss, and the mobile energy storage system is scheduled according to the situation of voltage violation. And the specific vehicle model and its scheduling are determined, which can better deal with the problem of distributed energy consumption and make prosumer operate safely and economically. Finally, according to the proposed N-1 security check constraint of distribution network with mobile energy storage system, the maximum open capacity of distribution network is calculated after the voltage regulation is completed. The example shows the practicability and correctness of the model in this paper. This paper formulates a mobile energy storage operation strategy to improve the open capacity of distribution network. The strategy not only fully meets users' needs, but also better guides the operation of power grid. It is conducive to releasing more potential power supply space of distribution network and improving asset utilization.

An Interval Mapping Model of Power/Uncertain Voltage Response and Its Application in Overvoltage Prevention Control

Intermittent distributed generation and stochastic loads cause uncertainty in power flow in distribution networks. To construct the relationship between power injections and node voltages over a long time scale and a wide operational region, an interval mapping model is proposed in this paper, which is composed of multiple affine power flow calculations and interval regression via quadratic programming. An acceleration mechanism using parallel processing and iterative acceleration is designed to improve modeling efficiency. The application of the interval model in overvoltage prevention coordinated control is further discussed. Numerical results tested by a modified IEEE 33-bus system demonstrate that the interval mapping model has good performance in assessing the impact boundaries of power injections on uncertain voltage responses. The acceleration mechanism for the modeling process gives the interval mapping model the potential for online application; the effect of overvoltage prevention control in simulation further shows its practical value.

Impact of Distributed Generation on Network Reconfiguration for Power Loss Minimization in Radial Distribution System by Hybrid Algorithm

Feeder reconfiguration is a planning to change the system configuration by altering the existing tie-line and sectionalizing switches status for minimizing the system losses. Hence, the network reconfiguration is essential in distribution system to minimizing system power losses. Reduction of power loss is much considerable role in power flow of distribution network in evaluating system performance. There are several methods have been proposed for reduction of system power losses and voltage improvement. This paper mainly employs feeder reconfiguration for power loss minimization and voltage improvement using opening and closing tie line and sectionalizing switches by hybrid binary particle swarm and cuckoo search algorithm. As a consequence in this operation, there is significant improvement of voltage profile, freeing up and power loss minimization. The system performance is evaluated and tested in 33 bus system, and simulation is carried out using Matlab simulation platform. For optimal switching strategy, the cuckoo search and hybrid particle swarm optimization algorithm are implemented and showed better improvement in voltage profile, minimization of real power loss and percentage of power loss reduction.

A per-node granularity decentralized optimal power flow for radial distribution networks with PV and EV integration

With the large scale of distributed energy resources integrated into distribution systems, the development of effective power management for controllable components is becoming an increasingly important concern. This paper focuses on solving the optimal power flow problem in a distribution network with a fully decentralized mode that has massive photovoltaics and electric vehicles. First, an optimal power flow model considering photovoltaics and electric vehicles as controllable agents was established to achieve low network loss, low curtailment of photovoltaic resources, and high satisfaction of electric vehicle owners. Second, a novel linearized power flow model was proposed to produce per-node granularity communication. Thus, each node only needed to exchange the voltage message with its neighboring nodes. Then a decentralized quadratically constrained quadratic programming model based on the alternating direction method of multipliers was built to solve the optimal power flow problem. Next, a closed-form iterative solution method for the decentralized optimization was developed to improve the calculation speed for each iteration. Finally, case studies for a real 35-bus distribution system and a real 110-bus distribution system in China were used to verify the effectiveness of the proposed method.

A high-frequency-link voltage matching phase-shift control strategy for high-frequency modular multilevel DC transformer in MVDC distribution networks

High-frequency modular multilevel DC transformer (MMDCT) plays an important role in the bus connection, voltage conversion and power transmission in MVDC distribution networks. However, the variation of power flow in distribution network leads to the high-frequency-link (HFL) voltages in MMDCT mismatch the HFL transformer voltage ratio, resulting in the increase of circulating power and current stress, and the decrease of power factor and efficiency in M2DCT. To solve this problem, a HFL voltage matching phase-shift control (VMPC) strategy for MMDCT is proposed in this paper. Different with the traditional phase-shift control (TPC), the proposed VMPC adjusts the HFL voltages by varying the number of inserted sub-modules (SMs) in real-time, ensuring the HFL voltages match the HFL transformer voltage ratio in the whole operating range, resulting in the improvement of efficiency and performance. The detailed operation principle, control architecture and corresponding capacitor voltage balance algorithm of VMPC are investigated. On this basis, the improvements on the current stress, power factor and efficiency of MMDCT under the proposed VMPC are also analyzed. The experiment results verify the correctness and effectiveness of the analysis and proposed strategy.

Chance-Constrained Frequency Regulation with Energy Storage Systems in Distribution Networks

One of the applications of energy storage systems (ESSs) is to support frequency regulation in power systems. In this paper, we consider such an application and address the challenges of uncertain frequency changes, limited energy storage, as well as distribution network constraints. We formulate a bi-level optimization problem that includes the operation objectives of the system operator and the ESSs, using chance constraints to account for uncertain frequency changes. The frequency regulation decision of the system operator depends on the ESSs decision to participate in the regulation service as well as the distribution network constraints. Due to the interdependencies between the ESSs demand fluctuations and the distribution network power flow changes, the system operator requires the ESSs’ operation information for frequency regulation decisions, which may not be available from the ESSs. Therefore, we propose a decentralized algorithm such that the system operator and the ESSs can pursue their own operation objectives, while ensuring the distribution network constraints are satisfied. We evaluate the performance of our method on IEEE 37-bus and 123-bus test feeders by considering combinations of ESSs with different sizes. Simulation results demonstrate that our approach can successfully coordinate the ESSs to regulate the frequency deviations.

A survey of power flow calculations considering distributed generation

With the construction of China’s smart grid and the gradual implementation of the power market, the traditional centralized power grid mode has been unable to meet the demand of electricity in today’s society. The introduction of distributed generation has become a new trend in the future development of power grids. Due to the introduction of distributed generation, many new node types will appear in the distribution network. It is often difficult to achieve the expected results when using traditional power flow algorithms when dealing with these nodes. Therefore, it is particularly important to study the power flow calculation of distribution networks with distributed generation. This paper discusses in detail the impact of distributed power sources on distribution networks and the current research status of distribution network power flow calculations with distributed generation.

Mobile model for distributed generations and battery energy storage systems in radial grids

In this paper, mobile distributed generations (DGs) and battery energy storage systems (BESSs) are modeled and integrated into the network. The optimal locations of DGs and BESSs are determined for each season over the year, and the installed DG-energy storage system (ESS) may be transferred to new buses at each season. The methodology is simulated on a radial electrical distribution network, and the location, size, and hourly operation of DGs and ESSs are optimized. DC power flow is adopted to model the power flow in the grid. In the DC power flow, the active power losses in the lines and reactive power of the loads are not included. Since the network is radial and the modeling is lossless, it is expected that the DGs and BESSs cannot present their positive abilities efficiently. Four cases are simulated including case 1: network without BESSs and DGs; case 2: fixed operation pattern and location for BESSs and DGs under all seasons; case 3: variable operation pattern and fixed location for BESSs and DGs under all seasons; and case 4: variable operation pattern and location for BESSs and DGs under all seasons. The planning installs one 0.0470 p.u. DG and one 0.0202 p.u. BESS on the network, resulting in 0.5 Million $/year reduction in the costs. However, the results verify that changing locations of the DGs and BESSs cannot have significant impacts on the results. This point confirms that the application of DC power flow in radial distribution networks is not suitable and cannot develop all advantages of BESSs and DGs.

Economic dispatch of distribution network with inn for electric vehicles and photovoltaic

Inn for electric vehicles (EVs) and photovoltaic (PV) is a typical integration of EVs locally consuming renewable energy sources (RES), with features of EV charging, energy storage, and RES consumption. In the existing research works, scholars focus on the energy storage system (ESS) as a medium to charge EVs and send back the power to the utility grid and alleviating the information asymmetry between EV owners and grid dispatching agencies with lower costs of distribution network. In this study, a mixed operational mode based on inn for EV and PV with a replaceable EV battery is analysed. The fragmented energy transferring can shift the load more effectively, balance fluctuation of RES, of great significance to optimise the operation of distribution network system. In summary, a comprehensive model of power flow in distribution network with inn for EV and PV is proposed. Based on an improved IEEE 33-node case, the effects of fragmented energy management mode are analysed. Numerical results show that replacing the full-charged battery for EV is more effective for peak load time-shifting and improving consuming of RES power based on the interaction among RES, ESS, and the replaceable EV battery.

Research on Distributed Source-Load Interaction Strategy Considering Energy Router-Based Active Distribution Network

With increasing penetration of distributed generation, surplus energy at some critical buses in distribution network will extremely challenge the stable operation of conventional power system. Energy routers (ERs) can be placed at the critical buses so as to achieve flexible management of power flow in active distribution network. It will offer more flexibility to realize the interaction between source and load. In this paper, energy routers are mainly catalogued as source-type and load-type, and then a novel distributed source-load interaction strategy for energy router based active distribution network is proposed, which only requires information exchange between neighbor routers. The interaction strategy includes three parts: the strategy for source-type ERs, the strategy for load-type ERs and the cooperation strategy for multiple source-type and load-type ERs. Moreover, a novel calculating method of power loss is proposed to make strategies applicable considering reverse and forward power flow. Finally, the correctness and effectiveness of the proposed strategies are verified by comparison with optimal routing paths derived by the typical centralized Dijkstra algorithm in the case study.

Unbalanced power flow algorithm for AC&DC hybrid distribution network with diverse‐controlled VSC‐MTDC converts

The paper aims to propose an algorithm to calculate the power flow of an AC&DC hybrid distribution system. AC&DC distribution networks have recently attracted increasing attention, for the distributed generations (DGs) and DC loads can be integrated in DC networks in more simple and flexible ways than AC networks. Many efforts have been made to deal with the power flow problem of hybrid networks, however, the DC-side power flow's effect on three-phase unbalanced AC side and the influence to entire distribution system which DG directly connected in the DC side are both not considered. Therefore, this paper discusses the grid architecture with multiple AC&DC feeders. Then, models of VSC-MTDC, DC/DC converters, DGs, and other elements are formulated for power flow calculation. Furthermore, power flow equations of DC distribution and VSC converters are deduced in detail. As for converters under different control strategies and diverse forms of linking combinations between AC&DC grids, calculating approaches are considered to be of partial differences. Considering these distinct cases, a specific and improved sequential method is employed to compute distribution network's power flow. Simulation results on a modified IEEE 13 Node Test Feeder demonstrate the rapidity, accuracy, and easy-convergence of the algorithm.

Study on Unbalanced Power Flow in Distribution Network with Distributed Generators of Power Grid

Study on Unbalanced Power Flow in Distribution Network with Distributed Generators of Power Grid