Problems In Distribution Networks Research Articles

Optimal scheduling of variable speed pumps with mixed integer linear programming

ABSTRACT Mixed integer linear programming (MILP) has been gaining traction as a method for solving optimal pump scheduling problems in water distribution networks (WDNs). However, inclusion of variable-speed pumps (VSPs) in MILP pump scheduling frameworks has not been given adequate treatment. This article addresses this gap by describing a methodology for formulating and solving optimal pump scheduling problems with VSPs using MILP and piece-linear approximations of network components. The methodology proceeds in four steps: (a) WDN simulation with initial pump schedule(s), (b) approximation of network components, including VSP, using linear and piece-linear functions around the chosen operating points, (c) formulation of a fully parameterised mixed integer linear programme, and (d) solution of the optimisation problem and WDN simulation with optimal pump schedule(s). The methodology is coded in MATLAB/OCTAVE and Python and is publicly available on GitHub. It was applied to solve a pump scheduling problem on a two variable speed pump single-tank network that allows the reader to easily understand how the methodology works and how it is applied in practice. The results show that the formulation is robust and the optimiser is able to return a globally optimal solution for a range of operating points.

Benders Decomposition-based Coordinated Optimization Method for Medium and Low Voltage Distribution Network with Photovoltaics Access

aims: From the perspective of improving the economic benefit of the distribution network and ensuring the safe operation of the distribution network, the medium and low voltage optimization model with the goal of reducing the operation cost is established. background: Double carbon background and new energy power system policy, a large number of distributed photovoltaic access distribution network caused a great influence, not only on the low voltage distribution network user side power quality impact, photovoltaic full hair also can happen when tide back phenomenon, for the stable operation of the medium voltage distribution network and scheduling, therefore, this paper puts forward a scheduling of the voltage distribution network and low voltage distribution network optimization method, to solve the problems of large-scale distributed photovoltaic access. objective: Reducing operating costs and ensuring the stable and safe operation of the distributed network. method: The optimization problem of medium and low voltage distribution network is decomposed into the main optimization problems of medium voltage distribution network and the sub-problems of optimizing the low-voltage distribution network. An optimal solution is obtained by coordinating the boundary coupling variables between the two problems and solving them iteratively. Finally, the effectiveness of the coordination algorithm is verified by simulating the medium and low voltage distribution network. result: A coordinated optimization method for medium and low voltage distribution network with photovoltaics access. conclusion: It reduces the operation cost, ensures the stable and safe operation of the power grid, thus improving the economic benefits. other: None

Phased optimization of active distribution networks incorporating distributed photovoltaic storage system: A multi-objective coati optimization algorithm

In this study, a phased operation optimization method for active distribution network with energy storage system is proposed for the operation optimization problem of active distribution network. The proposed model considers the PV and storage system output, the number of regulation equipment action, network loss and node voltage deviation for multi-objective optimization of the active distribution network. To achieve multi-objective optimization of the proposed optimal model, this study proposes a multi-objective coati optimization algorithm based on integrated crowding distance ranking, Bernoulli chaotic mapping, external archiving and non-dominated ranking mechanism. The proposed algorithm exhibits good performance as tested by ZDT and UF test functions, and obtaining optimal values in 75 % of the results. In the test of the improved IEEE30 and IEEE33 node system, the proposed method is improved by 21.55 %, 56.10 % and 4.12 % in the three aspects of network loss, node voltage deviation and minimum voltage of the whole network compared with the unoptimized case. Therefore, the proposed method in this study has a good application value for the optimization of active distribution network operation and can support the grid-connected operation of distributed new energy sources.

A Systematic Investigation into the Optimization of Reactive Power in Distribution Networks Using the Improved Sparrow Search Algorithm–Particle Swarm Optimization Algorithm

With the expansion of the scale of electric power, high-quality electrical energy remains a crucial aspect of power system management and operation. The generation of reactive power is the primary cause of the decline in electrical energy quality. Therefore, optimization of reactive power in the power system becomes particularly important. The primary objective of this article is to create a multi-objective reactive power optimization (MORPO) model for distribution networks. The model aims to minimize reactive power loss, reduce the overall compensation required for reactive power devices, and minimize the total sum of node voltage deviations. To tackle the MORPO problems for distribution networks, the improved sparrow search algorithm–particle swarm optimization (ISSA-PSO) algorithm is proposed. Specifically, two improvements are proposed in this paper. The first is to introduce a chaotic mapping mechanism to enhance the diversity of the population during initialization. The second is to introduce a three-stage differential evolution mechanism to improve the global exploration capability of the algorithm. The proposed algorithm is tested on the IEEE 33-node system and the practical 22-node system. The results indicate a reduction of 32.71% in network losses for the IEEE 33-node system after optimization, and the average voltage of the circuit increases from 0.9485 p.u. to 0.9748 p.u. At the same time, optimization results in a reduction of 44.07% in network losses for the practical 22-node system, and the average voltage of the circuit increases from 0.9838 p.u. to 0.9921 p.u. Therefore, the proposed method exhibits better performance for reducing network losses and enhancing voltage levels.

Distributed Energy Resources Based Two-Layer Delay-Independent Voltage Coordinated Control in Active Distribution Network

In order to solve serious voltage problem in active distribution networks and improve the utilization rate of renew-able energy resources, a distributed energy resources (DERs) based two-layer delay-independent voltage coordinated con-trol method is proposed. First, an upper-layer sensitivity-based voltage coordinated control strategy is designed by maximiz-ing the use of residual reactive power and minimizing active power reduction, where reactive power compensation and ac-tive power regulation from the most sensitive DERs are per-formed in a high priority. Then, a lower-layer delay-independ-ent coordinated controller is designed to dynamically regulate the reactive/active power of each DER unit, when communica-tion transmission delays are within allowable range estimated. A robust controller is designed with the local states of DER and the states of other coupling DERs with time delay, thereby overcoming the effects of coupling characteristics among DERs and parameter uncertainties. Finally, simulation results demonstrate the effectiveness of the proposed method.

Optimal dispatching of wind turbine-photovoltaic-pumped storage new energies and thermal generators combined distribution network

This paper mainly investigates the optimal dispatching problem of the combined distribution network consisting of wind turbine generators (WTGs), photovoltaic generators (PVGs), pumped storage generators (PSGs) and thermal generators (TGs). According to the load demand in the distribution network and the output conditions of different renewable energy generators, PSGs and TGs, a joint optimal dispatching model based on the operation cost of the distribution network is set up. Based on the power flow model of second-order cone relaxation (SOCR) technology, the nonlinear constraints on voltage and current in the distribution network are linearized, so as to solve the cost optimization scheduling problem more efficiently. Finally, an improved IEEE33-node distribution network is used as the basic grid model for simulation analysis, so as to verify the effectiveness of the proposed model.

Decentralized robust operation of the unbalanced microgrids in distribution networks: A convex relaxation approach

This work presents a distributed robust operation framework for the microgrids within the power distribution network. It addresses the uncertainties in photovoltaic generation, as well as active, and reactive loads in the network, by modeling them using polyhedral sets. The energy management problems are formulated as two-stage optimization problems in microgrids and power distribution networks for which Benders decomposition is used to solve the problems. The power flow constraints are relaxed using second-order cone relaxation and moment relaxation techniques in the power distribution network and microgrid energy management problems, respectively. The interaction between the microgrids and the power distribution network is represented using the price signal and the exchanged active and reactive power at the microgrids’ points of common coupling. The effectiveness of the proposed framework is shown using two case studies on IEEE 37-bus and IEEE 123-bus systems. The effect of the energy storage system on the operational cost of the system is assessed. It is shown that total operation cost is decreased by 9.69% when the energy storage system is integrated into the power distribution network. Additionally, the solution derived from the robust problem is compared with that of the deterministic problem.

A novel fuzzy programming approach for piece selection problem in P2P content distribution network.

Piece selection policy in dynamic P2P networks play crucial role and avoid the last piece problem. BitTorrent uses rarest-first piece selection mechanism to deal with this problem, but its efficacy is limited because each peer only has a local view of piece rareness. The problem of piece section is multiple objectives. A novel fuzzy programming approach is introduced in this article to solve the multiple objectives piece selection problem in P2P network, in which some of the factors are fuzzy in nature. Piece selection problem has been prepared as a fuzzy mixed integer goal programming piece selection problem that includes three primary goals such as minimizing the download cost, time, maximizing speed and useful information transmission subject to realistic constraints regarding peer's demand, capacity and dynamicity. The proposed approach has the ability to handle practical situations in a fuzzy environment and offers a better decision tool to each peer to select optimal pieces to download from other peers in dynamic P2P network. Extensive simulations are carried out to demonstrate the effectiveness of the proposed model. It is proved that proposed system outperforms existing with respect to download cost, time and meaningful exchange of useful information.

A Game-Theoretic Approach for Electric Vehicle Aggregators Participating in Phase Balancing Considering Network Topology

With the increasing popularity of electric vehicles (EVs), uncontrolled charging of single-phase plug-in EVs will result in severe three-phase unbalance problem in distribution networks. To solve the problem, a phase balancing (PB) scheme performed by EV aggregators (EVAs) based on the linear multiphase power flow model is proposed in this paper. In the scheme, the PB compensations are provided to encourage EVAs to help the distribution system operator reduce the phase unbalance of the entire grid. Considering all EVAs are selfish and rational, the PB scheme is formulated as a game problem, in which each EVA competes with other EVAs to determine its charging strategy to minimize the charging cost minus the PB compensation. The consideration of coupling voltage constraints leads this game model to a challenging generalized Nash equilibrium problem (GNEP). By employing the theory of variational inequality, the properties of solutions for the GNEP are investigated. Furthermore, a two-level distributed algorithm is designed to find the unique variational solution, a fair and stable solution. Finally, comprehensive case studies are conducted on the IEEE-13 and IEEE-123 test systems to corroborate that the proposed PB game model can effectively mitigate voltage unbalance and cut EV users’ costs.

Multi-Criteria Decision Making in Optimal Operation Problem of Unbalanced Distribution Networks Integrated With Photovoltaic Units

Multi-Criteria Decision Making in Optimal Operation Problem of Unbalanced Distribution Networks Integrated With Photovoltaic Units

Probabilistic spatiotemporal scenario generation method for dynamic optimal power flow in distribution networks

Due to the intricate intertwining of spatiotemporal characteristics and the substantial computational complexity caused by high dimensionality, the simultaneous consideration of both spatial and temporal correlations is a non-trivial problem in power system scheduling with variable renewable energy sources. This paper proposes a novel probabilistic spatiotemporal scenario generation (PSTSG) method for the dynamic optimal power flow problem in distribution networks, which generates probabilistic scenarios considering the spatial and temporal correlations among random variables simultaneously. First, static scenarios are generated by Latin hypercube sampling, and the probability of each static scenario is determined by copula-importance sampling theory, which is proposed to ensure the static scenarios yield the same probabilistic characteristics as the random variables. Next, a probability-based scenario reduction technique is implemented to retain effective scenarios and lower the computational burden. Then, multiple linear regression generalizes the static scenarios into dynamic ones with the same probabilities. Finally, a spatiotemporal scenario-based stochastic optimization is proposed for the dynamic optimal power flow problem, which considers uncertainties in variable renewable energy generation and aims to balance the output of controllable generators, renewable energy curtailment, and load shedding. Numerical simulations in a modified IEEE 33-node distribution network show that the proposed approach outperforms the existing methods that do not simultaneously consider spatial and temporal correlations in terms of computational efficiency and accuracy, proving that the proposed PSTSG method can efficiently capture the spatial and temporal correlation so as to make the optimal scheduling decision.

Solving probabilistic optimal power flow with renewable energy sources in distribution networks using fire hawk optimizer

The main contribution in this article is proposing a modern meta-heuristic algorithm for solving nonlinear, nonconvex, and complex OPF problems effectively in distribution networks, considering RES. The Fire Hawk Optimizer (FHO) algorithm is proposed in this work. The considered objective function (OF) is the combined minimization of generating cost, active power loss (Plosses), and load bus voltage deviation (VD). The proposed strategy is validated using the standard IEEE 69-bus benchmark. The obtained results are compared with various recent meta-heuristic techniques such as Capuchin Search Algorithm (CSA), Bear Smell Search Algorithm (BSSA), Black Widow Optimization (BWO) Algorithm, Walrus Optimization Algorithm (WaOA), and Prairie Dog Optimization (PDO) Algorithm. One-way ANOVA and the Tukey test, two common statistical tests, are used to compare algorithms effectively. The FHO shows the best and superior performance with minimum mean cost and standard deviation values of 51.2711 and 5.1131 respectively. This demonstrates that FHO results are more consistent and less diverse. The FHO shows a lower computational time of (25.3241 s) as compared with other strategies. The statistical results confirm the proposed approach's reliability, stability, and consistency. The proposed method provided reliable, high-quality results with faster computing times. Additionally, it has a significant convergence that makes it superior to solving OPF problems in distribution networks with variable RES and NRES.

Optimal Allocation and Energy Management of Units in Distribution Networks with Multiple Renewable Energy Sources and Battery Storage Based on Computational Intelligence

The paper deals with an optimization problem in an electricity distribution network with different types of distributed generation and a battery storage system in terms of a smart grid concept. The optimization problem considers two objectives, namely, the annual energy losses and the exchange of energy with the higher-level power grid. The decision variables of the problem are the allocation of the different distributed generation units and the battery storage system, the annual power profiles of the controllable distributed generation and the battery storage system, and the power factor profiles of the controllable and noncontrollable distributed generation. All decision variables are solved simultaneously in a single optimization problem. The variable load shapes of the grid consumers and the profiles of the photovoltaic and wind power systems are considered in the study. All data are observed at the annual level with hourly resolution. The problem solving method uses computational intelligence techniques, namely, metaheuristic optimization methods and artificial neural networks. The study proposes a framework for optimizing the decision variables in the planning phase of distributed generation and battery storage, and for controlling the variable power and power factor profiles based on an artificial neural network in the implementation phase. The optimization problem is solved with a power system simulation program and a metaheuristic optimizer in cosimulation synergy. The three cases of distributed generation and battery storage are considered simultaneously. The proposed method is applied to the test grid operator IEEE with 37 buses, and reductions in annual energy losses and energy exchange are obtained in the ranges 34–86% and 41–99%, respectively.

A Customer-Centric Distributed Data-Driven Stochastic Coordination Method for Residential PV and BESS

An aggregation scheme is an effective transactive manner of Distributed Energy Resources (DER) spreading across distribution networks. Distributed approach locally achieves cost minimization of an aggregator and customers. The uncertainties of wholesale market price and rooftop PV output will impact on aggregator's scheduling decision and each customer's cost, while solar energy fluctuation can cause an overvoltage problem in distribution networks. However, the probability distributions of these uncertainties always have errors, even in emerging data-based methods. There is no stochastic method using real data with an out-of-sample guarantee suitable for this distributed approach so far to help an aggregator avoid price risk and manage customers' energy against solar energy fluctuation. To address these unsolved issues, we propose a data-driven Wasserstein distributionally robust formulation of the aggregator's agent and customer's agent respectively. The Wasserstein metric is employed to construct the Wasserstein ambiguity set. The mathematical models are then reformulated equivalently to convex programming respectively so that the operating model can be solved by the off-the-shelf solver. To improve the efficiency of the distributed solving framework, an alternating optimization procedure (AOP) process is proposed to overcome the issue caused by binary variables in the alternating direction method of multipliers (ADMM). The proposed operation framework is verified on the modified IEEE 33-bus distribution network and realistic single-feeder LV network.

Integrated dynamic multi-threshold pattern recognition with graph attention long short-term neural memory network for water distribution network losses prediction: An automated expert system

Water loss is a common and critical problem in water distribution networks, resulting in a decrease in wastewater and user experience. In this research, prediction-classification framework based on deep learning (i.e., graph attention long short-term neural memory network (GA-LSTM)) is proposed. Dynamic multi-threshold pattern recognition (DMTPR) was developed to identify and classify losses. To improve the model's reliability, we performed hyperparameter optimisation, trained and verified using one year's operation data of a real pipe network, and compared it with the previous methods. In addition, the influence of different aggregation ranges on the accuracy and stability of the model was analysed. The results showed that the GA-LSTM-DMTPR framework can be used as a reliable tool for practical applications because it provides high-precision and high-stability water demand prediction and realises accurate loss identification and classification. This is owing the potential of the model to aggregate the spatial and temporal multi-dimensional information.

Co-simulation-based optimal reactive power control in smart distribution network

The increasing integration of distributed energy resources such as photovoltaic (PV) systems into distribution networks introduces intermittent and variable power, leading to high voltage fluctuations. High PV integration can also result in increased terminal voltage of the network during periods of high PV generation and low load consumption. These problems can be solved by optimal utilization of the reactive power capability of a smart inverter. However, solving the optimization problem using a detailed mathematical model of the distribution network may be time-consuming. Due to this, the optimization process may not be fast enough to incorporate this rapid fluctuation when implemented in real-time optimization. To address these issues, this paper proposes a co-simulation-based optimization approach for optimal reactive power control in smart inverters. By utilizing co-simulation, the need for detailed mathematical modeling of the power flow equation of the distribution network in the optimization model is eliminated, thereby enabling faster optimization. This paper compares three optimization algorithms (improved harmony search, simplicial homology global optimization, and differential evolution) using models developed in OpenDSS and DigSilent PowerFactory. The results demonstrate the suitability of the proposed co-simulation-based optimization for obtaining optimal setpoints for reactive power control, minimizing total power loss in distribution networks with high PV integration. This research paper contributes to efficient and practical solutions for modeling optimal control problems in future distribution networks.

A multi-objective cost-loss optimization framework for optimal feeder routing problem of radial distribution networks

A multi-objective cost-loss optimization framework for optimal feeder routing problem of radial distribution networks

Resilience assessment of mobile emergency generator-assisted distribution networks: A stochastic geometry approach

Escalation of extreme weather events represents substantial threat to power system infrastructure. Mobile emergency generators (MEGs) can form part of a flexible restoration strategy against such destructive events. However, with continued expansion of distribution networks, quantification of the impact of MEGs has become increasingly challenging owing to extreme-weather-event-induced uncertainties. In this paper, we propose a stochastic geometry-based method for assessing the impact of MEG deployment on distribution networks affected by extreme weather events through investigation of structural features. First, we propose a distance measure to represent the electrical connection between power grid components. Subsequently, we adopt the point process and Voronoi tessellation to describe the spatial distribution of power grid components and the service coverage provided by MEGs under different scenarios. Then, we propose a set of assessment metrics to evaluate the survivability of power grid components and the resilience of the entire distribution network under extreme weather events. Finally, we derive accurate analytical expressions for the distance distribution and resilience metrics, such as coverage probability and load shedding, enabling us to explore the relationship between MEG deployment decisions, structural features, and power grid resilience. The proposed method enables analytic assessment of the impact of MEG deployment on the resilience of distribution networks, and provides beneficial insights to help formulate efficient measures for enhancing resilience. Case studies demonstrated that the proposed method is accurate and efficient in dealing with network analysis and assessment problems for distribution networks under massive potential failure scenarios.

Distributed Optimal Power Flow in Unbalanced Distribution Grids With Non-Ideal Communication

The use of distributed optimization for solving optimal power flow (OPF) problems in distribution networks is increasing as the number of controllable devices and the span of service areas increase. However, the performance of the distributed optimization algorithm largely depends on the availability and quality of communication links between the computing entities. In this paper, we evaluate the performance of the alternating direction method of multipliers (ADMM) for solving the OPF problem for volt-VAr optimization (VVO) under non-ideal communication. The overall problem is formulated by considering the unbalanced operation of multi-phase distribution networks. The algorithm's performance is first analyzed, assuming there is an ideal communication between computing entities, which serves as a benchmark for further analysis. Then, two non-ideal communication models, namely (1) sporadic communication failure and (2) communication under a noisy transmission, are applied to the information exchange architecture of the ADMM. Extensive numerical experiments are conducted with two test systems, the IEEE 123-bus feeder and a 2522-bus network scaled down from the IEEE 8500-bus system; these are used to evaluate the performance of the algorithm. The results indicate that the ADMM-based distributed VVO algorithm has deteriorated performance under high levels of communication failure and high levels of noise injection. Additionally, although the centralized-VVO counterpart has some computational superiority when the overall problem is convex and no communication impairments exist, the distributed-VVO has superior immunized solution performance under realistic communication constraints.

Optimization study of overvoltage problem in PV distribution network based on electrical energy router

Photovoltaic power generation has the advantages of being clean and efficient, but it poses a threat to the voltage quality of distribution networks due to unstable power output. In order to solve the overvoltage and power utilization problems of a high-penetration PV distribution network, this paper proposes a tidal current analysis model based on a four-port power router. First, the steady-state modeling of different ports of the electrical energy router is carried out, and the corresponding voltage control strategy is proposed. Then, by establishing a unified tidal current calculation model, a solution for the optimal operation of the distribution network is proposed. Finally, based on the overvoltage data of a regional power grid, the impact on the voltage level of the grid-connected PV system before and after the addition of the power router is compared. From the analyzed data, it is concluded that the introduction of a four-port power router for corresponding port control strategies can effectively improve overvoltage problems in high-permeability PV distribution networks.