Distribution Network Constraints Research Articles

Centralised rehearsal of decentralised cooperation: Multi-agent reinforcement learning for the scalable coordination of residential energy flexibility

This paper investigates the use of deep multi-agent reinforcement learning (MARL) for the coordination of residential energy flexibility. Particularly, we focus on achieving cooperation between homes in a way that is fully privacy-preserving, scalable, and that allows for the management of distribution network voltage constraints. Previous work demonstrated that MARL-based distributed control can be achieved with no sharing of personal data required during execution. However, previous cooperative MARL-based approaches impose an ever greater training computational burden as the size of the system increases, limiting scalability. Moreover, they do not manage their impact on distribution network constraints. We therefore adopt a deep multi-agent actor–critic method that uses a centralised but factored critic to rehearse coordination ahead of execution, such that homes can successfully cooperate at scale, with only first-order growth in computational time as the system size increases. Training times are thus 34 times shorter than with a previous state-of-the-art reinforcement learning approach without the factored critic for 30 homes. Moreover, experiments show that the cooperation of agents allows for a decrease of 47.2% in the likelihood of under-voltages. The results indicate that there is significant potential value for management of energy user bills, battery depreciation, and distribution network voltage management, with minimal information and communication infrastructure requirements, no interference with daily activities, and no sharing of personal data.

Integration flexibility of renewable distributed energy resources in active distribution networks: A two-module data-driven characterization method

Characterizing the integration flexibility of renewable distributed energy resources (RDERs), which describes the feasible region of RDER accommodations with which the operational constraints of an active distribution network (ADN) can be respected, facilitates the ADN operations. However, traditional characterization methods face the challenge of concurrently dealing with inevitable AC power flow and numerous RDERs. To resolve this issue, this paper develops a novel characterization method that contains two interconnected modules: learning and updating modules. The two modules jointly and iteratively calculate the parameters to characterize the integration flexibility of RDERs (IFR). In the learning module, a new loss function is designed to train the IFR parameters using a training data set. In the updating module, two optimization problems are developed based on the optimization-based performance estimation of the trained parameters to generate more data points for performance improvement in the learning module. The effectiveness of the proposed method is corroborated in the IEEE 33-bus and IEEE 136-bus test systems.

A peer‐to‐peer joint energy and reserve market considering renewable generation uncertainty: A generalized Nash equilibrium approach

AbstractPeer‐to‐peer (P2P) energy trading enhances distribution network resilience by reducing energy demand from central power plants and enabling distributed energy resources to support critical loads after extreme events. However, adequate reserves from main grids are still required to ensure real‐time energy balance in distribution networks due to the uncertainty in renewable generation. This paper introduces a novel two‐stage joint energy and reserve market for prosumers, wherein local flexible resources are fully utilized to manage renewable generation uncertainty. In contrast to cooperative optimization methods, the interactions between prosumers are modelled as a generalized Nash game (GNG), considering that prosumers are self‐interested and should follow distribution network constraints. Then, linear decision rules are employed to ensure a feasible market equilibrium and develop a privacy‐preserving algorithm to guide prosumers toward the market equilibrium with a proven convergence. Finally, the numerical study on a modified IEEE 33‐power system demonstrates that the designed market effectively manages renewable generation uncertainty, and that the algorithm converges to the market equilibrium.

Generalized Nash Equilibrium Analysis for Peer-to-Peer Transactive Energy Market Considering Coupling Distribution Network Constraints

Generalized Nash Equilibrium Analysis for Peer-to-Peer Transactive Energy Market Considering Coupling Distribution Network Constraints

A Fault Restoration Method for DC-interconnected Distribution Systems with Renewable Resources Considering Multiple Fault Scenes

Background:: The distribution systems are gradually transformed into active systems with the large-scale integration of renewable resources, which brings greater potential to the fault recovery of the distribution networks and higher requirements for the power scheduling capability under fault conditions. Power electronic devices such as soft open points (SOPs) can break the radial constraints of the traditional distribution network, provide cross-station power support in fault scenarios, and enhance the resilience of the distribution networks. Methods:: This paper focuses on the distribution systems with multi-transformer flexible interconnection, and a multi-device coordinated fault restoration method is proposed. Firstly, the characteristics of different transformer fault scenes and the fault restoration process coordinated by the bus-bar switches and SOPs in each scene are sorted out. Secondly, an optimization model of the fault restoration for DC-interconnected distribution system is established considering the network operation and the equipment constraints in the fault restoration process. Result:: The proposed model aims at the maximization of the weighted load restoration amount, and is transformed into a second-order cone programming model to be solved quickly. Lastly, the effectiveness of the proposed method is verified in a typical flexible interconnection distribution system. Conclusion:: The simulation results prove that it can effectively improve the capability of preserving power supply for important loads after transformer failure.

Chance-constrained co-optimization of peer-to-peer energy trading and distribution network operations

Peer-to-Peer (P2P) energy markets enable participants to trade locally produced electrical energy at a mutually agreed-upon price. Distributed Energy Resources (DERs) and flexible loads are fundamental components of P2P energy markets, facilitating the market participants to supply or consume energy in accordance with trading agreements. Consequently, it is vital to account for the stochastic nature of DERs and load demand while designing the P2P energy trading model in order to attain optimal operation of P2P energy markets and secure operation of the distribution network. The scenario-based and robust optimization techniques commonly used to characterize uncertainty suffer from data requirement, computational burden, and solution conservatism standpoints. This paper, therefore, proposes a chance-constrained model for P2P energy trading considering renewable energy uncertainty and distribution network constraints. The uncertain behaviour of renewable generation resources is modelled using chance constraints and integrated with the decision-making process of the P2P energy market and distribution network operation. The chance-constrained P2P energy trading problem is reformulated as a deterministic equivalent problem that can be solved by readily available commercial solvers. The ex-ante and ex-post-performance of the proposed chance-constrained formulation is evaluated on a 15-bus radial distribution network, while the scalability of the proposed formulation is demonstrated on modified IEEE 33-bus and 69-bus test networks. The results showcase the effectiveness of the proposed chance-constrained model in handling the uncertainty and respecting the network constraints while deriving the P2P energy trading outcomes.

An AC-Feasible Linear Model in Distribution Networks With Energy Storage

With the increasing deployment of distributed energy resources (DERs), dispatching DERs subject to operational constraints in distribution networks draws much attention. One challenge is the non-convexities in 1) system-wide AC power flow constraints and 2) the individual complementarity constraint of energy storage. To resolve this challenge, this paper studies an AC-feasible linear model in distribution networks with energy storage, including its formulation, analysis, and applications. First, an AC-feasible linear model is formulated as a set of linear constraints on controllable DERs and uncontrollable power demand by 1) converting the non-convex system-wide constraints into linear constraints based on the Brouwer's fixed-point theorem and the second-order Taylor expansion, and 2) replacing the non-convex individual complementarity constraint of energy storage with one properly designed linear constraint. Furthermore, to analyze the power demand level at which the proposed linear model can provide a solution, this paper proposes an examination-based projection method under the Monte Carlo framework to handle projections of thousands of dimensions from linear constraints over time periods. Finally, the potential applications of our AC-feasible linear model are discussed. Numerical experiments are conducted in the IEEE 33-bus and 136-bus test systems to demonstrate the effectiveness of the proposed methods.

Direct Load Control Scheme for Flexible Loads under Automated Demand Response Program for Peak Demand Management, Loss Minimization, Asset Management, and Sustainable Development

Background: Nowadays implementation of Demand Response (DR) programs in the distribution grid is a necessary planning criterion for distribution utility. Implemented DR programs should be automated, intelligent, well-educated, and more competent than the conventional augmentation techniques to resolve Distribution Network (DN) constraints. Peak demand causes DN to approach its maximum capacities. Peak demand also exceeds the sustainable limit of the DN resulting disruption in electric supply, failures of various assets like transformers, feeders, etc. Objective: In this paper, a Direct Load Control (DLC) scheme for Flexible Loads (FLs) is modeled & implemented under Automated Demand Response (ADR) program and tested on real 54-bus DN. Methods: This ADR program is implemented through Demand Response Aggregator (DRA) and ADR Technology Solution Enablers (ADRTSE) to curtail the peak demand on the DN ADR is a recent technology that may put off new generation (conventional- and non-conventional both). Results: It also enables the distribution utility to curtail the peak demand & its period ensuring reliability of supply without restructuring, augmentation of existing infrastructure, and development of new infrastructure. Conclusion: The result validates the effectiveness of ADR program for peak demand curtailment, asset management, distribution network losses minimization, and for sustainable development of environment.

Risk-Based Hosting Capacity Analysis in Distribution Systems

Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set of the power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework.

Collaborative operation optimization of distribution system and virtual power plants using multi‐agent deep reinforcement learning with parameter‐sharing mechanism

AbstractWith the increasing integration of distributed energy resources (DERs) into distribution systems, the optimization of system operation has become complex, facing challenges such as inadequate consideration of market participants’ benefits, poor computational efficiency, and data privacy concerns. This paper introduces the concept of a virtual power plant (VPP) as a solution for energy integration and management. To strike a balance between operational safety and the interests of market participants, a dual‐layer model is proposed. This model considers the benefits of both Distribution System Operators (DSO) and VPP, while also enhancing the consideration of distribution network constraints. The DSO considers AC optimal power flow and utilizes penalty functions to ensure network security in case of violations. To enhance computational efficiency and privacy, the paper presents the parameter‐sharing twin delayed deep deterministic policy gradient approach. This approach allows multiple intelligent agents to share a neural network model, effectively reducing the computational load. During the training process, only essential data is exchanged among the agents, ensuring the privacy of sensitive information. The effectiveness of the proposed model and the algorithm is validated through a case study on an IEEE 33‐node system.

A Fully-Decentralized Transactive Energy Management Under Distribution Network Constraints via Peer-to-Peer Energy Trading

Peer-to-peer (P2P) energy trading is seen as a promising method for distributed transactive energy (TE) management. Since distribution network is used for electricity transfer, physical constraints should be imposed during the P2P trading. In this paper, we propose a P2P-based distributed TE management approach considering distribution network constraints and product differentiation for P2P energy trading between different buses. A multi-period AC optimal power flow (OPF) model is used to monitor power flow in distribution system, and the exactness of second-order cone relaxation is recovered by the convex-concave procedure, making sure that P2P transactions do not violate network constraints. Moreover, we propose a fully-decentralized variant of alternating direction method of multipliers for clearing P2P transactions in a fully-decentralized manner under AC power flow constraints. Our proposed variant does not need any interactions with the central supervisor in comparison with the traditional one. Finally, numerical results on IEEE 33-bus and 141-bus distribution systems verify the effectiveness of our proposed method in ensuring physical feasibility, lowering data communication and protecting data privacy during P2P energy trading.

Peer-to-peer energy trading under distribution network constraints with preserving independent nature of agents

In recent years, the use of distributed energy resources has accelerated to deal with global warming. As these resources are decentralized, the current centralized energy market must be modified to accommodate their characteristics. Advances in information technology have made it possible to implement peer-to-peer (P2P) markets. However, completely removing the distribution system operator from P2P exchanges can risk the network's security. Conversely, establishing network security only by the operator can decline the independence of agents. This paper proposes a decentralized framework for implementing the P2P market based on the alternating direction method of multipliers, which maintains the distribution system's constraints, considering the agents' independent nature. The agents reach convergence with minimal exchange of information while maintaining the network constraints, including voltage and current limits. The network constraints are included using a proposed sensitivity approach in the sub-problem of each agent. In this approach, by calculating the sensitivity coefficients of voltage and current, the network security can be evaluated with the changes of active and reactive powers by agents. The simulation results demonstrate that the proposed framework can efficiently maintain network constraints. The short running time of the P2P trading with the proposed framework makes it feasible for practical applications.

Multi-stage optimization for energy management and trading for smart homes considering operational constraints of a distribution network

The increase in the uptake of distributed energy resources (DERs) makes the distribution network more complex. Inadequate management of these DERs may lead to escalated power transmission, potentially resulting in challenges within the distribution network and provoking degradation of critical assets like distribution transformers. The smart home has a home energy management system (HEMS) to schedule the DERs at the home level based on the objectives of the end-user. However, HEMS is not coordinated with the distribution network operators, which can cause different network issues at the distribution level. To mitigate this, effective management of DERs across different levels of the distribution network is essential. This paper introduces a four-stage optimization within a three-level coordination framework that aims to maximize benefits for all stakeholders. A mixed integer linear programming (MILP)-based HEMS is formulated in the first stage to perform home energy management effectively. At the aggregator level, in the second stage, a MILP-enabled peer-to-peer (P2P) trading mechanism is designed. At the same level, a third-stage loss of life optimization is performed pertaining to the optimal power status of the HEMS and P2P trading. In the last stage, a three-phase optimal power flow-based optimization is proposed to maintain the operational constraints of the unbalanced distribution network. Optimizing HEMS and P2P trading while addressing transformer limitations, our proposed method reduces peak power by 38.85%. The transformer life loss using P2P is only 0.00059%, while in HEMS, it is 0.62% per day. Additionally, our method substantially lowers electricity costs for P2P prosumers. Thus, our proposed method outperforms other existing mechanisms from both financial and physical network operation suitability perspectives.

Chance-Constrained Optimization of Photovoltaic System Allocation considering Power Loss, Voltage Level, and Line Current

Changes are emerging that will significantly alter structure and operation of this century’s distribution networks, and photovoltaic (PV) systems will play greater role in energy sector, with implications for power system reliability. Considering uncertainties in solar irradiance and electrical loads and incorporating them into the optimization problem within an appropriate methodology is becoming increasingly important in reshaping distribution networks. In this paper, uncertainty scenarios are handled with Monte Carlo Simulation (MCS) under genetic algorithm (GA) and differential evolution- (DE-) based optimization, and probability distribution functions (pdf) of bus voltages and line current are obtained to be used in chance-constrained stochastic programming. This present study focuses on investigating impact of uncertainties in PV system operating under different irradiance scenarios on power loss with probabilistic constraints in distribution networks instead of precise deterministic limits to contribute more efficient and reliable use of energy. By combining meta-heuristic optimization and MCS technique under one framework, this paper contributes to knowledge base of how to allocate PV plants within distribution networks under chance-constrained strategy. In order to show the effectiveness of the proposed methodology, obtained optimization results are tested using MCS under set of uncertainty conditions and network constraints are evaluated for limit violation probabilities. The effectiveness of this method is investigated based on comparative results of two different optimization methods through probabilistic analysis and simulation.

Generalized Wardrop Equilibrium for Charging Station Selection and Route Choice of Electric Vehicles in Joint Power Distribution and Transportation Networks

This paper presents the equilibrium analysis of a game composed of heterogeneous electric vehicles (EVs) and a power distribution system operator (DSO) as the players, and charging station operators (CSOs) and a transportation network operator (TNO) as coordinators. Each EV tries to pick a charging station as its destination and a route to get there at the same time. However, the traffic and electrical load congestion on the roads and charging stations lead to the interdependencies between the optimal decisions of EVs. CSOs and the TNO need to apply some tolling to control such congestion. On the other hand, the pricing at charging stations depends on real-time distributional locational marginal pricing, which is determined by the DSO after solving the optimal power flow over the power distribution network. This paper also takes into account the local and the coupling/infrastructure constraints of EVs, transportation and distribution networks. This problem is modeled as a generalized aggregative game, and then a decentralized learning method is proposed to obtain an equilibrium point of the game, which is known as variational generalized Wardrop equilibrium. The existence of such an equilibrium point and the convergence of the proposed algorithm to it are proven. We undertake numerical studies on the Savannah city model and the IEEE 33-bus distribution network and investigate the impact of various characteristics on demand and prices.

Power Loss Minimization through Reconfiguration Using BPSO-Based Technique

Power loss is influenced by uncertain and ever increasing loads in the system but can be minimized by network reconfiguration where the topological structure of the system is changed by altering the switching operation. In this work, a multi-objective framework through reconfiguration is formulated with loss minimization as primary objective and reliability and voltage profile improvement as secondary objectives. A binary particle swarm optimization (BPSO) base method is developed to reconfigure the network by fulfilling all distribution network constraints. The influence of the BPSO parameters to obtain the optimal switches with minimized power loss, reliability indices, and voltage deviations are studied by a faster convergence. The results have been compared for different weights of the objective to give a comprehensive understanding of the nature of the objective attempted in this work. IEEE 33 bus and radial IEEE 69 bus systems were considered for testing the proposed method.

P2P flexibility markets models to support the coordination between the transmission system operators and distribution system operators

The increasing integration of Distributed Energy Resources (DER) in the distribution network has brought more importance to Peer-to-Peer (P2P) markets. However, energy traded in P2P markets can lead to voltage and congestion constraints in distribution networks operated by Distribution System Operators (DSOs). At the same time, Transmission System Operators (TSOs) may need to solve system problems, requesting the participation of DERs in frequency regulation services. To ensure competitive participation in P2P markets, as well as to ensure a correct operation of distribution networks and to contribute to mitigate problems at the system level, coordination mechanisms between the P2P market and the System Operators (SOs) are required. This paper introduces a set of mathematical models considering P2P flexibility trading at the distribution system, while assisting the DSO and TSO in solving the congestion, voltage and frequency problems, respectively. The models are assessed on an IEEE 37-bus distribution network with high DER penetration. The first and second models are based on product differentiation to avoid violating the lines’ thermal limits and the nodes’ voltage limits, respectively. The second model also considers reactive power control in order to impact voltage constraints. The third model uses a virtual load, connected to the TSO network (before the power transformer), to model frequency regulation services. The last model proposes the integration of all methods. Results showed that each model was effective in solving its constraint. However, they do not dismiss the use of the peers’ flexibility assets to assure an overall feasible techno-economic solution. The use of the methodology proposed in the present paper can significantly facilitate the adoption of full P2P markets as well as the confidence of the system operators in the integration of these markets.

Optimal Energy Management for Battery Swapping Based Electric Bus Fleets With Consideration of Grid Ancillary Services Provision

In this paper, a novel optimization model is formulated to optimize the scheduling of battery swapping stations (BSS) operating electrified public bus transit fleets. The BSS consists of a number of battery modules that are combined together to create a MW-scale battery storage system. As such, the formulated optimization problem aims at minimizing the running costs of the BSS via i) exploiting the low electricity prices in the market (i.e., charging the battery modules at low prices), and ii) utilizing the BSS in the provision of grid ancillary services. The proposed model considers the operational requirements of the bus transit fleet to satisfy the energy needs of the battery electric buses (BEBs) and maintain their defined timetable. Also, the model integrates the power distribution network constraints such as bus voltages and line capacity limits to ensure its reliable operation. The impact of the BSS participation in the provision of ancillary grid services on the operation, degradation, and lifetime of the battery modules is investigated in this work by using a proposed saving cost index (SCI). It is demonstrated that the proposed model propels the economic viability of the BSS operation concept.

Scheduling method for aggregated photovoltaic‐battery systems considering information notified by distribution system operator

AbstractIn recent years, the aggregation business has gained a lot of attention in Japan. Aggregators will make contracts with customers with photovoltaic (PV) power systems and battery energy storage systems (BESSs) including electric vehicles (EVs) to participate in electricity markets. Aggregators might have to pay electricity supply‐demand imbalance charges when generated and consumed energies contracted at the day‐ahead supply‐demand market are different from those at the current day operation due to distribution network constraints such as voltage and power flow limitations. Therefore, the information on network constraints is very important for aggregators to determine their day‐ahead schedules. In this paper, we evaluated the relationship between aggregator supply‐demand schedules and the distribution system operation. It was assumed that the reverse power flow limitations due to network constraints are notified to the aggregators by distribution system operator (DSO). Two cases of the aggregators’ schedules of PV systems and stationary BESSs were compared in the simulations. In addition, aggregator strategies for making adequate schedules were evaluated.

Coordinated active and reactive power operation of multiple dispersed resources for flexibility improvement

The purpose of this paper is to reach the optimal active and reactive power operation of multiple dispersed resources consisting of mobile energy storage system (MESS), demand response (DR) and photovoltaic (PV), for flexibility improvement of distribution network with uncertain PV and DR, minimization of power loss and operation cost whilst satisfaction of both power factor and voltage variation requirement. Especially, the flexibility aspect of distribution network is focused due to its significance for supporting economic operation without voltage rise issue during high PVs integration. Firstly, the active and reactive power operation spaces of MESS and PV inverter are discussed under power factor constraint. Then, the stochastic characteristics of PV generation and DR of microgrids are investigated using probability distribution. After that, the optimization framework coordination with dispersed MESS, PV inverter and DR to ensure operational flexibility of distribution network is proposed. Finally, the total cost minimization based flexibility improvement approach is presented by optimizing power loss, uncertain risk, operation cost of distribution network and MESS, satisfying operation constraints of both distribution network and dispersed resources. Simulation results conducted on the IEEE 69-bus system demonstrate the effectiveness of the proposed approach for PV accommodation, voltage quality improvement as well as peak load shaving.