Source-linked AI summary
Decentralized P2P Energy Trading under Network Constraints in a Low-Voltage Network
Jaysson Guerrero, Archie Chapman, Gregor Verbic
TL;DR
Local P2P energy trading can create network issues when exchanges ignore low-voltage network constraints. The paper incorporates network impacts into a continuous double auction, finding that constrained P2P trading preserves economic benefits while remaining within operating limits.
Problem
Many local energy-trading studies avoid network constraints, although uncontrolled household participation can cause overvoltage and reverse flows that trip protection equipment.
Method
The methodology models power injections and absorptions in the network, uses a continuous double auction for neighbor-to-neighbor trading, and internalizes technical-constraint costs.
Results
$75.92 market benefit was achieved in one-day household expenses and incomes while remaining within network operating limits; P2P also traded more energy and increased prosumer revenues than benchmark curtailment schemes.
Takeaways & Limitations
The proposed market reduces users’ energy costs, increases incomes, and achieves local generation-demand balance without violating technical constraints.
Abstract
from arXiv · showhide
The increasing uptake of distributed energy resources (DERs) in distribution systems and the rapid advance of technology have established new scenarios in the operation of low-voltage networks. In particular, recent trends in cryptocurrencies and blockchain have led to a proliferation of peer-to-peer (P2P) energy trading schemes, which allow the exchange of energy between the neighbors without any intervention of a conventional intermediary in the transactions. Nevertheless, far too little attention has been paid to the technical constraints of the network under this scenario. A major challenge to implementing P2P energy trading is that of ensuring that network constraints are not violated during the energy exchange. This paper proposes a methodology based on sensitivity analysis to assess the impact of P2P transactions on the network and to guarantee an exchange of energy that does not violate network constraints. The proposed method is tested on a typical UK low-voltage network. The results show that our method ensures that energy is exchanged between users under the P2P scheme without violating the network constraints, and that users can still capture the economic benefits of the P2P architecture.
NOMENCLATURE
The paper frames P2P energy trading as a decentralized local-market application for DER-enabled households, while emphasizing that network constraints must be incorporated into trading models.
- Context: DERs such as photovoltaic panels, batteries, smart appliances, and electric vehicles enable residential consumers to become prosumers.These resources create opportunities for local energy trading in distribution networks.
- P2P trading: Blockchain and distributed ledger technologies support decentralized transactions between prosumers and neighboring users.P2P architectures allow prosumers to trade energy surpluses directly with nearby users.
- Network constraints: Uncoordinated P2P electricity exchanges can violate hard network constraints because residential users share an electricity network.Physical constraints therefore need to be represented in energy-trading models.
- Research gap: Previous studies largely focused on distributed-ledger technologies or omitted transaction-level impacts on voltage and network capacity.Some prior work evaluated losses but not voltage and capacity effects for each transaction.
- Contribution: The paper extends P2P trading by validating transactions against distribution-network conditions and charging extra costs associated with physical energy losses.It presents a sensitivity-analysis methodology and a specific implementation for consumers and prosumers.
- Contribution: The contributions include assessing network constraints, internalizing exchange-related external costs, comparing alternative strategies, and demonstrating feasibility for P2P trading.The paper also positions the approach as beneficial for power systems and end-users.
II. PRELIMINARIES
The preliminaries define a decentralized P2P smart-grid setting in which households trade energy with neighbors or a retailer across time slots, using predicted demand and generation profiles.
- P2P architecture: Information flows among peers are decentralized, while financial interaction channels such as DLTs remain separate from physical electrical links.The system contains H households interacting over a finite decision horizon divided into time slots.
- System setting: The modeled P2P system is a low-voltage network where residential users buy and sell energy through an online platform under a decentralized scheme.Users remain self-interested and control their own energy use.
- Trading options: Households can trade with neighbors or a retailer, allowing surplus energy to be sold through feed-in arrangements or the local P2P market.This setup is presented as compatible with existing retail institutional arrangements.
- Household agents: Consumers bid according to demand profiles, while households are assumed able to predict demand and generation for each time slot.The household population is partitioned into consumers and prosumers.
- Energy accounting: Total purchased energy includes energy obtained from both the grid and the local market, while sold energy is represented separately for each time slot.The notation distinguishes purchase and sale quantities and their associated prices.
- Prosumer optimization: Type 2 prosumers optimize self-consumption by solving a mixed-integer linear program subject to device-operation constraints.The model uses decision variables and state variables to represent household operation.
C. Network Model
The network model represents a radial low-voltage distribution system with a slack substation, connected branch nodes, and voltage-related operating quantities used to describe network behavior.
- Topology: The distribution network is radial, with nodes connected by distribution lines and Node 0 serving as the feeder substation and slack bus.All other nodes represent branch nodes.
- Topology: Each line connects a child node to a parent node that is closer to feeder 0.The child set δ(j) contains nodes connected downstream of node j.
- Network impacts: Voltage issues worsen with higher conductor resistance, more prosumers, and peak photovoltaic generation around midday.The referenced figures compare household voltage problems across these network conditions.
- Electrical quantities: The model assigns complex current, impedance, complex power, voltage, and net complex power injection to each line or node.Squared voltage magnitude is defined as v_i := |V_i|2, with the feeder-root voltage fixed.
D. Local energy trading under network constraints
P2P trading in low-voltage networks must account for physical constraints because uncontrolled exchanges can cause voltage and capacity problems. The section contrasts centralized DOPF and decentralized alternatives while motivating constraint-aware trading.
- Uncontrolled household participation in P2P trading can cause overvoltage and reverse flows that trip protection equipment.
- 20% PV penetration causes voltage problems for 5–7 kW systems in the evaluated feeder’s worst case.Voltage issues also worsen around midday, with higher network resistance, and as the number of prosumers increases.
- DOPF produces DLMPs that reflect losses and binding capacity or voltage constraints across the network.A central entity solves the constrained scheduling problem and uses the resulting prices to attribute network costs.
- Centralized DOPF faces scalability, privacy, stochastic-consumption, and tariff-redesign barriers.The passage identifies the large number of consumers, household-level decomposition, compliance with allocated profiles, and incompatibility with existing tariffs as barriers.
- Decentralized P2P is presented as an alternative to DOPF, but it still needs to obey network constraints.
III. METHODOLOGY
The methodology estimates how bilateral P2P injections and withdrawals affect the distribution grid. It embeds sensitivity coefficients in the market mechanism to validate trades and internalize power-flow externalities.
- The method estimates grid impacts from a bilateral injection at one bus and absorption at another.The motivating example considers a consumer at Bus 4 purchasing energy from a prosumer at Bus 3.
- Analytically derived sensitivity coefficients are embedded to guarantee bilateral transactions and internalize external power-flow costs.
- Voltage sensitivity coefficients estimate voltage variations caused by network power injections.
- Power transfer distribution factors quantify active-power line-flow changes from exchanges between two nodes.
- Loss sensitivity factors represent the portion of system losses attributable to network power injections.
A. Voltage Sensitivity Coefficients Formulation
The voltage-sensitivity formulation links nodal power-injection changes to voltage changes. It replaces repeated full load-flow calculations with analytically derived sensitivities computed from network equations.
- The traditional VSC approach uses the Jacobian matrix after solving a Newton-Raphson power flow.
- The inverse Jacobian estimates voltage changes from changes in real and reactive nodal power injections.P and Q denote real and reactive injections, while θ and V denote voltage angles and magnitudes.
- Repeated full load-flow calculations may be infeasible or intractable as the network state changes.
- The study therefore uses analytically derived VSCs based on the compound admittance matrix.
- VSCs are obtained by computing voltage partial derivatives with respect to active-power injections at network buses.The resulting voltage changes can be calculated from power changes at specific buses.
B. Power Transfer Distribution Factors
The PTDF formulation uses ISFs and network susceptance relationships to estimate how bilateral active-power transfers redistribute flows across distribution branches.
- ISFs quantify branch-flow sensitivity to generation or load changes at a particular bus.
- The ISF is calculated using the reduced nodal susceptance matrix for a specified slack bus and fixed remaining quantities.
- The sensitivity calculation uses DC approximations, branch susceptances, and the branch-to-node incidence matrix.The incidence vector assigns 1 to the sending bus and -1 to the receiving bus.
- PTDFs capture branch-flow variation caused by an injection at one bus withdrawn at another.
- For branch (k, l), PTDFs represent sensitivity to an active-power transfer ∆Pij from Bus i to Bus j.
C. Loss Sensitivity Factors
The methodology calculates loss sensitivity factors and uses bilateral exchange coefficients to associate network losses with individual P2P transactions.
- C. Loss Sensitivity Factors: Loss sensitivity factors are derived using partial derivatives obtained from the voltage-sensitivity formulation and the conductance matrix.The loss sensitivities describe how losses change with power injection at one bus and power withdrawal at another.
- C. Loss Sensitivity Factors: The bilateral exchange coefficient associates losses with a bilateral transaction between two network buses.This coefficient supports allocating transaction-related losses to the participating agents.
- C. Loss Sensitivity Factors: The procedure begins by clustering complex-voltage information and building the matrix of a linear system of equations.These steps precede the calculation of the sensitivity factors.
- C. Loss Sensitivity Factors: The methodology overview contains modules for calculating voltage sensitivity coefficients, power transfer distribution factors, and loss sensitivity factors.These modules provide the network-impact quantities used in the broader validation process.
D. Illustrative example
An illustrative five-node case shows how a bilateral exchange is assessed for voltage variation, line utilization, congestion, and losses within the P2P market mechanism.
- D. Illustrative example: A five-node example examines power injected at Node 3 and withdrawn at Node 4 during a bilateral energy exchange.The transaction is used to illustrate its effects on real power losses, congestion, and voltage constraints.
- D. Illustrative example: Voltage sensitivity coefficients estimate transaction-induced voltage variations, and trades are disallowed when they cause voltage issues.This applies the network-permission logic to voltage constraints.
- D. Illustrative example: Power transfer distribution factors evaluate line utilization for the transaction and can support congestion charges for physical network use.The example calculates PTDF values for the relevant lines.
- D. Illustrative example: Total system losses are calculated using voltage sensitivities and loss equations, with the BEC34 coefficient assigning an extra loss-related cost.The participating agents pay for losses caused by their transaction.
- D. Illustrative example: The market mechanism combines a continuous double auction, agent bidding strategies, and a network permission structure.The continuous double auction matches buyers and sellers, while orders are submitted separately for each time slot.
- D. Illustrative example: Unmatched bids and asks remain in the order book, and partially covered orders can wait for subsequent matching orders during the trading period.The matching process continues as new bids and asks arrive.
B. Bidding Strategies
The bidding and trading model combines stochastic household behavior with network validation, allowing matched trades only while network constraints remain respected and incorporating curtailment implicitly.
- B. Bidding Strategies: HEMS agents respond to stochastic information, making participants unpredictable and potentially causing large swings in available energy and prices in a thin market.The paper therefore treats simple bidding heuristics as more practical than constructing an optimal bidding strategy.
- B. Bidding Strategies: A third-party entity validates matched transactions using network features and sensitivity coefficients, evaluating voltage variation and line congestion.Households receive a signal indicating whether they can continue participating without causing network problems.
- B. Bidding Strategies: Power curtailment is implicitly incorporated into trading, allowing users at weak network locations to participate when their orders are matched and permitted.The authors associate this with greater consumer participation and a better reflection of network conditions.
- B. Bidding Strategies: The model represents a low-voltage network with consumers, prosumers, a local market, and up to 100 agents in the simulation.The study uses a UK network with one feeder and 100 single-phase households over 24 hours divided into 15-minute intervals.
- B. Bidding Strategies: The case study includes 50 consumers and 50 prosumers, including 40 PV households and 10 households with PV, batteries, and HEMS.Prosumers have 5.0 kWp PV systems; Type 2 households additionally have 3 kW and 10 kWh batteries.
- B. Bidding Strategies: A 25 kW, 50 kWh community storage system buys midday surplus through the P2P market and resells energy during peak demand hours.The retailer-operated CES is intended to apply peak shaving during peak load hours.
- B. Bidding Strategies: Price bounds use time-of-use tariffs for maximum bids and feed-in tariffs for minimum asks.These constraints prevent buyers from paying above the retailer tariff and sellers from accepting below the export tariff.
- B. Bidding Strategies: The process initializes bids from load, generation, and tariffs, then evaluates network conditions whenever an ask and bid are matched.The market remains open while network constraints are respected.
B. Scenarios’ Description
The study evaluates two scenarios for network-constrained P2P trading, comparing the proposed local market with curtailment benchmarks. Scenario I shows market activity, compliant voltages, and household economic benefits.
- Two scenarios are evaluated to assess the proposed methodology and demonstrate P2P energy-trading benefits under network constraints.
- P2P matching promotes local demand-generation balance, with prosumers supplying surplus energy until consumer demand, including CES requirements, is covered.
- Scenario I uses the proposed local-market P2P method, alongside reduced-capacity and tripping curtailment benchmarks.The reduced-capacity benchmark limits each prosumer’s export to ≤3 kW.
- Most energy is traded between 8:00 and 14:00, with an additional sales peak around 11:00 linked to CES charging.
- 0.945 pu to 1.022 pu: user-node voltages remain within this range, with no overvoltage cases during the simulated day.Around 55% of observed voltages fall between 0.99 pu and 1 pu.
- $75.92: P2P trading delivers a market benefit while exchanges respect network constraints, decreasing users’ expenses and increasing their incomes.
D. Scenario II Results
Scenario II compares the network-constrained P2P market with curtailment schemes. The P2P approach trades more energy, increases prosumer revenues, and reduces spilled energy while retaining scalability and identifying future extensions.
- P2P trading increases energy traded and prosumer revenues compared with the benchmark curtailment methods.
- P2P reduces energy spillage and provides greater economic benefits to users than power-curtailment methods.
- 70% versus around 50%: the furthest prosumer’s spilled-energy share is higher under Tripping than in the P2P case.
- $0.7: the prosumer’s income increases in the P2P case because more energy is sold.
- The proposed method combines network-constrained P2P trading with a continuous double auction and internalizes technical costs in transactions.
- Future work will examine flexible-load bidding strategies and penalties for forecast deviations to enhance trading among nearby users.