P2Es: Community-Based Energy Systems

• P2Es is a community-scale framework that enables prosumers to trade locally, self-consume rooftop PV, and optimize energy flows through integrated scheduling.
• The approach combines local price formation with technical constraints, using tools like Dynamic Operating Envelopes and the Energy Trading Potential Index to guide trades.
• P2Es research demonstrates social-welfare maximization by incorporating flexible role switching, demand response, and multi-layer coordination between energy communities and the grid.

Searching arXiv for recent work on peer-to-peer energy systems and related terminology. P2Es, in the smart-grid usage treated here, denotes peer-to-peer energy systems or peer-to-peer energy trading and scheduling within an Energy Community (EC): a local market platform in which households act as prosumers, self-consume rooftop PV generation, exchange energy with neighbors, trade across ECs, and buy from or sell to the utility when needed. In this formulation, P2Es differs from centralized energy management because the community itself participates in price formation and resource allocation, and local trading is used before fallback to the retailer or utility. Recent work has expanded this notion along three axes: community-level scheduling for maximum social welfare, structural readiness assessment via the Energy Trading Potential Index (ETPI), and grid-aware peer-to-peer-to-grid (P2P2G) coordination through Dynamic Operating Envelopes (DOEs) (Alirezazadeh et al., 2024).

1. Core concept and system boundary

Within an EC, P2Es is organized around prosumers, local generation, flexible demand, storage, and external grid exchange. The architecture described in the literature includes prosumers / houses, Energy Communities, solar PV, demand response (DR), EV batteries, and parking-sharing services for guest EVs. A Community Energy Management Center (CEMC) coordinates each EC and interfaces with the utility; uninterruptible loads are supplied directly from the utility, while interruptible loads can be served by PV, DR, internal P2P exchanges, or the utility if still unmet. Guest EVs pay parking fees to ECs and charge or discharge within the scheduling framework (Alirezazadeh et al., 2024).

Formulation	Main unit of coordination	Primary purpose
P2P energy management (Alirezazadeh et al., 2024)	CEMC and ECs	Social-welfare-oriented scheduling
ETPI framework (Imran et al., 20 Jun 2026)	Community trading graph	Structural readiness assessment
DOE-embedded P2P2G (Jiang et al., 2023)	Prosumers and DSO	Grid-feasible decentralized trading

This system boundary is broader than simple bilateral energy exchange. It explicitly couples local electricity trading with EV charging/discharging, DR participation, and, in one formulation, parking allocation. A plausible implication is that the term P2Es, as used in this literature, refers not merely to a market-clearing rule but to an integrated socio-technical scheduling layer for residential communities.

2. Economic objective and scheduling model

The social-welfare-oriented formulation casts P2Es as a revenue-maximization problem over communities, users, and time periods. The objective function aggregates profit from trading with the utility, DR incentives and penalties, inter-community P2P exchange profit, an explicit social welfare term, parking-hosting revenue, standby payment for DR availability, penalty for unsupplied energy, and EV charging/discharging value. The social welfare term is written as

$${TPSW}_{c,u,t}=(P_{c,u,t}^{Self\,\,Supply}+{PT2P2P}_{c,u,t})\times c_{c,u,t}^{SWV},$$

with $c_{c,u,t}^{SWV}$ set to 0.055 $/kWh in the case study (Alirezazadeh et al., 2024).

The model distinguishes uninterruptible and interruptible loads. PV first covers internal needs; DR can reduce interruptible demand; remaining demand can be supplied by internal P2P imports or by the utility. The paper defines unsupplied energy as

$${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$

and imposes a global market-clearing equality for P2P exchange:

$$\sum\limits_{c\in C,u\in U}{PT2P2P}_{c,u,t}=\sum\limits_{c\in C,u\in U}{PTFP2P}_{c,u,t}.$$

Binary variables enforce seller/buyer exclusivity so that an entity is effectively either a seller or a buyer in a given period, not both simultaneously (Alirezazadeh et al., 2024).

Price formation is local rather than purely utility-imposed. The case study uses a local P2P price generated from an external methodology, with the average of the buying and selling prices used as the P2P equilibrium price. The paper explicitly notes that local prices are typically between retail and export prices, making P2P trading more attractive than selling excess PV back to the grid. Operationally, the implementation is scenario-based: 1000 EV scenarios are generated via Monte Carlo simulation, K-means scenario reduction selects 3 representative scenarios, and the resulting optimization is solved over a 24-hour horizon (Alirezazadeh et al., 2024).

3. Structural trading potential and the ETPI framework

A distinct strand of P2Es research asks a prior question: whether a community is structurally worth equipping with a full P2P trading stack at all. The Energy Trading Potential Index (ETPI) is introduced as a normalized, data-driven metric for community-level structural trading potential. The underlying Energy Trading Potential (ETP) is normalized as

$$\text{ETPI} = \frac{\text{ETP}}{\text{ETP}_{\max}},$$

so that ETPI lies in [0,1], making it dimensionless and comparable across community mixes and time windows (Imran et al., 20 Jun 2026).

The framework models the community as a generalized bipartite graph in each hourly trading round during daylight hours. For a prosumer $P_j$, the round-$r$ net balance is

$s_j^r = g_j^r - d_j^r.$

Under the static policy, prosumers are always treated as suppliers; if they have no surplus, they become inactive and cannot buy from others. Under the flexible policy, a prosumer with $s_j^r \le 0$ joins the buyer side. Pairwise buyer-seller interactions are scored using price compatibility $W_{ij}^r$, demand fulfillment $c_{c,u,t}^{SWV}$0, and network robustness $c_{c,u,t}^{SWV}$1, combined through

$c_{c,u,t}^{SWV}$2

and then classified into positive, neutral, or negative sentiment according to thresholds $c_{c,u,t}^{SWV}$3 and $c_{c,u,t}^{SWV}$4. Over a window of $c_{c,u,t}^{SWV}$5 rounds, edge weights are aggregated through positive, neutral, and active-round counts (Imran et al., 20 Jun 2026).

The formal mechanism by which flexibility changes market structure is explicit. If $c_{c,u,t}^{SWV}$6 prosumers have surplus in round $c_{c,u,t}^{SWV}$7, then

$c_{c,u,t}^{SWV}$8

so the per-round gain is

$c_{c,u,t}^{SWV}$9

which is always nonnegative and strictly positive when some prosumers are in deficit and some are in surplus. Quantitatively, the headline case is the (1:9) mix: ETPI = 0.61 under the flexible policy versus 0.15 under the static policy, with ETP = 23.3 versus 5.5. The flexible policy generated 45,594 total active edges versus 26,370 under the static policy, a 73% increase. By contrast, in the balanced (5:5) case the difference was much smaller: 79,676 versus 74,130, only a 7.5% difference (Imran et al., 20 Jun 2026).

This framework also overturns a common simplification that more distributed PV always increases P2P value. The reported result is more specific: in consumer-heavy mixes, ETP rises monotonically with PV capacity, but in prosumer-heavy mixes under the flexible policy, ETP can decrease as PV capacity increases because larger PV systems create more surplus while reducing the frequency with which prosumers fall into deficit and switch roles (Imran et al., 20 Jun 2026).

4. Grid-feasible P2Es and DOE-embedded P2P2G

Another major development is the integration of distribution-network integrity into P2Es through Dynamic Operating Envelopes. In the DOE-embedded P2P2G mechanism, prosumers negotiate bilateral P2P trades while simultaneously negotiating DOE export limits with the distribution system operator (DSO). For prosumer $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$0, the DOE is a time-varying export sequence

$${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$1

and if every prosumer stays within its DOE, the distribution grid remains within safe limits (Jiang et al., 2023).

The integrated optimization couples a DSO cost $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$2 with prosumer costs $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$3, subject to a robust feasibility condition over the DOE region. At prosumer level, the local objective includes grid purchase and sale, bilateral P2P prices, and device decisions. The key local constraint is the DOE-aware net injection bound

$${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$4

which is the point at which P2P trading is made explicitly grid-aware. On the network side, the DSO solves a radial-network-constrained problem with line thermal limits, voltage bounds, and power-balance constraints; expected network loss cost is minimized over scenarios inside the DOE region (Jiang et al., 2023).

Privacy preservation is achieved through ADMM-based negotiation with a consensus constraint

$${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$5

Prosumers submit intended export limits, the DSO returns DOE allocations and a DOE price signal, and neither side discloses the full internal variables that would reveal detailed P2P trades or private device data. To reduce peer communication, the P2P subproblem uses communication-censored ADMM (COCA), which suppresses transmission of small updates according to

$${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$6

The DOE price is further decomposed into congestion, voltage, energy, and loss components, and the paper derives a direct relation between the P2P price and the DOE price, so that grid constraints are embedded in price formation rather than appended as ex post penalties (Jiang et al., 2023).

Simulation results show the operational effect of this coupling. In a 15-bus case, P2P2G without DOE converged in 93 iterations but violated voltage and line-power limits; with DOE, convergence took 187 iterations, network integrity was restored, and daily loss dropped from 1.175 MWh to 0.245 MWh. Communication was reduced from 1122 peer communications under standard ADMM to 860 under COCA. In a 141-bus case, the DOE + COCA variant preserved technical performance while reducing peer communications from 179172 to 20731 (Jiang et al., 2023).

5. Performance, benefits, and recurrent misunderstandings

The scheduling-oriented P2Es formulation reports multiple benefit streams in a case study with three ECs with six houses each. The numerical outcomes are Total Profit from Grid = $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$7, Total Profit from Parking Hosting = $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$8, Total Social Welfare Profit of Customers = $${ENS}_{c,u,t}=[ID_{c,u,t}^{Subsequent\ PV}-{DR}_{c,u,t}-{PTIDFG}_{c,u,t}-{PTFP2P}_{c,u,t}],$$9, and Total Profit = $$\sum\limits_{c\in C,u\in U}{PT2P2P}_{c,u,t}=\sum\limits_{c\in C,u\in U}{PTFP2P}_{c,u,t}.$$0. In that formulation, guest EVs have a 25 kWh battery and must depart at 90% state of charge (Alirezazadeh et al., 2024).

Several recurrent misunderstandings are addressed directly by the literature. First, prosumer-heavy communities are not necessarily poor P2P candidates: under flexible role switching, a (1:9) community can have substantial latent activity even when a static seller-only model suggests very limited trading potential (Imran et al., 20 Jun 2026). Second, more installed PV does not automatically imply higher trading potential; this depends on whether sufficient buyers remain in the community (Imran et al., 20 Jun 2026). Third, purely economic P2P scheduling is not sufficient for feeder operation, because voltage violations, line congestion, and higher network losses can emerge when detailed network constraints are ignored (Jiang et al., 2023). Fourth, grid-aware P2Es need not require full DSO visibility of every bilateral trade, since DOE negotiation can preserve privacy while still guaranteeing network integrity (Jiang et al., 2023).

Taken together, these results suggest a layered interpretation of P2Es. At the market layer, it is a local exchange mechanism that rewards self-supply, local trading, DR, EV services, and parking provision. At the structural layer, it is a graph-constrained opportunity space whose value depends on role flexibility and community composition. At the network layer, it is viable only when export behavior is coordinated with feeder constraints.

6. Terminological ambiguity and cross-disciplinary usage

The acronym P2Es is context-dependent. In the smart-grid literature summarized above, it denotes peer-to-peer energy systems. In another supplied source, however, the paper’s “P2Es” content refers to a proposed direct positron/electron comparison measurement of two-photon exchange in Hall A, based on

$$\sum\limits_{c\in C,u\in U}{PT2P2P}_{c,u,t}=\sum\limits_{c\in C,u\in U}{PTFP2P}_{c,u,t}.$$1

with the charge-odd part of the amplitude isolating TPE effects in elastic scattering (Cline et al., 2021).

This suggests an editorial caution rather than a substantive contradiction: in interdisciplinary writing, the expansion of P2Es should be stated explicitly on first use. In the energy-systems sense, the term denotes a community-scale framework for local electricity exchange, scheduling, and infrastructure evaluation. In other fields, the same letter sequence can denote unrelated experimental programs.