Pith. sign in

REVIEW 4 major objections 4 minor 50 references

Online distributed optimization for spatio-temporally constrained real-time peer-to-peer energy trading

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Real-time peer-to-peer energy trading with storage and network constraints can be cleared online, distributively, within a bounded cost gap of the stochastic optimum.

desk verdict The algorithmic framework is worth a look, but the central near-optimality theorem has a sign error in the drift bound and the discomfort cost vanishes by definition, so the main theoretical claim doesn't stand as written. read the letter →

arxiv 2505.21884 v1 pith:V7X4UFK7 submitted 2025-05-28 eess.SY cs.SYmath.OC

Junhong Liu , Qinfei Long , Rong-Peng Liu , Wenjie Liu , Yunhe Hou This is my paper
classification eess.SYcs.SYmath.OC
keywords peer-to-peerenergytradingLyapunovoptimizationconsensusADMMstoragesystemnetworkconstraintsonlinedistributedreal-timemarketclearingnear-optimalperformancebound
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Real-time peer-to-peer electricity markets must clear trades before future demand, solar output, and prices are known, while respecting battery state-of-charge dynamics and distribution-network voltage and flow limits. This paper tries to establish that such markets can be operated online—decisions made from current data alone—at a time-averaged cost no worse than the optimal stochastic benchmark plus an explicit gap that depends only on storage parameters. The argument works by modifying Lyapunov optimization so the battery charge can move freely inside its bounds instead of jumping to boundary values, and by a consensus ADMM scheme whose per-agent updates are closed-form. If correct, the result offers a privacy-preserving, fast, near-optimal market-clearing method that needs no forecasts, no centralized solver, and no sharing of private cost functions.

What carries the argument

The load-bearing object is the shifted state-of-charge virtual queue $\tilde{S}_{i,t} = S_{i,t} + \epsilon_i$ with per-prosumer weight $\delta_i$, and the drift-plus-penalty objective of P2: minimize $f_t(\Phi_t) + \sum_{i\in\mathcal{N}_p} \delta_i\,[\kappa_i \tilde{S}_{i,t} w_{i,t} + (1-\kappa_i)\epsilon_i w_{i,t} + \tfrac{1}{2} w_{i,t}^2]$. Unlike standard Lyapunov storage control, the quadratic $w^2$ term is kept so the online problem is a quadratic program and the battery decision $w_{i,t}$ may take interior values inside its bounds rather than only boundary values; the paper argues this enlarges the feasible solution space and improves flexibility. The performance gap $\Theta$ is controlled by the variance bound $D[w^\dagger_{i,t}] \le (w_{\max} - w_{\min})^2$ from Lemma 2.2 and by the auxiliary problem P4, whose optimal value lower-bounds $\Psi^*_{P1}(\Phi)$. To distribute P2, each trading variable $e_{i,j,t}$ is duplicated as $u_{i,j,t}$ with the consensus constraint $u_{i,j,t} + u_{j,i,t} = 0$, and closed-form KKT updates for $e$, $w$, $p$, and $u$ are derived; the utility company plays the role of a network manager that returns the aggregated shadow price $R_{i,t}$ for voltage and line-flow constraints.

What would settle it

Evaluate the exact per-slot Lyapunov drift for a single prosumer with $\kappa_i < 1$ at its extreme SoC states and compare it with the claimed constant $M_i$ in Eq. (14); if the exact drift ever exceeds $M_i$, Lemma 2.1 fails and the chain in Theorem 2.1 breaks. A second test: run the closed-form updates on a two-bus one-buyer one-seller market with $\kappa_i < 1$ and check at every ADMM iteration whether the sign constraints (6a)-(6b) and the energy-balance equations (7a)-(7b) are actually satisfied.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is Theorem 2.1: if the random system states are i.i.d. over the operation period, then the time-averaged cost $\Psi_{P1}(\Phi^*)$ of the online decision sequence produced by the drift-plus-penalty problem P2 at each slot satisfies $\Psi^*_{P1}(\Phi) \le \Psi_{P1}(\Phi^*) \le \Psi^*_{P1}(\Phi) + \Theta$, where $\Psi^*_{P1}(\Phi)$ is the optimal value of the original spatio-temporally constrained stochastic problem and $\Theta$ is the explicit constant in Eq. (40) built from storage parameters (weight $\delta_i$, shift $\epsilon_i$, efficiency $\kappa_i$, and SoC bounds) together with the width of the charging window. The proof chain runs through Lemma 2.1 (drift upper bound), the auxiliary problem P4 whose optimum lower-bounds $\Psi^*_{P1}$, and Lemma 2.2 (existence of a stationary solution $\Phi^\dagger$ with bounded variance for the battery action), then sums the per-slot inequalities up to $T$ and lets $T \to \infty$. The reformulation from P2 to the distributed problem P3 via consensus ADMM is claimed to be exact, with zero additional performance gap, so the bound applies to the distributed algorithm; the closed-form KKT updates for $e$, $w$, $p$, and $u$ are said to make the distributed solution match the centralized optimum while only traded energies and shadow prices are exchanged between peers and active-power injections are sent to the utility company.

Load-bearing premise

The load-bearing premise is Lemma 2.1's drift inequality: the per-slot change in the shifted battery Lyapunov function must be bounded above by the constant $M_i$ for every feasible state, and if that inequality fails for some $\kappa_i < 1$ the whole gap argument in Theorem 2.1 loses its starting point.

Editorial extensions

If this is right

  • Decisions for the real-time P2P market can be made from current and past data alone, without forecasts or look-ahead, at a time-averaged cost within the explicit gap $\Theta$ of the stochastic optimum.
  • The consensus-ADMM implementation keeps prosumer cost functions and ESS parameters private: only traded energies and shadow prices are shared with peers, and only active-power injections are shared with the utility company.
  • The closed-form per-agent updates reduce the online clearing time on the tested 15- to 141-bus systems to roughly 1/100 to 1/450 of the centralized solver time, making sub-hourly market clearing practical.
  • The gap $\Theta$ depends only on ESS parameters, so it can be reduced offline by the SDP-based tuning of the shifting and weight parameters; the reported one-day simulation shows a 53.10% cost reduction over the greedy algorithm.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The i.i.d. assumption is likely not necessary in practice: the paper notes an extension to finite ergodic Markov chains, and a cheaper empirical test would be to run the same algorithm on historical solar, load, and price traces and compare its time-averaged cost with the offline optimum; if the gap stays near or below $\Theta$, the guarantee holds beyond i.i.d.
  • The drift-bound issue in Lemma 2.1 (the coefficient $(\kappa_i^2 - 1)$ is non-positive, so replacing the quadratic term by its maximum is not an upper bound) means a user should verify the constant $M_i$ numerically for their own battery parameters before relying on the guaranteed gap.
  • The claim that the distributed reformulation is exactly equivalent to P2 assumes the closed-form updates always respect the bilateral sign constraints and the utility-company balance equations at every iteration; this is worth a direct feasibility check, since the $[\cdot]^+$ projections in Eqs. (7a)-(7b) can in principle produce infeasible iterates when the trading graph is sparse.
  • The framework should extend to piecewise-linear or time-varying tariffs, since the closed-form updates come from KKT conditions; re-deriving the $\Theta$ formula for such tariffs would be a concrete testable extension of the paper's method.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes an online distributed method for real-time peer-to-peer energy trading with energy storage systems and distribution-network constraints. It formulates the problem as a stochastic program P1, uses a modified Lyapunov drift-plus-cost argument to obtain an online problem P2, then applies consensus ADMM to solve P2 in a distributed manner via P3, with closed-form primal updates. The central theoretical claim is Theorem 2.1, which asserts that the time-averaged cost of the online decisions is within a finite gap Θ of the stochastic optimum. Numerical experiments on 15- to 141-bus systems compare the method against greedy, regret-based, traditional Lyapunov, and offline benchmarks.

Significance. If the theoretical guarantee were valid, this would be a useful contribution: an online, privacy-preserving, distributed algorithm for P2P energy trading that handles ESS and network constraints without forecasts, with closed-form updates and a quantitative optimality gap. The paper deserves credit for a clearly stated problem formulation, for explicitly separating the temporal relaxation from the spatial ADMM decomposition, and for reporting concrete simulation comparisons including scalability on larger systems. However, the central near-optimality guarantee is not established as written: the drift bound in Lemma 2.1 has an algebraic sign error, the gap Θ inherits that error, and the closed-form updates do not enforce the bilateral sign constraints. The significance of the paper is therefore conditional on a substantial revision of the proof and of the algorithmic feasibility argument.

major comments (4)
  1. [§3.1, Lemma 2.1, Eqs. (13)–(15)] Lemma 2.1 is not a valid upper bound as stated. In the proof, the term 0.5(κ_i^2−1)·max{(S_min+ε_i)^2, (S_max+ε_i)^2} is used to bound 0.5(κ_i^2−1)·̃S_{i,t}^2. Since the paper assumes κ_i∈(0,1], the coefficient 0.5(κ_i^2−1) is non-positive, so replacing ̃S_{i,t}^2 by the maximum squared shifted queue produces the most negative value of that quadratic term, not an upper bound; a valid upper bound would need the squared shifted queue closest to zero. In addition, M_i in Eq. (14) contains the term κ_i(1−κ_i)̃S_{i,t}ε_i, which depends on the state ̃S_{i,t}, so M_i is not a constant for the listed parameters {δ_i, ε_i, κ_i, S_min_i, S_max_i}. Because Theorem 2.1 uses this lemma at Eq. (41a), the main near-optimality claim is currently unsupported.
  2. [§5.1, Theorem 2.1, Eqs. (40)–(43)] The performance gap Θ inherits the sign error from Lemma 2.1, and further steps in the proof are not justified. In Eq. (40a), the coefficient δ_i(κ_i−1/2−1/2κ_i^2) is non-positive for κ_i≤1, so using the maximum squared shifted queue makes the gap artificially small rather than providing an upper bound. The derivation of Θ_2 in Eqs. (42a)–(42c) is also not a valid chain: Eq. (42a) is asserted to equal an expression containing sqrt(max{(S_min+ε_i)^2, (S_max+ε_i)^2}), and that expression is then bounded by κ_i(1−κ_i)max{(S_min+ε_i)^2, (S_max+ε_i)^2}, without a correct intermediate inequality. Consequently, the proof chain (41a)–(41i) does not establish Ψ_P1(Φ*)≤Ψ*_P1+Θ. Since this is the paper's central advertised theoretical contribution, the issue is load-bearing rather than a local typo.
  3. [§2.1, Eqs. (5a) and (8)] The discomfort cost term in the objective is identically zero by the paper's own definitions. Equation (5a) defines p_{i,t}=g_{i,t}-d_{i,t}, and Eq. (8) contains the term γ_i(p_{i,t}-g_{i,t}+d_{i,t})^2. Substituting (5a) gives γ_i(0)^2=0 for every prosumer and every time slot. Thus the claimed load-rescheduling/discomfort cost has no effect on the optimization, and the variable d_{i,t} is not penalized as described. This affects the interpretation of the model and of the simulation results involving demand flexibility.
  4. [§4.2, Eqs. (26)–(30), and §5 preamble] The closed-form updates do not enforce the bilateral sign constraints (6a)–(6b), and the claimed zero performance gap between P2 and P3 is not established. Equations (26a)–(26b) are unconstrained stationary points of the augmented Lagrangian; no projection or inequality multipliers are introduced for the sign restrictions e_{i,j,t}≤0 or e_{i,j,t}≥0. Therefore the primal iterates may violate the buyer/seller sign constraints, so the algorithm is not guaranteed to produce feasible trades. Separately, Section 5 states that the ADMM reformulation P2→P3 is equivalent with zero performance gap, but the algorithm uses a finite stopping threshold r≤10^{-3} and a finite iteration cap k_max; ADMM convergence is asymptotic, and no bound on the suboptimality from early stopping is given. The theorem therefore applies, at best, to an exact solution of P2, not to the implemented distributed algorithm.
minor comments (4)
  1. [Eq. (14) and its proof] Equation (14) omits the squares on the max arguments, and the proof of Lemma 2.1 writes max{(S_min_i+ε_i)^2, (S_min_i+ε_i)^2} with the same term repeated; the second argument should be (S_max_i+ε_i)^2.
  2. [Figure 5 and §6.2] The text says Figure 5(b) shows traded energy and Figure 5(a) shows convergence, but the caption states the opposite; the figure parts and the textual references should be reconciled.
  3. [Eq. (26a)] The numerator uses “−β” without a subscript; it should presumably be −β_i, and the sign convention should be checked against Eq. (26b).
  4. [§6, numerical experiments] The performance comparisons appear to be based on a single simulation run or a single random draw of prosumer parameters, with no error bars or multiple-seed statistics, so the reported percentage improvements (e.g., 53.10% versus the greedy algorithm) are not accompanied by an indication of variability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the Lyapunov bound is self-contained, though it contains a soundness flaw rather than circularity.

full rationale

The paper's claimed derivation chain does not reduce to its own inputs by construction. P1 is reformulated into P2 via a drift-plus-cost surrogate, P2 to P3 via consensus ADMM, and Theorem 2.1 is meant to bound the gap between the original stochastic problem and the online decisions. No parameter is fitted to cost data and then renamed as a prediction: the offline tuning of δ_i and ϵ_i minimizes the bound Θ, not the realized cost, and the bound itself is an analytic expression in the ESS parameters. The stationary-solution Lemma 2.2 is referred to external Lyapunov and storage-control literature, and the ADMM convergence is cited to Boyd et al.; no load-bearing result rests on the authors' own prior work. The main risk is a correctness defect, not circularity: in Lemma 2.1 and the proof of Theorem 2.1, the term 0.5(κ_i²−1) times the squared shifted queue is bounded using max{(S_min+ϵ)²,(S_max+ϵ)²} even though the coefficient 0.5(κ_i²−1) is non-positive, so the stated inequality is not an upper bound; moreover, M_i in Eq. (14) still contains the state-dependent term κ_i(1−κ_i) ̃S_{i,t}ϵ_i, so it is not a constant. These are internal proof errors, but they are not cases of a conclusion being equivalent to its premise or a fitted value being presented as a prediction. Accordingly, the circularity score is 0.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

The central machinery is standard Lyapunov optimization and consensus ADMM, so the ledger is mostly assumptions about stochasticity, network modeling, and feasibility of unconstrained updates. The main invented object is the shifted virtual queue. Free parameters delta, epsilon, eta, and the dual step sizes are tuned or hand-picked; delta and epsilon also appear directly in the claimed bound Theta.

free parameters (5)
  • Lyapunov weight parameter delta_i = optimized by Algorithm 2; example range 1e-2 to 5e-2
    Controls drift-plus-cost tradeoff and appears linearly in the claimed bound Theta; tuned offline via SDP P6.
  • Virtual queue shift parameter epsilon_i = negative, often -S_max_i or S_max_i - X_i*(S_min_i + S_max_i)
    Shifts the virtual queue and appears in the bound Theta; tuned by Algorithm 2.
  • ADMM penalty factor eta = 12 in simulation
    Hand-tuned; affects convergence speed and residual balance.
  • Dual step sizes tau_p, tau_u, tau_f = not specified in text
    Used in multiplier update equations (31)-(33); values are not reported, hurting reproducibility.
  • Charging/discharging coefficient kappa_i = 0.998 in simulation
    Assumed constant per prosumer; directly affects ESS dynamics and the bound Theta.
assumptions (6)
  • domain assumption System states R_t are i.i.d. over the operation period, extendable to finite ergodic Markov.
    Invoked in Remark 2.5 and used by Lemma 2.2 to ensure a stationary optimal solution exists; real PV, load, and price time series are not i.i.d.
  • domain assumption Reactive power injection satisfies q_{j,t} = X_j * p_{j,t} with constant proportion.
    Remark 2.1 reduces the network variables; the authors note it can be lifted, but all theory and simulations use it.
  • standard math LinDistFlow is a valid linear approximation of the power flow with about 1% error.
    Equation (2) cites [34]; central to the network constraints but the error is not demonstrated on the test cases.
  • standard math There exists a stationary solution Phi^dagger_t for P4 satisfying Lemma 2.2.
    Borrowed from [42, 32, 37, 39]; not proved in this paper.
  • ad hoc to paper The unconstrained KKT closed-form updates satisfy the bilateral sign constraints and energy balance at every iteration.
    Equations (26)-(28) contain no projection; the paper asserts feasibility only through multipliers, with no proof.
  • ad hoc to paper The consensus ADMM reformulation P3 is equivalent to P2 with zero performance gap even with finite iterations and stopping tolerance 1e-3.
    Section 5 claims zero gap but only cites O(1/k) convergence from [41].
invented entities (2)
  • Shifted virtual queue tilde S_i,t = S_i,t + epsilon_i
    purpose: Converts the time-coupling ESS state constraint into a drift term for online Lyapunov optimization.
    Standard Lyapunov construct, not a physical quantity; it has no falsifiable prediction outside the paper.
  • Auxiliary trading variables u_i,j,t
    purpose: Duplicates of bilateral trades e_i,j,t to decouple spatial constraint (6c) for ADMM.
    Standard consensus variables; no independent evidence expected.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Online distributed optimization for spatio-temporally constrained real-time peer-to-peer energy trading." pith.science (2026). https://pith.science/paper/V7X4UFK7

@misc{pith2026250521884,
  author       = {Pith},
  title        = {Pith review of: Online distributed optimization for spatio-temporally constrained real-time peer-to-peer energy trading},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7X4UFK7}},
  note         = {Machine review of arXiv:2505.21884}
}
read the original abstract

The proliferation of distributed renewable energy triggers the peer-to-peer (P2P) energy market formations. To make profits, prosumers equipped with photovoltaic (PV) panels and even the energy storage system (ESS) can actively participate in the real-time P2P energy market and trade energy. However, in real situations, system states such as energy demands and renewable energy power generation are highly uncertain, making it difficult for prosumers to make optimal real-time decisions. Moreover, severe problems with the physical network can arise from the real-time P2P energy trading, such as bus voltage violations and line overload. To handle these problems, this work first formulates the real-time P2P energy trading problem as a spatio-temporally constrained stochastic optimization problem by considering ESS and the spatial physical network constraints. To deal with the uncertainties online, a modified Lyapunov optimization method is innovatively proposed to approximately reformulate the stochastic optimization problem into an online one by relaxing the time-coupling constraints. Compared with the state-of-the-art online methods, the proposed one renders more flexibility and better performance for the real-time P2P energy market operation. Additionally, to protect the prosumers' privacy, an online distributed algorithm based on the consensus alternating direction method of multipliers (ADMM) is developed to solve the reformulated online problem by decoupling the spatial constraints. The theoretical near-optimal performance guarantee of the proposed online distributed algorithm is derived, and its performance can be further improved by minimizing the performance gap. Simulation results demonstrate that the proposed online distributed algorithm can guarantee the fast, stable, and safe long-term operation of the real-time P2P energy market.

Figures

Figures reproduced from arXiv: 2505.21884 by the authors.

Figure 1
Figure 1. Scheme of the real-time P2P energy trading scenario. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Information exchange between the prosumers and utility company [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Scheme of the proposed online distributed algorithm. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (7 more)
Figure 6
Figure 6. Figure 6: Iterations needed to converge at different time slots. constraints, certain energy trading transactions can be accepted while they might cause the bus voltage violations. The net￾work constraints well help to regulate the per-unit voltage mag￾nitude within the normal r…
Figure 5
Figure 5. Figure 5: (a) The traded energy from two methods. (b) the convergence of the [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 7
Figure 7. Figure 7: (a) The voltage magnitude profiles at 14th hour. (b) the power flow [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: The energy profiles of bus-9. It is observed that the charged or discharged energy of ESS at each time slot are within the allowed limits. The SoC of ESS is also within its normal range, which is from 0 to 5(kWh). This demonstrates the effectiveness of the proposed onl…
Figure 10
Figure 10. Figure 10: Scalability analysis of the proposed algorithm. [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: Time-averaged costs under different scenarios: (a) minimum values of SoC. (b) maximum values of SoC. (c) charging/discharging coefficient. 0 10-3 10-2 5*10 -2 10 -1 5*10 -1 1 (¢/( kWh)) 0 0.2 0.4 0.6 0.8 1 R elativ e C h a n g e in Tr a d e d E n e r g y Prosumer (1,3…
Figure 12
Figure 12. Figure 12: (a) Traded energy with different τ. (b) relative change of traded energy with different τ. analysis is conducted with regard to δi . Boundary constraints (11) and (12) for ESS also work for the reformulated problems, which always ensure the norm operation of ESS under…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

50 extracted references · 49 canonical work pages

  1. [1]

    Morstyn, N

    T. Morstyn, N. Farrell, S. J. Darby, M. D. McCulloch, Using peer-to- peer energy-trading platforms to incentivize prosumers to form federated power plants, Nature energy 3 (2) (2018) 94–101

    work page 2018

  2. [2]

    Zhang, J

    C. Zhang, J. Wu, Y . Zhou, M. Cheng, C. Long, Peer-to-peer energy trad- ing in a microgrid, Applied energy 220 (2018) 1–12

    work page 2018

  3. [3]

    Y . Liu, Y . Li, H. B. Gooi, Y . Jian, H. Xin, X. Jiang, J. Pan, Distributed robust energy management of a multimicrogrid system in the real-time energy market, IEEE Transactions on Sustainable Energy 10 (1) (2017) 396–406

    work page 2017

  4. [4]

    Aminlou, B

    A. Aminlou, B. Mohammadi-Ivatloo, K. Zare, R. Razzaghi, A. Anvari- Moghaddam, Peer-to-peer decentralized energy trading in industrial town considering central shared energy storage using alternating direction method of multipliers algorithm, IET Renewable Power Generation 16 (12) (2022) 2579–2589

    work page 2022

  5. [5]

    Huang, S

    H. Huang, S. Nie, J. Lin, Y . Wang, J. Dong, Optimization of peer-to- peer power trading in a microgrid with distributed pv and battery energy storage systems. sustainability 2020; 12

    work page 2020

  6. [6]

    Nguyen, W

    S. Nguyen, W. Peng, P. Sokolowski, D. Alahakoon, X. Yu, Optimizing rooftop photovoltaic distributed generation with battery storage for peer- to-peer energy trading, Applied Energy 228 (2018) 2567–2580. 16

    work page 2018

  7. [7]

    M. A. Hannan, S. Wali, P. J. Ker, M. S. Abd Rahman, M. Mansor, V . Ra- machandaramurthy, K. Muttaqi, T. M. I. Mahlia, Z. Y . Dong, Battery energy-storage system: A review of technologies, optimization objec- tives, constraints, approaches, and outstanding issues, Journal of Energy Storage 42 (2021) 103023

    work page 2021

  8. [8]

    P. Song, Z. Xu, H. Dong, H. Cai, Z. Xie, Security-constrained line loss minimization in distribution systems with high penetration of renewable energy using upfc, Journal of Modern Power Systems and Clean Energy 5 (6) (2017) 876–886

    work page 2017

Show all 50 references
  1. [9]

    Pillai, M

    G. Pillai, M. Allison, T. P. Tun, K. Chandrakumar Jyothi, E. Kol- lonoor Babu, Facilitating higher photovoltaic penetration in residential distribution networks using demand side management and active voltage control, Engineering Reports 3 (10) (2021) e12410

    2021

  2. [10]

    C. H. Leong, C. Gu, F. Li, Auction mechanism for p2p local energy trad- ing considering physical constraints, Energy Procedia 158 (2019) 6613– 6618

    2019

  3. [11]

    Zhong, S

    W. Zhong, S. Xie, K. Xie, Q. Yang, L. Xie, Cooperative p2p energy trad- ing in active distribution networks: An milp-based nash bargaining solu- tion, IEEE Transactions on Smart Grid 12 (2) (2020) 1264–1276

    2020

  4. [12]

    Morstyn, A

    T. Morstyn, A. Teytelboym, M. D. McCulloch, Bilateral contract net- works for peer-to-peer energy trading, IEEE Transactions on Smart Grid 10 (2) (2018) 2026–2035

    2018

  5. [13]

    Q. Peng, S. H. Low, Distributed optimal power flow algorithm for radial networks, i: Balanced single phase case, IEEE Transactions on Smart Grid 9 (1) (2016) 111–121

    2016

  6. [14]

    Paudel, L

    A. Paudel, L. P. M. I. Sampath, J. Yang, H. B. Gooi, Peer-to-peer energy trading in smart grid considering power losses and network fees, IEEE Transactions on Smart Grid 11 (6) (2020) 4727–4737

    2020

  7. [15]

    Paudel, Y

    A. Paudel, Y . Jiawei, H. B. Gooi, Peer-to-peer energy trading in smart grids considering network utilization fees, in: 2020 IEEE Power & En- ergy Society General Meeting (PESGM), IEEE, 2020, pp. 1–5

    2020

  8. [16]

    J. Kim, Y . Dvorkin, A p2p-dominant distribution system architecture, IEEE Transactions on Power Systems 35 (4) (2019) 2716–2725

    2019

  9. [17]

    C. Feng, B. Liang, Z. Li, W. Liu, F. Wen, Peer-to-peer energy trading under network constraints based on generalized fast dual ascent, IEEE Transactions on Smart Grid 14 (2) (2022) 1441–1453

    2022

  10. [18]

    K. Umer, Q. Huang, M. Khorasany, M. Afzal, W. Amin, A novel commu- nication efficient peer-to-peer energy trading scheme for enhanced pri- vacy in microgrids, Applied Energy 296 (2021) 117075

    2021

  11. [19]

    W. Shi, N. Li, C.-C. Chu, R. Gadh, Real-time energy management in microgrids, IEEE Transactions on Smart Grid 8 (1) (2015) 228–238

    2015

  12. [20]

    Iqbal, M

    S. Iqbal, M. Nasir, M. F. Zia, K. Riaz, H. Sajjad, H. A. Khan, I. Mem- ber, A novel approach for system loss minimization in a peer-to-peer en- ergy sharing community dc microgrid, International Journal of Electrical Power & Energy Systems 129 (2021) 106775

    2021

  13. [21]

    Y . Jia, C. Wan, P. Yu, Y . Song, P. Ju, Security constrained p2p energy trading in distribution network: An integrated transaction and operation model, IEEE Transactions on Smart Grid 13 (6) (2022) 4773–4786

    2022

  14. [22]

    J. Li, C. Zhang, Z. Xu, J. Wang, J. Zhao, Y .-J. A. Zhang, Distributed trans- active energy trading framework in distribution networks, IEEE Transac- tions on Power Systems 33 (6) (2018) 7215–7227

    2018

  15. [23]

    Paudel, K

    A. Paudel, K. Chaudhari, C. Long, H. B. Gooi, Peer-to-peer energy trad- ing in a prosumer-based community microgrid: A game-theoretic model, IEEE Transactions on Industrial electronics 66 (8) (2018) 6087–6097

    2018

  16. [24]

    Zhang, R

    Z. Zhang, R. Li, F. Li, A novel peer-to-peer local electricity market for joint trading of energy and uncertainty, IEEE Transactions on Smart Grid 11 (2) (2019) 1205–1215

    2019

  17. [25]

    Khorasany, Y

    M. Khorasany, Y . Mishra, G. Ledwich, A decentralized bilateral energy trading system for peer-to-peer electricity markets, IEEE Transactions on industrial Electronics 67 (6) (2019) 4646–4657

    2019

  18. [26]

    G. M. Tina, C. Ventura, S. Ferlito, S. De Vito, A state-of-art-review on machine-learning based methods for pv, Applied Sciences 11 (16) (2021) 7550

    2021

  19. [27]

    Bouachir, M

    O. Bouachir, M. Aloqaily, ¨O. ¨Ozkasap, F. Ali, Federatedgrids: Federated learning and blockchain-assisted p2p energy sharing, IEEE Transactions on Green Communications and Networking 6 (1) (2022) 424–436

    2022

  20. [28]

    T. Chen, S. Bu, Realistic peer-to-peer energy trading model for microgrids using deep reinforcement learning, in: 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe), IEEE, 2019, pp. 1–5

    2019

  21. [29]

    Zhang, Q

    W. Zhang, Q. Li, Q. He, Application of machine learning methods in photovoltaic output power prediction: A review, Journal of Renewable and Sustainable Energy 14 (2) (2022)

    2022

  22. [30]

    Shahriar, A.-R

    S. Shahriar, A.-R. Al-Ali, A. H. Osman, S. Dhou, M. Nijim, Machine learning approaches for ev charging behavior: A review, IEEE Access 8 (2020) 168980–168993

    2020

  23. [31]

    G. Wang, W. Cai, Y . Zhang, K. Zhao, X. Xu, Lyapunov optimization based online energy flow control for multi-energy community microgrids, in: 2019 IEEE PES GTD Grand International Conference and Exposition Asia (GTD Asia), IEEE, 2019, pp. 706–711

    2019

  24. [32]

    J. Qin, Y . Chow, J. Yang, R. Rajagopal, Modeling and online control of generalized energy storage networks, in: Proceedings of the 5th interna- tional conference on Future energy systems, 2014, pp. 27–38

    2014

  25. [33]

    Z. Guo, P. Pinson, S. Chen, Q. Yang, Z. Yang, Online optimization for real-time peer-to-peer electricity market mechanisms, IEEE Transactions on Smart Grid 12 (5) (2021) 4151–4163

    2021

  26. [34]

    X. Zhou, Z. Liu, W. Wang, C. Zhao, F. Ding, L. Chen, Hierarchical distributed voltage regulation in networked autonomous grids, in: 2019 American Control Conference (ACC), IEEE, 2019, pp. 5563–5569

    2019

  27. [35]

    H. Zhu, H. J. Liu, Fast local voltage control under limited reactive power: Optimality and stability analysis, IEEE Transactions on Power Systems 31 (5) (2015) 3794–3803

    2015

  28. [36]

    M. H. Ullah, J.-D. Park, Peer-to-peer energy trading in transactive markets considering physical network constraints, IEEE Transactions on Smart Grid 12 (4) (2021) 3390–3403

    2021

  29. [37]

    J. Qin, Y . Chow, J. Yang, R. Rajagopal, Online modified greedy algo- rithm for storage control under uncertainty, IEEE Transactions on Power Systems 31 (3) (2015) 1729–1743

    2015

  30. [38]

    Zhong, K

    W. Zhong, K. Xie, Y . Liu, C. Yang, S. Xie, Y . Zhang, Online control and near-optimal algorithm for distributed energy storage sharing in smart grid, IEEE Transactions on Smart Grid 11 (3) (2019) 2552–2562

    2019

  31. [39]

    Neely, Stochastic network optimization with application to communi- cation and queueing systems, Springer Nature, 2022

    M. Neely, Stochastic network optimization with application to communi- cation and queueing systems, Springer Nature, 2022

    2022

  32. [40]

    Le Cadre, P

    H. Le Cadre, P. Jacquot, C. Wan, C. Alasseur, Peer-to-peer electricity mar- ket analysis: From variational to generalized nash equilibrium, European Journal of Operational Research 282 (2) (2020) 753–771

    2020

  33. [41]

    S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al., Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends® in Machine learning 3 (1) (2011) 1–122

    2011

  34. [42]

    Tushar, C

    W. Tushar, C. Yuen, T. K. Saha, T. Morstyn, A. C. Chapman, M. J. E. Alam, S. Hanif, H. V . Poor, Peer-to-peer energy systems for connected communities: A review of recent advances and emerging challenges, Ap- plied energy 282 (2021) 116131

    2021

  35. [43]

    Ouali, A

    S. Ouali, A. Cherkaoui, et al., An improved backward /forward sweep power flow method based on a new network information organization for radial distribution systems, Journal of electrical and Computer Engineer- ing 2020 (2020)

    2020

  36. [44]

    Pena-Bello, E

    A. Pena-Bello, E. Barbour, M. Gonzalez, M. K. Patel, D. Parra, Opti- mized pv-coupled battery systems for combining applications: Impact of battery technology and geography, Renewable and Sustainable Energy Reviews 112 (2019) 978–990

    2019

  37. [45]

    Grant, S

    M. Grant, S. Boyd, Cvx: Matlab software for disciplined convex pro- gramming, version 2.1 (2014)

    2014

  38. [46]

    Huang, Y

    Q. Huang, Y . Xu, T. Wang, C. A. Courcoubetis, Market mechanisms for cooperative operation of price-maker energy storage in a power network, IEEE Transactions on Power Systems 33 (3) (2017) 3013–3028

    2017

  39. [47]

    D. R. Conover, A. J. Crawford, V . V . Viswanathan, S. Ferreira, D. Schoen- wald, Protocol for uniformly measuring and expressing the perfor- mance of energy storage systems, Tech. rep., Pacific Northwest National Lab.(PNNL), Richland, W A (United States) (2014)

    2014

  40. [48]

    J. Yang, A. Paudel, H. B. Gooi, H. D. Nguyen, A proof-of-stake public blockchain based pricing scheme for peer-to-peer energy trading, Applied Energy 298 (2021) 117154

    2021

  41. [49]

    Baroche, P

    T. Baroche, P. Pinson, R. L. G. Latimier, H. B. Ahmed, Exogenous cost al- location in peer-to-peer electricity markets, IEEE Transactions on Power Systems 34 (4) (2019) 2553–2564

    2019

  42. [50]

    J. Shi, Z. Ye, H. O. Gao, N. Yu, Lyapunov optimization in online battery energy storage system control for commercial buildings, IEEE Transac- tions on Smart Grid 14 (1) (2022) 328–340. 17

    2022

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.