A cooperative model of photovoltaic and electricity-to-hydrogen including green certificate trading under the conditional value at risk

Cooperation in energy systems is no longer limited to the distribution of electricity,and more attention is paid to the trading of green certificates(GCs).This paper proposed a cooperative method for photovoltaic(PV)and electric-to-hydrogen(EH)trading,including GC trading under risk management.First,a novel PV and EH model is established and the cooperation mechanism is analyzed.Meanwhile,PV and EH models were risk-controlled using the conditional value at risk to reduce the impact of the uncertainty of PV electricity and EH loads.Then,the PV-EH cooperative model was established based on cooperative game theory;this was then divided into two subproblems of“cooperative benefit maximization”and“transaction payment negotiation,”and the above two subproblems were solved distributively by alternating direction multiplier method(ADMM).Only energy transactions and price negotiations were conducted between the PV and EH,which can protect the privacy and confidentiality of each entity.Finally,the effectiveness of the cooperation model was verified using a practical engineering case.The simulation results show that the cooperation of the PV-EH can significantly improve the operational efficiency of each entity and the overall efficiency of the cooperation and realize the efficient redistribution of electricity and GC.

EXTRAPUSH FOR CONVEX SMOOTH DECENTRALIZED OPTIMIZATION OVER DIRECTED NETWORKS

In this note, we extend the algorithms Extra [13] and subgradient-push [I0] to a new algorithm ExtraPush for consensus optimization with convex differentiable objective functions over a directed network. When the stationary distribution of the network can be computed in advance, we propose a simplified algorithm called Normalized ExtraPush. Just like Extra, both ExtraPush and Normalized ExtraPush can iterate with a fixed step size. But unlike Extra, they can take a column-stochastic mixing matrix, which is not necessarily doubly stochastic. Therefore, they remove the undirected-network restriction of Extra. Subgradient-push, while also works for directed networks, is slower on the same type of problem because it must use a sequence of diminishing step sizes. We present preliminary analysis for ExtraPush under a bounded sequence assumption. For Normalized ExtraPush, we show that it naturally produces a bounded, linearly convergent sequence provided that the objective function is strongly convex. In our numerical experiments, ExtraPush and Normalized ExtraPush performed similarly well. They are significantly faster than subgradient-push, even when we hand-optimize the step sizes for the latter.

Decentralized State Estimation of Combined Heat and Power System Considering Communication Packet Loss

In order to obtain an accurate state estimation of the operation in the combined heat and power system,it is necessary to carry out state estimation.Due to the limited information sharing among various energy systems,it is practical to perform state estimation in a decentralized manner.However,the possible communication packet loss is seldomly considered among various energy systems.This paper bridges this gap by proposing a relaxed alternating direction method of multiplier algorithm.It can also improve the computation efficiency compared with the conventional alternating direction of the multiplier algorithm.Case studies of two test systems are carried out to show the validity and superiority of the proposed algorithm.

Online Learning over a Decentralized Network Through ADMM

In this paper,we focus on the decentralized online learning problem where online data streams are separately collected and collaboratively processed by a network of decentralized agents.Comparing to centralized batch learning,such a framework is faithful to the decentralized and online natures of the data streams.We propose an online decentralized alternating direction method of multipliers that efficiently solves the online learning problem over a decentralized network.We prove its O(√T)regret bound when the instantaneous local cost functions are convex,and its O(log T)regret bound when the instantaneous local cost functions are strongly convex,where T is the number of iterations.Both regret bounds are in the same orders as those of centralized online learning.Numerical experiments on decentralized online least squares and classification problems demonstrate effectiveness of the proposed algorithm.

Decentralized Robust Energy Management of Multi-area Integrated Electricity-gas Systems

This paper proposes a fast and decentralized solution methodology for the robust operation of multi-area integrated electricity-gas systems(M-IEGSs).A deterministic reformulation is obtained for the two-stage robust model by applying the linear decision rule based electrical reserve utilization scheme as well as regulating the distributed gas storages.Two linear approximations are developed for the nonconvex Weymouth equation in the gas network to determine the gas flow directions.The penalty convex-concave procedure(P-CCP)is then adopted to refine a feasible local optimum for the nonconvex model with an acceleration strategy.The decentralized decision-making is enabled by the alternating direction multipliers method(ADMM).The convergence as well as computation performance of the overall solution procedure can be guaranteed as only convex optimizations are solved.Simulation results validate the effectiveness of the proposed methods as well as the benefits of the proposed convex programing based solution procedure.

Stochastic Accelerated Alternating Direction Method of Multipliers for Hedging Communication Noise in Combined Heat and Power Dispatch

Combined heat and power dispatch(CHPD)opens a new window for increasing operational flexibility and reducing wind power curtailment.Electric power and district heating systems are independently controlled by different system operators;therefore,a decentralized solution paradigm is necessary for CHPD,in which only minor boundary information is required to be exchanged via a communication network.However,a nonideal communication environment with noise could lead to divergence or incorrect solutions of decentralized algorithms.To bridge this gap,this paper proposes a stochastic accelerated alternating direction method of multipliers(SA-ADMM)for hedging communication noise in CHPD.This algorithm provides a general framework to address more types of constraint sets and separable objective functions than the existing stochastic ADMM.Different from the single noise sources considered in the existing stochastic approximation methods,communication noise from multiple sources is addressed in both the local calculation and the variable update stages.Case studies of two test systems validate the effectiveness and robustness of the proposed SAADMM.