This paper proposes a novel Peer-to-Peer (P2P) joint electricity and carbon (E&C) trading model to co-optimize the energy and carbon emissions permit transactions considering the trading preferences in the distribution network. To realize the secure and low-carbon network operation, a decomposable carbon-aware distribution locational marginal pricing (CDLMP)-based operation service pricing scheme of the distribution system operator (DSO) is proposed to guide the P2P transactions among prosumers. In practice, the coordination between the P2P market and the DSO is cast as a bi-level optimization. In the upper level, the network operation optimization of the DSO is modeled as a carbon-aware optimal power flow (COPF) problem based on a carbon emission flow model to ensure the security of network operation and derive the CDLMP. In the lower level, a decentralized P2P joint E&C trading is modeled to simultaneously clear energy and carbon permit. Later, this paper develops an l (p)-Box ADMM method to relax the binary variables originating from the peer-matching process of the carbon trading. Finally, a novel demurrage protocol is designed to facilitate the convergence of the bi-level interaction with an incentive for trading adjustments. Case studies illustrate the effectiveness of the proposed method in motivating “grid-friendly” and “low-carbon” P2P trading.

This paper presents a chance constrained information gap decision model for multi-period microgrid expansion planning (MMEP) considering two categories of uncertainties, namely random and non-random uncertainties. The main task of MMEP is to determine the optimal sizing, type selection, and installation time of distributed energy resources (DER) in microgrid. In the proposed formulation, information gap decision theory (IGDT) is applied to hedge against the non-random uncertainties of long-term demand growth. Then, chance constraints are imposed in the operational stage to address the random uncertainties of hourly renewable energy generation and load variation. The objective of chance constrained information gap decision model is to maximize the robustness level of DER investment meanwhile satisfying a set of operational constraints with a high probability. The integration of IGDT and chance constrained program, however, makes it very challenging to compute. To address this challenge, we propose and implement a strengthened bilinear Benders decomposition method. Finally, the effectiveness of proposed planning model is verified through the numerical studies on both the simple and practical complex microgrid. Also, our new computational method demonstrates a superior solution capacity and scalability. Compared to directly using a professional mixed integer programming solver, it could reduce the computational time by orders of magnitude.

Real-time dispatch in microgrid (MG) is to balance the fluctuating supply and demand resulted from load and renewable generation by dispatching the energy storage system (ESS) and controllable generators. However, it is difficult to evaluate the real-time charging and discharging costs of ESS. In this paper, two hidden costs, discharging opportunity cost and marginal charging cost, are proposed and modeled for ESS from the perspective of real-time operation, which lead to more efficient coordination between ESS and controllable generators. A two-layer model is presented for MG real-time operation. The upper layer is a look-ahead dispatch that optimally allocates power for each generator. Then, two hidden costs of ESS are analyzed and modeled according to the Lagrangian formulation of the look-ahead dispatch problem. On the basis of the two hidden costs, a practical, efficient, and time-saving corrective strategy is proposed for the lower layer real-time dispatch. Feasibility and effectiveness of the proposed method are verified on a typical MG system. Simulation results validate the correctness of the two hidden costs of ESS. Further, the proposed method has proven to outperform existing real-time dispatch methods by a comparative study.

The advanced switching techniques enable the topology reconfiguration of microgrids (MGs) in active distribution network. In this paper, we enhance and generalize the traditional reconfiguration strategy resorting to the concept of “dynamic MGs” (i.e., the reorganization of MGs boundaries), to achieve a higher operational feasibility against the emergency islandings. Also, a risk-averse two-stage mixed integer conic program model is presented to support the networked MGs planning with generalized reconfiguration decisions. The MGs capacity expansion and seasonal reconfiguration decisions are made in the first stage, and validated under stochastic islanding scenarios in the second stage, where the network operations are captured by a second-order conic program (SOCP). Furthermore, a conditional value-at-risk (CVaR) measure is involved to quantitatively control the islanding risks. By theoretically proving the strong duality of the SOCP subproblem, we develop and customize Benders decomposition method with the guaranteed finite convergence to the optimal value. Finally, numerical results on 33- and 56-bus networked MGs validate the effectiveness of proposed reconfiguration strategy as well as planning approach. Our method demonstrates a cost-saving up to 22.56% when comparing to the traditional scheme with fixed MGs boundaries.

This paper presents a chance constrained stochastic conic program model for networked microgrids planning. Under a two-stage optimization framework, we integrate a multi-site microgrids investment problem and two sets of operational problems that correspond to the grid-connected and islanding modes, respectively. To handle the uncertain nature of renewable energy generation and load variation, as well as the contingent islanding caused by external disruptions, stochastic scenarios are employed to capture randomness and a joint chance constraint is introduced to control the operational risks. A second-order conic program (SOCP) formulation is also utilized to accurately describe the AC optimal power flow (OPF) in operational problems. As the resulting mixed integer SOCP model is computationally difficult, we customize the bilinear Benders decomposition with non-trivial enhancement techniques to deal with practical instances. Numerical results on 5-and 69-bus networked microgrids demonstrate the effectiveness of the proposed planning model and the superior performance of our solution algorithm.

Compared with commonly-used point forecasting, probabilistic forecasting provides quantitative information on the uncertainty associated with wind power output. However, most studies focus on modelling only a fixed set of quantiles or intervals, which cannot provide the entire information of wind power distribution. In this paper, we propose a non-parametric and flexible method for probabilistic wind power forecasting. First, the distribution of wind power output is specified by spline quantile function, which avoids assuming a parametric form and also provides flexible shape for wind power density. Then, autoregressive recurrent neural network is used to build the non-linear mapping from input features to the parameters of quadratic spline quantile function. A novel loss function based on continuous ranked probability score (CRPS) is designed to train the forecasting model. We also derive the closed-form solution of the integral required in computing the CRPS-based loss function in order to improve the computational efficiency in training. The effectiveness of our proposed method has been validated with public real-world data from Global Energy Forecasting Competition 2014. Compared with some advanced benchmarks, our proposed approach outperforms them at least six percent in terms of CRPS, indicating that it can provide probabilistic wind power forecasting with high quality.