A day-ahead market-clearing model is proposed for smart distribution systems in this paper. Various types of distributed energy resources (DERs), such as distributed energy storage, distributed generators, microgrids, and load aggregators, can bid into the day-ahead distribution-level market. Considering system Volt/VAR control, network reconfiguration and interactions with the wholesale market, an optimization model is built to clear the day-ahead market, through which the distribution locational marginal pricing (DLMPs) for both active power and reactive power are determined. Through derivations of the Lagrangian function and sensitivity factors, DLMPs are decomposed to five components, i.e., marginal costs for active power, reactive power, congestion, voltage support, and loss, which provide price signals to motivate DERs to contribute to congestion management and voltage support. Finally, case studies demonstrate the effectiveness of the proposed method.

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 proposes a convex optimization based distributed algorithm to solve the multi-period optimal gas-power flow (OGPF) problem in coupled energy distribution systems. At the gas distribution system side, the non-convex Weymouth gas flow equations are convexified as quadratic constraints. Then the optimal gas flow (OGF) subproblem is solved by an iterative second-order cone programming (SOCP) procedure, whose efficiency is two orders of magnitudes higher than traditional nonlinear methods. A convex quadratic program based initiation scheme is suggested, which helps to find a high-quality starting point. At the power distribution system side, convex relaxation is performed on the non-convex branch flow equations, and the optimal power flow (OPF) subproblem gives rise to an SOCP. Tightness is guaranteed by the radial topology. In the proposed distributed algorithm, the OGF problem and the OPF problem are solved independently, and coordinated by the alternating direction multiplier method (ADMM). Numerical results corroborate significant enhancements on computational robustness and efficiency compared with existing OGPF calculation methods.

The reliable operation of Internet data centers (IDCs) is crucial to digitization transformation of society. However, the extreme fault on the IDC-located distribution network is fatal to IDC operation. The evolution of flexible distribution networks (FDNs) can satisfy the deep dependence of IDC on high-quality and reliable power supply. In FDNs, AC/DC feeders with multiple voltage levels can be flexibly interconnected and adjusted by flexible stations (FSs). It is promising to flexibly enhance operation performance of crucial IDCs after fault isolation in FDNs. In this paper, a coordinated supply restoration method of IDCs in FDNs with spatial-temporal regulation is proposed to minimize IDC data-dropping loss under complex faults. First, a spatial-temporal transfer strategy of IDC workloads is precisely formulated and an FS-based network reconfiguration strategy is proposed. Then, a mixed-integer second-order conic programming model is established for efficient solving. Spatial-temporal coordination among the source, network, storage, and demand sides can be realized without violating physical feasibility. Finally, the proposed method is validated on the modified IEEE 33-node and modified IEEE 123-node test cases. Case studies show that total outage loss is effectively reduced with sufficient utilization of available power. Operational performance of FDN is also enhanced under extreme faults.

Distribution-level electricity market provides a platform for trading energy and grid services from large-amount of small-scale distributed energy resources (DERs) located on distribution grids. The behavior of the DERs in the distribution electricity market may ultimately impact the market-clearing and locational marginal prices (LMPs) in the wholesale market. This paper proposes a bi-level optimization model for distribution market clearing and distribution locational marginal pricing (DLMP) considering the interactions between distribution and transmission wholesale markets. In the proposed model, the upper-level model represents the distribution system operator (DSO) market-clearing and the lower-level model represents the wholesale market-clearing by the independent system operator (ISO). The LMP at the substation will impact the DER dispatch and power demands of the DSO as well as the DLMP. In turn, the power demands of the DSO will further impact the ISO market and its LMPs. The equilibrium problem with equilibrium constraints (EPEC) approach is applied to find the equilibria of multiple DSOs and the ISO. The EPEC problem is transformed into a single-level mixed-integer convex problem in order to allow for efficient solving. The effectiveness of the proposed model and solution method are demonstrated through case studies.

The high-precision parameters in distribution networks are difficult to obtain, which brings difficulties to the model-based methods and analysis. With the widespread deployment of high-precision measurement units, data-driven methods have greater advantages in practice. In addition, with massive integration of distributed renewable generation and fast electric vehicle chargers, the fluctuations of net load increase significantly. The data-driven power flow calculation method based on the linear model becomes difficult to obtain accurate results for the low nonlinear adaptability. To improve the data-driven power flow calculation accuracy under high penetration of renewable distribution generation, this paper proposed an approach with high adaptability to the nonlinearity of power flow. Based on the thought of Koopman operator theory, the nonlinear relationship in power flow calculation is converted into a linear mapping in a higher dimension state space, which can significantly improve the calculation accuracy. Case studies on different IEEE cases have demonstrated that the proposed method can realize higher accuracy in power flow calculation with large-scale power fluctuations, compared to the existing data-driven method, in both mesh and radial networks. Finally, measurement data of a practical 10kV distribution network has been further used to verify the effectiveness of the proposed method in practical applications.