This manuscript proposes a time-series temperature-dependent power flow method for unbalanced distribution networks consisting of underground cables. A thermal circuit model for unbalanced three-phase multi-core cables is developed to estimate the conductor temperature and resistance of Medium and Low Voltage distribution networks. More specifically, a novel approach is proposed to model and estimate the parameters of the three-phase thermal circuit of 3/4-core cables, using the results of Finite Element Method and Particle Swarm Optimization. The proposed approach is generic and can be accurately applied to any kind of 3- or 4-core cables buried in homogeneous or non-homogeneous soil. Furthermore, it is applicable in cases where one or more adjacent cables exist. Using the proposed approach, the conductor temperature of each phase can be individually and precisely calculated even in networks with highly unbalanced loads. The proposed approach is expected to be an important tool for simulating the steady state of unbalanced distribution networks and estimating the conductor temperatures. The proposed thermal circuit is validated using two 4-core LV and one 3-core MV cables buried in different depths in homogeneous or non-homogeneous soil. Time-series power flow for a whole year is performed in a 25-bus unbalanced LV network consisting of multicore underground cables.

Local voltage controllers (LVCs) are important components of a modern distribution system for regulating the voltage within permissible limits. This manuscript presents a sensitivity-based three-phase weather-dependent power flow algorithm for distribution networks with LVCs. This Part I presents the theoretical development of the proposed algorithm, which has four distinct characteristics: a) it considers the three-phase unbalanced nature of distribution systems, b) the operating state of LVCs is calculated using sensitivity parameters, which accelerates the convergence speed of the algorithm, c) it considers the precise switching sequence of LVCs based on their reaction time delays, and d) the nonlinear influence of weather variations in the power flow is also taken into consideration. Simulations and validation results presented in Part II indicate that the proposed approach outperforms other existing algorithms with respect to the accuracy and speed of convergence, thus making it a promising power flow tool for accurate distribution system analysis.

This supplementary document is part of the original 2-Part manuscript titled “A SensitivityBased Three-Phase Weather-Dependent Power Flow Algorithm for Networks with Local Controllers.” This research focuses on proposing a novel sensitivity-based three-phase weather-dependent power flow algorithm for distribution networks with local voltage controllers (LVCs). The proposed algorithm has four distinct characteristics: a) it considers the three-phase unbalanced nature of distribution systems, b) the operating state of LVCs is calculated using sensitivity parameters, which accelerates the convergence speed of the algorithm, c) it considers the precise switching sequence of LVCs based on their reaction time delays, and d) the nonlinear influence of weather variations in the power flow is also taken into consideration. In this supplementary document, the relevant derivations of the sensitivity parameters are presented to complement the original 2-Part manuscript.

This letter presents a comprehensive model of on-load tap-changer (OLTC) transformers that connect 3-wire medium voltage (MV) with 4-wire multigrounded low voltage (LV) networks. The proposed model enables the inclusion of the 3-wire MV network and the 4-wire multigrounded LV network into a single YBUS matrix without any assumption or simplification. Its distinct feature is that the tap changer of the transformer is simulated outside the YBUS matrix, thus a refactorization of the YBUS matrix is not required in every tap change. The proposed transformer model has been validated in a 4-Bus network, while its performance has been tested in the IEEE 8500-Node and IEEE 906-Bus test networks.

Conventional power flow (CPF) algorithms assume that the network resistances and reactances remain constant regardless of the weather and loading conditions. Although the impact of the weather in power flow analysis has been recently investigated via the weather-dependent power flow (WDPF) approaches, the magnetic effects in the core of ACSR conductors have not been explicitly considered. ACSR conductors are widely used in distribution networks. Therefore, this manuscript proposes a three-phase weather-dependent power flow algorithm for 4-wire multi-grounded unbalanced microgrids (MGs), which takes into consideration the impact of weather as well as the magnetic effects in the core of ACSR conductors. It is shown that the magnetic effects in the core can significantly influence the power flow results, especially for networks composed of single-layer ACSR conductors. Furthermore, the proposed algorithm explicitly considers the multi-grounded neutral conductor, thus it can precisely simulate unbalanced low voltage (LV) and medium voltage (MV) networks. In addition, the proposed approach is generic and can be applied in both grid-connected and islanded networks. Simulations conducted in a 25-Bus unbalanced LV microgrid highlight the accuracy and benefit of the proposed approach.