This paper presents a generic and comprehensive distribution optimal power flow (DOPF) model that can be used by local distribution companies (LDCs) to integrate their distribution system feeders into a Smart Grid. The proposed three-phase DOPF framework incorporates detailed modeling of distribution system components and considers various operating objectives. Phase specific and voltage dependent modeling of customer loads in the three-phase DOPF model allows LDC operators to determine realistic operating strategies that can improve the overall feeder efficiency. The proposed distribution system operation objective is based on the minimization of the energy drawn from the substation while seeking to minimize the number of switching operations of load tap changers and capacitors. A novel method for solving the three-phase DOPF model by transforming the mixed-integer nonlinear programming problem to a nonlinear programming problem is proposed which reduces the computational burden and facilitates its practical implementation and application. Two practical case studies, including a real distribution feeder test case, are presented to demonstrate the features of the proposed methodology. The results illustrate the benefits of the proposed DOPF in terms of reducing energy losses while limiting the number of switching operations.

https://uwaterloo.ca/sustainable-energy-policy/sites/ca.sustainable-energy-policy/files/uploads/files/Sumit-poster_IEEE_GM_July_2010-recd15Feb2011.pdf

Optimal Operation of Distribution Feeders in Smart Grids

An algorithm based on a nonlinear interior-point method and discretization penalties is proposed in this paper for the solution of the mixed-integer nonlinear programming (MINLP) problem associated with reactive power and voltage control in distribution systems to minimize daily energy losses, with time-related constraints being considered. Some of these constraints represent limits on the number of switching operations of transformer load tap changers (LTCs) and capacitors, which are modeled as discrete control variables. The discrete variables are treated here as continuous variables during the solution process, thus transforming the MINLP problem into an NLP problem that can be more efficiently solved exploiting its highly sparse matrix structure; a strategy is developed to round these variables off to their nearest discrete values, so that daily switching operation limits are properly met. The proposed method is compared with respect to other well-known MINLP solution methods, namely, a genetic algorithm and the popular GAMS MINLP solvers BARON and DICOPT. The effectiveness of the proposed method is demonstrated in the well-known PG&E 69-bus distribution network and a real distribution system in the city of Guangzhou, China, where the proposed technique has been in operation since 2003.

Reactive Power and Voltage Control in Distribution Systems With Limited Switching Operations

In recent years, fuzzy set theory applications have received increasing attention in various areas of power systems such as operation, planning, and control. A number of research articles appeared which indicate applicability of fuzzy systems to power systems for wider operating conditions under uncertainties. While most of these systems are still under investigation, however, there already exist several practical applications of fuzzy systems. This paper presents a comprehensive set of references on fuzzy set theory applications in power systems.

Bibliography on the fuzzy set theory applications in power systems (1994-2001)

Reactive power optimization with time-varying load demand in distribution systems is investigated in this paper. The objective of this paper is to determine the proper setting values of capacitor banks and transformer taps for the 24 hours in the next day. A heuristic and algorithmic combined approach is proposed in this paper. The approach simplifies the mathematical model of the daily setting values of reactive power/voltage control devices, solves the temporal optimization of each control device by heuristic rules, and then converts the optimization model with time-varying load into the same one as conventional optimization model with constant load. Therefore, the algorithms applied to the conventional optimization model can be easily used to solve the optimization model with time-varying load demand. Results from numerical examples show that a proper dispatch schedule for capacitor banks and transformer taps can be reached by this approach efficiently.

A heuristic and algorithmic combined approach for reactive power optimization with time-varying load demand in distribution systems

This study presents a comprehensive optimisation model that combines reactive power (VAR) optimisation and network reconfiguration to minimise power losses and eliminate voltage violations. In this model, the reactive power of distributed generators (DGs), VAR compensators, the position of tap-changer and the states of branches are formulated as continuous and discrete decision variables. The original non-convex three-phase optimisation model was converted to a mixed-integer second-order cone programming model using the second-order cone relaxation, big-M method and piecewise linearisation. The results of numerical tests showed that the proposed model can achieve significant additional gains in network loss reduction and voltage violation mitigation. This developed method can be used as a basic analysis tool for active distribution networks operation schedule or planning.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-gtd.2015.1228

Mixed-integer second-order cone programing model for VAR optimisation and network reconfiguration in active distribution networks

Reactive power/voltage control in a distribution substation is investigated in this work. The purpose is to determine proper capacitor on/off status and suitable load tap changer (LTC) positions for the 24 hours in the next day. To reach this goal, an artificial neural network (ANN) is designed to reach a preliminary dispatch schedule for the capacitor and LTC. The inputs to the ANN are main transformer real power and reactive power and primary and secondary bus voltages and the outputs are the desired capacitor on/off status and LTC tap positions. The preliminary dispatch schedule is further refined by fuzzy dynamic programming in order to reach the final schedule. To demonstrate the effectiveness of the proposed method, reactive power/voltage control is performed on a distribution substation in Taipei, Taiwan. Results from the example show that a proper dispatch schedule for capacitor and LTC can be reached by the proposed method in a very short period.

Feng-Chang Lu

Papers

A combined artificial neural network-fuzzy dynamic programming approach to reactive power/voltage control in a distribution substation