Author: Li, Qing Title: A linear approximation of unified branch flow for reactive power optimization with wind turbines Advisors: Chan, Ka-wing Kevin (EE) Degree: M.Sc. Year: 2019 Subject: Wind turbines -- AerodynamicsWind powerElectric power distributionHong Kong Polytechnic University -- Dissertations Department: Department of Electrical Engineering Pages: viii, 74 pages : color illustrations Language: English Abstract: The optimal power flow (OPF) calculation plays an important role in both the planning and operation of a distribution network. This project aims to study and apply a new linearization approximation (LA) method based on the unified branch flow model to solve the challenging mixed-Integer AC-OPF problem in reactive power optimization of a distribution network with wind turbines using modern linear programming software.In the first part of this dissertation, the basic theory of reactive power optimization in distribution network is firstly reviewed. Common devices implemented in the reactive optimization project are described. Next, general optimization methods are classified and introduced. Then, typical artificial intelligent algorithms applied in optimal power flow calculation are outlined briefly.In the second part of this dissertation, typical algorithms, including the bus class algorithm and the Newton algorithm, are depicted for the power flow calculation in the distribution network. The Dist Flow algorithm is described elaborately with explicit mathematical model, which paves a way for the branch flow analysis in reactive optimization model. In order to support the modeling of stochastic model of wind turbine output, theories for random power flow calculation are presented in detail.Considering the impact of randomness fluctuation of intermittent power supply, evaluating the wind power output by the method of probability statistics, combining the probability of random outage of power systems, a multi-state discrete random probability model of wind turbines output has been firstly built. Next, the reactive optimization model in radial distribution network with wind turbines is built. A particular branch flow analysis has been performed. The objective function, which takes the reduction of operating cost derived from reactive power compensation into consideration, has been defined based on the net present value (NPV) principle. Then, the optimization problem constraints, which is comprise of branch power flow constraints, line transmission capacity constraints, voltage limit constraints and capacitor volume limit constraints, are described in detail. Because the group number of capacitors that can be installed at one node is an integer, this reactive optimization configuration problem is a mixed-integer AC-OPF problem.Based on the proposed reactive power optimization model, as the sending end and receiving end forms of BFM are specified with a system of linear-quadratic equations, the quadratic equality constraints will be firstly relaxed by replacing equality with inequality. The inequality constraints is converted to the form of second-order cone, thus the unified BFM is a SOCP problem [7] to ensure the global convergence of the solution of the Mixed-Integer AC-OPF problem.According to the proposed method of polyhedral approximation of second-order cone by Ben-Tal and Nemirovski [20], a linearization scheme is derived with an arbitrary prescribed accuracy ε. The principle that lies behind this polyhedral approximation can be divided into two steps: decomposition and projection. The first step is to represent the cone of dimension n+1 by a system of cones of dimension 3, the second step is projection which build polyhedral approximation of the L2 generated from the decomposition [7].The reactive optimization model in radial distribution network with wind turbines is applied in IEEE 33-node test case and IEEE 69-node test case, and solved with both the conventional MISOCP algorithm and the proposed LA algorithm. The total cost saving, the capacitor volume calculated by the reactive planning, node voltage profile and computing time based on the two methods are evaluated and compared. Lastly, the effect of the variation of polyhedron size v on the feasibility of LA algorithm applied in mixed-integer AC-OPF calculation is investigated precisely. The correlation between the polyhedron size v and computing time is demonstrated and analyzed in detail. Rights: All rights reserved Access: restricted access

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