فرمولاسیون و راه حل ولتاژ سیستم توزیع و کنترل VAR همراه با تولید پراکنده به عنوان یک مشکل برنامه ریزی غیرخطی عدد صحیح مختلط

Coordinated voltage and VAR control (VVC) can provide major economic benefits for distribution utilities. Incorporating distributed generations (DG) for VVC can improve the efficiency and reliability of distribution systems. This paper presents an approach to formulate and solve distribution system VVC with DG units as a mixed integer non-linear programming (MINLP) problem. The method can be utilized to create an effective control scheme for both the traditional VVC devices and DG units. The MINLP formulation is based on three-phase power flow formulation, and is solved with an open-source BONMIN optimization solver with outer approximation (OA) algorithm. BONMIN is interfaced with Matlab via a third-party optimization toolbox. The proposed approach is applied to several distribution feeder models with promising results.

Power factor (PF) correction and conservation voltage reduction (CVR) can reduce distribution losses and overall power demand. PF correction is performed with fixed and switchable capacitor banks in traditional feeders. PF correction reduces line losses by limiting the amount of current drawn by reactive power (VAR) loads. The traditional voltage control devices include load tap changer (LTC) transformers and voltage regulators (VRs). In North America, the node voltages have to be kept within the ANSI specified operational range [1], between 114 V and 126 V for all secondary buses on a 120 V voltage base. Studies have shown that reducing feeder voltage can noticeably reduce feeder power demand in real utility systems if a large portion of the loads are constant impedance and constant current loads [2] and [3]. Applying PF correction and voltage control together is commonly referred to as voltage and VAR control or optimization (VVC or VVO). There are several existing methods for VVC and VVO. References [4], [5], [6] and [7] present local control approaches for capacitor banks and VR devices. The local control methods are generally simple, provide no coordination between devices, and are often limited to a single directional power flow. Supervisory control and data acquisition (SCADA) based VVC usually provides coordination of control devices, as described in [8], [9], [10] and [11]. These approaches are based on complicated rule structures. They consider VAR and voltage decisions separately, and generally do not yield optimal solutions. Analytical approaches, like the one presented in this paper, consider VVC as an analytical problem. Existing analytical techniques include non-linear programming (NLP) with interior point algorithm [12], sensitivity based approaches [13], dynamic programming [14], discrete coordinated descent method [15], and mixed integer linear programming (MILP) [16] and [17]. Artificial intelligence (AI) methods, such as artificial neural networks [18], fuzzy systems [19] and genetic algorithms [20], could be useful tools for VVC. With increasing DG penetration into distribution feeders, DG units could participate in VVO. Inverter coupled DG units can provide real and reactive power to offset some of the system power demand, as described in [21], [22] and [23]. Direct MINLP formulation and solution has been difficult due to the fact that commercial optimization solvers cannot generally solve MINLP problems. With advances in open-source MINLP algorithms, a direct MINLP formulation of VVO can be presented and solved. The MINLP approach can provide value to VVO since it reduces the need for linearization in problem formulation and the need to transform continuous values into discrete values. This paper proposes a new formulation method for VVO problem with DGs as a direct MINLP problem. The proposed approach solves VVO for all three phases, works for different load types, incorporates integer decisions, and allows for non-linear voltage, current and control equations. The method has shown promises to yield optimal solutions effectively.

This paper has investigated an approach of presenting and solving distribution system VVO with DG as MINLP problem. The presented optimization approach was constrained by Cartesian power flow constraints, voltage and current constraints, and control device constraints. The solutions were obtained with BONMIN open-source optimization solver interfaced with Matlab via third-party toolbox. The method was applied to three unbalanced distribution test feeders with VRs, capacitor banks, and DGs. Results obtained from the test systems showed that the approach can produce quality results with reasonable computational effort. The approach is suitable for unbalanced three phase systems with varying loads and load types. Comparison with traditional voltage control showed that MINLP based VVO can reduce overall system demand significantly.