A Simple and Efficient Power Flow for Distribution Networks

Technology and Economics of Smart Grids and Sustainable Energy https://doi.org/10.1007/s40866-022-00135-0 (2022) 7:10 ORIGINAL PAPER A Simple and Efficient Power Flow for Distribution Networks Yogambari Venkatesan1 · Arun Nambi Pandian1 · Aravindhababu Palanivelu1 Received: 19 December 2020 / Accepted: 19 January 2022 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2022 Abstract This paper presents an efficient power flow (PF) for distribution networks (DN). The proposed PF method uses basic circuit laws in deriving the final PF expression and appears like the classical Gauss-Seidel PF algorithm of transmission systems. It possesses the advantages of forward and backward sweeps (FBS) based PF methods but avoids the FBS and formation of a Jacobian matrix. It primarily depends on a constant transformation matrix, formed only once from the network topology and feeder parameters. The transformation matrix relates the node currents with effective feeder voltage drops, and helps to compute the node voltages directly from the given set of load powers. The proposed PF was studied on 15, 33 and 69 node DNs, and the study exhibited that the performances in terms of accuracy, robustness to different r/x ratios of distribution lines and computational efficiency of the proposed method are superior to those of existing methods. Keywords Distribution power flow · Forward and backward sweeps · Compensation based power flow · Distribution management systems Introduction The concept of smart-grid for distribution networks (DN) has attracted many developing countries and steps have been initiated to modernize the existing DNs with advanced metering, distribution automation and distributed energy sources (DES). Such smart DNs require repeated and fast power flow (PF) solutions for performing various distribution management functions such as VAR control, load curtailment, DES placement, reconfiguration and so on. The PF techniques such as Gauss-Seidel, Newton-Raphson (NR), fast decoupled PF, etc. are not suitable for DNs, as DNs are ill-conditioned and different from transmission systems in respect of network topology, feeder parameters and operating voltages [24]. PF is a computational procedure of determining steady state node voltages at fundamental frequency for a given load powers of DNs. The essential requirements of a PF method are fast convergence, lower memory requirement, lower computation time, and robust to wide variations in feeder parameters. Considering these requirements, several PF techniques have been suggested in recent years. These techniques are * Yogambari Venkatesan 1 Department of Electrical Engineering, Annamalai University, Annamalainagar, Tamil Nadu, India divided into node based and branch based techniques. The node based techniques usually solve a set of linearized PF equations involving Jocabian matrices for voltage corrections iteratively, while branch based techniques solve a set of basic circuit laws for steady state voltages by forward and backward sweeps (FBS) without involving Jacobian matrices. A compensation based PF (CPF) adapting FBS was suggested for DNs [21, 28]. A G-matrix based decoupled PF (GDPF) using equivalent load currents was presented for DNs [18, 26]. A feeder-to-bus matrix based PF for DNs for eliminating FBSs by modelling the PF equations in compact form was outlined [6, 30]. The PF of DNs was formulated as a convex optimisation problem and interior point algorithm was applied for solving the tailored problem for overcoming numerical ill-conditioning issues [14]. A loop-based PF was presented for 3-phase DNs [32]. A rotation based decoupled PF (RDPF) that eliminates the off-diagonal sub-Jacobian matrices by multiplying the PF equations with feeder’s admittance angles was proposed for DNs [4]. A robust PF using the topology of unbalanced DNs was explained for eliminating matrix inversion and FBSs [2]. A PF adapting fuzzy logic for DNs with composite loads was developed for modelling the uncertain data [15]. A graph theory based 3-phase PF adapting a loop as reference unlike node reference was described [11]. A robust line current based decoupled PF (LDPF) was presented by discarding 13 Vol.:(0123456789) 10 Page 2 of 7 Technology and Economics of Smart Grids and Sustainable Energy Fig. 1  Sample Network (2022) 7:10 3 8 f3 0 1 f1 2 f2 5 f5 f4 4 the off-diagonal sub-Jacobian matrices through transformations [5]. A net node power based PF for DNs was proposed in addition to presenting a sensible strategy for choosing starting voltages for achieving better convergence [25]. A distribution PF using basic laws was developed for studying many load models and different line r/x ratios [13]. Several existing PF methods of DNs were reviewed [17]. The NR and FBS schemes with changing load patterns and different line r/x ratios were studied and portrayed that FBS scheme was better than NR technique [20]. An AC PF relating the voltages, feeder currents and powers was proposed for DNs. This method can be used as fundamental tool for developing several online distribution management functions [9]. An interactive software for carrying out the PF and DES placement in DNs was developed [1]. A Z-bus based 3-phase PF by modelling different models of loads and network parameters without considering the radial nature of DNs was suggested for DNs [8]. A PF method employing power loss derivatives with advantages of being non-iterative and efficient was outlined for DNs with DES [3]. A simple PF scheme adapting fixed matrices for relating load currents with line currents and then with bus voltages was proposed [31]. The convergence of bus-impedance matrix based PF methods of DNs was studied and an acceleration technique was suggested for enhancing the convergence of the PF [33]. The transmission and 3-phase DNs were mathematically modelled and applied for solving PF problems with advantage of realizing reliable convergence [23]. A compact modelling of DNs in phasor domain was formulated by altering the nodal equations, and used for iteratively solving the PF [19]. A simple PF technique was outlined for DNs comprising FACTS devices and DES plants [29]. A NR based PF technique suitable for ring DNs was developed [27]. Sequence components based three-phase PF was suggested for DNs with intent of lowering the dimension of the PF problem and simplifying the solution procedure 13 7 f8 f7 f9 f6 9 6 [12]. A PF method adapting simple circuit laws and equations was outlined for DNs [22]. Most of the FBS based methods calculate the load currents from the initial node voltages, and then successively compute the feeder currents starting from last feeder to first feeder, evaluate the feeder voltage drops, and update the node voltages from first node to last node. These calculations represent an iteration, and are repeated till convergence. While the Newton based methods require inversion/factorization of time con (...truncated)