Distributed Optimal Power Flow Algorithm for Radial Networks, I: Balanced Single Phase Case

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally, OPF is solved in a centralized manner. With increasing penetration of renewable energy in distribution system, we need faster and distributed solutions for real-time feedback control. This is difficult due to the nonlinearity of the power flow equations. In this paper, we propose a solution for balanced radial networks. It exploits recent results that suggest solving for a globally optimal solution of OPF over a radial network through the second-order cone program relaxation. Our distributed algorithm is based on alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative method, our decomposition allows us to derive closed form solutions for these subproblems, greatly speeding up each ADMM iteration. We illustrate the scalability of the proposed algorithm by simulating it on a real-world 2065-bus distribution network

Distributed Optimal Power Flow Algorithm for Radial Networks, I: Balanced Single Phase Case

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally, OPF is solved in a centralized manner. With increasing penetration of renewable energy in distribution system, we need faster and distributed solutions for real-time feedback control. This is difficult due to the nonlinearity of the power flow equations. In this paper, we propose a solution for balanced radial networks. It exploits recent results that suggest solving for a globally optimal solution of OPF over a radial network through the second-order cone program relaxation. Our distributed algorithm is based on alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative method, our decomposition allows us to derive closed form solutions for these subproblems, greatly speeding up each ADMM iteration. We illustrate the scalability of the proposed algorithm by simulating it on a real-world 2065-bus distribution network

Placement analysis of combined renewable and conventional distributed energy resources within a radial distribution network

System islanding, relay tripping, and reverse power flow-like issues in the distribution network are all caused by randomly placed distributed energy resources. To minimize such problems, distributed energy resource (DER) optimal placement in the radial distribution network (RDN) is essential to reduce power loss and enhance the voltage profile. When placing DERs, consideration of constraints like size, location, number, type, and power factor (PF) should be considered. For optimal placement, renewable and nonrenewable DERs are considered. The effects of different types and PFs of DER placements have been tested on the IEEE 33 bus RDN to satisfy all limitations. Using various intelligent techniques, distributed energy resource units of optimal type, PF, size, quantity, and position were placed in the IEEE 33 bus RDN. These intelligent strategies for minimizing power loss, enhancing the voltage profile, and increasing the convergence rate are based on an adaptive neuro-fuzzy inference system, a genetic algorithm, and enhanced particle swarm optimization.publishedVersio

Distributed Optimization for Power Systems with Radial Partitioning

This paper proposes group-based distributed optimization algorithms on top of intelligent partitioning for the optimal power flow (OPF) problem. Radial partitioning of the graph of a network is introduced as a systematic way to split a large-scale problem into more tractable sub-problems, which can potentially be solved efficiently with methods such as convex relaxations. The simple implementation of a Distributed Consensus Algorithm (DiCA) with very few parameters makes it viable for different parameter selection methods, which are crucial for the fast convergence of the distributed algorithms. The DiCA algorithm returns more accurate solutions to the tested problems with fewer iterations than component-based algorithms. Our numerical results show the performance of the algorithms for different power network instances and the effect of parameter selection. A software package DiCARP is created, which is implemented in Python using the Pyomo optimization package.Comment: 7 pages, 4 figure

Distributed Load Control in Multiphase Radial Networks

The current power grid is on the cusp of modernization due to the emergence of distributed generation and controllable loads, as well as renewable energy. On one hand, distributed and renewable generation is volatile and difficult to dispatch. On the other hand, controllable loads provide significant potential for compensating for the uncertainties. In a future grid where there are thousands or millions of controllable loads and a large portion of the generation comes from volatile sources like wind and solar, distributed control that shifts or reduces the power consumption of electric loads in a reliable and economic way would be highly valuable. Load control needs to be conducted with network awareness. Otherwise, voltage violations and overloading of circuit devices are likely. To model these effects, network power flows and voltages have to be considered explicitly. However, the physical laws that determine power flows and voltages are nonlinear. Furthermore, while distributed generation and controllable loads are mostly located in distribution networks that are multiphase and radial, most of the power flow studies focus on single-phase networks. This thesis focuses on distributed load control in multiphase radial distribution networks. In particular, we first study distributed load control without considering network constraints, and then consider network-aware distributed load control. Distributed implementation of load control is the main challenge if network constraints can be ignored. In this case, we first ignore the uncertainties in renewable generation and load arrivals, and propose a distributed load control algorithm, Algorithm 1, that optimally schedules the deferrable loads to shape the net electricity demand. Deferrable loads refer to loads whose total energy consumption is fixed, but energy usage can be shifted over time in response to network conditions. Algorithm 1 is a distributed gradient decent algorithm, and empirically converges to optimal deferrable load schedules within 15 iterations. We then extend Algorithm 1 to a real-time setup where deferrable loads arrive over time, and only imprecise predictions about future renewable generation and load are available at the time of decision making. The real-time algorithm Algorithm 2 is based on model-predictive control: Algorithm 2 uses updated predictions on renewable generation as the true values, and computes a pseudo load to simulate future deferrable load. The pseudo load consumes 0 power at the current time step, and its total energy consumption equals the expectation of future deferrable load total energy request. Network constraints, e.g., transformer loading constraints and voltage regulation constraints, bring significant challenge to the load control problem since power flows and voltages are governed by nonlinear physical laws. Remarkably, distribution networks are usually multiphase and radial. Two approaches are explored to overcome this challenge: one based on convex relaxation and the other that seeks a locally optimal load schedule. To explore the convex relaxation approach, a novel but equivalent power flow model, the branch flow model, is developed, and a semidefinite programming relaxation, called BFM-SDP, is obtained using the branch flow model. BFM-SDP is mathematically equivalent to a standard convex relaxation proposed in the literature, but numerically is much more stable. Empirical studies show that BFM-SDP is numerically exact for the IEEE 13-, 34-, 37-, 123-bus networks and a real-world 2065-bus network, while the standard convex relaxation is numerically exact for only two of these networks. Theoretical guarantees on the exactness of convex relaxations are provided for two types of networks: single-phase radial alternative-current (AC) networks, and single-phase mesh direct-current (DC) networks. In particular, for single-phase radial AC networks, we prove that a second-order cone program (SOCP) relaxation is exact if voltage upper bounds are not binding; we also modify the optimal load control problem so that its SOCP relaxation is always exact. For single-phase mesh DC networks, we prove that an SOCP relaxation is exact if 1) voltage upper bounds are not binding, or 2) voltage upper bounds are uniform and power injection lower bounds are strictly negative; we also modify the optimal load control problem so that its SOCP relaxation is always exact. To seek a locally optimal load schedule, a distributed gradient-decent algorithm, Algorithm 9, is proposed. The suboptimality gap of the algorithm is rigorously characterized and close to 0 for practical networks. Furthermore, unlike the convex relaxation approach, Algorithm 9 ensures a feasible solution. The gradients used in Algorithm 9 are estimated based on a linear approximation of the power flow, which is derived with the following assumptions: 1) line losses are negligible; and 2) voltages are reasonably balanced. Both assumptions are satisfied in practical distribution networks. Empirical results show that Algorithm 9 obtains 70+ times speed up over the convex relaxation approach, at the cost of a suboptimality within numerical precision.</p

Application of the Multiverse Optimization Method to Solve the Optimal Power Flow Problem in Alternating Current Networks

In this paper, we solve the optimal power flow problem in alternating current networks to reduce power losses. For that purpose, we propose a master–slave methodology that combines the multiverse optimization algorithm (master stage) and the power flow method for alternating current networks based on successive approximation (slave stage). The master stage determines the level of active power to be injected by each distributed generator in the network, and the slave stage evaluates the impact of the proposed solution on each distributed generator in terms of the objective function and the constraints. For the simulations, we used the 10-, 33-, and 69-node radial test systems and the 10-node mesh test system with three levels of distributed generation penetration: 20%, 40%, and 60% of the power provided by the slack generator in a scenario without DGs. In order to validate the robustness and convergence of the proposed optimization algorithm, we compared it with four other optimization methods that have been reported in the specialized literature to solve the problem addressed here: Particle Swarm Optimization, the Continuous Genetic Algorithm, the Black Hole Optimization algorithm, and the Ant Lion Optimization algorithm. The results obtained demonstrate that the proposed master–slave methodology can find the best solution (in terms of power loss reduction, repeatability, and technical conditions) for networks of any size while offering excellent performance in terms of computation time

Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition technique

This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature

Optimal Allocation of Energy Storage and Wind Generation in Power Distribution Systems

The advent of energy storage technologies applications for the electric power system gives new tools for planners to cope with the operation challenges that come from the integration of renewable generation in medium voltage networks. This work proposes and implements an optimization model for Battery Energy Storage System (BESS) and distributed generation allocation in radial distribution networks. The formulation aims to assist distribution system operators in the task of making decisions on energy storage investment, BESSs\u27 operation, and distributed generation penetration\u27s level to minimize electricity costs. The BESSs are required to participate in energy arbitrage and voltage control. In addition, due to the complexity of the model formulated, a genetic algorithm combined with an AC multi-period optimal power flow implementation is used to solve the problem. The methodology provides the optimal connection points and size of a predetermined number of BESSs and wind generators, and the BESS\u27s operation. The model considers the BESSs\u27 charging/discharging efficiency, depth of discharge level, and the network\u27s operation constraints on the nodal voltage and branches power flow limits. The proposed methodology was evaluated in the IEEE 33-bus system. The results show that BESSs investment in radial distribution systems facilitates the deployment of distributed generation and favors the reduction of generation costs despite its still high capital cost. Adviser: Fred Choobine