Nonlinear optimal power flow by a noninterior-point method based on Chen-Harker-Kanzow NCP-functions

In some countries, the electric power systems are operating near to their limits due to the absence of investments in the transmission network expansion and natural growth of the electricity demand. This operation condition can also occur in electric power systems in which the transmission expansion is carried out in appropriate way. In this case, the excessive loading of the transmission network is usually originated by the loss of interconnections that transport large energy blocks. The two operation scenarios described above have caused Voltage Stability problems in the electric power systems. The voltage instability states are mainly characterized by the presence of two mechanisms: the unsolvability of the power flow equations and the controllability loss. The disturbances that originate these two mechanisms are of stochastic nature. Consequently, the voltage instability indices, used to analyze the unsolvability and controllability loss, are random variables. In this way, the voltage stability assessment would recognize the uncertainties associated with the parameters of the electric network, for example: load fluctuations and equipment availability. Generally, the uncertainties modeling in the voltage stability is carried out using the following probabilistic methods: the Monte Carlo Simulation and the State Enumeration. The main index estimated by these methods is the voltage instability risk. However, the voltage instability risk evaluation is usually carried out considering only one of the mechanisms that cause voltage instability scenarios. Furthermore, the severity of the unstable states has not been properly investigated. The aim of this thesis is to develop a method to carry out a probabilistic assessment of the voltage stability that take into account the two mechanisms that cause the voltage instability in the evaluation of its risk. Probabilistic indices, based on Well-Being Analysis, are also proposed to express the severity of the voltage instability states. The proposed method is based on the combination of the following techniques: State Enumeration Method, Monte Carlo Simulation, D' Matrix Method and Nonlinear Optimal Power Flow. The State Enumeration and Monte Carlo Simulation Methods are used to select the system states resulting of equipment failures and load forecast errors. The identification of the controllability loss and the solvability restoration of the power flow equations for the selected states are carried out by the D' Matrix Method and by the Nonlinear Optimal Power Flow, respectively. The combination of the methods cited above was used to obtain the following probabilistic indices: voltage instability risk, expected value of the voltage instability margin for the buses, and Well-Being states probabilities. The results of the tests with the proposed method revealed that the probabilities of unstable states, associated with the two voltage instability mechanism, are very significant. Additionally, the Well-Being Analysis was able to identify the root cause and the severity of the voltage instability problems.

This paper investigates potential of modified differential evolution (MDE) algorithm, to find solution for optimal power flow (OPF) problem of power system. The performance of the proposed MDE algorithm is experienced on the modified IEEE-30 bus test systems integrating flexible ac transmission systems (FACTS) devices, that is, thyristor controlled phase shifter (TCPS) and thyristor controlled series capacitor (TCSC) at preset locations. The OPF problem of the present work is formulated with five different objective functions viz. (a) fuel cost (with valve point effect) minimization, (b) power transmission losses minimization, (c) emission reduction (d) fuel cost (without valve point effect) minimization and (e) minimization of combined economic and environmental cost. The proposed implementation exploits MDE, resulting in a much shorter execution time while retaining the best possible solution of OPF problem.

In this article, various nonlinear and non-convex optimal power flow (OPF) objective functions are optimized using eight different optimization algorithms, i.e., moth-flame optimization algorithm (MFO), gray wolf optimizer (GWO), dragonfly algorithm (DA), sine–cosine algorithm (SCA), antlion optimizer (ALO), multi-verse optimizer (MVO), grasshopper algorithm (GOA) and ion motion algorithm (IMO) for different test systems, i.e., IEEE 57-bus test system and IEEE 118-bus test system. As per no free lunch algorithm, in general, no algorithm can be considered better than other, and hence, the performance of algorithm relies heavily upon system under consideration. Applications through 22 different case studies are pursued to assess efficiency of algorithms under consideration. An attempt has been made to evaluate algorithms based on the best solution, average solution, average simulation time and trend of convergence. Different statistical tests are performed to identify the efficiency of algorithms under consideration. Test results suggest that MFO performs better as compared to rest of the algorithms for most test cases proving its mettle in dealing with nonlinear and non-convex OPF problem.

Since conventional optimal power flow (OPF) algorithms are limited and too slow for operational planning, power system operation and planning engineers have been seeking efficient OPF algorithms for three decades. The interior point method is one of the most efficient algorithms. In this paper, an improved quadratic interior point (IQIP) method is used to solve comprehensive OPF problems with a variety of objective functions, including economic dispatch, VAr planning and loss minimization. The IQIP method features a general starting point (rather than selected good point as in the general interior point method) and fast convergence. Consequently, the OPF package described in this paper offers huge improvements in speed, accuracy and convergence in solving multi-objective and multi-constraint optimization problems. It will be a very useful tool for the power industry.

The optimal power flow (OPF) has been commonly used as an efficient tool in the power system planning and operation for many years. OPF is an important tool in modern Energy Management System (EMS). It plays an important role in maintaining the economy of the power system. The problem of OPF subjected to set of equality and inequality constraints was originally formulated in 1962 by Carpentier [1]. The OPF problem is a nonlinear, non-convex, large scale, static optimization problem with both continuous (generator voltage magnitudes and active powers) and discrete (transformer taps and switchable shunt devices) control variables. Even in the absence of discrete control variables, the OPF problem [2] is non convex due to the existence of the nonlinear (AC) power flow equality constraints. The presence of discrete control variables, such as switchable shunt devices, transformer tap positions further complicates the problem solution.

Optimal power flow using gravitational search algorithm

Large-scale nonlinear optimal power flow (OPF) problems have been efficiently solved lately by extensions from linear programming to nonlinear programming of the primal-dual logarithmic barrier interior-point method and its predictor-corrector variant. Motivated by the impressive performance of the nonlinear predictor-corrector extension, in this paper we extend from linear programming to nonlinear OPF the efficient multiple centrality corrections (MCC) technique that was developed by Gondzio. The numerical performance of the proposed MCC algorithm is evaluated on a set of power networks ranging in size from 118 buses to 2098 buses. Extensive computational results demonstrate that the MCC technique is fast and robust, and outperforms the successful predictor-corrector technique.

The optimal power flow (OPF) problem is a well-known non-convex optimization problem that aims to minimize the cost of electric power generation subject to consumer demand, the physics of power flow, and technological constraints. To find an optimal solution to this problem, local search techniques such as interior point methods are typically used. However, due to the non-convex nature of the problem, these methods are likely to result in a sub-optimal solution. The goal of this paper is to characterize the worst-case performance of local search on the OPF problem. To accomplish this, we formulate the OPF problem as a canonical quadratically-constrained quadratic program (QCQP). Then, we study the problem of finding the worst-case local minimum of this QCQP, which is non-convex and hard to solve in general. We find a relaxation of this problem into a semidefinite program (SDP) and show that it is exact for certain cases. Using some test cases which are known to have multiple local minima, we demonstrate the effectiveness of the proposed relaxation to bound the worst-case local minimum. We compare the obtained upper bound on local minima to the lower bound provided by the standard SDP relaxation of the OPF problem to understand how much SDP outperforms local search for a given problem.

Strengthened SOCP Relaxations for ACOPF with McCormick Envelopes and Bounds Tightening

Although a significant amount of research has been directed to developing necessary and sufficient conditions for the optimal solutions of several engineering problems, there is little work on the development of a necessary and sufficient condition for optimal power flow (OPF) solutions. This paper seeks to develop the following: (1) a necessary and sufficient condition for a local OPF solution, and (2) a necessary and sufficient condition for an OPF Karush-Kuhn-Tucker (KKT) solution. The derived necessary and sufficient conditions were numerically verified on IEEE 30-, 57- and 118-bus systems. Computationally, the derived necessary and sufficient condition is also useful in assisting existing OPF methods to obtain OPF solutions instead of KKT solutions (i.e., KKT saddle points).

The optimal design of grid-connected distributed energy systems (DES) has been previously investigated, but most studies exclude nonlinear multiphase optimal power flow (MOPF) constraints which capture imbalances in alternating current (AC) distribution networks. Previous DES design studies considering AC power flow assume balanced loads and networks, which is an assumption that does not hold for distribution networks that are often inherently unbalanced. This is the first study to present an optimisation framework for designing grid-connected DES while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution. This study proposes a new algorithm for obtaining DES designs subject to nonlinear multiphase power flow constraints with regularised complementarity reformulations for operational constraints containing binary variables. DES design models with either MOPF or OPF are tested using an unbalanced distribution network, where rooftop solar, gas boilers, and battery storage are considered as distributed resources. Despite the increased complexity, DES design with MOPF obtains the best solution, with 81% greater solar capacity and 6% lower total annualised cost when compared to DES with OPF. Designs from a commonly-used linear DES design framework based on direct current (DC) approximations produce the highest costs (8% more than initially predicted) when tested with MOPF. The proposed algorithm with complementarity reformulations achieves a 19% improvement in the objective value over a previous two-stage decomposition for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within unbalanced distribution networks.

Incorporating time-coupled storage restrictions in the nonlinear dynamic optimal power flow poses a major challenge in terms of performance and solvability. As a consequence, the application of existing works that combine AC optimal power flow with integration of storage are usually restricted to problems of small size or short periods of time coupling. In this work, an approach using an augmented Lagrangian algorithm for the decoupling of the storage component has been developed, which is suitable for solving large-scale problems. The iterative methodology, which is highly scalable and allows for parallelization up to the total amount of time steps, takes multiple storage units into account. The approach has been tested using a data set of the German transmission network consisting of 950 buses and 26 hydro storage units. The proposed method shows robust results in terms of convergence as well as a promising performance characteristic for an increasing number of simulated time steps.

This study proposes an improved particle swarm optimization method to find optimal power flow by using the power transmission loss as an objective function. In the literature, PSO is a well — known intelligent search method to handle the solution of optimal power flow problem. A novel scheme which is called Improved PSO (IPSO) is defined by modifying the initialization step of PSO algorithm and choosing the load bus voltages, generator active and reactive powers, line flow capacities as penalty functions in the objective function. PSO and IPSO-based optimal power flow solutions are compared with each other on IEEE 118 and 300 bus systems. According to the test results, the power loss obtained by IPSO-based solution has less power loss than PSO-based solution. This proposed method can be used to obtain faster desirable solutions and better power loss results for the optimal power flow problem in case of power loss minimization.

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area.

An interior point method (IPM) for solving the optimal power flow (OPF) problem is presented. The IPM uses a combination of the predictor corrector, multiple predictor corrector and multiple centrality correction methods (all belong to the family of higher order interior point methods). The proposed IPM uses the best properties of each method to obtain a more robust IPM with faster convergence characteristics. The active power loss minimisation, minimum load shedding and maximum loadability problems are formulated as an OPF problem and solved with the proposed methodology. The IEEE 30, 57, 118, and 300 bus systems, and two realistic power systems, a 464 bus corresponding to the interconnected Peruvian system, and a 2256 bus corresponding to part (South–Southeast) of the interconnected Brazilian system were tested successfully. Results have indicated that good convergence performance is obtained and the computational time is small.