Optimal Power Flow Solution Methods Research Articles

Accuracy enhancement of second-order cone relaxation for AC optimal power flow via linear mapping

• Mapping second-order cone AC OPF equations via semi-Lorentz transformation. • Transforming both variables and network parameters in Model-A. • Applying the proposed linear transformation on the network parameters in Model-B. • Developing an empirical analysis to obtain a good value for the semi-Lorentz factor. • Improving both optimality gap and relaxation error compared to other methods. Optimal power flow (OPF) has always been one of the most crucial tools for power system operations. OPF problem formulation involves non-linear alternative current (AC) power flow equations, and a wide range of challenges occur as a result. This is because the resulting non-convex optimization problems are not only complex and time-consuming, but also difficult to find a global optimum as many local optimums are present. So far, different relaxations have been provided to address these issues. One of the most effective strategies for convexifying such formulations is second-order cone programming (SOCP). Although SOCP is an efficient instrument for convexifying AC OPF equations, it is unable to reach the global optimal solution compared to other methods. The aim of this paper is therefore to provide a new method to approach the global optimum of AC OPF relaxed by SOCP. This method is obtained with the aid of a new linrear tranfsormation called semi-Lorentz transformation as it similar to the Lorentz transformation in the special relativity theory. In this method second-order cone AC OPF equations are mapped to a new model via semi-Lorentz transformation. In addition, an approximation approach is also presented to reach the best semi-Lorentz factor, the main driver in semi-Lorentz transformation, for each particular problem based on the network parameters. From the comparative analysis in case studies, the proposed OPF solution method has robust precision and higher efficiency while consuming less computing time.

On the Solution of the Optimal Power Flow for Three-Phase Radial Distribution Networks With Energy Storage

We study a multiperiod optimal power flow (OPF) problem in unbalanced three-phase radial distribution networks with batteries. To address this problem, we first take the resistance-line battery model that treats lossy batteries by adding resistive lines and virtual buses. Then, we derive a linearization for the power flow equations, called generalized three-phase simplified DistFlow, which accounts for shunt elements. Also, it is exact at a freely chosen point while having globally good performance. Using it, we extend the heuristic iterative OPF algorithm, CoDistFlow, to unbalanced three-phase networks. At convergence, three-phase CoDistFlow gives a solution that satisfies the exact nonlinear power-flow equations and the exact security constraints. To theoretically guarantee the convergence of three-phase CoDistFlow, we develop the forced convergent three-phase CoDistFlow. Moreover, we show how to adapt the three-phase CoDistFlow to solve a scenario-based OPF in the presence of uncertainties, whereas other existing OPF solution methods may not offer this possibility. Finally, we perform evaluations on the IEEE 123-bus test feeder and comparisons with Ipopt.

Optimal power flow incorporating renewable uncertainty related opportunity costs

AbstractIn this paper, an optimal power flow solution method incorporating a cost model that associates the uncertainty‐related expense incurred with the use of renewable energy sources, viz., solar and wind, is demonstrated. Wind speed and solar radiation are assumed to follow Weibull and normal distributions and the uncertainty is simulated using Monte‐Carlo approach. Wind turbine mathematical model is used to estimate the wind generator output, while the same for solar PV is estimated using PV‐inverter models. The uncertainty‐induced opportunity cost for both the renewable sources is composed of the costs due to both power excess and deficit. These cost components are indicative of the reserve requirement and loss of benefit, due to the unavailability of the corresponding generation. This research models and integrates the opportunity costs of renewable generation into a conventional OPF formulation, which is then solved using four variants of particle swarm optimization method. Among these, mutation‐based PSO approach provided better results than others. The test system used is modified IEEE 39‐bus network and the performance of the method as well as the effect of the uncertainty cost is evaluated under multiple renewable penetration levels. The results also indicate that solar generation is preferred over wind in terms of the uncertainty cost, while the use of stochastic natured renewable systems is economically justified and preferred over thermal generators.

A Sufficient Condition for Global Optimality of Solutions to the Optimal Power Flow Problem

Recent applications of a semidefinite programming (SDP) relaxation to the optimal power flow (OPF) problem offers a polynomial time method to compute a global optimum for a large subclass of OPF problems. In contrast, prior OPF solution methods in the literature guarantee only local optimality for the solution produced. However, solvers employing SDP relaxation remain significantly slower than mature OPF solution codes. This letter seeks to combine the advantages of the two methods. In particular, we develop an SDP-inspired sufficient condition test for global optimality of a candidate OPF solution. This test may then be easily applied to a candidate solution generated by a traditional, only-guaranteed-locally-optimal OPF solver.

A New Approach for Optimal Power Flow Solution Based on Two Step Initialization with Multi-Line FACTS Device

In this article, a new intelligent search evolution algorithm (ISEA) is proposed to minimize the generator fuel cost in optimal power flow (OPF) control with multi-line flexible alternating current transmission systems (FACTS) device which is interline power flow controller (IPFC). Unlike the OPF solution methods existing in the literature, in the proposed algorithm, a two step initialization process have been adopted which eliminates the mutation operation and also it gives optimal solution with less number of generations. The proposed algorithm has been examined and tested on a standard IEEE-30 bus system without and with IPFC. The test results indicate that the proposed algorithm with IPFC can obtain better solution than without IPFC.

SENSITIVITY FACTOR BASED SHORT TERM DYNAMIC OPTIMAL POWER FLOW

ABSTRACT In general, conventional Optimal Power Flow(OPF) solutions utilize some optimization techniques at a single case. In the OPF solution method, all the available variables are used to solve the problem. In practical operation, such a solution is not a practical consideration because the control actions would be too many to be implemented. In this paper, sensitivity factors combined with dynamic programming technique are used to solve short term (one day) dynamic optimal power flow. A two-step real time real power dispatch method considering inconforming load change is used to solve real power dispatch, and then, the sensitivity factors are used to solve reactive power dispatch with some constraints. Finally, the dynamic programming technique is used to minimize the control actions to as little as possible. The advantages of this method are simple and easy to implement, and it would greatly enhance the operators' planning.

Large-scale optimal power flow: effects of initialization, decoupling and discretization

Extensive numerical testing of a second-order OPF (optimal power flow) solution method was conducted using a 1500 bus network under various loading conditions. The results show that properly implemented second-order OPF solution methods are robust with respect to different starting points, the decoupled OPF solution is expected to be close to the full OPF solution, and the effects of discretization of load tap changing (LTC) transformer taps are very small and usually negligible. The test procedure required two optimizations. During the first optimization, the transformer taps were treated as continuous variables. Using the continuous solution, the LTC taps were moved to their closest allowable discrete values. During the second optimization the LTC transformer taps were held fixed at their discretized values. The second solution was compared to the first. A small difference between these two solutions indicates that the effects of the transformer tap discretization were minimal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>