AC Optimal Power Flow Solution Research Articles

Stochasticity agnostic solution to the AC optimal power flow by recursive bound tightening with top‐down heuristically inducted binary decision trees

The efficient solution of the AC optimal power flow (OPF) for all cases and electrical grids is not guaranteed. Heuristics, approximations and relaxations have been proposed aplenty, each with pros and cons. This work proposes to solve the AC OPF with binary decision trees (BDTs). The solution starts with the full feasible set of an AC OPF instance, and, iteratively, BDTs tighten the constraints/bounds of that set, to improve the occurring feasible set by the median of the objective function of the preceding set. The medians of the objective function of the progressively tightened feasible sets will converge to the global optimum of the AC OPF. Recent proofs for the estimate performance of top-down BDT learning heuristics ensure convergence of the method to the global optimum, provided the feasible set is adequately sampled for the BDT training. The recursive implementation of the method and the inductive nature of BDTs may also yield dispatches at multiple optimality levels for the same AC OPF instance, to account for stochastic resources. The performance of the proposed AC OPF solution is assessed over multiple cases by NICTA and the IEEE PES task force on benchmarks for validation of emerging power system algorithms.

Hybrid Learning Aided Inactive Constraints Filtering Algorithm to Enhance AC OPF Solution Time

The optimal power flow (OPF) problem contains many constraints. However, equality constraints and a limited set of inequality constraints encompass sufficient information to determine the problem feasible space. This article presents a hybrid supervised regression-classification learning-based algorithm to predict active and inactive inequality constraints before solving AC OPF solely based on nodal power demand information. The proposed algorithm is structured using a mixture of classifiers and regression learners. Instead of directly mapping OPF results from demand, the proposed algorithm removes inactive constraints to construct a truncated AC OPF. This truncated optimization problem can be solved faster than the original problem with less computational resources. Numerical results on several test systems show the proposed algorithm's effectiveness for predicting active and inactive constraints and constructing a truncated AC OPF.

Collaborative Distributed AC Optimal Power Flow: A Dual Decomposition Based Algorithm

This paper proposes a novel dual decomposition based algorithm that solves the AC optimal power flow (ACOPF) problem in the radial distribution systems and microgrids in acollaborative and distributed manner. The proposed algorithm adopts the second-order cone program relaxed branch flow ACOPF model. In the proposed algorithm, bus-level agents collaboratively solve the global ACOPF problem by iteratively sharing partial variables with its 1-hop neighbors as well as carrying out local scalar computations that are derived using augmented Lagrangian and primal-dual subgradient methods. In addition to the algorithm innovation, this paper proposes two distributed computing platforms, i.e. high performance computing based and hardware-in-the-loop platforms, to validate and evaluate the proposed distributed algorithm. The computationand communication performances of the proposed algorithm are quantified and analyzed over typical IEEE test distribution systems. Experimental results indicate that 1) the proposed collaborative distributed ACOPF solver can be executed on a fully distributed computing structure and yield accurate ACOPF solution; and 2) the proposed distributed algorithm has a low communication overhead.

Equivalent Circuit Formulation for Solving AC Optimal Power Flow

In this paper, we formulate and solve the ac optimal power flow (AC-OPF) as an equivalent circuit problem in terms of current, voltage, and admittance state variables. The generator models are represented using conductance and susceptance state variables, and the operational and network constraints are translated to corresponding current/voltage constraints without loss of accuracy or generality. To understand the physics behind the optimality conditions of the optimization problem, we extend the linear adjoint circuit theory to translate them to equivalent circuit domain. It is shown that the operating point that defines the equivalent circuit solution precisely represents an AC-OPF solution. We then further exploit the equivalent circuit representation to use power flow simulation techniques to robustly solve the optimization problem. The efficiency of our approach is demonstrated for several AC-OPF benchmark test cases (up to 70 k buses) under nominal and congested operating conditions, and the runtime and scalability properties are presented.

Beyond Relaxation and Newton–Raphson: Solving AC OPF for Multi-Phase Systems With Renewables

This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this paper leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm—a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using single- and multi-phase distribution networks with renewables, as well as several transmission systems.

A Linearized OPF Model With Reactive Power and Voltage Magnitude: A Pathway to Improve the MW-Only DC OPF

In this study, a linearized and convergence-guaranteed optimal power flow (OPF) model with reactive power ( Q ) and voltage magnitude ( v ) is proposed. Based on a linearized network model, a fully linearly-constrained OPF model is formulated with constraints on Q and v and limits on the apparent branch flow. Compared with the commonly used DC OPF method, the proposed method narrows the deviation from the AC OPF solution without requiring any additional information of the power grid. The locational marginal price (LMP) of the proposed method is closer to the AC OPF solution than the DC OPF method. The marginal price of the reactive power (Q-LMP) is provided, which offers the opportunity to price the reactive power. Case studies on several IEEE and Polish benchmark systems show that the proposed OPF method substantially enhances the performance of the prevalent DC OPF method. In addition, it is shown that if the accuracy of the linearized network model needs to be further improved, such as that during the iterative quasi-optimization process that reconstitutes the AC feasibility, a solution that is notably close to the optimum of the AC OPF model can be obtained by taking only one more iteration.

Stochastic Dynamic AC Optimal Power Flow Based on a Multivariate Short-Term Wind Power Scenario Forecasting Model

The deterministic methods generally used to solve DC optimal power flow (OPF) do not fully capture the uncertainty information in wind power, and thus their solutions could be suboptimal. However, the stochastic dynamic AC OPF problem can be used to find an optimal solution by fully capturing the uncertainty information of wind power. That uncertainty information of future wind power can be well represented by the short-term future wind power scenarios that are forecasted using the generalized dynamic factor model (GDFM)—a novel multivariate statistical wind power forecasting model. Furthermore, the GDFM can accurately represent the spatial and temporal correlations among wind farms through the multivariate stochastic process. Fully capturing the uncertainty information in the spatially and temporally correlated GDFM scenarios can lead to a better AC OPF solution under a high penetration level of wind power. Since the GDFM is a factor analysis based model, the computational time can also be reduced. In order to further reduce the computational time, a modified artificial bee colony (ABC) algorithm is used to solve the AC OPF problem based on the GDFM forecasting scenarios. Using the modified ABC algorithm based on the GDFM forecasting scenarios has resulted in better AC OPF’ solutions on an IEEE 118-bus system at every hour for 24 h.

Transmission expansion planning based on Locational Marginal Prices and ellipsoidal approximation of uncertainties

This paper proposes an algorithm for transmission expansion planning (TEP) which minimizes the congestion surplus calculated from optimized nonlinear (AC) Optimal Power Flow (OPF) and Locational Marginal Prices (LMPs). Uncorrelated and correlated uncertainties related to operating conditions of the future transmission network and expected costs of the submitted energy bids to the energy market are constrained by bounding hyper-ellipsoid around base case AC OPF solution, with assumption of additive uncertainties. Perturbed uncertain points inside a hyper-ellipsoid are selected by proposed quasi-random sampling algorithm. For these points, the linearized OPF around base case AC OPF solution is proposed. The Genetic Algorithm (GA) does selection of lines and years for transmission expansion, where the increments of the fitness function are calculated by proposed linearized AC OPF model. The results and practical aspects of the proposed methodology are illustrated on 12- and 118-bus test power system examples.

Differential evolution based method for total transfer capability evaluation

The application of Differential Evolution (DE) to compute the Total Transfer Capability (TTC) in deregulated market is proposed in this paper. The objective is to maximize a specific point-to-point power transaction without violating system constraints using DE. This algorithm is based on full ac optimal power flow solution to account for the effects of active and reactive power flow, voltage limits, and line flow limits. The real power output of generators in source area and the real power of the loads in the sink area were adjusted to obtain the maximum transfer capability. In order to calculate TTC more accurately, Transmission Reliability Margin is incorporated in the calculation of TTC by considering single and multiline outages and also a three phase to ground fault near a bus and clearing it by isolating the faulty line after certain time interval. The performance of the proposed method is tested on the modified IEEE-30 bus system and results are compared with that of Particle Swarm Optimization method (PSO). Further, the results are compared with other published results using CPF and EP. It is found that DE provides more reliable results than other methods. Keywords: Total transfer capability, available transfer capability, transmission reliability margin, differential evolution, particle swarm optimization.