Proposed Optimal Power Flow Formulation Research Articles

Optimal power flow for bipolar DC microgrids

This paper proposes an optimal power flow (OPF) formulation for bipolar DC microgrids. The bipolar DC microgrid can integrate distributed generations (DGs) and supply power to end-users with high effectiveness and reliability. In comparison with the existing power flow methods for DC grids, which are based on power injection, the current injection power flow method should be adopted for bipolar DC microgrids to entirely consider the bipolar structure. In this regard, the OPF established herein is based on the current injection power flow method. The output current of DGs as well as pole voltages should be adopted as decision variables to utilize the linearity of the power flow equation. The optimal set point of the output power and balanced voltage level of the DGs are determined with respect to three objective functions: generation cost, voltage unbalance, and network loss. Depending on the existence of the constant power load and the generation cost function that cause bilinear equality constraints, the proposed OPF model is classified as a convex quadratic programming (QP) or a nonconvex quadratically constrained QP problem, which can be solved using commercial solvers. The case study validates that the proposed OPF formulation can find the optimal operating point with low computational burden at various grid conditions and operational priority.

Fast Coscheduling of Discrete and Continuous Resources in Active Distribution Systems

This article proposes a novel fast method for flexibility scheduling and steady-state voltage control in smart distribution systems enabled with both conventional discrete controllable devices (DCDs), e.g., capacitor banks and <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> -load tap changers, and continuous and faster control devices, e.g., distributed energy resources, renewable resources, and static voltage regulators. By approximating the active and reactive losses, a linear branch flow model is presented for the optimal power flow (OPF) problem in distribution systems. Accurate models are also proposed for DCDs which suit the proposed OPF formulation and require fewer binary variables compared to those available in the literature. Conservation voltage reduction (CVR) scheme is modeled in the proposed OPF methodology. The CVR effects on energy saving, peak-load reduction, line losses, and transformer losses are analyzed in the case studies. As shown in various case studies, the proposed method is fast enough for quasi-real-time applications and is efficacious in minimizing the system operation cost, holding an acceptable level of power quality based on the available standards and evading the conflict between control actions.

Loss Minimization With Optimal Power Dispatch in Multi-Frequency HVac Power Systems

Low-frequency high-voltage ac transmission scheme has recently been proposed as an alternative approach for bulk power transmission. This paper proposes a multi-period optimal power flow (OPF) for a multi-frequency HVac transmission system that interconnects both conventional 50/60-Hz and low-frequency grids using back-to-back converters with a centralized control scheme. The OPF objective is to minimize system losses by determining the optimal dispatch for generators, shunt capacitors, and converters. The OPF constraints include the operational constraints of all HVac grid and converter stations. The resulting mixed-integer nonlinear programing problem is solved using a proposed framework based on the predictor-corrector primal-dual interior-point method. The proposed OPF formulation and solution approach are verified using a multi-frequency HVac transmission system that is modified from the IEEE 57-bus system. The results with the optimal dispatch from the proposed method during a simulated day show a significant loss reduction and an improved voltage regulation compared to those when an arbitrary dispatch is chosen.

Distributionally Robust Chance-Constrained Approximate AC-OPF With Wasserstein Metric

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed in the proposed OPF formulation combines an exact ac power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on the IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate ac model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties.

Optimal power flow using hybrid differential evolution and harmony search algorithm

In this paper, Optimal Power Flow (OPF) with non-convex and non-smooth generator fuel cost characteristics is proposed using Hybrid Differential Evolution and Harmony Search (Hybrid DE-HS) algorithm. The proposed OPF formulation includes active and reactive power constraints; prohibited zones, and valve point loading effects of generators. In the problem formulation, transformer tap settings and reactive power compensating devices settings are also considered as the control variables. Therefore, OPF is a complicated optimization problem, hence there is a need to solve this problem with an accurate algorithm. The OPF solution is obtained by considering generator fuel cost, transmission loss and voltage stability index as objective functions. The effectiveness of the proposed hybrid algorithm is validated on IEEE 30, 118 and 300 bus test systems, and the results obtained with proposed Hybrid DE-HS algorithm are compared with other optimization techniques reported in the literature. For example, the quadratic fuel cost obtained by the hybrid DE-HS algorithm for IEEE 30 bus system is 799.0514 $/h, saving 0.31% of the cost obtained by the General Algebraic Modeling System (GAMS) software. This benefit increases further with the size of the system.

Optimal power flow using clustered adaptive teaching learning-based optimisation

In this paper, optimal power flow (OPF) with non-convex and non-smooth generator cost characteristics is presented using clustered adaptive teaching learning-based optimisation (CATLBO) algorithm. The proposed OPF formulation includes active and reactive power constraints; prohibited zones, and valve point loading (VPL) effects of generators. In the problem formulation, transformer tap settings and reactive power compensating devices settings are also considered as control variables. OPF is a complicated optimisation problem, hence there is a need to solve this problem with an accurate algorithm. In the proposed CATLBO algorithm, the class is divided into different sections, and allot different teacher to every section depending on the performance of that particular section. This sectioning of the class makes the proposed technique more robust and less prone to trapping in local optima. The OPF solution is obtained by considering generator fuel cost, transmission loss and voltage stability index as objective functions. The effectiveness of proposed CATLBO algorithm is validated on IEEE 30 bus test system, and the simulation results obtained with CATLBO algorithm are compared with other optimisation techniques presented in the literature.

Efficiency Improvements in Meta-Heuristic Algorithms to Solve the Optimal Power Flow Problem

AbstractThis paper proposes the efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of power flows needed in the solution process. The proposed efficient approaches uses the lower and upper bounds of objective function values. By using this approach, the number of power flows to be performed are reduced substantially, resulting in the solution speed up. The efficiently generated objective function bounds can result in the faster solutions of meta-heuristic algorithms. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, etc., are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) and Prohibited Operating Zones (POZs) effects of generating units. The effectiveness of proposed approach is examined on IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approach is generic enough to use with any type of meta-heuristic algorithm based OPF.

Efficiency improvements in meta-heuristic algorithms to solve the optimal power flow problem

This paper presents three efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of load flows/power flows needed in the solution process. The proposed efficient approaches uses the concept of incremental power flow model based on sensitivities, and lower, upper bounds of objective function values. By using these approaches, the number of load flows/power flows to be performed are substantially, resulting in the solution speed up. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) effects and Prohibited Operating Zones (POZs) of generating units. The effectiveness of proposed approaches are examined on the IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approaches are generic enough to use with any type of meta-heuristic algorithm based OPF.

Optimal Power Flow using Clustered Adaptive Teaching Learning Based Optimization

In this paper, optimal power flow (OPF) with non-convex and non-smooth generator cost characteristics is presented using clustered adaptive teaching learning-based optimisation (CATLBO) algorithm. The proposed OPF formulation includes active and reactive power constraints; prohibited zones, and valve point loading (VPL) effects of generators. In the problem formulation, transformer tap settings and reactive power compensating devices settings are also considered as control variables. OPF is a complicated optimisation problem, hence there is a need to solve this problem with an accurate algorithm. In the proposed CATLBO algorithm, the class is divided into different sections, and allot different teacher to every section depending on the performance of that particular section. This sectioning of the class makes the proposed technique more robust and less prone to trapping in local optima. The OPF solution is obtained by considering generator fuel cost, transmission loss and voltage stability index as objective functions. The effectiveness of proposed CATLBO algorithm is validated on IEEE 30 bus test system, and the simulation results obtained with CATLBO algorithm are compared with other optimisation techniques presented in the literature.

Optimal power flow algorithm and analysis in distribution system considering distributed generation

This study investigates the optimal power flow (OPF) problem for distribution networks with the integration of distributed generation (DG). By considering the objectives of minimal line loss, minimal voltage deviation and maximum DG active power output, the proposed OPF formulation is a multi-object optimisation problem. Through normalisation of each objective function, the multi-objective optimisation is transformed to single-objective optimisation. To solve such a non-convex problem, the trust-region sequential quadratic programming (TRSQP) method is proposed, which iteratively approximates the OPF by a quadratic programming with the trust-region guidance. The TRSQP utilises the sensitivity analysis to approximate all the constraints with linear ones, which will reduce the optimisation scale. Active set method is utilised in TRSQP to solve quadratic programming sub-problem. Numerical tests on IEEE 33-, PG&E 69- and actual 292-, 588-, 1180-bus systems show the applicability of the proposed method, and comparisons with the primal-dual interior point method and sequential linear programming method are provided. The initialisation and convergence condition of the proposed method are also discussed. The computational result indicates that the proposed algorithm for DG control optimisation in distribution system is feasible and effective.

A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect

In this paper, an effective and reliable algorithm, based on Shuffle Frog Leaping Algorithm (SFLA) and Simulated Annealing (SA) is proposed for solving the optimal power flow (OPF) problem with non-smooth and non-convex generator fuel cost characteristics. Also, the proposed OPF formulation contains detailed generator constraints including active and reactive power generation limits, valve loading effects, and Prohibited Operating Zones (POZs) of units. OPF is spontaneously a complicate optimization problem, and becomes more and more complex considering the above constraints. Therefore, it needs to be solved with an accurate algorithm. Recently researchers have presented a new evolutionary method called SFLA algorithm. The original SFLA often converges to local optima. In order to avoid this shortcoming we propose a new method that profits from SA algorithm to improve local search near the global optima. The possibility of convergence to global optima is increased using the proposed method. For validating the proposed algorithm, it has been examined on the standard IEEE 30-bus test systems. The hybrid SFLA-SA provides better results compared to the original SFLA, SA, and other methods recently reported in the literature as demonstrated by simulation results.

Security constrained optimal power flow considering detailed generator model by a new robust differential evolution algorithm

This paper presents a new multiobjective model, including two objective functions of generation cost and voltage stability margin, for optimal power flow (OPF) problem. Moreover, the proposed OPF formulation contains a detailed generator model including active/reactive power generation limits, valve loading effects, multiple fuel options and prohibited operating zones of units. Furthermore, security constraints, including bus voltage limits and branch flow limits in both steady state and post-contingency state of credible contingencies, are also taken into account in the proposed formulation. To solve this OPF problem a novel robust differential evolution algorithm (RDEA) owning a new recombination operator is presented. The proposed RDEA has a minimum number of adjustable parameters. Besides, a new constraint handling method is also presented, which enhances the efficiency of the RDEA to search the solution space. To show the efficiency and advantages of the proposed solution method, it is applied to several test systems having complex solution spaces and compared with several of the most recently published approaches.

A method for voltage stability‐constrained optimal power flow (VSCOPF)

AbstractThis paper presents a novel formulation for solving optimal power flow (OPF) problems with voltage stability constraints. The proposed Voltage Stability Constrained OPF (VSCOPF) formulation is based on voltage sensitivity with respect to total load demand representing the gradient of the P‐V curve at the operating point. In the formulation, voltage constraints are given by a set of equality constraints which must be satisfied by the voltage sensitivity. Since the voltage stability constraints retain a sparse matrix structure, the method based on the proposed OPF formulation may effectively solve large‐scale problems. The feasibility and effectiveness of the proposed method are demonstrated on test problems with 2‐, 49‐, and 2312‐bus systems. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 29–39, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10125

電圧安定度制約を考慮した最適潮流計算手法

This paper presents a novel formulation for solving optimal power flow (OPF) problems with voltage stability constraints. The proposed Voltage Stability Constrained OPF (VSCOPF) formulation is based on voltage sensitivity with respect to total load demand representing the gradient of the P-V curve at the operating point. In the formulation, voltage constraints are given by a set of equality constraints which must be satisfied by the voltage sensitivity. Since the voltage stability constraints retain a sparse matrix structure, the method based on the proposed OPF formulation may effectively solve large-scale problems. The feasibility and effectiveness of the proposed method are demonstrated on test problems with 2-, 49-, and 2312-bus systems. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 29–39, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10125