Optimal Power Flow Formulation Research Articles

Optimal Power Flow with Reactive Power Compensation for Cost and Loss Minimization On Nigerian Power Grid System

One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile

Optimal Power Flow with Reactive Power Compensation for Cost and Loss Minimization On Nigerian Power Grid System

One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.

Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation

Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This paper explores a solution method for multiperiod AC OPF that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The SOCP relaxation's solution is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. This combined method is demonstrated on several test cases with up to 4259 nodes and a time horizon of eight time steps. A comparison of initialization schemes indicates that the SOCP-based approach offers improved convergence rate, execution time, and solution quality.

Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we adopt a chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows, and voltages remain within their bounds with a predefined probability. We then discuss different chance-constraint reformulations and solution approaches for the problem. We first describe an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterative solution scheme which alternates between solving a deterministic AC optimal power flow problem and assessing the impact of uncertainty. The flexibility of the iterative scheme enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample-based reformulations that do not require any approximation or relaxation of the AC power flow equations. In a case study based on four different IEEE systems, we assess the performance of the method, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical reformulations outperforms the two alternative, sample-based chance constraint reformulations.

Load Curtailment Sensitivity Indices Through Optimal Placement of Unified Power Flow Controller

The optimal power flow (OPF) is one of the key tasks to be performed in the complicated operation and planning of a power system. Directing the power in such a way that the lightly loaded branches are loaded to reduce the system load curtailment is an option which can be achieved by making use of FACTS devices. This paper proposes a set of load curtailment sensitivity indices for optimal placement of Unified Power Flow Controller (UPFC) in power system network. An OPF formulation considering the minimization of load curtailment requirement as an objective has been developed in this paper to study the impact of optimal placement of UPFC. The effectiveness of the proposed method has been tested on IEEE-14 bus test system. The obtained results have been presented in terms of change in system load curtailment with respect to changes in UPFC controller parameters for the best location. The optimal location of UPFC in a line has been decided based on the calculated sensitivity indices. Conclusion is made on different results to see the benefit of UPFC in power system.

Hybrid Stochastic-Deterministic Multiperiod DC Optimal Power Flow

Stochastic optimal power flow (OPF) formulations that minimize the expected operating costs over forecast scenarios generally result in lower costs than the standard (deterministic) OPF problem for power systems with significant forecast error, for example, from renewable energy sources. However, this type of stochastic OPF problem is more computationally demanding than the deterministic OPF, and even more so when storage units or ramp-constrained generators are included, as they require solving a multi-period OPF problem. We propose a hybrid method approaching the cost performance of the stochastic OPF problem and the computational burden of the deterministic OPF problem. Our method decomposes the problem into stochastic and deterministic subproblems, and relies on Benders’ Cuts to interface them. We present three versions of the method, which achieve different cost/computational burden trade-offs. The versions can be parametrized so that they scale well with the problem dimension. For one of the versions, we develop a multi-dimensional formulation of the Sandwich Algorithm , which is used to iteratively approximate a convex function. Through a case study using a 118-bus system, we find that our hybrid method achieves between 25% and 81% of the cost improvement of the stochastic OPF, but requires only 12 to 41% of the increased computation time required by the stochastic OPF. Both the hybrid method and the multi-dimensional Sandwich Algorithm can be used for problems outside of the field of power systems.

Robust optimisation for AC–DC power flow based on second‐order cone programming

This study presents an adjustable robust optimisation method for AC–DC optimal power flow (OPF) considering the uncertainty of renewable energy source (RESs). The optimal power flow of AC–DC system is modelled as a second-order cone (SOC) problem, and the affinely adjustable robust OPF (AAROPF) formulation is proposed. To apply AAROPF, the base-point generation is calculated and determined to match the power with forecasted RES output before the realisation of the uncertainty. Also once the uncertainty is revealed, generators reschedule its output through participation factors responding to the uncertain fluctuation of RES output to ensure a feasible solution for all realisations of RES output within a prescribed uncertainty set. Numerical results are obtained on a modified AC–DC IEEE 30-bus to minimise the expected operational cost. Results reveal a higher cost using AAROPF than the deterministic case, but it obtains a more robust solution with higher successful rates.

Implementation of lossy FTRs for perfect risk hedging under the marginal loss pricing

In this study, a market framework is proposed for the practical implementation of lossy financial transmission rights (FTRs). The advantage of lossy FTRs over conventional FTRs is that the lossy FTRs can be settled directly according to locational marginal prices (LMPs) without requiring any LMP decomposition. Therefore, the price risk for a forward contract can be perfectly hedged if the power transaction involved perfectly matches the corresponding FTR. Although proposed long back, lossy FTRs still did not find an entry to the market because of the prejudice of market complexity and inefficiency. The principal aim of this study is, thus, to create the necessary environment so as to make those fine risk-hedging tools available in the market. First of all, a suitable format for forward contracts is prescribed to enable proper utilisation of lossy FTRs. The detailed lossy FTR auction model is prepared based upon a suitable optimal power flow (OPF) formulation. In addition, the implementation of lossy FTRs is shown for an AC-DC system by appropriately modelling the DC-line power flow behaviour according to the chosen OPF framework. The lossy FTR auction model prepared is thoroughly verified for the FTR issuance as per the market expectations.

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.

Optimal Power Flow with Reactive Power Compensation for Cost and Loss Minimization on Nigerian Power Grid System

One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile.

Multi‐objective optimal power flow considering the system transient stability

This study presents a new formulation for optimal power flow (OPF) to enhance the overall transient stability of the power system in addition to the traditional fuel cost minimisation. To overcome the shortcomings of the traditional formulation, this study formulates OPF as a true multi-objective optimisation problem. One objective is to operate the system economically within the system physical bounds. The other objective is to withstand severe contingencies by enhancing the system transient stability. To overcome the inconsistency and sub optimality problems, strength Pareto evolutionary algorithm is developed for solving multi-objective OPF (MOOPF) problem. Time domain simulations (TDSs) are employed for handling transient stability problem that knocks out the numerical inaccuracy and convergence problems. To speed up the transient stability assessment, a hybrid stability classifier is developed that combines TDS and transient energy function methods. To demonstrate the effectiveness of the proposed strategy, two standard test systems have been considered. The results show the effectiveness of the proposed approach to solve the MOOPF and enhance greatly the system transient stability. The results also show the superiority of the proposed approach compared with those reported 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.

A Robust Approach to Chance Constrained Optimal Power Flow With Renewable Generation

Optimal Power Flow (OPF) dispatches controllable generation at minimum cost subject to operational constraints on generation and transmission assets. The uncertainty and variability of intermittent renewable generation is challenging current deterministic OPF approaches. Recent formulations of OPF use chance constraints to limit the risk from renewable generation uncertainty, however, these new approaches typically assume the probability distributions which characterize the uncertainty and variability are known exactly. We formulate a Robust Chance Constrained (RCC) OPF that accounts for uncertainty in the parameters of these probability distributions by allowing them to be within an uncertainty set. The RCC OPF is solved using a cutting-plane algorithm that scales to large power systems. We demonstrate the RRC OPF on a modified model of the Bonneville Power Administration network, which includes 2209 buses and 176 controllable generators. Deterministic, chance constrained (CC), and RCC OPF formulations are compared using several metrics including cost of generation, area control error, ramping of controllable generators, and occurrence of transmission line overloads as well as the respective computational performance.

An introduction to optimal power flow: Theory, formulation, and examples

ABSTRACTThe set of optimization problems in electric power systems engineering known collectively as Optimal Power Flow (OPF) is one of the most practically important and well-researched subfields of constrained nonlinear optimization. OPF has enjoyed a rich history of research, innovation, and publication since its debut five decades ago. Nevertheless, entry into OPF research is a daunting task for the uninitiated—both due to the sheer volume of literature and because OPF's ubiquity within the electric power systems community has led authors to assume a great deal of prior knowledge that readers unfamiliar with electric power systems may not possess. This article provides an introduction to OPF from an operations research perspective; it describes a complete and concise basis of knowledge for beginning OPF research. The discussion is tailored for the operations researcher who has experience with nonlinear optimization but little knowledge of electrical engineering. Topics covered include power systems modeling, the power flow equations, typical OPF formulations, and common OPF extensions.

Impact analysis of RES-based DGs with economical considerations in restructured electricity market

ABSTRACTThe integration of distributed generators (DGs) into the grid is of great importance in improving system reliability. The criterion of minimizing total system cost used previously by many researchers for locating the optimal sites for DGs using optimal power flow (OPF) formulations was considered in this work. Here, three different cost functions are formulated for three kinds of renewable energy source (RES). Three different objectives were considered separately for determining the optimal locations for each kind of RES using the mixed integer non-linear programming (MINLP) method. Having many alternatives with these three objectives, the analytic hierarchy process (AHP) was used to reach a decision over getting the optimal locations for various kinds of RES. The proposed methodology was demonstrated on a 15-node distribution system.

Optimal Fast Control and Scheduling of Power Distribution System Using Integrated Receding Horizon Control and Convex Conic Programming

In this paper, a convex optimal power flow (OPF) formulation integrated within receding horizon control (RHC) architecture using second-order conic programming (SOCP) is proposed. The main advantages of the proposed method are 1) global optimal scheduling with faster computation time; 2) dynamic models with online control within optimization routine; and 3) integration of uncertain resources and measurements. The effectiveness of this method is evaluated using modified IEEE 32-bus and IEEE 119-bus distribution test systems considering network constraints such as energy market interactions, storage dynamics, and uncertain model of wind generation. The efficiency of the proposed method compared to RHC ac optimal power flow (RHC-ACOPF) is also evaluated using real-time simulator. The results show that the proposed method outperforms the RHC-ACOPF and guarantees global optimal solution. The proposed method also provides effective usage of energy storage system since dynamic modeling of energy storage within the optimization algorithm is possible using RHC integration.

Linear approximated formulation of AC optimal power flow using binary discretisation

This study presents a novel linear approximated methodology for full alternating current-optimal power flow (AC-OPF). The AC-OPF can provide more precise and real picture of full active and reactive power flow modelling, along with the voltage profile of buses compared to the commonly used direct current-optimal power flow. While the AC-OPF is a non-linear programming problem, this can be transformed into a mixed-integer linear programming environment by the proposed model without loss of accuracy. The global optimality of the solution for the approximated model can be guaranteed by existing algorithms and software. The numerical results and simulations which represent the effectiveness and applicability of the proposed model are given and completely discussed in this study.

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.

Finding a representative network losses model for large-scale transmission expansion planning with renewable energy sources

The global drive for integration of RESs (renewable energy sources) means that TEP (transmission expansion planning) has to be carried out over geographically wide and large-scale networks under high levels of uncertainty. This leads to complex combinatorial TEP optimization problems, requiring a huge amount of OPF (optimal power flow) computations. The algorithm employed to calculate the OPF must be reasonably accurate but computationally very efficient, because it has to be run for a lot of operational conditions. Overly simplified OPF formulations are not adequate, since they neglect aspects which play a relevant role in TEP. Specifically, network losses significantly influence TEP solutions, but they are often disregarded due to their computational burden. Given their potential impact on the optimal TEP solution, the main focus of this paper is to find an appropriate losses model in the context of medium to long-term TEP for large-scale power systems. Keeping the balance between accuracy and computation time is essential in such problems. The paper presents two alternative linear losses models, as well as two variants of existing ones. These models are compared and tested using case studies, including small, medium and large-scale networks. Practical conclusions and recommendations are drawn from numerical results.