Power Flow Solution Research Articles

Multi-objective solution of optimal power flow based on TD3 deep reinforcement learning algorithm

With the increasing proportion of renewable energy generator units in power grid, the research on how to coordinate and control the optimal power flow (OPF) problem of traditional power generation and renewable energy power generation is gradually being paid attention to. In this paper, considering the line constraints and generator set constraints, an OPF problem including thermal power units and renewable energy units is established, and multiple solution objectives are set. The goals include line safety, renewable energy output, unit generation capability and unit operating costs. As an off-policy learning strategy, TD3 reinforcement learning method outperforms other reinforcement learning methods in learning strategies which include dual critic networks, actor network delayed update, replay buffer sampling and target policy smoothing regularization. As a result, for this multi-objective solution problem, we adopt the TD3 reinforcement learning solution method and verify the effects through an example. It reveals in the experiments that TD3 learning method can achieve better results through algorithm comparison and line disconnection analysis. Algorithm analysis shows TD3 method can achieve faster convergence while the disconnection analysis shows the robustness of the proposed method. Through this solution method, a reasonable generator set output arrangement can be obtained. At the same time, in the case of using different weight coefficients, it will have different effects on the control strategy.

Optimal power flow solution based on gorilla troops optimization technique considering uncertainty of renewable energy sources: A case study of Adrar’s isolated power network

This paper proposes an efficient Gorilla troops-inspired algorithm to cope optimal power flow (OPF) problem considering uncertainty of renewable energy sources (RES). The problem is formulated as large-scale constrained optimization problem with non-linear characteristics. Its degree of complexity increases with incorporation of intermittent energy sources, making it harder to be solved using conventional optimization techniques. However, could be efficiently resolved by nature-inspired optimization algorithms and solvers. The objective function is the overall cost of system, including reserve cost for over-estimation and penalty cost for under-estimation of two types of PV-solar and wind energy. To demonstrate the consistency and robustness of the developed algorithm a case study on the modified IEEE 30-bus system and and Adrar’s power network (isolated grid) is carried out. Simulation results show the capability of GTO to find high quality optimal feasible solutions and ranked first among the compared algorithms, and so, over different function landscapes.

An Extensive Study Using the Beetle Swarm Method to Optimize Single and Multiple Objectives of Various Optimal Power Flow Problems

An electric energy generation system, under the economic operation mode, is an imperative mission in the power system function. This article deals with the use of beetle swarm optimization algorithm (BSOA), for optimal power flow (OPF) solution, in an effective approach. BSOA is a competent optimization technique, to handle multimodal, nonlinear, and nondifferentiable objective functions. The proposed OPF is modeled by numerous objective functions, formulations with constraints, examined with thirty-one different cases, on the three distinguished test systems (IEEE 30, 57, and 118-bus), using single and weighted sum multiobjectives. Six new multiobjective cases are also studied. The control variables, such as real generation of power, tap setting ratio of transformers, bus voltages magnitudes, and the values of shunt capacitor, are also optimized. Potency and robustness of this proposed method were investigated and evaluated with more recent findings reported in the literature. This extensive study revealed the preeminence of the presented technique, applied to OPF problem, with intricate and nonsmooth objective functions.

Development and Validation of a Load Flow Based Scheme for Optimum Placing and Quantifying of Distributed Generation for Alleviation of Congestion in Interconnected Power Systems

The energy supply entities widely adopt distributed generators (DG) to meet the additional power requirement due to scheduled or unscheduled interruptions. The expansion of transmission and distribution systems via the inclusion of loads and generators and the occurrence of line interruptions are significant causes of congestion of transmission lines in interconnected systems. The management and alleviation of congested lines is a primary requirement for a power system network’s reliable and efficient operation. The researchers investigated the potential scope of distributed generation (DG) to alleviate the congested branches in interconnected transmission systems. The development of a reliable scheme to arrive at the best location and size of local generators for alleviating congestion deserves considerable importance. This paper attempted to develop a simple and reliable strategy for the optimum placement and sizing of DGs to be integrated with a transmission line system of DGs for congestion relief in transmission lines by analyzing power flow solutions. This research work considered the 14-bus system of IEEE for the preliminary analysis to identify the parameters employed for assessing the severity of line congestion and the best placement and sizing of DGs for congestion relief. This work analyzed power flows by load flow algorithms using ETAP software in the 14-bus IEEE system for different line outage cases. The analysis of power flow solutions of the 14-bus system of IEEE revealed that the percentage violation of the system can be regarded as an essential parameter to assess the extent of congestion in an interconnected system. A detailed power flow analysis of the system with various capacities of DG integration at several buses in the system revealed the application of two indices, namely the index of severity (SI) and sensitivity factor (SF), for optimum placement with the best capacity of DGs for congestion alleviation in the system. This work proposed a reliable algorithm for the best siting and sizing of DGs for congestion relief by using the identified indices. The proposed methodology is system indices allied load flow-based algorithm. This work produced a fast simulation solution without any mismatch through this developed scheme. The approximations linked with the algorithm were very minute, resulting in comprehensive bests instead of inexact limited bests with less simulation time and more convergence probability and availing the benefits of the mathematical approach. The work investigated the feasibility of the proposed methodology for optimum placing and quantifying DGs for congestion solutions for a practical interconnected bus system in the supply entity of the Kerala grid with many buses. Any transmission system operator can adopt this method in similar connected systems anywhere. The proposed algorithm determined the most severe cases of congestion and the optimum site and size of DGs for managing congested feeders in the grid system. The analysis of the losses in the system for different cases of DG penetration by load flow analysis validated the suitability of the obtained results.

Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy

The paper applies jellyfish search algorithm (JSA) for reaching the maximum profit of IEEE 30-node and IEEE 118-node transmission power networks considering electrical market and wind turbines (WTs). JSA is compared with the particle swarm optimization (PSO), genetic algorithm (GA), moth swarm algorithm (MSA), salp swarm algorithm (SSA), and water cycle algorithm (WCA) for three study cases. The same and different electric prices for all nodes are, respectively, considered in Case 1 and Case 2, whereas Case 3 considers different prices and the placement of one WT. As a result, JSA can reach higher profit than MSA, SSA, WCA, PSO, and GA by 1.2%, 2.44%, 1.7%, 1.3%, and 1.02% for Cases 1, 2, and 3. Then, JSA is applied for optimizing the placement of from two to four WTs for the first system, and from zero to five wind farms (WF) for the second systems. Comparison of profits from the study cases indicates that the network can reach higher profit if more WTs and WFs are optimally placed. The placement of four WTs can support the two systems to reach higher profit by $130.3 and $34770.4, respectively. The greater profits are equivalent to 2.6% and 97.2% the profit of the base system. On the other hand, the obtained results also reveal the important order of location for installing wind power generators. The important order of nodes is, respectively, Nodes 5, 2, 1, and 10 for the first system, as well as Nodes 29, 31, 71, 45, and 47 for the second system. Thus, it is recommended that renewable energies are very useful in improving profit for transmission power systems, and the solutions of installing renewable energy-based generators should be determined by high performance algorithms, such as JSA.

A phasor rotation-based approach to represent PV buses on the current injection power flow

The power flow formulation based on current injection was first introduced to cope with the problem of updating the Jacobian matrix in the conventional Newton Raphson power flow. In the case of PQ buses, the current injection method is very efficient, as all elements in the Jacobian matrix are constant. However, when PV buses are present, non-constant elements are introduced in the Jacobian matrix, deteriorating the methodôs performance. This paper presents a novel approach for representing PV buses in the current injection power flow by applying the concept of single-phase phasor rotation. In the proposed formulation, the elements introduced in the Jacobian matrix by the presence of PV buses are constant; therefore, the Jacobian needs to be built and factorized just once, reducing the computational burden and speeding up the power flow solution process. Case studies were conducted on transmission and distribution systems containing up to 2313-buses, considering several R/X line ratios and loading conditions to illustrate the validity and merits of the proposed formulation. The results indicate that the proposed approach leads to a computationally efficient power flow that can be successfully applied to single-phase transmission and distribution networks.

Multi-Objective Optimal Power Flow Solutions Using Improved Multi-Objective Mayfly Algorithm (IMOMA)

This paper realizes the implementation of Improved Multi-objective Mayfly Algorithm (IMOMA) for getting optimal solutions related to optimal power flow problem with smooth and nonsmooth fuel cost coefficients. It is performed by considering Simulated Binary Crossover, polynomial mutation and dynamic crowding distance in the existing Multi-objective Mayfly Algorithm. The optimal power flow problem is formulated as a Multi-objective Optimization Problem that consists of different objective functions, viz. fuel cost with/ without valve point loading effect, active power losses, voltage deviation and voltage stability. The performance of Improved Multi-objective Mayfly Algorithm is interpreted in terms of the present Multi-objective Mayfly Algorithm and Nondominated Sorting Genetic Algorithm-II. The algorithms are applied under different operating scenarios of the IEEE 30-bus test system, 62-bus Indian utility system and IEEE 118-bus test system with different combinations of objective functions. The obtained Pareto fronts achieved through the implementation of Improved Multi-objective Mayfly Algorithm, Multi-objective Mayfly Algorithm and Nondominated Sorting Genetic Algorithm-II are compared with the reference Pareto front attained by using weighted sum method based on the Covariance Matrix-adapted Evolution Strategy method. The performances of these algorithms are individually analyzed and validated by considering the performance metrics such as convergence, divergence, generational distance, inverted generational distance, minimum spacing, spread and spacing. The best compromising solution is achieved by implementing the Technique for Order of Preference by Similarity to Ideal Solution method. The overall result has shown the effectiveness of Improved Multi-objective Mayfly Algorithm for solving multi-objective optimal power flow problem.

Load Flow Analysis and the Impact of a Solar PV Generator in a Radial Distribution Network

The distribution system acts as a conduit between the consumer and the bulk power grid. Due to characteristics such as a high resistance/reactance ratio, distribution networks cannot be solved using conventional methods, such as the Gauss-Seidel and Newton–Raphson. This research proposes a method for the calculation of the power flow in radial networks that considers their wide range of resistance and reactance values, PV generator characteristics, and radial structure. An iterative methodology is employed, with each iteration beginning with the branch that has the highest accurate power flow solution. The procedure is reliable and effective over various workloads and network configurations. To confirm the effectiveness of the suggested technique on the simple and IEEE 33-bus radial distribution system, simulations were carried out in MATLAB. The implications of including a renewable energy source, such as a PV generator, in the network under consideration are investigated by simulation result comparison. The optimal location of the PV generator was also determined using an Artificial Neural Network (ANN) controller. The results of the identification process improve the already exceptional efficacy and performance of the ANN controller.

Optimal power flow solution with current injection model of generalized interline power flow controller using ameliorated ant lion optimization

<span lang="EN-US">Optimal power flow (OPF) solutions with generalized interline power flow controller (GIPFC) devices play an imperative role in enhancing the power system’s performance. This paper used a novel ant lion optimization (ALO) algorithm which is amalgamated with Lévy flight operator, and an effectual algorithm is proposed named as, ameliorated ant lion optimization (AALO) algorithm. It is being implemented to solve single objective OPF problem with the latest flexible alternating current transmission system (FACTS) controller named as GIPFC. GIPFC can control a couple of transmission lines concurrently and it also helps to control the sending end voltage. In this paper, current injection modeling of GIPFC is being incorporated in conventional Newton-Raphson (NR) load flow to improve voltage of the buses and focuses on minimizing the considered objectives such as generation fuel cost, emissions, and total power losses by fulfilling equality, in-equality. For optimal allocation of GIPFC, a novel Lehmann-Symanzik-Zimmermann (LSZ) approach is considered. The proposed algorithm is validated on single benchmark test functions such as Sphere, Rastrigin function then the proposed algorithm with GIPFC has been testified on standard IEEE-30 bus system.</span>

The sequential power flow in complex plane for solving the VSC-MTDC hybrid AC/DC transmission grids

This paper presents new methodologies and modeling aimed at studying interwoven AC and DC subsystems of a power system in the complex plane. It is well known that the development of any former power flow application in real domain addressed to embedding FACTS devices is preceded by an arduous algebra task. To overcome this difficulty, a novel power flow solution method is proposed in this work. Thanks to the Wirtinger calculus, a Newton–Raphson method based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates is developed. Thus, the voltage-source-converter multi-terminal direct current is formulated in complex plane without any loss of accurateness and is termed as VSC-MTDC. Its performance is assessed through IEEE-test systems interconnected across a DC network prone to several scenarios, e.g., topology, loading magnitude and interchanging of active power.

Calculating multiple loadability points in the power flow solution space

Calculating loadability margins is indispensable for maintaining secure and stable operations of electric power grids. Loadability margins closely resemble boundedness placed by the Power-Flow (PF) equations solution space. Estimating these limits is a computationally demanding task linked to the non-convex structure of the PF solution space, technological constraints, and intricate grid topology. Furthermore, multiple loadability points exist within the PF solutions space due to the non-convex topology, representing either a structural change in the number of equilibria or the disappearance of all system equilibria. To address the problem of accurately estimating loadability margins, we present a computationally robust two-stage algorithmic framework that guarantees to identify all isolated loadability points within the PF solution space for a given set of parameters. Numerical results from different test cases validate the proposed algorithmic framework computational performance and also illustrate the convoluted structure of the PF solution space with disjoint sections.

Optimal Power Flow Solution for Bipolar DC Networks Using a Recursive Quadratic Approximation

The problem regarding of optimal power flow in bipolar DC networks is addressed in this paper from the recursive programming stand of view. A hyperbolic relationship between constant power terminals and voltage profiles is used to resolve the optimal power flow in bipolar DC networks. The proposed approximation is based on the Taylors’ Taylor series expansion. In addition, nonlinear relationships between dispersed generators and voltage profiles are relaxed based on the small voltage voltage-magnitude variations in contrast with power output. The resulting optimization model transforms the exact nonlinear non-convex formulation into a quadratic convex approximation. The main advantage of the quadratic convex reformulation lies in finding the optimum global via recursive programming, which adjusts the point until the desired convergence is reached. Two test feeders composed of 21 and 33 buses are employed for all the numerical validations. The effectiveness of the proposed recursive convex model is verified through the implementation of different metaheuristic algorithms. All the simulations are carried out in the MATLAB programming environment using the convex disciplined tool known as CVX with the SEDUMI and SDPT3 solvers.

Relation between the Branch-to-Node Incidence and Triangular Matrices in Radial Distribution Networks

The power flow solution is a classical problem in electrical engineering that has been studied for more than 60 years [1]. One of the most widely used methods corresponds to the Newton-Raphson approach, which is currently employed for analyzing power systems with meshed configurations and multiple generation sources, i.e., it is typically employed for power systems in high-voltage levels [2].

Constraints on OPF Surrogates for Learning Stable Local Volt/Var Controllers

We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power setpoints that approximate optimal power flow (OPF) solutions. We propose an incremental control algorithm and identify two different sets of slope conditions on the local surrogates such that the network is collectively steered toward desired configurations asymptotically. Our results reveal the trade-offs between each set of conditions, with coupled voltage-power slope constraints allowing an arbitrary shape of surrogate functions but risking limitations on exploiting generation capabilities, and reactive power slope constraints taking full advantage of generation capabilities but constraining the shape of surrogate functions. AC power flow simulations on the IEEE 37-bus feeder illustrate their guaranteed stability properties and respective advantages in two DG scenarios.

An optimal power flow solution to deregulated electricity power market using meta-heuristic algorithms considering load congestion environment

In this article, the Improved Mayfly Algorithm (IMA) is used as an upgraded form of the Mayfly Algorithm (MA), featuring simulated binary crossover and polynomial mutation operators replacing the arithmetic crossover and standard distribution mutation operators of the MA. With MA, IMA's achievements and significance are acknowledged. The algorithms achieve a final best solution for the investigated objective functions of the optimal power flow problem in a deregulated electrical power market under different load conditions. The overall load of the power system varies between half of the base load (-50%) and twice the base load (+100%). The investigated objective functions are associated with the financial worth of generators, dissipation of active power in transmission lines, variation of voltage magnitudes at the system bus, and voltage stability index at the load bus of the power system networks. The result achieved by GA, PSO, MA and IMA are attained using the IEEE-30 bus test system in a deregulated power system. Investigations are conducted on the best solutions for each objective function; offers of generators and bids of loads; generator sales and load purchases; and system revenues associated with different load scenarios. The simulated outcomes have confirmed that IMA would triumph over GA, PSO and MA.

Reduction of Active and Reactive Power Losses on Transmission Lines using SSSC

This paper discusses a comprehensive study on reduction of power (active and reactive) losses in transmission lines using a second generation FACTS device, Static Synchronons Series Compensator (SSSC). Modern restructured power systems sometimes operate with heavily loaded lines resulting in power losses and higher voltage deviations, which may lead to mal-operation of power system and eventual collapse of the system. This is mainly due to continuous and uncertain growth in demand for electrical power. The paper presents a methodology to solve the problem of power losses in the Nigerian 28 – bus power system by incorporating Static Synchronons Series Compensator in the network using Newton-Rahson power flow algorithm. Simulation of power flow solution without and with the FACTS device was done using a Matlab software. The results showed that the maximum power (active and reactive) loss in the system without SSSC occurred in the transmission line connecting bus 17 (Jebba) to bus 23(Shiroro) and a 19.32% loss reduction was obtained on the line after the incorporation of the SSSC FACTS device giving a power saving of 80.68%. The total system active and reactive power losses before the application of SSSC was 205.183MW and 1594.683MVAR respectively. However, when the FACTS device was applied at the weak buses the total system active and reactive power losses reduced to 144.571MW and 1136.863MVAR respectively giving a percentage loss reduction in active and reactive power of 29.54% and 28.71% respectively resulting in a power saving of 70.46% and 71.29%. Hence, more power was available in the network when compared to the base case due to the installation of SSSC. Also an improvement in the voltage magnitude at the weak buses and other buses were noticed as they were all maintained at 1.0 PU.

Parallel primal‐dual interior point method for the solution of dynamic optimal power flow

Parallel primal‐dual interior point method for the solution of dynamic optimal power flow

On the accuracy of power flow and load margin calculation caused by incorrect logical PV/PQ switching: Analytics and improved methods

Power Flow (PF) and Continuation Power Flow (CPF) are key tools for power system static calculation and analysis. This paper shows that the widely used logical PV/PQ switching method can lead to calculating non-physical power flow solutions and incorrect load margin calculations. From a computational viewpoint, several small and large numerical examples are presented to show the non-physical power flow solution and inaccurate load margin calculation made by the outer loop PF method. The existence of a non-physical power flow solution caused by logical PV/PQ switching and its impact on incorrect load margin calculation will be demonstrated. To address these issues, two smooth functions to approximate the generator Q-V curve and an active-set scheme will be presented. The Type-I smooth model is suitable for calculating physically feasible power flow solution, in addition it will be shown to contribute to faster convergence than the logical PV/PQ switching methods. The type-II smooth model is suitable for continuation power flow calculation for accurate load margin and speed improvement. A smooth-model-based active-set-assisted power flow method is then developed and its effectiveness in converging to the feasible (physical) power flow solution and the correct calculation of load margins will be shown. Numerical studies on several test systems were conducted to demonstrate the effectiveness of the proposed method in computing physical power flow solutions and achieving faster speed. For example, the proposed method for 70,000-bus PF computation is 1.7 times faster than that of the inner loop-based method and for the 25,000-bus CPF computation is about 3 times faster than that of the outer loop-based method.

Application of Three-Phase Power Flow Analysis to the Nigerian Distribution Networks

Single-phase power flow analysis is used to study most distribution networks in Nigeria. The use of single-phase-power flow analysis assumes that the network is balanced and that the conductor phases act identically. However, Nigerian distribution networks are highly imbalanced because of untransposed lines, irregularly distributed loads in conductor phases, mismatched conductor sizes, and spacing. Consequently, single-phase modeling of the networks fails to reflect actual network behavior, resulting in an incorrect power flow solution. This research presents the three-phase modeling of radial distribution networks for a three-phase-power flow study of Nigerian distribution networks. Olusanya's 54-bus and Ajinde's 62-bus distribution networks in Nigeria were evaluated, both of which were very imbalanced. Without making any assumptions about the network components, these two distribution networks were properly modeled. Each network's three-phase power flow study was carried out in the MATLAB environment. The power flow solutions for each network demonstrated unevenness in the voltage profile for each network phase, as well as inequality in the real and reactive power losses in each phase, indicating that the deployed three-phase-power flow analysis properly mirrored the underlying network characteristics. Therefore, applying three-phase power flow analysis to distribution networks is critical for proper assessment of distribution network performance.

Toward Models of Impact and Recovery of the US Western Grid from Earthquake Events

A Cascadia Subduction Zone (CSZ) earthquake will cause widespread damage to numerous lifelines and infrastructure along the northern US west coast. The goal of the presented research is to provide a bottom up estimate of the impact on and subsequent recovery of a Cascadia Subduction Zone earthquake on the US western grid to supplement and enhance the expert opinion estimates provided to date. The scope is limited to only consideration of shaking damage to utility substation equipment components of a power system model. The analysis utilizes probabilistic models of damage and recovery for substation power system assets, along with graph techniques for modeling connectivity, and Monte Carlo quasi steady state power flow solutions. The results show that a conservative estimate of the initial damage and loss of load is approximately 4000 MW, with a recovery estimate of 230 days.