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Optimal power flow problem with the integrated renewable energy sources: A survey
Abstract
In a transmission network, optimal power flow (OPF) is considered as one of the most widely studied non-linear, non-convex and highly constrained problem. While solving the conventional OPF problem, power generation system mainly consists of fossil fuel thermal generators; however, with the increased energy demand, renewable energy sources like wind turbines, solar photovoltaic panels and hydro plants are also introduced. OPF problem is solved using traditional and heuristic approaches to attain the stated objectives that mainly include fuel cost reduction, power loss minimization and emission reduction. These objectives are either optimized individually or in combination where two or more objectives are optimized simultaneously to achieve multi-objective optimization. Further, this study gives an overview of how these economical, environmental and technical objectives are achieved.
The transformation of conventional grid into Smart Grid (SG) requires strategic implementation of the demand-sensitive programs while considering the varying fluctuations in the consumers’ load. The core challenges faced by existing electric system are that how to utilize electrical devices, how to tackle large amount of data generated by end devices and how to meet energy demands of consumers in limited resources. This dissertation is focused on the energy management of residential sector in the SG. For this purpose, we have proposed the Energy Management Controllers (EMCs) at three levels: at home level (including the single and multiple homes), at building level and at regional level. In addition, cloud and fog based environments are integrated to provide on-demand services according to the consumers’ demands and are used to tackle the problems in existing electric system. At first level, heuristic algorithms based EMC is developed for the energy management of single and multiple homes in residential sector. Five heuristic algorithms: genetic algorithm, binary particle swarm optimization algorithm, bacterial foraging optimization algorithm, wind driven optimization algorithm and our proposed hybrid genetic wind driven algorithm are used to develop the EMC. These algorithms are used for scheduling of the residential load during peak and off peak hours in a real time pricing environment for minimizing both the electricity cost and peak to average ratio while maximizing the user comfort. In addition, the advancements in the electrical system, smart meters and implementation of Renewable Energy Sources (RESs) have yielded extensive changes to the current power grid for meeting the consumers’ demand. For integrating RESs and Energy Storage System (ESS) in existing EMCs, we have proposed another Home EMC (HEMC) that manages the residential sector’s load. The proposed HEMC is developed using the earliglow algorithm for electricity cost reduction. At second level, a fuzzy logic based approach is proposed and implemented for the hot and cold regions of the world using the world-wide adaptive thermostat for the residential buildings. Results show that the proposed approach achieves a maximum energy savings of 6.5% as compared to the earlier techniques. In addition, two EMCs: binary particle
swarm optimization fuzzy mamdani and binary particle swarm optimization fuzzy sugeno
are proposed for energy management of daily and seasonally used appliances. The comfort evaluation of these loads is also performed using the Fanger’s Predicted Mean Vote method. For increasing the system automation and on-demand availability of the resources, we have proposed a cloud-fog-based model for intelligent resource management in SG for multiple regions at next level. To implement this model, we have proposed a new hybrid approach of Ant Colony Optimization (ACO) and artificial bee colony known as Hybrid Artificial Bee ACO (HABACO). Moreover, a new Cloud to Fog to Consumer (C2F2C) based framework is also proposed for efficiently managing the resources in the residential buildings. C2F2C is a three layered framework having cloud, fog and consumer layers, which are used for the efficient resource management in six regions of the world. In order to efficiently manage the computation of the large amount of data of the residential consumers, we have also proposed and implemented the deep neuro-fuzzy optimizer. The simulation results of the proposed techniques show that they have outperformed the previous techniques in terms of energy consumption, user comfort, peak to average ratio and cost optimization in the residential sector.
Economic-environmental power dispatch is one of the most popular bi-objective non-linear optimization problems in power system. Classical economic power dispatch problem is formulated with only thermal generators often ignoring security constraints of the network. But importance of reduction in emission is paramount from environmental sustainability perspective and hence penetration of more and more renewable sources into the electrical grid is encouraged. However, most common forms of renewable sources are intermittent and uncertain. This paper proposes multiobjective economic emission power dispatch problem formulation and solution incorporating stochastic wind, solar and small-hydro (run-of-river) power. Weibull, lognormal and Gumbel probability density functions are used to calculate available wind, solar and small-hydro power respectively. Some conventional generators of the standard IEEE 30-bus system are replaced with renewable power sources for study purpose. Network security constraints such as transmission line capacities and bus voltage limits are also taken into consideration alongwith constraints on generator capabilities and prohibited operating zones for the thermal units. Decomposition based multiobjective evolutionary algorithm and summation based multiobjective differential evolution algorithm are applied to the problem under study. An advanced constraint handling technique, superiority of feasible solutions, is integrated with both the multiobjective algorithms to comply with system constraints. The simulation results of both the algorithms are summarized, analyzed and compared in this study.
IIn this paper, we propose a home energy management system which employs load shifting strategy of demand side management to optimize the energy consumption patterns of a smart home. It aims to manage the load demand in an efficient way to minimize electricity cost and peak to average ratio while maintaining user comfort through coordination among home appliances. In order to meet the load demand of electricity consumers, we schedule the load in day-ahead and real-time basis. We propose a fitness criterion for proposed hybrid technique which helps in balancing the load during On-peak and Off-peak hours. Moreover, for real-time rescheduling, we present the concept of coordination among home appliances. This helps the scheduler to optimally decide the ON/OFF status of appliances in order to reduce the waiting time of appliance. For this purpose, we formulate our realtime rescheduling problem as knapsack problem and solve it through dynamic programming. This study also evaluates the behavior of the proposed technique for three pricing schemes including: time of use, real-time pricing and critical peak pricing. Simulation results illustrate the significance of the proposed optimization technique with 95% confidence interval.
The exhaustive knowledge of optimal power flow (OPF) methods is critical for proper system operation and planning, since OPF methods are utilized for finding the optimal state of any system under system constraint conditions, such as loss minimization, reactive power limits, thermal limits of transmission lines, and reactive power optimization. Incorporating renewable energy sources optimized the power flow of system under different constraints. This work presents a comprehensive study of optimal power flows methods with conventional and renewable energy constraints. Additionally, this work presents a progress of optimal power flow solution from its beginning to its present form. Authors classify the optimal power flow methods under different constraints condition of conventional and renewable energy sources. The current and future applications of optimal power flow programs in smart system planning, operations, sensitivity calculation, and control are presented. This study will help the engineers and researchers to optimize power flow with conventional and renewable energy sources.
The problem of voltage collapse in power systems due to increased loads can be solved by adding renewable energy sources like wind and photovoltaic (PV) to some bus-bars. This option can reduce the cost of the generated energy and increase the system efficiency and reliability. In this paper, a modified smart technique using particle swarm optimization (PSO) has been introduced to select the hourly optimal load flow with renewable distributed generation (DG) integration under different operating conditions in the 30-bus IEEE system. Solar PV and wind power plants have been introduced to selected buses to evaluate theirs benefits as DG. Different solar radiation and wind speeds for the Dammam site in Saudi Arabia have been used as an example to study the feasibility of renewable energy integration and its effect on power system operation. Sensitivity analysis to the load and the other input data has been carried out to predict the sensitivity of the results to any deviation in the input data of the system. The obtained results from the proposed system prove that using of renewable energy sources as a DG reduces the generation and operation cost of the overall power system.
Generations from several sources in an electrical network are to be optimally scheduled for economical and efficient operation of the network. Optimal power flow problem is formulated with all relevant system parameters including generator outputs and solved subsequently to obtain the optimal settings. The network may consist of conventional fossil fuel generators as well as renewable sources like wind power generators and solar photovoltaic. Classical optimal power flow itself is a highly non-linear complex problem with non-linear constraints. Incorporating intermittent nature of solar and wind energy escalates the complexity of the problem. This paper proposes an approach to solve optimal power flow combining stochastic wind and solar power with conventional thermal power generators in the system. Weibull and lognormal probability distribution functions are used for forecasting wind and solar photovoltaic power output respectively. The objective function considers reserve cost for overestimation and penalty cost for underestimation of intermittent renewable sources. Besides, emission factor is also included in objectives of selected case studies. Success history based adaptation technique of differential evolution algorithm is adopted for the optimization problem. To handle various constraints in the problem, superiority of feasible solutions constraint handling technique is integrated with success history based adaptive differential evolution algorithm. The algorithm thus combined and constructed gives optimum results satisfying all network constraints.
Optimal Power flow considered the backbone tool in the complex power system. The expanding in demands lead to increasing in generation that requires increase the transmission capacity, for these reasons the problem of optimal power flow OPF still under many studies in order to minimize the cost, losses, emission of harm gases, etc. FACTS is the main articles of this paper include the last nontraditional OPF methods, hybrid methods, multi-objective OPF, and OPF with FACTS devices. Also there are three Tables contain the recent stander and hybrid methods used, mostly, in solving OPF problems with their advantages, disadvantages, and their applications that may help the researchers in this field, eventually some important points have been concluded.
This article demonstrates an appositeness of a novel metaheuristic optimization algorithm viz. the Moth Flame Optimization (MFO) to solve various non-convex, non-linear optimum power flow (OPF) objective functions. MFO is based on movement of moths with respect to the source of light. In this paper, five single objective functions are selected for solving the OPF problem: generator fuel cost minimization under various realistic conditions, real power loss reduction, and emission minimization. Simulations are performed on the IEEE 30-bus system to identify efficacy of the proposed method. Results obtained by MFO are collated with other stochastic methods reported in literature. Comparison reflects that MFO obtains optimum value with rapid and smooth convergence. Statistical tests like Wilcoxon test, Quade test, Friedman test and Friedman aligned test are also carried out to check the effectiveness of the MFO. Comparison of MFO with other stochastic algorithms demonstrates superiority of MFO in terms of solution excellency and solution feasibility, substantiating its effectiveness and competence.
Power flow study (load-flow study) is a steady-state analysis whose target is to determine the voltages, currents, and real and reactive power flows in a system under a given load conditions. The objective of an Optimal Power Flow (OPF) study is to find steady state operation point which minimizes generation cost, loss, emission etc. Over the past half-century, OPF has become one of the most important and widely studied nonlinear optimization problems while maintaining an acceptable system performance in terms of limits on generators' real and reactive powers, line flow limits, output of various compensating devices etc. Traditionally, classical optimization methods were used to effectively solve OPF. But more recently due to incorporation of FACTS devices and deregulation of a power sector, the traditional concepts and practices of power systems are superimposed by an economic market management. Therefore, OPF has become complex. In recent years, Artificial Intelligence (AI) methods have been emerged which can solve highly complex OPF problems. The purpose of this paper is to present a comprehensive survey of various optimization methods like traditional and AI methods used to solve OPF problems.
The incorporation of renewable energy resources (RERs) into electrical grid is very challenging problem due to their intermittent nature. This paper solves an optimal power flow (OPF) considering wind–solar–storage hybrid generation system. The primary components of the hybrid power system include conventional thermal generators, wind farms and solar photovoltaic modules with batteries. The main critical problem in operating the wind farm or solar PV plant is that these RERs cannot be scheduled in the same manner as conventional generators, because they involve climate factors such as wind velocity and solar irradiation. This paper proposes a new strategy for the optimal power flow problem taking into account the impact of uncertainties in wind, solar PV and load forecasts. The simulation results for IEEE 30 bus system with genetic algorithm (GA) and two-point estimate method have been obtained to test the effectiveness of the proposed optimal power flow strategy. Results for a sample system with GA and two-point estimate OPF, and GA and Monte Carlo simulation have been obtained to ascertain effectiveness of the proposed method.
A new evolutionary hybrid algorithm (HA) has been proposed in this work for Environmental Optimal power flow (EOPF) problem. The EOPF problem has been formulated in a nonlinear constrained multi objective optimization framework. Considering the intermittency of available wind power a cost model of the wind and thermal generation system is developed. Suitably formed objective function considering the operational cost, cost of emission, real power loss and cost of installation of FACTS devices for maintaining a stable voltage in the system has been optimized with HA and compared with particle swarm optimization algorithm (PSOA) to prove its effectiveness. All the simulations are carried out in MATLAB/SIMULINK environment taking IEEE30 bus as the test system.
In this paper, a new fuzzy adaptive artificial physics optimization (FAAPO) algorithm is used to solve security-constrained optimal power flow (SCOPF) problem with wind and thermal power generators. The stochastic nature of wind speed is modeled as a Weibull probability density function. The production cost is modeled with the overestimation and underestimation of available wind energy and included in the conventional SCOPF. Wind generation cost model comprises two components, viz. reserve capacity cost for wind power surplus and penalty cost for wind power shortage. The selection of optimal gravitational constant (G) is a tedious process in conventional artificial physics optimization (APO) method. To overcome this limitation, the gravitational constant (G) is fuzzified in this work. Therefore, based upon the requirement, the gravitational constant changes adaptively. Hence, production cost is reduced, settles at optimum point and takes less number of iterations. The proposed algorithm is tested on IEEE 30-bus system and Indian 75-bus practical system, including wind power in both the test systems. It is observed that FAAPO can outperform BAT algorithm and APO algorithm. Hence, the proposed algorithm can be used for integration of wind power with thermal power generators.
Distributed Generation (DG) sources based on Renewable Energy (RE) can be the fastest growing power resources in distribution systems due to their environmental friendliness and also the limited sources of fossil fuels. In general, the optimal location and size of DG units have profoundly impacted on the system losses in a distribution network. In the present article, the Particle Swarm Optimization (PSO) algorithm is employed to find the optimal location and size of DG units in a distribution system. The optimal location and size of DG units are determined on the basis of a multi-objective strategy as follows: (i) the minimization of network power losses, (ii) the minimization of the total costs of Distributed Energy Resources (DERs), (iii) the improvement of voltage stability, and (iv) the minimization of greenhouse gas emissions. The related distribution system was assumed to be composed of the fuel cells, wind turbines, photovoltaic arrays, and battery storages. The electrical, cooling, and heating loads were also considered in this article. The heating and cooling requirements of the system consist of time varying water heating load, space heating load, and space cooling load. In this study, the waste and fuel cell were used to produce the required heating and cooling loads in the distribution system. In addition, the absorption chiller was used to supply the required space cooling loads. A detailed performance analysis was carried out on 13 bus radial distribution system to demonstrate the effectiveness of the proposed methodology.
The rapid development of distributed generation in different forms and capacities is transforming the conventional planning of distribution networks. Despite the benefits offered by renewable distributed generation technologies, several economic and technical challenges can result from the inappropriate integration of distributed generation in existing distribution networks. Therefore, the optimal planning of distributed generation is of paramount importance to ensure that the performance of distribution network can meet the expected power quality, voltage stability, power loss reduction, reliability and profitability. In this paper, we firstly discuss several conventional and metaheuristic methodologies to address the optimal distributed generation planning problem. Metaheuristic algorithms are often used as they offer more flexibility, particularly for multi-objective planning problems without the pursuit of globally optimized solution. Analytical techniques are considered suitable for modeling power system mechanisms and validating numerical methods. Then, this paper conducts a comprehensive review and critical discussion of state-of-the-art analytical techniques for optimal planning of renewable distributed generation. The analytical techniques are discussed in detail in six categories, i.e. exact loss formula, loss sensitivity factor, branch current loss formula, branch power flow loss formula, equivalent current injection and phasor feeder current injection. In addition, a comparative analysis of analytical techniques is presented to show their suitability for distributed generation planning in terms of various optimization criteria. Finally, we present conclusive remarks along with a set of recommendations and future challenges for optimal planning of distributed generation in modern power distribution networks.
A new optimal power flow model for wind, solar, and solar-thermal bundled power scheduling and dispatch is proposed, incorporating the deviation incentive/penalty charges for renewable energy introduced in India. The multiobjective function is solved using the flower pollination algorithm; the scheme is successfully tested on the IEEE 30-bus and Indian utility 30-bus systems. The forecasting error constraints introduced in renewable energy scheduling and dispatch are demonstrated to be beneficial in several aspects. Solar-thermal bundling is shown to create win-win situations for thermal and solar generators. The effectiveness of the flower pollination algorithm in solving optimal power flow models is proved.
Several potential benefits to the quality and reliability of delivered power can be attained with the installation of distributed generation units. To take full advantage of these benefits, it is essential to place optimally sized distributed generation units at appropriate locations. Otherwise, their installation could provoke negative effects to power quality and system operation. Over the years, various powerful optimization tools were developed for optimal integration of distributed generation. Therefore, optimization techniques are continuously evolving and have been recently the focus of many new studies. This paper reviews recent optimization methods applied to solve the problem of placement and sizing of distributed generation units from renewable energy sources based on a classification of the most recent and highly cited papers. In addition, this paper analyses the environmental, economic, technological, technical, and regulatory drivers that have led to the growing interest on distributed generation integration in combination with an overview about the challenges to overcome. Finally, it examines all significant methods applying optimization techniques of the integration of distributed generation from renewable energy sources. A summary of common heuristic optimization algorithms with Pro-Con lists are discussed in order to raise new potential tracks of hybrid methods that haven't been explored yet.
An energy storage system (ESS) is a promising tool for improving the power system's technical and economical functionalities. This device possesses diverse applications in terms of system operation and planning. One of the main applications of the ESS in the power system operation, specially a large scale unit, is defined as load leveling. To this end, in the literature, various ESS models are integrated into two main power system operation frameworks, i.e., optimal power flow (OPF) and unit commitment (UC). But the question is that in which framework the obtained benefit from the load leveling by ESS is maximum and why. In other words, should ESS units schedule before generating unit commitment (UC) or after OPF and how. In this context, this paper performs three works. First, it proposes OPF and UC frameworks integrated with large scale ESS units. Second, the proposed models are implemented with identical parameters. Third, the obtained results are considered with respect to various outcomes, especially operation cost. This study is implemented on an IEEE 24 bus RTS system. The simulation results are analyzed and compared with respect to various parameters, and relevant conclusions are drawn based on the results.
Abstract Considering the importance of clean energy, the combined operation of hydro-thermal-wind (HTW) system is formulated in optimal power flow (OPF) framework. The objective is to find an optimal generation schedule for the HTW system where the system will work economically and in a voltage secure manner with reduced loss during normal as well as stressed system operation. As system voltage may be vulnerable especially during under estimation (UE) situation, provision of additional reactive power (Q) support is essential as a possible solution. This is achieved by installing shunt facts devices i.e. (STATCOM) at the weak nodes of the power network. A comparative assessment between wind-thermal (WT) and HTW system operation with STATCOM at different wind penetration levels is also depicted. The optimum operational paradigms are obtained by optimizing the objective with Genetic Algorithm (GA), Hybrid Algorithm (HA) and modified bacteria foraging algorithm (MBFA). After several tests, superiority of MBFA optimization over HA and GA is revealed so that the IEEE30-bus system operates in a voltage secure and cost-effective manner.
The term smart grid refers to a modernization of the electrical network consisting in the integration of various technologies such as dispersed generation, dispatchable loads, communication systems and storage devices which operates in grid-connected and islanded modes. As a result, traditional optimization techniques in new power systems have been seriously influenced during the last decade. One of the most important technical and economical tools in this regard is the Optimal Power Flow (OPF). As a fundamental optimization tool in the operation and planning fields, OPF has an undeniable role in the power system. This paper reviews and compares the OPF approaches mainly related to smart distribution grids. In this work, the main OPF approaches are compared in terms of their objective functions, constraints, and methodologies. Furthermore, computational performances, case study networks and the publication date of these methods are reported. Finally, some basic challenges arising from the new OPF methodologies in smart grids are addressed.
Meta heuristic algorithms have been introduced as a powerful method to solve the nonlinear optimization problems. These algorithms have been employed in many complex engineering problems due to their high capability in finding the solutions and reaching the optimal results within a short period of time. Optimization of distributed generation units in distribution systems, which have profoundly impacted on the system losses and voltage profile, is one of these nonlinear problems. In this study, a novel objective function was proposed for optimization procedure by meta-heuristic algorithms. The related objective function consists of the total cost of distributed generation units, cost of the purchased natural gas, cost of distribution system power losses, and penalty for greenhouse gas emissions. The electrical, cooling, and heating loads were considered in this study. In the distribution system, the waste and fuel cell were used to supply the required heating and cooling loads. The meta-heuristic algorithms including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Imperialist Competitive Algorithm (ICA) were employed to find the optimal location and size of distributed generation units in a distribution system. A detailed performance analysis was done on 13 bus radial distribution system. The performances of three algorithms were compared with each other and results showed that the PSO was the fastest; and had the best solution and optimum results. Furthermore, the PSO reached the optimum solution in a fewer number of iterations than the GA and ICA algorithms.
Distributed generation, with respect to its ability in utilizing the alternative resources of energy, provides a promising future for power generation in electric networks. Distributed generators contribution to power systems include improvement in energy efficiency and power quality to reliability and security. These benefits are only achievable with optimal allocation of distributed resources that considers the objective function, constraints, and employs suitable optimization algorithm. In this paper, a comprehensive review on the optimal allocation of distributed generators was carried out for different objectives, constraints, and algorithms. Current review highlights how the methods and algorithms for optimal distributed generation allocation play an important role in improving the accuracy and efficiency of the results.
The intermittent volatility of wind power integrated into the grid poses a great threat to the stable operation of power systems on the supply side. Conversely, large-scale charging of electric vehicles (EVs) also brings new challenges to dispatch on the demand side. In response, the randomness and temporal-spatial correlations of stochastic wind power generation are considered in this paper. Additionally, the EV charging infrastructure is studied. A dynamic stochastic optimal power flow (DSOPF) for wind farms and EVs integrated power system based on the chance-constrained programming model is proposed. An optimal dispatch scheme is obtained by solving the dynamic optimal power flow. After that, dynamic probabilistic power flow based on cumulants is performed under the scheme to obtain the probability distribution of state variables. The upper and lower bounds of chance constraints are adjusted according to the probability distribution function until they are all satisfied. Illustrative examples demonstrate the effectiveness of DSOPF for firming the variable wind energy, and EV charging is performed on the Institute of Electrical and Electronics Engineers systems. On this basis, different EV charging modes and the temporal-spatial correlations are specifically discussed.
Due to different viewpoints, procedures, limitations, and objectives, the scheduling problem of distributed energy resources (DERs) is a very important issue in power systems. This problem can be solved by considering different frameworks. Microgrids and Virtual Power Plants (VPPs) are two famous and suitable concepts by which this problem is solved within their frameworks. Each of these two solutions has its own special significance and may be employed for different purposes. Therefore, it is necessary to assess and review papers and literature in this field. In this paper, the scheduling problem of DERs is studied from various aspects such as modeling techniques, solving methods, reliability, emission, uncertainty, stability, demand response (DR), and multi-objective standpoint in the microgrid and VPP frameworks. This review enables researchers with different points of view to look for possible applications in the area of microgrid and VPP scheduling.
This article proposes a reliable computational paradigm for solving the optimal voltage regulation problem in power distribution systems in the presence of distributed generators. The main idea is to integrate elements of multi-objective optimization theory and decision analysis for computing a reliable problem solution, considering all the system uncertainties, and describing the multi-criteria aspects of the regulation problem. Detailed numerical simulations obtained from both balanced and unbalanced power systems are presented and discussed to demonstrate the effectiveness of the proposed methodology in the task of solving the optimal voltage regulation problem under different operating scenarios.
The drying up of the fossil energy sources and the damage from unchecked carbon emissions demand the development of low carbon economy, which promotes the development of new energy sources, such as wind power and photovoltaic. However, the direct connections of wind/photovoltaic power into power grid bring great impacts on power systems, thus affecting the security and stability of power system operations, which challenges the power system dispatching. In despite of many methods for power system dispatch, lack of the models, for power system containing wind power and photovoltaic considering carbon trading and spare capacity variation (PSCWPCCTSCV), restricts the further optimal operations of power systems. This paper studies the economic dispatch modeling problem of power system containing wind power and photovoltaic, establishes the model of economic dispatch of PSCWPCCTSCV. On this basis, adaptive immune genetic algorithm is applied to conduct the economic operation optimization, which can provide the optimal carbon trading price and the optimal power distribution coefficient. Finally, simulations based on the newly-proposed models are made to illustrate the economic dispatch of PSCWPCCTSCV. The results show that optimization with the proposed model can not only weaken the volatility of the new energy effectively, but also reduce carbon emissions and reduce power generation costs.
Increasing penetration of wind power in power systems causes difficulties in system planning due to the uncertainty and non dispatchability of the wind power. The important issue, in addition to uncertain nature of the wind speed, is that the wind speeds in neighbor locations are not independent and are in contrast, highly correlated. For accurate planning, it is necessary to consider this correlation in optimization planning of the power system. With respect to this point, this paper presents a probabilistic multi-objective optimal power flow (MO-OPF) considering the correlation in wind speed and the load. This paper utilizes a point estimate method (PEM) which uses Nataf transformation. In reality, the joint probability density function (PDF) of wind speed related to different places is not available but marginal PDF and the correlation matrix is available in most cases, which satisfy the service condition of Nataf transformation. In this paper biogeography based optimization (BBO) algorithm, which is a powerful optimization algorithm in solving problems including both continuous and discrete variables, is utilized in order to solve probabilistic MO-OPF problem. In order to demonstrate performance of the method, IEEE 30-bus standard test case with integration of two wind farms is examined. Then the obtained results are compared with the Monte Carlo simulation (MCS) results. The comparison indicates high accuracy of the proposed method.
In this work the variability of WP (wind power) has been suitably modelled and incorporated with the thermal generating units. The goal is to operate the wind-thermal generation system in a cost effective manner while maintaining a voltage secure operation with reduction in system loss. These objectives have been formulated in an OPF (optimal power flow) framework. As the wind generation cost model is subjected to intermittent WP, the voltage security aspect is considered during both UE (under estimation) and OE (over estimation) of available WP. This is achieved by suitably incorporating shunt facts devices (STATCOM) to provide reactive power (Q) support during UE scenario and maintaining a spinning reserve of thermal generators during OE scenario. To further utilize the Q-support, the DFIG (doubly fed induction generators) are used in the wind turbine. The combinations of optimum operational paradigms are obtained by optimizing the objective function with ACO (ant colony optimization) and MBFA (modified bacteria foraging algorithm). Finally, after performing several tests the superiority of MBFA optimized scenario over ACO is revealed so that the IEEE30-bus system operates in a voltage secured manner when subjected to N-1 contingencies.
This paper describes teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal power flow (MOOPF) problems while satisfying various operational constraints. To improve the convergence speed and quality of solution, quasi-oppositional based learning ( QOBL) is incorporated in original TLBO algorithm. The proposed quasi-oppositional teaching learning based optimization (QOTLBO) approach is implemented on IEEE 30-bus system, Indian utility 62-bus system and IEEE 118-bus system to solve four different single objectives, namely fuel cost minimization, system power loss minimization and voltage stability index minimization and emission minimization; three bi-objectives optimization namely minimization of fuel cost and transmission loss; minimization of fuel cost and L-index and minimization of fuel cost and emission and one tri-objective optimization namely fuel cost, minimization of transmission losses and improvement of voltage stability simultaneously. In this article, the results obtained using the QOTLBO algorithm, is comparable with those of TLBO and other algorithms reported in the literature. The numerical results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal non-dominated solutions of the multi-objective OPF problem. The simulation results also show that the proposed approach produces better quality of the individual as well as compromising solutions than other algorithms.
This paper presents an optimal energy management model of a solar photovoltaic-diesel-battery hybrid power supply system for off-grid applications. The aim is to meet the load demand completely while satisfying the system constraints. The proposed model minimizes fuel and battery wear costs and finds the optimal power flow, taking into account photovoltaic power availability, battery bank state of charge and load power demand. The optimal solutions are compared for cases when the objectives are weighted equally and when a larger weight is assigned to battery wear. A considerable increase in system operational cost is observed in the latter case owing to the increased usage of the diesel generator. The results are important for decision makers, as they depict the optimal decisions considered in the presence of trade-offs between conflicting objectives.
This paper focuses primarily on implementation of optimal power flow (OPF) problem considering wind power. The stochastic nature of wind speed is modeled using two parameter Weibull probability density function. The economic aspect is examined in view of the system wide social cost, which includes additional costs like expected penalty cost and expected reserves cost to account for wind power generation imbalance. The optimization problem is solved using Gbest guided artificial bee colony optimization algorithm (GABC) and tested on IEEE 30 bus system. The simulation results obtained using proposed method are compared with other methods available in the literature for a case of conventional OPF as well as OPF incorporating stochastic wind. Subsequently an extensive simulation study is conducted to investigate the effect of wind power and different cost components on optimal dispatch and emission. Numerical simulations indicate that the operation cost of system and emission depends upon the transmission system bottlenecks and the intermittency of wind power generation.
A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method.
A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses. The solution is feasible with respect to constraints on control variables and dependent variables such as load voltages, reactive sources, and tie line power angles. The method is based on power flow solution by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints. A test program solves problems of 500 nodes. Only a small extension of the power flow program is required to implement the method.
The paper describes a new approach to the optimal-power-flow
problem based on Newton's method which it operates with an augmented
Lagrangian function associated with the original problem. The function
aggregates all the equality and inequality constraints. The first-order
necessary conditions for optimality are reached by Newton's method, and
by updating the dual variables and the penalty terms associated with the
inequality constraints. The proposed approach does not have to identify
the set of binding constraints and can be utilised for an infeasible
starting point. The sparsity of the Hessian matrix of the augmented
Lagrangian is completely exploited in the computational implementation.
Tests results are presented to show the good performance of this
approach
A Newton optimal power flow program was developed for the Ontario Hydro Energy Management System. Each iteration minimizes a quadratic approximation of the Lagrangian. All the equations are solved simultaneously for all the unknowns. A new technique based on linear programming is used to identify the binding inequalities. All binding constraints are enforced using Lagrange multipliers. The algorithm combines the fast convergence of the Newton technique with the speed and reliability of Linear programming. Most cases converged in three iterations or less.
This work presents a linear programming based algorithm to solve reactive power dispatch problems. A mixed set of variables (generated voltages and reactive power injections) and the reactive power model of the fast decoupled load flow algorithm are used to derive linear sensitivities. A suitable criterion is suggested to form a sparse reactive power sensitivity matrix. The sparse sensitivity matrix is in turn modeled as a bipartite graph which is used to define an efficient constraint relaxation strategy to solve linearized reactive power dispatch problems. The penalty function - linear programming technique method is used in a complete reactive power dispatch solution algorithm, the performance of which is discussed by solving a 256-node, 58 control-variable test system.
A new optimal reactive power flow (ORPF) model in rectangular form is proposed in this paper. In this model, the load tap changing (LTC) transformer branch is represented by an ideal transformer and its series impedance with a dummy node located between them. The voltages of the two sides of the ideal transformer are then used to replace the turn ratio of the LTC so that the ORPF model becomes quadratic. The Hessian matrices in this model are constants and need to be calculated only once in the entire optimal process, which speed up the calculation greatly. The solution of the ORPF problem by the predictor corrector primal dual interior point method is described in this paper. Two separate prototypes for the new and the conventional methods are developed in MATLAB in order to compare the performances. The results obtained from the implemented seven test systems ranging from 14 to 1338 buses indicate that the proposed method achieves a superior performance than the conventional rectangular coordinate-based ORPF.
This paper presents a reactive power optimization model that is
based on successive quadratic programming (SQP) methods. Mathematical
formulation and unified algorithm suppose different objective functions
(OF) of reactive power optimization, depending on type and purposes of
current reactive power control or planning problem. A bicriterion
reactive power optimization model, that represents compromise between
economical and security objective functions, is proposed. An efficient
algorithm for approximation of initial problem by quadratic programming
problem is described. The quadratic programming problem (QP) is solved
on the basis of the Newton type quadratic programming method. A modified
successive quadratic programming method was developed, that provides
reliable convergence of the SQP method
Advances in distribution system analysis with distributed resources: Survey with a case study
- K Joshi
- N Pindoriya
Joshi, K. and Pindoriya, N., 2017. Advances in distribution system
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