Multi-objective optimization operation with corrective control actions for meshed AC/DC grids including multi-terminal VSC-HVDC

This paper presents a multi-objective optimal operation of meshed AC/DC power grids including multi-terminal voltage-source-converter-based high-voltage direct current (VSC-MTDC) systems. The proposed approach is modeled as a corrective security-constrained optimal power flow (CSC-OPF) problem, with the minimization of both the operation cost and power loss as the objectives. Moreover, it provides a cost-effective solution to assist in decision-making, and improves the system security during operation. The N − 1 contingency security criterion is enforced for both AC and DC transmission networks, and corrective control is used to eliminate or alleviate post-contingency security violations. The corrective control actions used in this paper include not only secure operation control actions, but also economical post-contingency corrective control of the multi-terminal VSC-HVDC. To increase the computation speed, a contingency screening technique is applied to CSC-OPF by efficiently selecting the most severe case of the N − 1 contingency, as obtained using a voltage security index (VSI). The proposed approach uses the non-dominated sorting genetic algorithm (NSGA-II) to find multi-objective OPF solutions by checking the post-contingency state feasibility while taking into account post-contingency corrective actions. Simulation results confirm the validity and effectiveness of this approach.     

Security-based multi-objective congestion management for emission reduction in power system

Power system operation in the era of post-restructuring faces several challenges: transmission congestion frequently occurs, security is deterred more than in the past, emission reduction is becoming a matter of importance and intermittent renewable power generation resources (RPGR) have been widely promoted. This paper intends to solve these challenges in a multi-objective optimisation framework. The proposed procedure comprises two stages: in the a priori stage, transmission congestion management cost (TCMC) and emission are traded-off via a proposed stochastic augmented ε-constraint technique which yields a set of non-dominated solutions. In the a posteriori stage, a solution is selected by considering power system security. For this purpose, two strategies are proposed: in the first strategy, based on a proposed managerial vision, a combination of data envelopment analysis introduced by Charnes, Cooper, and Rhodes (CCR-DEA), cross-efficiency technique and robustness analysis is deployed to select the most robust super-efficient solution. The advantage of the proposed a posteriori approach is that selecting the final solution is not subjected to assigning weights to the objective functions and/or providing higher-level information. In the second strategy, first the effective scenarios due to outage of transmission components are identified using CCR-DEA and next, each scenarios’ degree of severity (DOS) is obtained using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The sums of the DOS of non-dominated solutions’ effective scenarios are evaluated for final decision making. The proposed approach is applied to IEEE 24 bus test system and the results are analysed.     

A PSO based approach for multi-stage transmission expansion planning in electricity markets

This paper presents a particle swarm optimization (PSO) based approach to solve the multi-stage transmission expansion planning problem in a competitive pool-based electricity market. It is a large-scale non-linear combinatorial problem. We have considered some aspects in our modeling including a multi-year time horizon, a number of scenarios based on the future demands of system, investment and operating costs, the N − 1 reliability criterion, and the continuous non-linear functions of market-driven generator offers and demand bids. Also the optimal expansion plan to maximize the cumulative social welfare among the multi-year horizon is searched. Our proposed PSO based approach, namely modified PSO (MPSO), uses a diversity controlled PSO to overcome the problem of premature convergence in basic PSO (BPSO) plus an initial high diversity swarm to cover the search space efficiently. The MPSO model is applied to the Garver six-bus system and to the IEEE 24-bus test system and compared to the BPSO model and a genetic algorithm based model.     

Congestion management solution under secure bilateral transactions in hybrid electricity market for hydro-thermal combination

The deregulation of power system has created an environment of competitiveness among different market players and the transmission lines are forced to operate near to their thermal or stability limits. It is a challenge with System Operators (SO) to ensure a secure and reliable transmission of power under these conditions. This paper proposes a rescheduling based congestion management strategy in hybrid (pool + bilateral) electricity market structure for a combination of hydro and thermal units. The proposed congestion management problem has been formulated as mixed integer nonlinear programming (MINLP) problem with an objective to minimize the congestion management cost by suitably rescheduling the hydro and thermal units based on their up and down generation cost bids. The hydro units having lowest operational cost and fast startup time have been used to alleviate the congestion by considering non-concave piecewise linear performance curves for them. The secure bilateral transactions have been ensured while rescheduling of the generators for alleviating the congestion. The performance of the proposed model has been demonstrated by solving the congestion management problem on modified IEEE-24 bus system.     

Evolutionary computation based multi-objective pole shape optimization of switched reluctance machine

This paper presents the application of elitist Non-dominated Sorting Genetic Algorithm version II (NSGA-II) to determine optimum pole shape design for performance enhancement of Switched Reluctance Machine (SRM). In SRM, torque output and torque ripple are sensitive to stator and rotor pole arcs and their selection is a vital part of SRM design process. The problem of determining optimal pole arc is formulated as a multi-objective optimization problem with the objective of maximizing average torque, minimizing torque ripple and copper loss. In order to account for the geometry as well as for the nonlinearity of material utilized, the Finite Element Method (FEM) is used to determine the performance of the machine. The proposed optimization technique is applied to determine optimal pole shape of an 8/6, four-phase, 5 HP, 1500 rpm SRM. The results show the effectiveness of the proposed approach and confirm the application of NSGA-II as a promising tool for solving SRM design problems. The results obtained by NSGA-II are compared and validated with classical multi-objective approach based on weighted sum method using Differential Evolution (DE) algorithm.     

Particle swarm optimization algorithm for capacitor allocation problem in distribution systems with wind turbine generators

This paper aims at adopting the Particle Swarm Optimization (PSO) technique to find the near-optimal solutions for the capacitor allocation problem in distribution systems for the modified IEEE 16-bus distribution system connected to wind energy generation based on a cost function. The proper allocation and the optimized number of capacitors have led to adequate power losses reduction and voltage profile enhancement. Because of the wind power generation variations due to the nature of wind speed intermittency and the lack of reactive power compensation, the problem under study have been presented involving a nonlinear fitness function. In order to solve it, the corresponding mathematical tools have to be used. The formulated fitness cost function has consisted of four terms: cost of real power loss, capacitor installation cost, voltage constraint penalty, and capacitor constraint penalty. PSO technique has been used to obtain the near-optimum solution to the proposed problem. Simulation results demonstrate the efficiency of the proposed fitness cost function when applied to the system under study. Furthermore, the application of PSO to the modified IEEE 16-bus system has shown better results in terms of power losses cost and voltage profile enhancement compared to Genetic Algorithm (GA). In order to verify the successful adaptation of PSO toward attaining adequate near-optimal capacitor allocations in distribution systems, this metaheuristic technique has been employed to the large-scale IEEE 30-bus system. The proposed PSO technique has provided adequate results while modifying the objective function and constraints to include the power factor and transmission line capacities for normal and contingency (N-1) operating conditions.     

Evaluation of voltage and current profiles and Joule losses for a half-wavelength power transmission line

Half-wavelength lines (HWLLs) have been studied as an option to be applied to power transmission regarding line lengths around 2500 km for a 60 Hz frequency. The main advantage of this type of transmission line, which has not yet been put in commercial operation in any country, is the elimination of reactive compensation, which contributes to cost reduction if compared to a conventional ac transmission. This paper presents a demonstration of voltage and current magnitude profiles along the line, using phasors and graphic calculations. In addition, an algebraic expression for Joule losses is proposed, to be used in economical evaluation of a HWLL solution.     

Short-term hydrothermal generation scheduling by a modified dynamic neighborhood learning based particle swarm optimization

The main objective of the short-term hydrothermal generation scheduling (SHGS) problem is to determine the optimal strategy for hydro and thermal generation in order to minimize the fuel cost of thermal plants while satisfying various operational and physical constraints. Usually, SHGS is assumed for a 1 day or a 1 week planing time horizon. It is viewed as a complex non-linear, non-convex and non-smooth optimization problem considering valve point loading (VPL) effect related to the thermal power plants, transmission loss and other constraints. In this paper, a modified dynamic neighborhood learning based particle swarm optimization (MDNLPSO) is proposed to solve the SHGS problem. In the proposed approach, the particles in swarm are grouped in a number of neighborhoods and every particle learns from any particle which exists in current neighborhood. The neighborhood memberships are changed with a refreshing operation which occurs at refreshing periods. It causes the information exchange to be made with all particles in the swarm. It is found that mentioned improvement increases both of the exploration and exploitation abilities in comparison with the conventional PSO. The presented approach is applied to three different multi-reservoir cascaded hydrothermal test systems. The results are compared with other recently proposed methods. Simulation results clearly show that the MDNLPSO method is capable of obtaining a better solution.     

Robust non-fragile power system stabilizer

This paper presents a step towards the design of robust non-fragile power system stabilizers (PSSs) for single-machine infinite-bus systems. To ensure resiliency of a robust PSS, the proposed approach presents a characterization of all stabilizers that can guarantee robust stability (RS) over wide range of operating conditions. A three-term controller (x₁ + x₂s)/(1 + x₃s) is considered to accomplish the design. Necessary and sufficient stability constraints for existing of such controller at certain operating point are derived via Routh–Hurwitz criterion. Continuous variation in the operating point is tackled by an interval plant model where RS problem is reduced to simultaneous stabilization of finite number of plants according to Kharitonov theorem. Controller triplets that can robustly stabilize vertex plants are characterized in a similar manner. The most resilient controller is computed at the center of maximum-area inscribed rectangle. Simulation results confirm robustness and resiliency of the proposed stabilizer.     

Stochastic mid-term generation scheduling incorporated with wind power

A challenge now facing system operator is how to schedule optimally the generation units in a wind integrated power system over a one year time horizon considering the effects of wind forecasting and variability; also, regarding the effects of load uncertainty. By the same token, this paper first develops a new formulation for Stochastic Mid-term Generation Scheduling (SMGS). In the formulation, 2m + 1 point estimate method is developed to accurately estimate the output variables of Mid-term Generation Scheduling (MGS) problem. Then, the formulation is combined with adaptive modified gravitational search algorithm and a novel self-adaptive wavelet mutation strategy for the establishment of new robust algorithm for the present problem. It is noteworthy to say that the classical methods considered certain wind information in the deterministic solution of the MGS problem which is not the realistic approach. However, this study improves modeling of wind–thermal system in the MGS problem by considering possible uncertainties when scheduling the generators of power system. The proposed model is capable of taking uncertainty of load and wind into account. The proposed method is applied on two test cases and the numerical results confirmed the efficiency and stability of the proposed algorithm.     

Voltage distribution constant versus losses in medium-voltage distribution transformer: A polynomial interpolation approach

This paper aims to calculate an estimate of the initial stress voltage distribution in the transformer windings through their losses (that can be reduced by varying the construction parameters such as conductor section and size of the core window) through the numerical interpolation applied in capacitances of distribution transformers 30, 45, 75 and 112.5 kVA, 15 kV class. The calculations of the projects were organized into sets, with simultaneous variation of three construction parameters, totaling analysis of 10,648 projects of each power transformers arranged in three-dimensional arrays. The equation of the constant voltage distribution (α-factor) according to the losses through the quadratic polynomial and cubic splines for the of LV and HV windings is formulated.     

Modified parameter optimization of distribution transformer design using covariance matrix adaptation evolution strategy

Optimal transformer design (TD) is a complex multi-modal, multi-objective, mixed-variable and non-linear problem. This paper discusses the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for distribution TD, minimizing four objectives; purchase cost, total life-time cost, total mass and total loss individually. Two independent variables; voltage per turn and type of magnetic material are proposed to append with the usual TD variables, aiming at cost effective, reduced weight, and energy efficient TD. Three case studies with three sets of TD vectors are implemented on 400 KVA, 20/0.4 KV transformer to demonstrate the superiority of Modified Design Variables (MDV), in terms of cost savings, material savings, and loss reduction. Simulation results of CMA-ES provide better TD on comparison with conventional transformer design procedure, branch and bound algorithm tailored to a mixed-integer non-linear programming, Self Adaptive Differential Evolution (SaDE), and real coded GA (RGA). Statistical analysis has proven the faster convergence and consistency of CMA-ES. Moreover, NSGA-II is applied for solving multi-objective TD optimization problem with the aim of providing tradeoff between conflicting TD objectives.     

Model of distribution system total supply capability considering feeder and substation transformer contingencies

This paper proposes a model for calculating the total supply capability (TSC) for distribution system considering both feeder and substation transformer contingencies. Existing models and methods for TSC only consider substation transformer contingencies and ignore feeder contingencies. However, the feeder contingencies occur much more frequently than substation transformer contingencies in practice. Moreover, some operation state fail the feeder contingencies N − 1 verification even they pass the transformer contingencies N − 1 verification. In this paper, a TSC model is firstly proposed in which feeder and transformer N − 1 contingencies are fully considered. This model is designed in feeder level, which means the topology of interconnection among feeders is accurately modeled. Secondly, a supplementary model for load balancing is set up for a better load distribution solution on feeders and transformers at TSC loading. Finally, the method is tested in a test distribution system and a real partial distribution network and the results are verified by the traditional N − 1 simulation.     

A new optimal unified power flow controller placement and load shedding coordination approach using the Hybrid Imperialist Competitive Algorithm-Pattern Search method for voltage collapse prevention in power system

As power systems become more complex and heavily loaded, voltage collapse has become one of the most destructive events in modern power systems leading to blackouts in electric utilities worldwide. Voltage collapse is mainly caused by operating power systems at lower stability margins due to a surge in electric power demand. This paper presents an optimal unified power flow controller (UPFC) placement and load shedding coordination approach for voltage collapse prevention in N − K (K = 1, 2 and 3) contingency condition using Hybrid Imperialist Competitive Algorithm-Pattern Search (HICA-PS). ICA is the main optimizer of the proposed algorithm while pattern search is applied to further fine tune the results of the ICA. To show the effectiveness of the proposed approach in preventing voltage collapse in complex power systems, we implemented it on the New-England 39 bus power system. Its performance was also compared to that of some classical optimization techniques. Decrease in load shedding amounts, continuity of energy supply and voltage collapse prevention is the main positive features of the proposed approach.     

Transmission congestion management in bilateral markets: An interruptible load auction solution

This paper demonstrates that appropriate invocation of interruptible loads by the independent system operator (ISO) can aid in relieving transmission congestion in power systems. An auction model is proposed, for an ISO operating in a bilateral contract dominated market, for real-time selection of interruptible load offers while satisfying the congestion management objective. The proposed congestion management scheme using interruptible loads can specifically identify load buses where corrective measures are needed for relieving congestion on a particular transmission corridor. The N − 1 contingency criterion has been taken into account to simulate various cases, and hence, examine the effectiveness of the proposed method. It has been shown that the method can assist the ISO to remove the overload from lines in both normal and contingency conditions in an optimal manner.     

Optimal design of a robust discrete parallel FP + FI + FD controller for the Automatic Voltage Regulator system

The purpose of this paper is to design a good tracking controller for the generator Automatic Voltage Regulator (AVR) system. A fuzzy logic-based controller that is called Fuzzy P + Fuzzy I + Fuzzy D (FP + FI + FD) controller has been designed optimally and applied to AVR system. In the proposed method, optimal tuning of controller parameters is very important to achieve the desired level of robust performance. Thus, a hybrid of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) (HGAPSO) technique has been used to find a better fuzzy system control. The motivation for using this hybrid method is to increase disturbance rejection effort, reduce fuzzy system efforts and take large parametric uncertainties into account. The developed FP + FI + FD control strategy leads to a flexible controller with simple structure that is easy to implement. The simulation results have been compared with the conventional Proportional–Integral–Derivative (PID) and fuzzy PID controllers. Three cases of simulation have been performed, case 1: comparing the tracking capability of the controllers, case 2: comparing the disturbance rejection capability of the controller and case 3: evaluating the performance of the controllers assuming that amplifier and exciter system parameters have 50% uncertainty. The simulation results shows that the proposed parallel FP + FI + FD controller has good performance from the perspective of overshoot/undershoot, settling time, and rise time in comparison with both conventional and fuzzy PID controllers.     

Optimization models based on GM (1, 1) and seasonal fluctuation for electricity demand forecasting

In this paper, a novel combined approach which combines the first-order one-variable gray differential equation (GM (1, 1)) model derived from gray system theory and seasonal fluctuation from time series method (SFGM (1, 1)) is proposed. This combined model not only takes advantage of the high predictable power of GM (1, 1) model but also the prediction power of time series method. To improve the forecasting accuracy, an adaptive parameter learning mechanism is applied to SFGM (1, 1) model to develop a new model named APL-SFGM (1, 1). As an example, the statistical electricity demand data from 2002 to 2011 sampled from South Australia of Australia are used to validate the effectiveness of the two proposed models. Simulation and graphic results indicated that both of two proposed models achieve better performance than the original GM (1, 1) model. In addition, the APL-SFGM (1, 1) model, which is actually an adaptive adjustment model, obtains a higher forecasting accuracy as compared to the SFGM (1, 1) model.     

Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller

This article presents the automatic generation control of an unequal three area thermal system. Single stage reheat turbines and generation rate constraints of 3%/min are considered in each control area. Controllers such as Integral (I), Proportional – Integral (PI), Proportional – Integral – Derivative (PID), and Proportional – Integral – Derivative Plus Second Order Derivative (PID + DD) are treated as secondary controllers separately. A nature inspired optimization technique called Ant Lion Optimizer (ALO) algorithm is used for simultaneous optimization of the controller gains. Comparison of dynamic responses of frequencies and tie line powers corresponding to ALO optimized I, PI, PID and PID + DD controller reveal the better performance of PID + DD controller in terms of lesser settling time, peak overshoots as well as reduced oscillations. Robustness of the optimum gains of best controller obtained at nominal conditions is evaluated using sensitivity analysis. Analysis exposed that the optimum PID + DD controller gains obtained at nominal are robust and not necessary to reset again for changes in loading, parameter like inertia constant (H), size and position of disturbance. Furthermore, the performance of PID + DD controller is found better as compared to PID controller against random loading pattern condition.     

Maclaurin–Newton algorithms in 132 kV subtransmission security simulations

This paper examines how applicable approximate Jacobian inversions are when implemented in the security analysis simulations of 132 kV power subtransmission. The complete Scottish 400/275/132 kV power transmission network was simulated, including the 132 kV subtransmission network with its high r/x ratios. Both the coupled and decoupled Maclaurin–Newton load flow algorithms were tested. It was proved that high r/x ratios found in the 132 kV level, five times higher than in 400/275 kV, have an important influence on convergence and accuracy of the inversion Jacobian load flow algorithms. It was found that the decoupled inversion load flow was applicable for 132 kV, it converged regularly, but had worse convergence and accuracy characteristics, compared to 400/275 kV applications, while the coupled inversion load flow was not applicable at all for 132 kV, it always diverged.     

Distributed generation planning using differential evolution accounting voltage stability consideration

This paper describes a technique for selection of buses in a sub transmission system for location of distributed generation (DG) and determination of their optimum capacities by minimizing transmission losses. The buses have been selected based on incremental voltage (dV/dP) sensitivities. Line flow constraints have been accounted. Type-3 DG i.e. wind turbine along with induction generator has been considered for the study. Differential evolution (DE) has been used to evaluate the optimum DG capacity and results have been compared with those obtained using bare bones particle swarm optimization (BBPSO) and multi-membered non-recombinative (μ + λ) evolution strategy (MMNRES). The developed algorithms have been implemented on standard 6-bus and 30-bus test systems.