Transient stability constrained optimal power flow using particle swarm optimisation

A novel approach based on the particle swarm optimisation (PSO) technique is proposed for the transient-stability constrained optimal power flow (TSCOPF) problem. Optimal power flow (OPF) with transient-stability constraints considered is formulated as an extended OPF with additional rotor angle inequality constraints. For this nonlinear optimisation problem, the objective function is defined as minimising the total fuel cost of the system. The proposed PSO-based approach is demonstrated and compared with conventional OPF as well as a genetic algorithm based counterpart on the IEEE 30-bus system. Furthermore, the effectiveness of the PSO-based TSCOPF in handling multiple contingencies is illustrated using the New England 39-bus system. Test results show that the proposed approach is capable of obtaining higher quality solutions efficiently in the TSCOPF problem     

Investigation of static transmission expansion planning using the symbiotic organisms search algorithm

Transmission expansion planning (TEP) has become a complex problem in restructured electricity markets. This article presents the symbiotic organisms search (SOS) algorithm, a novel metaheuristic optimization technique for solving TEP problems in power systems. The SOS algorithm is inspired by the interactions among organisms in an ecosystem. The TEP problem is formulated here as an optimization problem to determine the cost-effective expansion planning of electrical power systems. Several constraints, such as power flow of the lines, right-of-way validity and maximum line addition, are taken into consideration. First, the SOS algorithm is tested with several benchmark functions. Then, it is applied on three standard power system networks (IEEE 24-bus system, Brazilian 46-bus system and Brazilian 87-bus system) in a TEP study to demonstrate the optimization capability of the proposed SOS algorithm. The results are compared with those produced by other state-of-the-art algorithms.     

Restoration strategy for secondary power network with grey relational analysis

An operational strategy for secondary power system restoration using grey relational analysis (GRA) is presented. The restoration scheme can be divided into three steps involving fault section determination, recovering process and voltage correction process. Three GRAs are incorporated to design the overall restoration scheme. The first GRA uses the network-switching status to identify the fault. The second GRA combines the switching states and load levels for network recovery. The third GRA uses capacitor bank control (CBC) to support bus voltages. Optimal power flow (OPF) is also used to verify the proposed scheme by off-line analysis to confirm a secure overall network operation including load-power balance, power generation limits, voltage limits and power flow limits. Computer simulations were conducted with an IEEE 30-bus power system to show the effectiveness of the proposed restoration scheme.     

A mixed logic dynamical modeling formulation and optimal control of intelligent robots

By considering the dexterous hand manipulation problem as a hybrid system, we propose a mixed logic dynamical (MLD) modeling formulation which encapsulates phases of continuous motion, switching between types of motion, and occurrence of impacts. We first formulates the multi-contact manipulation system into a general nonlinear dynamical equation subject to (in)equality and complementarity constraints, then transform the constrained system to a MLD system model. Based on the derived MLD model, dexterous hand manipulation can be realized optimally via mixed integer quadric programming (MIQP) algorithm. This modeling formulation and an optimization approach are applied to a whole body manipulation task as an example.     

Market power analysis in the oligopoly electricity markets under network constraints

Market power (MP) analysis under network constraints is a specific feature of electricity markets and, as well, one of the major concerns of the regulators. The goal, in the analysis, is to assess the impacts of network constraints on the market outcomes because of the strategic behaviour of the producers that may or may not take advantage of the knowledge of the network structure and of the constraints. In this work, different factors to the MP that can be used by the strategies of the producers are studied and the impacts of the network constraints in providing additional opportunities to exert MP are considered. The ex-ante analysis of the market is undertaken resorting to a supply function equilibrium (SFE) for which the authors propose a new approach for deriving the best slope for slope bidding strategy by an equivalent intercept iteration method. A set of indices, specifically devised for considering network impacts, are proposed to assess the MP of the producers in a constrained market. The application of the proposed approach is shown and tested on an IEEE 30 bus system.     

Integral methodology for distribution systems reconfiguration based on optimal power flow using Benders decomposition technique

A new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach is presented. The objective minimises power losses, balancing load among feeders and subject to constraints such as capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. A variant of the generalised Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS mathematical modeling language. The effectiveness of the proposal is demonstrated through two examples extracted from the specialised literature.     

Simultaneous Solution Strategies for Inclusion of Input Saturation in the Optimal Design of Dynamically Operable Plants

Recent work has considered the inclusion of input saturation in optimization-based integrated plant and control system design. Two mathematical formulations have been derived which allow saturation to be included within a simultaneous optimization framework; these are mixed-integer and bilinear formulations. The MIP formulation applied within an integrated design and control framework was found to be computationally intensive. This paper reviews these formulations and proposes an alternative solution strategy that uses an interior point approach to handle the complementarity constraints present in the bilinear formulation. A solution algorithm is presented and applied to an example problem.     

A Primal-Dual Interior-Point Method to Solve the Optimal Power Flow Dispatching Problem

This paper presents a primal-dual path-following interior-point method for the solution of the optimal power flow dispatching (OPFD) problem. The underlying idea of most path-following algorithms is relatively similar: starting from the Fiacco-McCormick barrier function, define the central path and loosely follow it to the optimum solution. Several primal-dual methods for OPF have been suggested, all of which are essentially direct extensions of primal-dual methods for linear programming. Nevertheless, there are substantial variations in some crucial details which include the formulation of the non-linear problem, the associated linear system, the linear algebraic procedure to solve this system, the line search, strategies for adjusting the centring parameter, estimating higher order correction terms for the homotopy path, and the treatment of indefiniteness. This paper discusses some of the approaches that were undertaken in implementing a specific primal-dual method for OPFD. A comparison is carried out with previous research on interior-point methods for OPF. Numerical tests on standard IEEE systems and on a realistic network are very encouraging and show that the new algorithm converges where other algorithms fail.     

A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorithm and Applications to Contact Problems

We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.     

求解非线性系统的信赖域方法

本文给出了一个求解非线性系统的信赖域方法。通过引入松驰变量将非线性系统问题转化为带非负约束的非线性最优化问题,新算法借助于KKT条件和F-BNCP函数,在每次迭代时,不必求解二次信赖域子问题,只需求解一个线性方程组。在一定的假设条件下,该算法还是全局收敛和局部超线性收敛的。数值试验结果表明该算法是有效的。     

Solving multi-objective optimal power flow using differential evolution

A differential evolution approach to solve optimal power flow problem with multiple and competing objectives is presented. Two sub-problems of optimal power flow namely active power dispatch and reactive power dispatch are considered. The problem is formulated as a nonlinear constrained true multi-objective optimisation problem with competing objectives. Constrain-domination approach have been used to handle inequality constraints, which eliminates the use of penalty factors. The performance of the proposed approach was tested on standard IEEE 30-bus system and is compared with a conventional method. The result demonstrates the capability of the proposed approach to generate diverse and well-distributed Pareto-optimal solutions.     

Complex dynamics of Cournot game with bounded rationality in an oligopolistic electricity market

In order to accurately simulate the dynamic decision-making behaviors of market participants, a novel dynamic Cournot game model with bounded rationality of electricity market that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of consumption benefits. The Nash equilibrium of electricity market and its stability are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e. congestion and non-congestion, and even in some cases there is no Nash equilibrium at all. Numerical simulations with the 2-node and IEEE 30-node systems are carried out to evaluate the dynamic behaviors of electricity market, especially the periodic and chaotic behaviors when the market parameters are beyond the stability region of Nash equilibrium.     

A hybrid optimization model for proficient bidding strategies with no Karush–Kuhn–Tucker optimality conditions

The computational complexity behind the bi‐level optimization problem has led the researchers to adopt Karush–Kuhn–Tucker (KKT) optimality conditions. However, the problem function has more number of complex constraints to be satisfied. Classical optimization algorithms are impotent to handle the function. This paper presents a simplified minimization function, in which both the profit maximization problem and the ISO market clearance problem are considered, but with no KKT optimality conditions. Subsequently, this paper solves the minimization function using a hybrid optimization algorithm. The hybrid optimization algorithm is developed by combining the operations of group search optimizer (GSO) and genetic algorithm (GA). The hybridization enables the dispersion process of GSO to be a new mutated dispersion process for improving the convergence rate. We evaluate the methodology by experimenting on IEEE 14 and IEEE 30 bus systems. The obtained results are compared with the outcomes of bidding strategies that are based on GSO, PSO, and GA. The results demonstrate that the hybrid optimization algorithm solves the minimization function better than PSO, GA, and GSO. Hence, the profit maximization in the proposed methodology is relatively better than that of the conventional algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Three‐dimensional quasi‐static frictional contact by using second‐order cone linear complementarity problem

A new formulation is presented for the three‐dimensional incremental quasi‐static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a second‐order cone linear complementarity problem is formulated, which consists of complementarity conditions defined by bilinear functions and second‐order cone constraints. The equilibrium configurations are obtained by using a combined smoothing and regularization method for the second‐order cone complementarity problem. Copyright © 2005 John Wiley & Sons, Ltd.     

POST-BUCKLING ANALYSIS WITH FRICTIONAL CONTACTS COMBINING COMPLEMENTARITY RELATIONS AND AN ARC-LENGTH METHOD

A linear complementarity problem formulation combined with an arc-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The arc-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc-length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints.     

Unified solution of security-constrained unit commitment problem using a linear programming methodology

With the advent of open markets trading of power as a commodity, secure operation is an enduring concern of the independent system operator. A comprehensive security-constrained unit commitment (SCUC) methodology to coordinate a secure and economic generation pattern for the day-ahead market is an urgent requirement. An ineffective coordination of electric power transfer over the transmission lines could result in congestion, and inadvertently an outage cause through line overloading. In the current practice, the SCUC is solved by decoupling the cost evaluation aspect from the network security aspect. The primary frequency regulation reserve deployable in a manner after a (n - 1) contingency has not been fully utilised in the present approaches. A unified approach to the solution of the SCUC using a linear programming methodology with an extended DC network model embedded in the main algorithm is presented. The line-flow-based power flow equations are used to couple the economic dispatch (ED) and the network security process, and the proposed SCUC will include primary reserve as a part of the security constraint. Unlike the traditional SCUC programs that solve the ED first and then check it with the network for any violation, the proposed method solves the optimisation by fixing the line limits to solve the ED from the UC. A six-bus three generator and a modified IEEE 30-bus nine generator systems illustrate the implementation of the proposed SCUC formulation.     

Mathematical programs with complementarity constraints in traffic and telecommunications networks

Given a suitably parametrized family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for improving or optimizing the equilibrium state. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. Here, a Wardrop equilibrium describes the traffic response to each toll design. Communication networks also have a deep literature on equilibrium flows that suggest some MPECs. We focus on mathematical programs with complementarity constraints (MPCCs), a subclass of MPECs for which the lower level equilibrium system can be formulated as a complementarity problem and therefore, importantly, as a nonlinear program (NLP). Although MPECs and MPCCs are typically non-convex, which is a consequence of the upper level objective clashing with the users' objectives in the lower level equilibrium program, the last decade of research has paved the way for finding local solutions of MPCCs via standard NLP techniques.     

Economic dispatch using an efficient real-coded genetic algorithm

The authors present a new formulation of the economic dispatch (ED) problem considering more practical constraints and nonlinear characteristics than previous works in the area. The proposed formulation includes ramp rate limits, prohibited operating zones, system spinning reserve, valve loading effects, multiple fuel options, which usually be found simultaneously in realistic power systems. To solve the ED formulation, an efficient real-coded genetic algorithm (RCGA) with arithmetic-average-bound crossover and wavelet mutation is presented. To show the effectiveness of the solution method, it is applied to five test systems having non-convex solution spaces and compared with some of the most recently published approaches. The obtained results reveal the performance of the proposed RCGA.     

Optimal Operation of Integrated Heat and Electricity Systems: A Tightening McCormick Approach

Combined heat and electricity operation with variable mass flow rates promotes flexibility, economy, and sustainability through synergies between electric power systems (EPSs) and district heating systems (DHSs). Such combined operation presents a highly nonlinear and nonconvex optimization problem, mainly due to the bilinear terms in the heat flow model—that is, the product of the mass flow rate and the nodal temperature. Existing methods, such as nonlinear optimization, generalized Benders decomposition, and convex relaxation, still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency. To resolve this problem, we herein first reformulate the district heating network model through an equivalent transformation and variable substitution. The reformulated model has only one set of nonconvex constraints with reduced bilinear terms, and the remaining constraints are linear. Such a reformulation not only ensures optimality, but also accelerates the solving process. To relax the remaining bilinear constraints, we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model. To improve the quality of the McCormick relaxation, we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables. We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution. Case studies show that, compared with the interior point method and the method implemented in a global bilinear solver, the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.     

OPF-based security redispatching including FACTS devices

An Optimal Power Flow (OPF)-based security-driven redispatching procedure to archive an appropriate security level is provided. The proposed procedure is particularly suited for security redispatching by an independent system operator. This procedure uses full ac equations and explicitly considers security limits through a stressed loading condition. Furthermore, a variety of FACTS devices can be incorporated in the redispatching problem to enhance system security. Several case studies based on the IEEE 24-bus system and on a real size model of the Italian system are analysed and discussed.