Abstract
Supply Function Equilibrium (SFE) and Conjectured Supply Function Equilibrium (CSFE) are some of the approaches most used to model electricity markets in the medium and long term. SFE represents the generators' strategies with functions that link prices and quantities, but leads to systems of differential equations hard to solve, unless linearity is assumed (Linear Supply Function Equilibrium, LSFE). CSFE also assumes linearity of the supply functions but only around the equilibrium point, also avoiding the system of differential equations. This paper analyzes the existence and uniqueness of G-CSFE (a CSFE previously proposed by the Authors) for both elastic and inelastic demands. In addition, it also proves that the iterative algorithm proposed to compute G-CSFE has a fixed point structure and is convergent, and that LSFE is a particular case of G-CSFE when demand and marginal costs are linear. Selected examples show the performance of G-CSFE and how it can be applied to market power analysis with meaningful results.

Abstract
The continuous penetration of intermittent technologies is gradually reinforcing the technical and economic importance of electricity ancillary services, which are responsible for guaranteeing the reliability and security of the power systems. Generation companies', regulating entities, system operators and other institutions (such as researchers on these fields) are more and more concerned on using market models to forecast most relevant outcomes for particular markets (such as energy and reserves cleared quantities and prices), under different simulation scenarios (such as costs or demand) and under different markets structures (such as more competitive or more oligopolistic). This paper reviews most energy and reserve markets implementations (mainly focusing on reserve types and dispatching methods), and discusses different approaches to model them. A theoretical equilibrium model for energy and reserve markets is also proposed.

Abstract
This paper attempts to propose a fair solution in generation scheduling problem in the presence of inherent uncertainties in short-term power system operation. The proposed methodology incorporates probabilistic methodology in the uncertainties representation section, while harmony search algorithm is adopted as a fast and reliable soft computing algorithm to solve the proposed nonlinear, non-convex, large-scaled and combinatorial problem. As an indispensable step towards a more economical power system operation, the optimal generation scheduling strategy in the presence of mixed hydro-thermal generation mix, deemed to be the most techno-economically efficient scheme, comes to the play and is profoundly taken under concentration in this study. This paper devises a comprehensive hybrid optimisation approach by which all the crucial aspects of great influence in the generation scheduling process can be accounted for. Two-point estimation method is also adopted probabilistically approaching the involved uncertain criteria. In the light of the proposed methodology being implemented on an adopted test system, the anticipated efficiency of the proposed method is well verified. © 2014 Taylor & Francis.

Abstract
This paper presents a new adaptive scheme for doubly fed induction generators (DFIGs) in order to augment their flexibility confronting with unpredicted operational conditions. Due to large fluctuations in the wind velocity, the proposed scheme would handle system unreliable operational conditions. In such system, which has multi-input, multi-output and is also represented as a nonlinear control system, the uncertain parameters would affect the operational conditions. So, in order to have a robust controlling scheme, the mentioned characteristics should be considered in the proposed method. The adaptive control scheme proposed in this paper satisfies the expected constraints and could also be implemented in real-world platforms, especially in large-scale wind farms with DFIG turbines. © 2014 Taylor & Francis.

Abstract
In this paper, the problem of optimal economic scheduling of multi-reservoir cascaded hydrothermal units is investigated in the presence of an individual pumped-storage generating unit in the network. The proposed problem is modeled in a multi-objective framework comprising two objective functions. The goal of the first objective function is to minimize the operation costs and the second one is set to minimize the emissions caused by the thermal units while all the technical constraints are satisfied. Furthermore, the valve loading effect is included in the first objective function as a sinusoidal function. The problem is modeled and solved as a Mixed Integer Non-Linear Programming (MINLP). The augmented É"-constraint technique and lexicographic optimization are employed to solve the problem. Numerical results obtained from implementing the model on a case study are discussed. Also, the decision making procedure has been done using a fuzzy satisfying method to select the most preferred solution among the Pareto solutions derived through solving the multi-objective problem.

Abstract
This paper presents a new computational technique in composite generation and transmission expansion planning considering reliability and cost assessment. The proposed procedure incorporates a virtual database in order to hedging the repetitive calculation by optimisation solver. Since generation and transmission expansion planning is a large scale, mixed-integer, nonlinear and non-convex optimisation task, the proposed technique accelerates the convergence time and reduces computational burden. The composite generation and transmission expansion planning problem is represented as a multi-objective optimisation problem. The virtual database-supported non-dominated sorting genetic algorithm (VDS-NSGA-II) is applied due to comparative assessment potential and good handling of the non-convex problems and non-commensurable objective functions. The virtual database eliminates the repetitive computational efforts in both reliability and hourly operational assessments. In this study, the expected energy not served at hierarchical level II is taken into account as a reliability index, whereas the entire system cost, including annually operational and investment costs, is considered as another objective function. The incidence matrix-based DC optimal power flow is adopted to reflect transmission flow constraint in a framework in which the disconnected bus problem would be handled in both objective functions. To numerically evaluate the efficiency of the proposed method, simulation results on a simple three-bus test system and the modified IEEE 24-bus reliability test system are provided. In spite of huge computation burden at HL-II reliability assessment, the results indicate high efficiency of the proposed VDS-NSGA-II. © 2014 Taylor & Francis.