Componente Biótico

The research described in this Thesis is focused on the investigation of the linear SFE methods and the analysis of the impact of various network constraints and operational conditions on the electricity market equilibrium. The implementation of an advanced nonlinear primal-dual interior point algorithm that considers AC network representation is undertaken, and the efficiency and robustness of the algorithmic iterative procedure is investigated and assessed. Numerous numerical tests on several subject matters related to the electrical network operation and the issue of market power in the electricity market are performed, in order to examine particular and general situations that affect the individual market participants and the market as a whole. The observations and conclusions are compared with those from the existing literature and discussions are provided for several issues that have not been addressed well in the literature. The reasons for choosing the particular methodology and the modelling assumptions are given below.

The electricity market equilibrium analysis was chosen over the market concentration analysis with indices and the ex-post estimation of pricing behaviour methods, since it is a much better representation of the interactions between the strategic firms in the oligopolistic environment of the electricity market. As discussed in Section 1.9, the oligopolistic equilibrium analysis is an efficient method for the evaluation of the sources and degree of market power, and hence it can provide a better depiction of the outcome of bid-based electricity pool markets.

The modelling of the market mechanism is based on the SFE theory, which was chosen due to its perceived advantages over the other available equilibrium methods. As discussed in Chapter 2, the market players are able to adapt better to the uncertain environment of the electricity market owing to the unknown load demand, by implementing function bids that relate different supply quantities to different prices rather than discrete quantity or price bids, as in the Cournot and Bertrand competitions. Hence the price predictions from the SFE model are more reliable than the Cournot prices, since they are not very sensitive to demand, and are more realistic than Bertrand prices, which resemble perfect competition behaviour. In addition, the supply function bids, which are increasing in price, reflect the generating costs for power production that are increasing with the quantity produced; such features cannot be represented successfully by applications of the Cournot and Bertrand settings.

In particular, the linear SFE model has been chosen for this investigation over the other SFE forms for several reasons. The study in [81] has shown that the linear SFE solution is a reasonable approximation for the general SFE form at low levels of demand, while it still remains an equilibrium at higher demand levels. The analysis on the California energy market in [163] is in agreement with this by showing that the cumulative supply function bids in a practical market appear to be 2-segment linear curves and modelling with linear bids is reasonably accurate. Furthermore, the study in [102] has shown that, in the absence of capacity constraints, the only stable SFE between the most competitive and the Cournot solution is the linear SFE, if quadratic cost functions (linear marginal costs) are modelled, and hence the only possible to appear in practice. In addition, this model results in considerably reduced mathematical complexity compared with the other available models, being able to handle multiple asymmetric firms with quadratic cost functions [79], while it can offer intelligible interpretations of the resulting market equilibrium solution. Since the above findings support the functionality of the linear SFE model, the study in this Thesis employs this theory with the prospect of further contributing to the literature.

The proposed electricity market model is implemented by considering AC power flow analysis and the representation of various network constraints. As discussed in Chapter 2, the AC model has several advantages over the DC model, since the latter is a linearized version of the nonlinear AC system that stems from the real characteristics and physical properties of practical power systems. Hence, in the context of market equilibrium analysis, the DC representation cannot identify the sources of market power related to the nonlinearities of real-life power systems and electricity markets. In this Thesis, the AC representation is employed in order to account for a more realistic market outcome, since the strategic interactions between the generating firms are directly dependent on the operational constraints and conditions. The market clearing price is determined in terms of nodal prices to represent both the energy price and the short-term transmission costs. The network constraints considered include the active and reactive power flow equations accounting for flows through transmission line and transformer branches, the bus voltage limits, the MVA transmission capacity limits and transmission losses for both transmission line and transformer branches, the transformer tap-ratio control to represent on-load tap-changing transformers, and the active and reactive generation capacity limits. The power load demand is price-responsive and represented by both active and reactive components, which are interrelated by means of the power factor angle. In addition, modelling of grid-connected solar PV systems that accounts for both PV active and reactive generation has been undertaken, considering the effect of the intensity of the applied solar irradiance. The model for the operation of the PV systems is based on real PV output performance data recorded in an experimental PV park. The purpose of the implementation of such a complicated network model, apart of enhancing the accuracy and realism of the market results, is aiming to investigate the effects of the individual network constraints and different system operational conditions on the market equilibrium. Several of these features, such as the transformer representation, the optimisation of the tap- ratios, the price-responsive reactive load demand, and the representation of PV systems in the electricity market equilibrium model, have not been addressed in the literature so far.

The implemented market model accounts only for supply-side bidding, while it considers competitive loads, for the following reasons. The study in [109] discusses that strategic demand-side bidding may result in instability due to the absence of pure strategy equilibria with low prices, or in market prices that are much higher than the marginal costs, being in agreement with [164], which examines a different market structure. Furthermore, the numerical results in [115] have shown that strategic bidding by the consumers lowers the economic efficiency and conceals market signalling of the need for new transmission investment, as already discussed in Chapter 2. Since the strategic demand-side bidding exhibits these adverse effects on the electricity market, it is not considered in this investigation. However, note that the competitive load demand function in this model is price-responsive.

The bi-level problem is formulated in a similar manner as in [134,137], where the 1st order KKT conditions of the lower level (ISO problem) are incorporated into the upper level to give a combined problem for the market equilibrium solution. The associated complementarity constraints of certain KKT condition equations are transformed into nonlinear mathematical expressions using the Fischer-Burmeister merit function in order to avoid possible complications due to ill-conditioning problems. Such modelling techniques are expected to be robust and applicable for large systems and, in addition, the analysis in [116] has shown that the resulting Nash stationary equilibria from such formulations are in fact local Nash equilibria. This finding further enhances the realism of the market model, since local equilibria are possible to be observed in practice.

In order to implement a market algorithm that involves the aforementioned network and market features, a numerical approach that is able to tackle successfully the associated mathematical complexity is required. In the past, formulations using the nonlinear primal-dual interior point method have been used to solve a wide variety of large scale OPF problems, while this method is also applicable to problems of bi-level nature, such as the bid-based electricity pool market equilibrium problem. This method has been chosen for the investigation that takes place in this Thesis, because it can easily handle the nonlinearities of the AC model and the inequality constraints required for the

representation of the network operation. Such iterative processes, based on the primal-dual interior point method, converge within a reasonable number of iterations, which is expected to enhance the computational performance. A comprehensive review of the mathematical theory and the advantages of the primal-dual interior point method is provided in Section 3.2.

The mathematical formulation for the power flow equations, the representation of the losses for the transmission lines and transformer branches, the bus voltages, and the complex power components is derived using rectangular coordinates instead of employing the polar representation. By using this technique, advantages that enhance the computational efficiency of the algorithm arise due to the fact that the resulting objective functions and the constraints of the bi-level market problem will appear in quadratic form. A quadratic function has the desirable properties of constant Hessian (2nd derivatives of the objective function and the power flow equations), Taylor series expansion that terminates at the 2nd order term without truncation error, and easy evaluation of the higher order term. These features allow for an attractive matrix setup and reduce the number of iterations for the convergence of the primal-dual interior point algorithm [165]. Furthermore, no trigonometric functions are incorporated in the primary formulations as in the case of the polar coordinates representation. More information about the rectangular coordinates representation is given in subsequent sections.

Major contributions of this Thesis:

The major contributions of the work presented in this Thesis include the following:

a) Implementation of a nonlinear primal-dual interior point algorithm to

solve the bi-level electricity market equilibrium problem based on linear SFE theory and considering advanced AC network modelling.

b) Achievement of superior computational performance of the electricity

market algorithm in providing SFE solutions for complicated realistic systems in the presence of binding functional constraints.

c) Modelling of the transformer in the equilibrium market algorithm and investigation of the impact of the transformer tap-ratio control on the electricity market equilibrium.

d) Determination of the impact of reactive power control on the

electricity market equilibrium, in terms of voltage control, limitations on the reactive power generation and absorption, and power factor adjustments.

e) Analysis of the effects of a new generating unit’s location for a new

entry in the electricity market, on the interactions between the strategic firms and the market outcome.

f) Modelling of grid-connected PV generating units in the electricity

market algorithm, with representation of the economic and technical aspects based on PV output performance data recorded from an outdoor experimental PV park.

g) Investigation of the effects of introducing PV generation in the

electricity market with respect to the applied solar irradiance, and determination of the impact of representing the nonlinear PV reactive power generation in the electricity market model.

h) Implementation of the four different parameterization methods in the

linear SFE market model and investigation of the respective market equilibrium solutions.

i) Determination of the interrelation between network congestion and

the individual network components, such as the transformer tap-ratio control and the PV generating units, and the different linear SFE parameterization methods.