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Register a new userThe Optimal Division of the Energy Market into Zones: Comparison of Two Methodologies under Variable Wind Conditions
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Anna Kad{\\l}ubowska MSc
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We compare two competing methodologies of market zones identification under the criterion of social welfare maximization: (i) consensus clustering of Locational Marginal Prices over different wind scenarios and (ii) congestion contribution identification with congested lines identified across variable wind generation outputs. We test the division of market into zones based on each of the two methodologies using a welfare criterion, i.e., comparing the cost of supplying energy on uniform market (including readjustments made on a balancing market to overcome the congestion) with cost on k-zone market. A division which maximizes the welfare is considered as the optimum.
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Adopting a zonal structure of electricity market requires specification of zones borders. One of the approaches to identify zones is based on clustering of Locational Marginal Prices (LMP). The purpose of the paper is twofold: (i) we extend the LMP methodology by taking into account variable weather conditions and (ii) we point out some weaknesses of the method and suggest their potential solutions. The offered extension comprises simulations based on the Optimal Power Flow (OPF) algorithm and twofold clustering method. First, LMP are calculated by OPF for each of scenario representing different weather conditions. Second, hierarchical clustering based on Wards criterion is used on each realization of the prices separately. Then, another clustering method, i.e. consensus clustering, is used to aggregate the results from all simulations and to find the global division into zones. The offered method of aggregation is not limited only to LMP methodology and is universal.
One of the methodologies that carry out the division of the electrical grid into zones is based on the aggregation of nodes characterized by similar Power Transfer Distribution Factors (PTDFs). Here, we point out that satisfactory clustering algorithm should take into account two aspects. First, nodes of similar impact on cross-border lines should be grouped together. Second, cross-border power flows should be relatively insensitive to differences between real and assumed Generation Shift Key matrices. We introduce a theoretical basis of a novel clustering algorithm (BubbleClust) that fulfills these requirements and we perform a case study to illustrate social welfare consequences of the division.
Adopting a zonal structure of electricity market requires specification of zones borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational Marginal Prices (LMP) methodology presented in paper [1], which takes into account variable weather conditions. The offered method of assessment of a proposed division of market into zones is however not limited to LMP approach but can evaluate the social welfare of divisions obtained by any methodology.
Zonal configuration of energy market is often a consequence of political borders. However there are a few methods developed to help with zonal delimitation in respect to some measures. This paper presents the approach aiming at reduction of the loop flow effect - an element of unscheduled flows which introduces a loss of market efficiency. In order to undertake zonal partitioning, a detailed decomposition of power flow is performed. Next, we identify the zone which is a source of the problem and enhance delimitation by dividing it into two zones. The procedure is illustrated by a study of simple case.
Quantum teleportation is one of the crucial protocols in quantum information processing. It is important to accomplish an efficient teleportation under practical conditions, aiming at a higher fidelity desirably using fewer resources. The continuous-variable (CV) version of quantum teleportation was first proposed using a Gaussian state as a quantum resource, while other attempts were also made to improve performance by applying non-Gaussian operations. We investigate the CV teleportation to find its ultimate fidelity under energy constraint identifying an optimal quantum state. For this purpose, we present a formalism to evaluate teleportation fidelity as an expectation value of an operator. Using this formalism, we prove that the optimal state must be a form of photon-number entangled states. We further show that Gaussian states are near-optimal while non-Gaussian states make a slight improvement and therefore are rigorously optimal, particularly in the low-energy regime.
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