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.
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.
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 algorith
m 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.
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 identifica
tion 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.
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 m
ethodology 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.
In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously degenerated syst
em, when only one agent is involved. The prediction is the most efficient if the agent is equipped with all strategies from the Full Strategy Space. Each of these filters is evaluated and, in each step, the best one is chosen. Despite the casual simplicity of the method its usefulness is invaluable in many cases including real problems. The significant power of the method lies in its ability to fast adaptation if lambda-GCMG modification is used. The success rate of prediction is sensitive to the properly set memory length. We considered the feasibility of prediction for the Minority and Majority games. These two games are driven by different dynamics when self-generated time series are considered. Both dynamics tend to be the same when a feedback effect is removed and an exogenous signal is applied.
We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be represented as a Mar
kov process with substantially reduced number of states with explicitly computable probabilities. For any payoff, the finiteness of the number of states is proved. Interesting features of an extensive random variable, called aggregated demand, viz. its strong inhomogeneity and presence of patterns in time, can be easily interpreted. Using Markov theory and quenched disorder approach, we can explain important macroscopic characteristics of the game: behavior of variance per capita and predictability of the aggregated demand. We prove that in case of linear payoff many attractors in the state space are possible.
We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=sgn (x)$ we explicitly represent the game as the Markov process
and prove the finitness of number of states. We also demonstrate boundedness of the utility function. Using these facts we can explain all interesting observable features of the aggregated demand: appearance of strong fluctuations, their periodicity and existence of prefered levels. For another payoff, $g(x)=x$, the number of states is still finite and utility remains bounded but the number of states cannot be reduced and probabilities of states are not calculated. However, using properties of the utility and analysing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies.
Generalization of the minority game to more than one market is considered. At each time step every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of utility th
en market occupancies become inhomogeneous with preference given to this market where the fluctuation occured first. There exists a critical size of agent population above which agents on bigger market behave collectively. In this regime there always exists a history of decisions for which all agents on a bigger market react identically.
