CONFINT – Model for Reliability Evaluation of Interconnected Hydrothermal Subsystems
The objective of the CONFINT model is to evaluate the reliability of hydrothermal interconnected power systems considering the scheduled and random forced outages of power plants generators, system load curve, capacity limits of interconnections among subsystems (system areas), and inflow uncertainties. It allows the calculation of power reserve margins and estimates the maximum peak load that a generation system can supply, considering a multi-area reliability criterion based on adequacy analysis. In addition, the CONFINT model provides siting indication of additional generation capacity and/or interconnection reinforcements in order to eliminate any power deficits.
In CONFINT model, the power system is represented by a linear network flow, where the nodes represent the areas, and the arcs represent the interchanges among areas. The generation in each area is modeled as an arc coming from a “source” node, S and arriving to respective area node. In turn, the area load is represented as an arc leaving the node to a “sink” node, T. Figure 1 illustrates a system composed by four areas.
The power system adequacy analysis is performed by using the Maximum Flow-Minimum Cut Theorem. The power system states evaluated by the CONFINT model are composed by: (i) generators states; (ii) interconnections states; (iii) load levels; and (iv) hydrologic scenarios.
The reliability indices are calculated analytically by direct integration method or by stochastic (Monte Carlo) simulation. This program calculates a wide set of reliability indices, such as
• Loss of Load Probability – LOLP (%);
• Loss of Load Expectation- LOLE (hours);
• Expected Power Not Supplied - EPNS (MW);
• Expected Energy Not Supplied- EENS (MWh);
• Loss of Load Frequency- LOLF (occurrences/h);
• Loss of Load Duration - LOLD (hours);
• System severity index (minutes).
These indices are computed considering the power system modeled as a "single area", thus providing adequacy reliability indices for the generation capacity, or as multi-area system, thus disaggregating those indices by areas or subsystems, and for each considered load level.
Additionally, CONFINT model provides areas and interconnections sensitivity indices, i.e., power marginal costs, which are useful to identify the need of generation and interconnections reinforcements.
CONFINT also comprises a module for modeling load curves - the MODCAR program - which, from a chronological load curve with any temporal discretization, performs its aggregation in a (pre-defined or not) number of load levels. The used methodology is based on the combination of clustering analysis statistical techniques and exploratory data analysis (EDA), and comprises the following steps: (i) previous analysis of load data and use of filtering techniques and trend evaluation; (ii) statistical aggregation of the load curve using the Ward method; (iii) determination of appropriate numbers of clusters, using specific metrics; (iv) refinement of the load curve aggregation, when the number of clusters is selected, by using the K-Means method; (v) post-processing to determine typical daily load profiles, through EDA techniques and the construction of loadplot curves, which consist of mapping boxplots for each hour of the day in conjunction with the aggregate levels of the load curve; and (vi) determination of durations and depths (p.u.) associated with the typical daily load profiles.
Besides providing a chronological and aggregate load curve, the MODCAR program computes other parameters necessary for reliability studies by the frequency and duration method, such as occurrence probability of each load level and the transition diagram (Markov diagram) of the load curve, represented by the transition rates among the different load levels.
The MODCAR program has been used to define the new energy load levels used in expansion and operation planning of the National Interconnected System and in the calculation of the electricity spot prices in Brazil.
Figure 1 – Representation of Brazilian interconnected system as a network flow model for reliability analysis.
CONFINT program is part of ENCAD (Graphical User Interface for CEPEL’s Energy Models), developed by CEPEL. This GUI allows:
• to import and export input data of an already existing case;
• A more friendly data edition;
• Autorun of CONFINT program;
• Visualization of graphics and output reports in text formats.
Figure 2 shows the screen of graphical interface to edit input data. Figure 3 illustrates the screen for graphic visualization of results.
Figure 2 – Screen for data edition.
Figure 3 – Plot of LOLP index.
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