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In August 2005, UniSoma delivered to CPFL the Load Curve Estimation for Distribution Transformers through Micro Regional Typologies module, developed in AIMMS. This module is the heart of the system proposed by the R&D project 129-04, which aims to guarantee a complete environment for transformer load curves collection, storing, processing and analysis.
Problem Description
A load curve is a graphical representation of the temporal evolution of electrical energy demand in 
a fixed point throughout the electrical grid. Normally, the values are shown in a daily horizon and 15-minute time buckets. The transformer load curve consolidates the demand for all consumers served by it, as well as possible losses due to the energy distribution.
Monitoring the evolution of load curves is a fundamental task for energy commercialization companies, such as CPFL. By monitoring the curves, it is possible to establish forecast models for load curve growth and, consequently, optimized policies for expanding the electrical distribution grid. However, this requires the use of sophisticated and expensive measuring equipment. In practical terms, this level of monitoring is economically prohibitive, given the large number of distribution transformers throughout the electrical grid.
The Challenge
Electrical energy consumers are classified into consumer or activity classes such as, for example, residential, commercial, industrial, rural, etc. A so-called PU represents the typical (or average) client consumer behavior for a determined category and a determined geographical micro region. This dimensionless curve (the sum of all represented points equals 1) multiplied by the total daily energy consumption generates the load curve for this category (or type). The load curve of a transformer is a sum of load curves of several types. In short, it is possible to estimate the transformer load curve cross-referencing its client's consumption (categorized by consumer classes) with the typical typology of the several classes.
The expected consumption of a transformer is easily identified; to do this, accessing the companies billing information is enough. The same cannot be said with respects to typologies, which indicate long-term consumer tendencies. In first place, there are different typologies for a same consumer class. The typical consumer behavior for a higher-class residential neighborhood is not the same as a lower-class neighborhood; this is why typologies are divided into micro regions. Besides this, with time even the regions change given the effects of social-economical variation of the geographical region.
In 2004, CPFL, through its R&D Program, financed UniSoma, in partnership with SEST (Specialized Services), to develop the “Load Curve Estimation for Distribution Transformers through Micro Regional Typologies” project.
Two fundamental ideas conceived the Project. The first was to conceive a methodology to estimate typologies based on cross-referencing billing information with measured load curves, from a sub-set of all available transformers. The second involved the developing of a low cost load curve meter, to subsequently allow a large scale production for collecting sample data compatible with the required precision to estimate typologies. Through the methodology and the load curve meter, it would be possible, with the necessary precision level, to estimate load curves of all transformers in the electrical grid.
The Solution
The following description summarizes the typology estimation methodology developed for the project, which resulted in the “Load Curve Estimation for Distribution Transformers through Micro Regional Typologies” system. Such a system, developed in AIMMS, has a mathematical programming model as its main component which, as previously described, estimates typologies for several consumer classes using market information and load curve field samples.
The estimation process with the model consists in searching a solution for the various categories of PUs that will minimize the difference between measured and estimated load curves throughout the several measure points of the calibration data. The estimated curve for each distribution transformer is calculated as a sum of several class PUs, weighted by the average number of consumers (market information).
Another important component of the Typology Estimation System is its User Interface, which was implemented to allow for practical and automated data input and displaying results as clear as possible. The System also has a database for internal use and, externally, a Preprocessing application to treat and collect billing and measurement data, located in CPFL Information Systems.
The Results
The test data used to for model calibration and validation consisted of 70 CPFL distribution transformers, whose load curves were measured. The calibration process demanded for System improvements, such as:
- Sample Load Curve Smoothing – preprocessing procedure to exclude data resulting from the effects of load curve oscillation which do not represent consumer tendencies;
- Correction Factor – an additional degree of freedom was incorporated to the model, to treat mismatching information from billing and measured load curves. For example: a distribution transformer is billed for 250 kWh/day, but field measurements indicate 500 kWh/day; even though they are of the same typologies, the resulting load curves will be different;
- Public Illumination – consumption due to public illumination, taking into account the seasonality, was counted for to prevent this factor affecting other categories of consumer typologies;
- Different Adjustment Criteria – there are several possible objectives to be used in the estimation process, each having a different effect over results. The adjustment possibilities are:
- Absolute Norm and Absolute Mean Square Error: prioritizes distribution transformers with higher revenues, because the error will be minimized with priority proportional to the energy consumption.
- Relative Norm and Relative Mean Square Error: provides a more homogeneous setting for all transformers (not necessarily according to consumption).
- Peak Weighted Norms: prioritizes the curve adjustment according to consumption peaks.
To solve the calibration instances, XA 13 and CONOPT 3.14 solvers were used for linear and non linear programming, respectively.
The application of the estimation model to the validation sample data demonstrated the methodology robustness, with respect to the homogeneity, representative and information quality of the calibration data. For most validation transformers (70 had their load curve measured throughout time) the estimated load curve generated by the model were completely representative of the sample. For some transformers, a significant difference was noticed between estimated load curves (based on billing registry) and measured load curves; subsequent analysis (including field visits) showed that such deviations occurred due to differences between market and measured information, which demonstrated that the system could, as well, be used to identify problems such as losses in distribution and billing.
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