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The TESLA Model

We're proud of our Model. Here we offer a full discussion of our modelling philosophy for those who want to understand the details.

The TESLA Model is an extremely accurate menu-driven system for energy load analysis and forecasting. It consists of two major components: the forecasting module and the weather correction module.

The forecasting module predicts load over a wide range of time horizons. It can provide very timely operational forecasts based on near term weather forecasts, and in the same modelling environment deliver medium and long-term estimates based on economic projections and alternative weather scenarios. TESLA can also be used for long-term strategic planning simulations involving alternative projections of both weather and economic conditions.

The weather correction module decomposes the observed load based on observed weather, seasonal normal weather and other causal variables. The result is a breakdown of load into the portion that would have occurred under normal weather and that which occurred due to weather deviations from seasonal norms.

Both modules are packaged with an operator interface that provides a standard set of Windows type controls for using and maintaining the model. It automates initialization of forecasts and analyses and displays the results on an hourly, sub-hourly, or summarized basis, in either tabular or graphical form. It also automates data maintenance tasks. The accuracy, power and flexibility of the TESLA system have led to its application to solve several management problems in the power industry.

How We Approach a Problem

Our modelling philosophy is to use as much information as possible. Since load is determined as a consequence of various factors and multiple decisions by many different people, we believe that accuracy in forecasting requires that we take into account a large number of relevant factors.

To apply this philosophy to the estimation of electricity or gas industries, we view load as arising from multiple processes. These processes can be grouped into four categories, each of which must be approached with different analytical tools:

Identifiable load is the load arising from identifiable, quantifiable influences, mainly consisting of human behaviour within a physical environment that can be predicted based on the clock and calendar, weather effects, and effects arising from macroeconomic and demographic considerations. The appropriate techniques for forecasting this component of load are very large scale, highly parameterized regression analysis, time-varying parameter estimation, and Bayesian estimation.

Latent load arises from slow moving processes which can be readily observed in the data, particularly once the identifiable load is removed, but which cannot reliably be attributed directly to any particular factor. The techniques we use for this component are Box-Jenkins analysis with time-varying autocorrelation parameters, path analysis, principal components analysis, response surface estimation and other latent variable techniques.

Exceptional load is observed in response to exceptional events, where the events can be predicted or are known in advance, and there is a body of experience from similar events. Appropriate techniques for this component of load include neural nets, and intensive close client contact and reporting.

Unpredictable load is that part of load arising from unforeseeable events, or from foreseeable events for which there is no body of experience. Useful techniques for this component include fuzzy logic systems, contingency analyses and Monte Carlo simulation.

The Effects of Weather

The primary weather variables used in the TESLA Model include temperature, wind speed and direction, cloud cover, humidity and precipitation, as well as the interaction among these factors and between them and other load determinants.

The effects of an aspect of weather (say temperature) depend on many other factors, including other weather conditions (is it raining, is the wind blowing, etc.). The model explicitly captures relevant interactions, which typically include:

• Time of day
• Season of the year
• Calendar events such as holidays and weekends
• Angle of the sun
• Other weather measures

Modeling Approach in the TESLA System

The TESLA Model is estimated using the hourly or sub-hourly measures available on weather variables reported by weather forecasting services. Interactions among these and other variables are then calculated and entered into the data set, along with a lag structure that captures delayed effects. Experience has shown that delays of more than a day (and longer) are common before the full effects of a particular weather event are felt.

Isolation of Weather Effects

Estimating the effect of weather on load requires complete specification of all the weather variables and their interactions, including the delays in their effects. It also requires that other factors correlated with weather phenomena be carefully accounted for as well, to prevent contamination of the weather effect estimates through cross correlations.

To correct for weather and to analyze the effects of weather deviations on a contingent basis, there is no substitute for a completely specified model that gives explicit weight to the entire available weather database.

Weather Correction in the TESLA Model

The TESLA Model can estimate historic load corrected for the effects of actual weather conditions that deviate from those “normally” observed. That is, it will produce an estimate of the load that would have occurred if "normal" weather had prevailed, and therefore identify that portion of the load that is due to weather variations. The same features permit scenario-type evaluations of the effect of future weather patterns on load.

Using All Available Information

A great variety of factors contribute to electric load, gas demand and other measures of energy consumption. In our electricity models, where coefficients are allowed to vary on an hourly or sub-hourly basis, using 2000 or more parameters in a particular model is not unusual. To handle estimations of this complexity, we have developed a process that we refer to as Very Large Linearized Systems (VLLS). The VLLS approach enables us to build models that:

• Are very responsive to their inputs
• Make intensive use of all available information
• Support the estimation of detailed and accurate nonlinear responses to the input variables, especially weather

Variables

Weather Variables

TESLA models use six primary weather variables (when available): temperature, relative humidity, cloud cover, wind speed, wind direction, and precipitation. Although useful models can be constructed with fewer variables, even just temperature-related ones, the other weather variables have both a direct physical impact on energy usage, and an indirect impact through people’s expectations. TESLA models, ideally, incorporate all of these effects.

We also include interaction variables involving weather. This group includes both the interaction among the weather variables themselves (e.g. the interplay between temperature and humidity) and interactions between weather variables and other measures (e.g. the interaction between cloud cover and the angle of the sun above the horizon, as a measure of effective insolation).

Clock and Calendar Variables

The clock and calendar have an enormous impact on energy usage. People begin and end the day and vary their energy consumption in a very regular manner. When the time of day and the calendar are both taken into account, we can tell a great deal about how consumption will respond: 2.00 a.m. [02:00] is a great deal different from 4.00 p.m. [16:00]; and 4:00 p.m. [16:00] on Sunday is quite different from 4.00 p.m. [16:00] on Wednesday, within the same week. Energy consumption also follows very strong seasonal patterns, with breaks in normal patterns occurring on and around holidays. TESLA models are tailored to the particular patterns experienced in each franchise area, including any tendency of those patterns to shift.

Radiative Energy

TESLA models incorporate measures of the amount of solar energy reaching the earth at any point in time. Generally, a history of insolation values (energy/light from the sun, generally called “solar radiation” or “light index”), long enough for model calibration is often not available for historical periods. In some cases, even if the data are available, a weather forecaster may not forecast such variables. However, the amount of energy arriving at a point on the earth's surface can always be approximated knowing the angle of the sun above the horizon and the amount of cloud cover present.

Special Events Data

Some special events have an important impact on load, but are not predictable from knowledge of the calendar and regular weekends and holidays. Special events include factors such as transportation strikes that affect the patterns of daily work and energy use, special sporting events and the like. They are important for two reasons. First, by taking them into account we prevent the results from an "unusual" day from influencing the model when an otherwise similar day occurs. Second, while one may not be able to predict such events, careful analysis of the effects of the event gives some insight into what would be the likely consequences of a similar event in the future.

Economic and Demographic Measures

Economic and demographic variables are used to track and project system scale. TESLA models operate on an hourly, subhourly or daily basis. However, economic and demographic variables are usually available only quarterly or annually and then often on a regional basis that does not match the service area being analyzed. TESLA can integrate such economic and demographic data into the model. This is particularly useful for projecting on a medium- to long-term basis.

Data Management

While TESLA models use weather information intensively, most of the variables that the models use are internally generated. In most field applications, there are only two kinds of update requirements: weather history and weather forecast, and the load history. Both of these requirements can be automated.

For model development and estimation, we desire at least a five-year history of hourly or sub-hourly load and hourly weather observations. Ideally, we like to have eleven years of data, which allows us to see every moving holiday on every day of the week at least once, and gives an adequate sample of extreme weather days. However, we recognize that not everyone has data back that far.

For most accurate forecast operation, the model requires access to a 30-day weather history and a 7-day load history. The load history is used in a final-stage error correction filter, and should be kept as close to current as possible. The weather history is used in the model's look-back computation, in order to capture the effects, for example, of a sustained period of abnormally hot or cold weather.

Common Problems

Probably the most common problem with historical data is phasing errors: observations recorded against the wrong time. The most frequent error is a one-hour displacement, most often seen following the change from standard time to daylight savings or British summer time.

We have methods to detect these errors over time, but they cannot readily be discerned from one or two observations.

TESLA Output

Modelling of load can readily be done for a client's entire service area, for larger areas (e.g. a region or country), or for smaller areas or units (franchise sub-areas, busses, feeders and stations, customer classes and large individual commercial/industrial users). A variety of different statistics can be derived and displayed. The precise layout of each type of display and computational variations in how certain statistics are to be derived are customized for each user. Depending on selections made by the user during implementation, any or all of the following statistics, along with many others, can be provided:

• Load forecast:
  • Every hour or sub hour
  • Scale and location of peak in the day
  • In-sample comparisons of actual versus forecasted
  • Standard error of estimate measurements
• Weather effects decomposition
• Temperature response profiles (and other weather response profiles)
• Shape of the temporal load profile
  • Around peak/“peak duration”
  • Deformations in shape over time, and by day type and season

Customized Reports

In addition to the standard TESLA output, we can supply customized reports to fulfil any need. TESLA is also available integrated with the SORITEC programmable econometric package, which allows the user to extend and modify the system. SORITEC has presentation-quality graphics capability, a spreadsheet tool that facilitates data exchange with other software and a report writer/table generator, as well as a large array of statistical capabilities.

Performance

Forecasting accuracy can be evaluated in terms of overall performance and in terms of predicting critical events. When forecasting electric load, the critical event is most often peak load, both in timing and in the level of load. The TESLA Model provides outstanding results on both scores.

A commonly used standard of accuracy for a load model is the mean absolute percentage error, or MAPE. In sample, TESLA distribution system models in the field demonstrate MAPEs in the range of 0.84 percent to 1.56 percent. These figures are based on using the actual weather data, but without employing any final-stage filters to update forecasts based on recent load experience. If final stage filters are used to improve the forecast based on recent load data, the MAPE will be reduced by an amount ranging from 0.15 percent to 0.30 percent. If the basic model is used with forecast weather, our experience is that the fit degrades by about 0.5 to 1.0 percent, depending of course on the accuracy of the weather forecast. Note: These figures include weekends and holidays.

While TESLA is over all an extremely accurate product, it performs particularly well near peak usage times in predicting both the time and the level of load. The VLLS approach offers great strength at critical turning points, particularly peaks and troughs. In fact, TESLA tends to have lower average errors near peaks than in general.

Forecasting accuracy like this enables us to offer TESLA on a pay-for-performance basis. Under such an arrangement, the contract contains a pay-for-performance schedule which varies TESLA’s compensation according to an agreed upon schedule. One basis for setting the compensation schedule, for example, is a measure of savings to the client due to increased forecast accuracy. TESLA Inc., will also negotiate a payment plan that is part fixed-fee and part pay-for-performance. TESLA Inc. welcomes opportunities to demonstrate the superiority of the TESLA Model through competitive benchmarks.