A novel time-permuting forecast method Colin Singleton & Billiejoe Charlton 7/11/2012

Why forecast at the household level? Understanding customers' energy usage helps energy suppliers to: communicate and engage with their customers -credible, informative forecasts get customers on-side manage their networks -such as by using smart battery storage to handle peak demand plan for the future -particularly in light of changes brought about by adoption of Low Carbon Technologies With the coming smart meter roll out, the time has come for new ideas about household-level forecasting

Household-level forecasting Suppose we have half-hourly smart meter readings from a household for, say, the N previous Tuesdays: is from the previous week, is from two weeks ago, etc. We want to make a good forecast for next Tuesday’s energy use. But what is a “good” forecast anyway?

But it gives counter-intuitive results: Here, blue forecast is “better”: (2-norm) error for blue forecast: 11.4Kwh, for red forecast: 15.6Kwh The p-norm (often with p=2) is a common way to measure error between forecast F and actual usage A:

What do we want from our forecasts? Subjectively the red forecast is much better than the flat blue one: - it has the right number of peaks, in roughly the right places - peak heights are nearly correct Red forecast more useful for smart control of energy storage systems Red forecast is much more believable to a customer

A better error measure: adjusted error where is the set of permutations that displace components by no more than w half-hours So you can move each forecast value up to places before measuring the error We will take to penalise large errors (missed peaks) much more than small errors, and

Adjusted error in action The forecast (red) is permuted onto the actual usage (green):

A yardstick forecast: the mean We will compare our forecasts to a simple yardstick forecast, the mean of the previous N usage profiles (on the same day of the week): When daily peaks do not coincide, the mean forecast becomes flattened, and hence less informative and would not be believed as a forecast

The mean forecast (in red) is quite flat

The averaged adjustment (AA) forecast Idea: If we shift the peaks to line them up before averaging, the forecast will not be flattened Start with a basis forecast (e.g. mean) Successively merge in each day - permute to make it as close as possible to current forecast - take a weighted average

The AA forecast has a bigger, clearer peak

AA forecast in action

Number of historical days used (same day of the week) Average daily Adjusted Error per household (kWh)

Number of historical days used (same day of the week) RMSE per half-hour per household (kWh)

Issues with the AA forecast The peak forecast by AA is still lower than we would like -Using the mean forecast as the basis drags the height down -But it’s not obvious what a better basis is AA gives recent history much more importance than distant history -because recent days get merged in first

Another forecasting idea Idea: a usage profile F which is “close to” the historical usage profiles (for that day of the week) will make a good forecast One way to interpret “close to”: sum of adjusted errors between F and historical usage profiles is small So forecast: We approximate this with a genetic algorithm (GA) All history days treated equally (we could add weights)

The GA forecast has an even bigger, even clearer peak

Number of historical days used (same day of the week) Average daily Adjusted Error per household (kWh)

Summary We described the adjusted error measure, which captures quality of household-level forecasts better than the 2-norm We illustrated two forecasts which beat the mean under adjusted error: -The averaged adjustment (AA) forecast -A genetic algorithm (GA) based forecast Future work includes refinement of the error measure and forecasts and individualising the forecasts Reference: “A New Error Measure for Forecasts of Household-level, High Resolution Electrical Energy Consumption” Stephen Haben, Jonathan A. Ward, Danica Vukadinovic-Greetham, Peter Grindrod and Colin Singleton