IEEE Power & Energy Magazine - May/June 2020 - 30

8:00 a.m. and noon, working hours. SMEs are considered
consumers with low uncertainties due to their regular working hours.
The accuracy of a day-ahead, peak-load forecasting model
can be used to quantify the magnitude of uncertainty. An
autoregressive integrated moving average (ARIMA) model
presented in this article captures the autocorrelations of
the standardized demand. The predictabilities of different
customer types are evaluated through a mean absolute error
(MAE), with a lower MAE indicating a better forecasting
performance. Groups R1, R2, and SME are highly predictable, with low uncertainties resulting from regular lifestyles
or consistent working hours. Group R3, consumers with
PVs, is less predictable as a result of the intermittent nature
of renewable energy. Group R4 is the least predictable group
across customer types, which could be due to irregular EV
charging behaviors (see Table 2).

Uncertainties Across Network Voltage Levels
Uncertainties are not evenly distributed across the distribution network because they vary drastically from one level to
another. At a granular [i.e., low-voltage (LV)] level, demand
is usually more volatile and shows higher uncertainties, while

load variations tend to cancel out when they are more aggregated at HV levels. In addition, different types of customers
demonstrate dissimilar demand patterns due to factors such
as energy usage behaviors, energy prices, and technologies. In
this section, we investigate the uncertainties across three network voltage levels: LV (0.415-11 kV), medium-voltage (MV)
(11-33 kV), and HV (66-132 kV). Both temporal and magnitude uncertainties are discussed.
Data were collected from the homes and substations from
selective areas, including South Wales, Ireland, and London.
Figure 3 depicts the distribution of daily peak occurrences for
annual data collected for HV, MV, and LV levels. The temporal distribution across all network voltage levels skewed
toward evening periods, which indicates a coincident peak
time. Nevertheless, the peak time is more scattered as the
voltage level drops. At the LV level, 37% of the peak times
are spread between 4:00 and 10:00 p.m., while 11% of peaks
occurred from 8:00 a.m. to noon, with the rest randomly distributed. At the HV level, more than half of the sample values
fall within a narrow interval between 4:00 and 8:00 p.m. The
standard deviations (in hours) of the peak time distributions
are 1.13, 1.55, and 2.48 for the HV, MV, and LV levels, respectively, which are consistent with those shown in Figure 3.

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figure 1. The temporal distribution of residential consumers' peak demands. (a) R1: The residential customers without stimulus (demand response) or special tariffs. They are billed an existing flat rate and currently the most representative residential consumers. (b) R2: Consumers billed using TOU tariffs reflecting different unit prices through the day. (c) R3: Consumers
with PVs. (d) R4: Consumers with EVs.
30

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