How to construct a stochastic power plant - A -Trial

How to construct a stochastic power plant - A -Trial
Pantelis Koutroumpis, Zeynep Gurguc, Ralf Martin⇤,
Mirabelle Muûls†, Tamaryn Napp and Ian Staffel
13th May 2014
The threat of climate change combined with a will to decrease imported energy dependency has
resulted in a policy-driven increase in renewable power production. This trend is bound to increase
in the coming decades. Figure 1 illustrates this by plotting the half-hourly (log) changes in power
demand together with the half hourly changes in wind power for the UK during the first 3 days of
2009. Wind power often grows or shrinks by more than 20% whereas power demand never exceeds
a change of 10%. A central challenge for the provision of larger shares of renewable power is their
intermittency. Compared to fossil fuel alternatives, renewable power sources are typically more
variable and less easy to predict. However, the power market is no stranger to variability and
uncertainty. Power demand varies heavily throughout the day, the days of the week and times
of the year. What’s more, there can be sudden demand peaks or troughs depending on arbitrary
factors such as how entertaining a TV program is or the outcome of a football match. Equally, the
power market equilibrium can be heavily affected by technical faults in power plants. At present
this variability is by and large managed from the supply side; i.e. power plants are switched on and
off to keep a balanced equilibrium of demand and supply. However, many have suggested that it
could be vastly more cost effective to address some of this variability through better management
of the demand side.
Economists in particular have long suggested that the key to demand side management is a more
variable pricing of electricity at the retail level (Faruqui and Sergici, 2010, Faruqui and Malko 1983).
However, dynamic pricing can only work if power consumers spend cognitive resources on the state
of the power market. It’s effect also needs to be persistent through time, yet the literature’s findings
on the impact of financial rewards on energy consumption are mixed. Abrahamse et al. (2005)
find these to be short lived, while others show they can be large and persistent over time (Dolan
and Metcalfe, 2013). Besides, feedback and information to consumers in addition to financial
incentives are effective measures to reduce energy consumption (Abrahamse et al. 2005; Allcott
Imperial College Business School, South Kensington Campus, London SW7 2AZ, United Kingdom, Grantham
Institute on Climate Change, and Centre for Economic Performance (CEP), London School of Economics (LSE).
Email: [email protected]
Grantham Institute for Climate Change and Imperial College Business School, South Kensington Campus,
London SW7 2AZ, United Kingdom, and CEP. Email: [email protected]
Figure 1: Wind power versus total power demand (First 3 days of 2009)
half hours
and Rogers 2012; Dolan and Metcalfe 2013), whereas social interaction and norms have been
proposed as other power demand shifters, though their effect also decreases through time (Hori
et al. 2013, Dolan and Metcalfe 2013). This raises the question as to whether ‘social’ demand
side management, which is currently being researched by utility companies and others (McMichael
2013, Kellet 2007,Lockwood and Platt 2009) would be persistent enough to face the huge flexibility
requirements of an increasingly renewable power provision.
Alternatively, there is now much discussion of smart grids and smart devices that interact with
smart grids, which would allow to achieve the needed demand side response automatically, without
relying on the customer’s behaviour. At present grids are not terribly smart yet and most electrical
devices are not smart enough to talk to smart grids. As an alternative we examine in this study
a device that is not terribly smart but that potentially allows smart people to manage power
demand at low cost and with current grid technology: the Power Balance Plug (POWBP). The
POWBP is a simple power plug that can be fitted to any existing power plug. It has a wifi chip
that allows it to connect to now common WiFi routers (73.3% of UK households have a WiFi
network1 ), allowing to remote control the plug. We have trialled this setup in the context of a
university student hall. We thereby contribute to the literature in two dimensions. First, , we
assess the effectiveness of the POWBP as a short-term alternative to smart devices. Second, in
subsequent waves of experiments, we hope to add to existing literature on the behavioral aspects
of low-carbon technologies usage (Jaffe and Stavins 1994) and energy consumption responses to
pricing. In this note we discuss our initial findings.
kdensity kWh
Figure 2: Average Consumption: Trial versus control group average half-hourly electricity consumption
Control group
Trial group
We are conducting our trial at a new student residence of Imperial College, comprising of more
than 500 identical self contained studio flats with bathroom and kitchenette. The trial group
consists of 12 students who were given POWBPS.2 The trial group was non-randomly selected on
a first come first serve basis after an email was sent round inviting students to participate. Figure 2
shows density plots of the average (pre-trial) energy consumption of trial and control group. Both
groups have a by and large a common support but the trial group consumes on average slightly
more energy (0.09 vs 0.07) kWh per 30 minutes.3 Figure 3 shows how consumption varies over
the course of a day. Not surprisingly peak consumption is in the evening. The lowest average
consumption is in the early morning hours. This is comparable to the average UK household
consumption pattern as shown in Figure 4.
Our main experiment are a series of randomly spaced switch off events. POWBPS plugs were
given to each student from the trial group together with a 4-socket extension lead and instructions
on how to use the plug. The plugs were then switched off at random points in time for 30 minutes.
There would be at least a gap of 3 hours between two switch off events. The trial was conducted
from January 14 until March 30. Figure 5 illustrates one week of the trial period (February 20
to 26). The blue vertical lines show the switch off events during this period, whereas the red line
shows average consumption.
We are adapting wifiplugs from for that purpose.
All our experiments below are in conducted within 30 minute intervals. This is the time resolution of the UK
wholesale electricity spot-market. To ease comparison we report all figures in terms of 30 minute intervals.
Figure 3: Average (half-hourly) Consumption over hours of a day
Linear Prediction
Adjusted Predictions of hours#betaid with 95% CIs
Data analysis
In this section we look first across all households, for the whole year. Then we pick out a few
different sub-groups of households: first single pensioners and other single-person households
(because single person households raised some unexpected findings in the initial study), and
second we examine electricity use in flats and detached houses (because these dwelling types are
at opposite ends of the scale and occupancy spectrums). Finally we compare the electricity profiles
for all homes monitored during the coldest and the warmest months. The figures do not match
0 presented
1 2 3 in
4 the
5 original
6 7 analysis
8 9 10
13 14 15
16 17 18
19 because
20 21 22
similar figures
of 11
of 23
hours households where more than 10% of
improved data cleaning. The original analysis also excluded
the energy use was unknown. In contrast, we have opted to include all households, in order to
keep sample sizes as large as possible. betaid=0
This analysis uses raw data, unadjusted for seasonal effects. This means the sample sizes for short
periods of the year are rather small, since the analysis includes only the dwellings monitored over
the period selected.
All households, whole year
Water heating
Figure 4:
The mean daily profile for all homes included in the study across the whole year indicates that on
average cold appliances draw very similar power from the grid throughout the day, see chart
below. Conversely, audiovisual, lighting, electric cooking and ‘washing/drying’ (which also includes
dishwashing) vary quite significantly through the day. In fact the averaging across homes and times
of year reduces the variability of these components of the profile, and in reality they fluctuate
more than
the graph suggests
for specific
of a day
- UK
Cold appliances
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00
The evening peak is very pronounced, and made up largely of electricity used for cooking in the
early evening, transferring to lighting and audiovisual later in the evening.
The evening peak is much more pronounced than the morning peak, and accounts for 50% higher
peak load when averaged across all homes and periods. Overall, although there is an identifiable
morning peak at about 7.30am, lower demand for lighting, space heating and cooking are almost
Power Consumption (kWh)
Figure 5: Seven days of switch off events
Evaluation of the experiment
We use a flexible linear regression model to evaluate the effect of the switch off events on the trial
group. Our most general specification is as follows:
kW hit = SW IT CHt ⇥ CON N ECTit + ↵t + ↵hhi + ✏it
where i indexes an individual participant, t indexes a specific half hourly period, SW IT CHt is
an indicator variable equal to 1 during a switch off event, CON N ECTit is an indicator variable
equal to 1 if a particular plug is connected to our server, ↵t is a period specific effect and ↵hhi is
a half-hourly period of a day specific effect for every participating individual.
Table 1 shows the regression results. The results suggest that for the average connected plug a
switch off event leads to a reduction of consumption by 0.0101 kWh. Put differently: the average
user has been connecting a 0.0202kWh (= 0.0101 ⇥ 2) device during the average switch off period.
That’s about the combined wattage of an iPad and an iPhone charger. Compared to the overall
average consumption it is typically more than 10% (compare with Figure 3). In column 3 we
investigate how this impact varies across different times of the day we look at 3 periods: Night
(from 1 to 8 o’clock), Day (from 8 to 18 o’clock), Evening (from 18 to 1 o’clock). This suggest
that during the night and day the impact is uniformly 0.01 kWh, whereas in the evening it is only
0 .007kWh. In columns 4 and 5 we also look at the level of electricity consumption. This suggests,
that trial group residents consume more energy (as we have seen before), that energy consumption
goes up over time, that trial group residents consume more during periods when their plugs were
Table 1: Seven days of switch off events
Dependant Variable
Switch off event X Connected
Change in Power Consumption
-0.0101*** -0.00974***
Trial group
Trial Period X Trial Group
Trial Period
Switch X Connected X Night
Switch X Connected X Day
Switch X Connected X Evening
Period fixed effects
Room X Half hour of day fixed effectsYes
Power Consumption
-0.00503* -0.00150
(0.00272) (0.00311)
0.00606*** 0.0133***
(0.00111) (0.00112)
-0.0308*** -0.0326***
(0.00110) (0.00126)
connected and that compared to the pre-trial period trial participants’ consumption increased less
than consumption of the control. This latter effect could be a result of the incentive scheme we
offered to participants which rewarded both, load balancing services as well as reductions in overall
The initial results are promising. We can identify a statistically significant and economically
meaningful effect of the plugs on energy consumption. In particular this effect appears considerably
stronger than the effects identified by studies looking into real time pricing.4 In future work we plan
to conduct similar experiments with a larger sample of consumers as well as different types.
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