Forecasting Peak Electricity Demand 2014

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Forecasting Peak Electricity Demand 2014
Peak Electricity Demand in Mauritius: Evolution and Forecasting
Jameel Khadaroo
July 2014
Executive Summary
This paper provides a thorough examination of the evolution of peak electricity demand in
Mauritius from January 2002 to December 2013. Peak demand is a key determinant of
investment in electricity generation. Inadequate generation capacity results in power blackout
while excessive generation capacity implies wasted public money. The forecasting of peak
demand therefore constitutes a real challenge to policymakers. Indeed peak demand has recently
been evoked at the highest decision-making level several times and this has spurred a public
debate. Adopting an objective non-controversial approach the present study proposes a statisticsbased model, called the seasonal autoregressive integrated moving average (SARIMA) model,
for forecasting peak electricity demand in Mauritius from January 2014 to June 2020. The
SARIMA is shown to provide reliable forecasts that are high enough to prevent power failure but
not too high to urge wasteful investment. The SARIMA forecasts tend to imply that the forecasts
of the Central Electricity Board (CEB) are on the high side. This prompts a call to the authorities
for a re-examination of CEB forecasts and for the use of the SARIMA model as one of the means
for forecasting peak electricity demand in Mauritius. Reliable forecasts shall prove useful to the
authorities who are currently contemplating additional generation capacity, from renewable and
non-renewable sources, and who are due to renegotiate power purchase agreements (PPAs) with
the major independent power producers (IPPs).
1
1. Introduction
The intensity of electricity consumption is not constant over time but broadly varies with the
levels of household, commercial and industrial activities. Electric cooking, lighting and
showering at home boost electricity demand in the evening while air conditioning in offices
during a hot summer raises electricity consumption in the middle of the day. Buoyant
commercial activity during the end-of-year festive season puts pressure on existing energy
infrastructure to meet unusually high demand for electricity. There is a time slot during which
electricity demand peaks up – this characterizes the concept of peak demand.
The distinction between peak demand and total demand for electricity has to be made. Peak
demand relates to an instant or a short time interval, usually a half-hourly or an hourly period,
while total demand relates to aggregate consumption over a longer period, such as a week,
month, quarter or even year.
Electricity consumption is expressed in multiples of Watt (W). In Mauritius, peak demand is
usually measured in Megawatt (MW) [1 MW = 1 million W] and total demand in Gigawatt hours
(GWh) [1 GWh refers to consumption of 1 GW during 1 hour and 1 GW = 1 billion W].
Peak demand is important as it determines investment requirements for adequate electricity
generation or supply. A deficiency in electricity supply results in power cut thereby disrupting
the smooth running of the economic machinery in a country and even undermining business
confidence. Peak demand forecasting is thus a key exercise undertaken to avoid power failure.
The challenge is to formulate peak demand forecasts that safeguard electricity supply and
completely eliminate the risk of power blackout while at the same time not engaging a country
into excessive wasteful spending on electricity generation.
The present paper undertakes an analysis of the evolution of monthly peak demand in Mauritius
using data over the period January 2002 – December 2013, in order to highlight systematic
patterns, uncover useful trends and more importantly formulate forecasts from January 2014 to
June 2020. This exercise is all the more useful at the current juncture since the Mauritian
authorities are evaluating additional electricity generation capacity, from renewable and nonrenewable sources, and are also due to renegotiate power purchase agreements (PPAs) with
major independent power producers (IPPs) who account for about 60% of total production.
2
2. Evolution of Peak Electricity Demand January 2002 – December 2013
With the process of economic growth over time and the consequent rise in purchasing power,
peak demand has not surprisingly been on an upward trend. Interestingly though, monthly peaks
have been displaying a more or less systematic consumption pattern every year.
Peak Demand (right axis) and Total Demand for Electricity Jan 2002 - Dec 2013
450
220
400
200
350
180
160
300
140
250
120
100
02
03
04
05
06
07
08
09
10
11
12
13
Peak Demand (MW)
Total Demand (GWh)
Starting at 282 MW in January 2002, monthly peak demand ends up at 441 MW in December
2013, representing an increase of 56%. The above graph also plots monthly total demand,
implying a close relationship with peak demand – the correlation coefficient is 0.97. Further
investigation reveals that this close relationship emanates from the commercial sector, as shown
in the following correlation matrix.
3
4
2012
2013
420
440
380
400
420
400
380
2009M12
420
2013M12
2008
2009M11
2005M12
2005M11
2005M10
2004
2013M11
Commercial
(GWh)
2005M09
0.65
2009M10
0.51
2013M10
0.76
2005M08
0.72
2009M09
Industrial
2013M09
1.00
2005M07
0.86
2009M08
0.97
2013M08
0.97
2005M06
Commercial
2009M07
1.00
2005M05
0.91
2009M06
0.84
2005M04
Domestic
2009M05
2005M03
1.00
2009M04
2005M02
0.97
2013M07
360
2009M03
Total
2013M06
380
2005M01
1.00
2013M05
380
2009M02
Peak
2013M04
400
2013M03
400
2009M01
310
2013M02
2004M12
2004M11
2004M10
2004M09
2004M08
315
2013M01
2008M12
2008M11
2008M10
2008M09
2004M07
2004M06
2004M05
2004M04
2004M03
Domestic
(GWh)
2012M12
2012M11
360
2012M10
2011
2012M09
340
2008M08
330
2012M08
350
2008M07
340
2012M07
2007
2008M06
340
360
2004M02
2003
2012M06
350
350
2008M05
340
370
2012M05
370
360
2008M04
350
380
2012M04
380
370
2008M03
300
2012M03
305
2004M01
320
2008M02
300
2008M01
2003M12
2003M11
2003M10
2003M09
2003M08
Total
(GWh)
2012M02
2007M12
2007M11
2007M10
2007M09
2003M07
2003M06
325
2012M01
2011M12
2011M11
2011M10
2011M09
2007M08
2007M07
2003M05
2003M04
2003M03
2003M02
Peak
(MW)
2011M08
2010
2007M06
2007M05
2006
2011M07
350
2003M01
2002
2011M06
370
2011M05
390
2007M04
320
2011M04
330
2007M03
360
2011M03
370
2007M02
280
2007M01
2002M12
2002M11
2002M10
2002M09
2002M08
2002M07
2002M06
2002M05
2002M04
2002M03
2002M02
2002M01
290
2011M02
2006M12
2006M11
2006M10
2006M09
2006M08
2006M07
2006M06
2006M05
2006M04
2006M03
2006M02
2006M01
310
2011M01
2010M12
2010M11
2010M10
2010M09
2010M08
2010M07
2010M06
2010M05
2010M04
2010M03
2010M02
2010M01
Correlation Matrix
Industrial
(GWh)
1.00
Peak Demand (MW) by Year (2002 - 2013)
340
2005
330
350
320
340
310
330
300
320
390
2009
360
330
To better understand the prevalence of systematic patterns in peak demand, the above collective
graph contains the evolution of peak electricity consumption by year. Every year, monthly peak
demand tends to be higher in the early part and the latter part of the year but lower during midyear. The following table records the months in which peak demand is highest and lowest every
year, from 2002 to 2013.
Year
Highest Peak Month (MW)
Lowest Peak Month
2002
November (308)
January
2003
December (324)
July
2004
November (333)
July
2005
December (353)
August
2006
December (367)
August
2007
November (368)
July
2008
March (378)
September
2009
February (389)
July
2010
March (404)
August
2011
December (413)
August
2012
December (430)
July
2013
December (441)
August
Every year, the highest or global peak occurs basically in November or December while the
lowest peak arises in July or August.
The global annual peak, which is the highest recorded load in a year, is of particular interest for
its direct relevance in the determination of electricity generation investment requirements.
5
Peak Demand (MW) by Year (2002 - 2013)
460
440
420
400
380
360
340
320
300
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
The annual peaks have increased steadily at an average growth rate of 3.1% per annum, from 308
MW in 2002 to 441 MW in 2013. The 2013 peak is 17% higher than the 2008 peak of 378 MW.
Assuming the authorities had a five-year planning horizon, this peak-to-peak comparison would
imply the need for additional net investment in order to cater for 17% additional peak demand
plus a reasonable safety margin.
A close examination of the above graph reveals that peak demand has switched to a lower trend
as from 2007, most probably as a result of the financial crisis which originated in August 2007 in
the US sub-prime mortgage market and subsequently metamorphosed into a full-fledged global
economic crisis that is still biting the Mauritian economy.
The evolution of peak demand is also analysed by month of the year, to uncover the relative
dominance of specific monthly peaks over the course of a typical year.
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Average Peak Demand (MW) by Month (Jan 2002 - Dec 2013)
380
370
360
Overall Mean = 354 MW
350
340
330
1
2
3
4
5
6
7
8
9
10
11
12
The monthly average peak demand over the 12-year period 2002 – 2013 is shown above. The
month of December dominates with an average peak of 375 MW while the month of August has
the lowest average peak of 333 MW. The average peaks for November, December, January,
February, March, April and May are above the overall monthly average peak of 354 MW while
the average peaks for June, July, August, September and October are below the overall mean.
This indicates the dominance of summer peaks over winter peaks and possibly suggests heavier
use of cooling appliances in summer compared to use of warming appliances in winter.
3. Peak Electricity Demand Forecasts January 2014 – June 2020
Given the presence of seasonal influence, monthly peak demand in Mauritius is forecasted using
a SARIMA (seasonal autoregressive integrated moving average) model. Assuming peak demand
in month
7
t is denoted by PDt , the SARIMA model is formulated below.
ln PDt   0   1t  ut
 ( L). ( L)ut   ( L). ( L)vt
Where
ln PDt is the natural logarithm of peak demand
p
 ( L)  (1   i Li ) is an autoregressive lag polynomial of order p
i 1
 ( L)  (1   L12 ) is a seasonal autoregressive lag polynomial that is compatible with monthly
seasonality
q
 ( L)  (1    j Lj )
is a moving average lag polynomial of order
q
j 1
 ( L)  (1   L12 )
is a seasonal moving average lag polynomial that is compatible with
monthly frequency
ut is deviation of log peak demand from trend
vt is a white-noise error term
Parameter
1
captures the systematic average monthly growth component in peak demand. The
orders of lag polynomials
 ( L)
and
 ( L)
are chosen by starting from the lowest lag order of
1 and extending on the basis of statistical significance. The SARIMA is estimated using monthly
peak demand from Jan 2002 to Dec 2013 and is shown below.
8
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
T
AR(1)
AR(4)
SAR(12)
MA(1)
SMA(12)
5.789558
0.001544
0.852644
-0.477721
0.801858
-0.426743
-0.923231
0.026441
0.000157
0.026487
0.025059
0.043395
0.089180
0.017572
218.9624
9.849658
32.19157
-19.06358
18.47827
-4.785162
-52.54044
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Inverted AR Roots
Inverted MA Roots
0.968020
0.966435
0.016240
0.031913
349.3690
610.4414
0.000000
.98
.85-.49i
-.00+.98i
-.49+.85i
.99
.50-.86i
-.50+.86i
-.99
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
.85+.50i
.49+.85i
-.43-.55i
-.85-.49i
.86+.50i
.43
-.50-.86i
.85-.50i
.49-.85i
-.43+.55i
-.85+.49i
.86-.50i
.00+.99i
-.86-.50i
5.883979
0.088643
-5.349516
-5.193546
-5.286145
2.066264
.85+.49i
.00-.98i
-.49-.85i
-.98
.50+.86i
-.00-.99i
-.86+.50i
The estimated model is stationary, has considerable explanatory power and passes the BreuschGodfrey (BG) LM serial correlation test (orders 1, 2, 3), the Breusch-Pagan-Godfrey (BPG)
heteroscedasticity test as well as the ARCH conditional heteroscedasticity test (orders 1, 2, 3).
In light of these reasonable diagnostics, the SARIMA model is next used for dynamic stochastic
forecasting of peak electricity demand in Mauritius over the period Jan 2014 – June 2020, using
a thousand replications.
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Peak Demand Forecasts (MW) from SARIMA Model Jan 2014 - June 2020
600
In-Sample Simulation
Jan 2005 - Dec 2013
550
500
450
400
Forecasts
Jan 2014 - Jun 2020
350
300
250
2002
2004
2006
2008
2010
2012
2014
2016
2018
2020
Actual
Forecast (97.5th Quantile)
The actual monthly peaks from Jan 2002 to Dec 2013 are shown in yellow. To assess the
reliability of the SARIMA for forecasting purposes, an in-sample dynamic stochastic simulation
is conducted from Jan 2005 to Dec 2013 and the 97.5th quantiles of the simulated values are
recorded for each month and shown in green. An extreme quantile (here the 97.5th) is considered
because peak demand is, by definition, an extreme event occurring in the upper tail of the
electricity demand statistical distribution. There is thus only 2.5% chance that actual peak
demand turns out to exceed the simulated peak value.
The simulated values do track the actual values but more importantly they are comfortably above
the actual values – this is essential for ensuring no power blackout. The degree of comfort is
measured by a safety margin, defined as:
 Simulated Value - Actual Value 
Safety Margin = 100*

Actual Value


10
If investment in electricity generation had been made on the basis of the 2005 – 2013 simulated
values for peak electricity demand, the following safety margins would have been observed.
Specifically, the minimum safety margins arising every year are shown below – this implies a
conservative approach which submits the simulation exercise to a rigorous test.
Minimum Safety Margin by Year (%) 2005 - 2013
7
6
5
4
3
2
1
2005
2006
2007
2008
2009
2010
2011
2012
2013
The minimum safety margins vary from 1.3% in 2005 to 7% in 2011, implying that adoption of
the SARIMA model would not have resulted in power failure. Indeed the safety margins depict
an upward trend, so that the degree of comfort does not seem to fade over time. These
observations provide support to the use of the SARIMA model for obtaining peak demand
forecasts in Mauritius from Jan 2014 to June 2020, shown in green above.
The SARIMA and (Central Electricity Board) CEB peak demand forecasts for the years 2014 –
2019 are next graphed below.
11
SARIMA vs CEB Peak Demand Forecasts (MW)
650
630
605
600
571
541
550
561
506
500 480
485
450 461
439
400
2014
533
513
502
544
534
521
508
492
475
453
446
2015
Low
2016
Base
460
2017
High
467
2018
474
2019
SARIMA
The CEB peak demand forecasts are made on the basis of three scenarios, namely Low, Base and
High, respectively pertaining to economic growth rates of 0.5%, 1.5% and 3.6% in Mauritius in
forthcoming years. The SARIMA forecasts, on the other hand, are obtained by exploiting
previous trend and seasonal information in peak demand. The SARIMA forecasts are higher than
the Low and Base forecasts but lower than the High forecasts.
Given broad-based consensus that growth rate of the Mauritian economy is likely to remain in
the vicinity of 3.5% in the near-term, the applicable scenario from CEB is the High scenario. The
CEB High forecasts increasingly diverge from the SARIMA forecasts over time. Assuming an
investment planning horizon which extends to 2019 and given an observed peak demand of 441
MW in 2013, the SARIMA forecasts suggest that the authorities have to prepare for net extra
generation capacity of 27% (561 MW) compared to 43% (630 MW) implied by the CEB High
forecasts.
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4. Conclusion
After analyzing the evolution of peak electricity demand in Mauritius from 2002 to 2013, this
paper proposes an alternative statistics-based model, called SARIMA, for forecasting peak
demand from 2014 to mid 2020. The concept of peak demand has recently been evoked several
times at the highest decision-making level in Mauritius. Reliable peak demand forecasts are
critical for determining future investment requirements in electricity generation, for eliminating
risks of power blackout and for avoiding unwarranted spending on generation capacity. The
difference between the SARIMA forecasts and the CEB High forecasts gets considerable (69
MW) by 2019. Given the demonstrated reliability of the SARIMA model in this paper, the
authorities may judiciously contemplate a re-examination as to whether CEB forecasts are on the
high side – such an exercise has the potential to save public money. The authorities may also
wish to adopt the SARIMA model as one of the means for forecasting peak demand in Mauritius,
especially at the current juncture where additional generation capacity is being contemplated and
PPAs with the major IPPs are due for renegotiation.
Sources of Information:
Statistics Mauritius
Central Electricity Board
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