​A Technical paper on ‘Applicability of Error Limit in Forecasting & Scheduling of Wind & Solar Power in India’’ by Abhik Kumar Das​ at India SMART GRID Week 2017 organised by India Smart Grid Forum & Government of India at Manekshaw Centre, New Delhi.

2. 30 ISGW 2017: Compendium of Technical Paper
Applicability of Error Limit in Forecasting &
Scheduling of Wind and Solar Power in India
Abhik Kumar Das
del2infinity Energy Consulting, India
abhik@del2infinity.xyz
Abstract : Forecasting of power generation is an essential
requirement for high penetration of variable renewable energy in
existing grid system as the major purpose of forecasting is to reduce
the uncertainty of renewable generation, so that its variability can be
more precisely accommodated. This paper focuses on the statistical
behaviour of error in solar and wind power forecasting considering
Indian regulations and analyse the applicability of the error limit in
calculating the energy accuracy of forecasting and the stability of
the grid.
Keywords : Forecast error, Variability, Penalty due to deviation
Introduction
One of the major challenges in renewable enabled smart grid
is to ensure the demand-supply balance for electricity. Wind
and solar energy are two major components of renewable
energy generation in India [1-4] but the variability and
unpredictability inherent to wind and solar create a threat
to grid reliability due to balancing challenge in load and
eneration. he unscheduled uctuations of ind and solar
generation produce ramping events and hence the integration
of si nificant ind and solar ener y into e istin supply
system is a challenge for large scale renewable energy
penetration [5-11]. To accommodate the variability, the day-
ahead and short-term renewable energy forecasting is needed
to effectively integrate renewable energy to the smart grid
and hence the forecasting and scheduling of wind and solar
energy generation has become a widely pursued area of
research at Indian context [12, 13].
The concept of forecasting and scheduling (F&S) of
renewable energy generators and the commercial settlement
was introduced in Indian context by CERC through
Indian Electricity Grid Code (IEGC), 2010 [14] and the
Renewable Regulatory Fund mechanism [15]. Due to several
implementation issues, the mechanism was never made
operational. To formulate an implementable framework,
CERC also issued 2nd amendment to regulation for
Deviation settlement mechanism and other related matters
[16]. After CERC regulation, Forum of Regulators (FOR)
[17] and other state regulators issued or drafted regulation
related to the forecasting and scheduling of Wind and Solar
power generation Since the system operators in India have
to do curtailment on variable renewable energy due to
intermittency and variability of the wind and solar power
generation, the forecasting takes an important role in creating
a sustainable solution for maximum utilization of renewable
energy.
The most usable and conventional strategies in F&S of
wind and solar power generation is predicting the weather
parameters using of NWP (Numerical Weather Prediction)
models and converting the values of weather parameters
into power generation using the turbine or PV models
considering the CFD based analysis in local regions. The
recent development of deep learning algorithms in ANN
rtificial eural et or based methodolo ies ha e
created a huge scope in forecasting the power generations.
Considering the uncertainty in the initial value vector in
NWP and learning vectors in DNN (Deep Neural Network)
, a powerful perspective regarding forecasting methodology
is to regard it fundamentally as a statistical rather than
deterministic solutions as the stability of the grid needs
not just the prediction of power generation but also the
uncertainty associated with it. Thus from a mathematical
viewpoint, forecasting is best considered as the study of the
temporal evolution of probability distributions associated
with variables in the power generation. Forecasting with
proper uncertainty analysis is required since the initial value
vector and the neural architecture of DNN can never be
precisely defined and there are obser ational limitations in
different variables required to predict the power generation.
Without proper forecasting models considering non-linear
dynamics approaches, a small but appreciable fraction of
error can create a large error due to temporal evolution.
In this paper, a simple functional relation is established
considering the variability of power generation and error limit
in forecasting for different regulations. The average penalty
due to deviation is calculated using the exponential model
of forecast error distribution. The remaining of the paper
is or ani ed as follo s he section brie y describes the
forecast error and the functional relationship of variability of
actual power generation is derived in section III. Section IV
shows the computational model of penalty due to deviations.
The results and brief analysis is discussed in Section V and
conclusion is presented in section VI.
II. Forecast Error
he most usable mathematical techni ues in definin the
forecast error are MAE (Mean Absolute Error), RMSE (Root
Mean Square Error). But considering the system stability, the
error at each Time Block (1 Time Block = 15 minute) has
more practical consequences and the error at i-th time block
is defined as

3. ISGW 2017: Compendium of Technical Paper 31
1
| ( ) |A Sx i x
AvC
(1)
Where AvC is the available capacity; xA
(i) and xS
(i) are
actual generation and scheduled generation respectively.
Considering the Indian regulation, the penalty due to
deviation can be generalized as shown in Table I [13].
Table I: Generalized Structure of Deviation charge
Error Band Deviation Charge per kw-Hr (Rs)
PPA Based [15] Fixed (depends on Regulations)
e ≤ m No penalty 0
m < e ≤ m1
10% of PPA INR 0.50
m1
< e ≤ m2
20% of PPA INR 1.00
m2
< e ≤ m3
30% of PPA INR 1.50
III. Variability in Power Generation
Variability of power represents the change of generation
output due to unscheduled uctuations of ind elocity or sun
radiation patterns while uncertainty describes the inability to
predict in advance the changes in generation output. Large
unscheduled changes in wind or solar power generation are
called ramp events which hamper the penetration of variable
power in the existing grid [13]. The variability can be
uantified as a measure of dispersion in ariable rene able
po er eneration and be easily uantified usin the concept
of Lorenz curve [18]. Though there are different ways to
quantify variability, the simplest way to measure variability
is using the normalized squared deviation about mean of the
actual generation for some time block n as follows,
2 2
1
1
( ( ) )
n
A A Ai
x i x
n Avc
(2.A)
Similarly the dispersion in the schedule generation for
the same time span can be represented as
2 2
1
1
( ( ) )
n
S S Si
x i x
n Avc
(2.B)
Here andS Ax x are the mean of the power generation in
the time span of n. For a good forecast in which S Ax x and
A S , we can show that (A.1)
2(1 )
A
m
r
(3)
Here r is the correlation coefficient of the schedule
and actual power generation. The relationship (3) shows
how much variability a forecast model can effectively
accommodates considering the no-penalty is 100m%, the
alue of hich is defined by the re ulation. s sho n in fi .
1, for some value of r, the maximum permissible variability of
the forecast model can be calculated for different regulations
i.e. no penalty error limit as 5% (m = 0.05), 10% (m = 0.10)
and 15% (m = 0.15). The value of r depends on the choices of
models and methodologies used in forecasting.
Figure 1: Shows the relation of correlation coefficient of actual
and schedule generation and the variability of the actual power
generation which the forecast model effectively accommodates.
IV. Penalty Due to Deviation
The penalty per available capacity can be represented as
( ) ( )C ec e h e de (4)
Where c(e) is the penalty due to the error and h(e) can
be represented as probability of error in the forecast models.
Here considering the Indian regulations, for simple statistical
calculation we can assume that
c(e) = k(e – m) if e > m (5)
= 0 , otherwise
Considering the phenomenological models of forecast
error, the probability distribution can be viewed as an
e ponential distribution of parameter as follo s
h(e exp(– e) (6)
As shown in Fig. 2, the frequency plot of forecast error in
solar and wind forecasting for different days. The frequency
plot closely match the e ponential distribution define in
for different alues of .
(A)

4. 32 ISGW 2017: Compendium of Technical Paper
(B)
Figure 2: Shows the normalized frequency distribution of
forecast error for different days of (A) solar forecasting and (B)
wind forecasting
Using mathematical manipulation, we can state that
(A.2)
C k[(m e
)2
e
2
](1 – P(m)) (7)
Here P(m) is the probability the error is under no penalty
error band i.e.
0
( ) ( ) ( )
m
P m Prob e m h e de (8)
nd e
is defined as the standard de iation of the error
distribution. Though the average penalty due to deviation is
al ays positi e fi . . and . and can be ero hen P(m)
= 1 i.e. prediction of power generation with 100% accuracy
s sho n in fi . . and . .
V. Results and Analysis
Equation (3) represents an interesting relationship connecting
physical parameter of the po er eneration A
), regulatory
parameter (m hich is defined in able as no penalty
error limit) and accuracy parameter (r hich is defined
as correlation coefficient of po er eneration forecast.
This relationship shows the ability to forecast model to
accommodate the maximum variability in the actual power
generation considering different regulations (m) as the
accuracy of the forecast model depends on the variability of
the actual power generation.
s an e ample the fi . sho s the daily forecast of a
160 MW plant in India, though there are variations in the
po er eneration the del infinity s based al orithm is
useful to forecast the pattern of uctuations.
Fig. 3 and 4 shows the actual and schedule power
generation of wind and solar plant. It is interesting to see
that though there are some penalties due to deviation in
some days, but achieving high predictability of the forecast
model, the penalty due to deviation in some days can
become zero.
(A)

5. ISGW 2017: Compendium of Technical Paper 33
(B)
Figure 3: Shows the actual and forecast power generation of wind and its penalty due to deviation per actual generation
occur again. Though there is a paucity of historical data and
the data related to weather parameters of different solar plants
in ndia but the del infinity s based solution can be used
for forecasting and scheduling solution which can minimize
the penalty due to present regulation and can work even when
there is unscheduled ariability. s an e ample the fi .
shows the forecast of 40 MW and 10 MW solar plants.
Due to stochastic behavior of weather parameters related
to solar power generation and the variability distribution of
power, the temporal evolution of predicted variables creates
uncertainties in forecasting. Though numerous forecast models
are available using different methodologies, a good forecast
is that which captures the genuine patterns which exist in the
historical data, but do not replicate past events that will not
(A)

6. 34 ISGW 2017: Compendium of Technical Paper
(B)
Figure 4: Shows the actual and forecast power generation of solar and its penalty due to deviation as percentage of revenue.
VI. Conclusion
Forecasting and Scheduling (F&S) of variable renewable
power generation like wind and solar is an essential
requirement for a sustainable energy future as the proper
forecast methodology reduces the uncertainty and helps
to accommodate the variable energy in existing grid. The
temporal evolution of predicted variables is non-deterministic
and the statistical prediction of the distribution of power
generation plays an important role in forecasting with
acceptable uncertainties. The relationship of variability of
actual po er eneration and correlation coefficient in forecast
for different regulations can be useful in forecasting and the
statistical formulation of average penalty due to deviation
can be used in analysis of different forecast strategies.
References
[1] National Action Plan on Climate Change, GOI (http://www.
moef.nic.in/downloads/home/Pg01-52.pdf last visited on 30
Sept. 2016)
[2] INDIA’S INTENDED NATIONALLY DETERMINED
CONTRIBUTION: WORKING TOWARDS CLIMATE
JUSTICE
(http://www4.unfccc.int/submissions/INDC/Published%20
Documents/India/1/INDIA%20INDC%20TO%20UNFCCC.
pdf last visited on 30 Sept. 2016)
[3] Report of the Expert Group on 175 GW RE by 2022,
ayo http niti. o .in ritereaddata files
writereaddata/files/document_publication/report-175-GW-
RE.pdf last visited on 30 Sept. 2016)
[4] Strategic Plan for new and renewable Energy Sector for the
period 2011-17, Ministry of New and Renewable Energy,
Government of India, 2011
[5] Das Abhik Kumar, “An analytical model for ratio based
analysis of wind power ramp events”, Sustainable Energy
Technology and Assessments, Elsevier vol. 9, pp.49-54,
March 2015
[6] Das Abhik Kumar et al., “An Empirical Model for Ramp
Analysis of Utility-Scale Solar PV Power”, , Solar Energy,
Elsevier, vol. 107, pp. 44-49, September 2014
[7] Kamath, C. 2010. “UnderstandingWind Ramp Events through
Analysis of Historical Data.” Transmission and Distribution
Conference and Exposition, 2010 IEEE PES in New Orleans,
LA, United States., April 2010
[8] Das Abhik Kumar & Majumder Bishal Madhab, “Statistical
Model for Wind Power based on Ramp Analysis”,
International Journal of Green Energy, 2013
[9] Gallego C., Costa A., Cuerva A., Landberg L., Greaves B.,
Collins J., “A wavelet-based approach for large wind power
ramp characterisation”, Wind Energy, vol. 16(2), pp. 257-
278, Mar. 2013
[10] Bosavy A., Girad R., Kariniotakis G., “Forecasting ramps of
wind power production with numerical weather prediction
ensembles”, Wind Energy, vol. 16(1), pp. 51-63, Jan. 2013
[11] Kirby B., Milligan M., “An exemption of capacity and
ramping impacts of wind energy on power systems”, The
Electricity Journal, vol.2(7), Sept. 2008, pp.30-42
[12] Steffel, S.J., 2010. Distribution grid considerations for large
scale solar and wind installations. IEEE, 1–3, Transmission
and Distribution Conference and Exposition, 2010 IEEE PES

7. ISGW 2017: Compendium of Technical Paper 35
[13] Das Abhik Kumar, ‘Forecasting and Scheduling of Wind and
Solar Power generation in India’, NTPC’s Third International
technology Summit „Global Energy Technology Summit’
2016
[14] Indian Electricity Grid Code, Central Electricity Regulatory
Commission, 2010
(http://cercind.gov.in/2010/ORDER/February2010/IEGC_
Review_Proposal.pdf last visited on 30 Sept. 2016)
[15] Procedure for implementation of the mechanism of
Renewable Regulatory Fund , Central Electricity Regulatory
Commission, 2011 ( http://www.cercind.gov.in/Regulations/
Detailed_Procedure_IEGC.pdf last visited on 30 Sept. 2016)
[16] Framework on Forecasting, Scheduling and Imbalance
Handling for Variable Renewable Energy Sources (Wind and
Solar), Central Electricity Regulatory Commission,
(http://www.cercind.gov.in/2015/regulation/SOR7.pdf last
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[17] Model Regulations on Forecasting, Scheduling and Deviation
Settlement of Wind and Solar Generating Stations at the State
level
(http://www.forumofregulators.gov.in/Data/study/MR.pdf
last visited on 30 Sept. 2016 )
[18] Das Abhik Kumar, “Quantifying photovoltaic power
variability using Lorenz curve”, Journal of Renewable and
Sustainable Energy, AIP, vol.6 (3), June 2014
Appendix
A1.
1
( ) | ( ) ( ) |A Se i x i x i
AvC
=
1
| ( ) ) ( ( ) ) ( ) |A A s S A Sx i x x i x x x
AvC
For a good forecasting system we can consider, S Ax x and
A S . Hence using the no penalty band in Table I, for
some n we can state that
m2
2
1
1
( )
n
i
e i
n
=
2
1
1 1
(( ( ) ) ( ( ) )
n
A A S S
i
x i x x i x
AvC n
=
2
2 2
1
1 1
(( ( ) ) ( ( ) ) 2( ( )
n
A A S S A
i
x i x x i x x i
AvC n
)( ( ) )]A S Sx x i x
A
2
S
2
– 2r A S
= 2(1 – r A
2
, which implies (3).
A.2. Using (4) and (6),
2
exp( )
m
C k e e de
Integrating,
2 2
1 1
exp( )C k m m
Using (8), P(m e p m) and for exponential
distribution e
. ence replacin e p m and e
get (7).
Author: Abhik Kumar Das
AbhikholdsaDualDegree(B.TechinElectronics&Electrical
Communication Engineering & M.Tech in Automation
and Computer Vision) from Indian Institute of Technology,
Kharagpur, India. He has a vast experience in computational
modelling of complex systems. He contributed in different
verticals of analytical modelling related to renewable energy
and techno-economics and published several well-cited
research articles in internationally acknowledged journals
and peer-reviewed conferences. He is founding member
of del infinity an accurate ind ner y olar ner y
Forecasting and Scheduling Solutions Company. (e-mail:
contact del infinity. y .