Applicability of Error Limit in Forecasting & Scheduling of Wind & Solar Power in India

30 ISGW 2017: Compendium of Technical Paper

Applicability of Error Limit in Forecasting &

Scheduling of Wind and Solar Power in India

Abhik Kumar Dasdel2infinity Energy Consulting, [email protected]

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

IntroductionOne 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 Errorhe 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

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 ≤ m

2 20% of PPA INR 1.00

m2 < e ≤ m

3 30% of PPA INR 1.50

III. Variability in Power GenerationVariability 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( ( ) )

V �Ç n

A A Aix 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( ( ) )

V �Ç n

S S Six 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 V � VA S , we can show that (A.1)

2(1 )

V ��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 DeviationThe penalty per available capacity can be represented as ( ) ( ) ÔC 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)


(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 e2](1 – P(m)) (7)

Here P(m) is the probability the error is under no penalty error band i.e.

0

( ) ( ) ( ) � Ôm

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 AnalysisEquation (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)


(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)


(B)

Figure 4: Shows the actual and forecast power generation of solar and its penalty due to deviation as percentage of revenue.

VI. ConclusionForecasting 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%20Documents/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. “Understanding Wind 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


[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 visited on 30 Sept. 2016)

[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 xAvC

� � � � �

For a good forecasting system we can consider, �S Ax x and V � VA S . Hence using the no penalty band in Table I, for some n we can state that

m2 2

1

1( )

n

i

e in Ç =

2

1

1 1(( ( ) ) ( ( ) )

n

A A S Si

x i x x i xAvC n

È Ø � � �É ÙÊ Ú Ç

= 2

2 2

1

1 1(( ( ) ) ( ( ) ) 2( ( )

n

A A S S Ai

x i x x i x x iAvC n

È Ø � � � � �É ÙÊ Ú Ç)( ( ) )]A S Sx x i x� �

A2 S

2 – 2r A S = 2(1 – r A2, which implies (3).

A.2. Using (4) and (6),2 exp( )

mC k e e de

�� O �OÔ

Integrating,2 21 1

exp( )C k m mË ÛÈ Ø È Ø� � � �OÌ ÜÉ Ù É ÙÊ Ú Ê ÚO OÌ ÜÍ Ý

Using (8), P(m e p m) and for exponential distribution e . ence replacin e p m and e get (7).Author: Abhik Kumar DasAbhik holds a Dual Degree (B.Tech in Electronics & 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 .

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Applicability of Error Limit in Forecasting & Scheduling of Wind & Solar Power in India