On recent advances in pv output power forecast

Review
On recent advances in PV output power forecast
Muhammad Qamar Raza ⇑
, Mithulananthan Nadarajah, Chandima Ekanayake
Power and Energy System Group, School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia
a r t i c l e i n f o
Article history:
Received 25 December 2015
Received in revised form 28 June 2016
Accepted 29 June 2016
Available online 7 July 2016
Keywords:
Photovoltaic
Artificial intelligence (AI)
Regressive techniques
PV output forecasting
Hybrid forecast models
Artificial neural network (ANN)
Auto-regressive moving average
Fuzzy Logic
Persistence method
Statistical methods
a b s t r a c t
In last decade, the higher penetration of renewable energy resources (RES) in energy market was encour-
aged by implementing the energy polices in several developed and developing countries due to increas-
ing environmental concerns. Among wide range of RES, Photovoltaic (PV) electricity generation get higher
attention by researcher, energy policy makers and power production companies due to its economic and
environmental benefits. Therefore, a large PV penetration was observed in energy market with rapid
growth in the last decade. The PV output power is highly uncertain due to several meteorological factors
such as temperature, wind speed, cloud cover, atmospheric aerosol levels and humidity level. The inher-
ent variability of PV output power creates different issues directly or indirectly for power grid such as
power system control and reliability, reserves cost, dispatchable and ancillary generation, grid integra-
tion and power planning. Therefore, there is need to accurately forecast the PV output over the spectrum
of forecast horizon at different chronological scales. In this paper, a comprehensive and systematic review
of PV output power forecast models were provided. This review covers the different factors affecting PV
forecast, PV output power profile and performance matrices to evaluate the forecast model. The critical
analysis regressive and artificial intelligence based forecast models are also presented. In addition, the
potential benefits of hybrid techniques for PV forecast models are also thoroughly discussed.
Ó 2016 Elsevier Ltd. All rights reserved.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2. Factors affecting PV output power forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.1. Forecast horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.2. Forecast model performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.3. Preprocessing of input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
2.4. Forecast model inputs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3. Solar output power profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.1. UQ center array PV output profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4. Classification of forecast techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.1. Persistence forecast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.2. Physical models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3. Statistical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.4. Linear models or time series models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.1. ARMA model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.2. ARIMA techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.3. CARDS model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
http://dx.doi.org/10.1016/j.solener.2016.06.073
0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
Abbreviations: AI, artificial intelligence; AM, air mass; ANN, artificial neural network; AR, auto-regressive; ARIMA, Auto-Regressive Integrated Moving Average; ARIMAX,
ARIMA exogenous; ARMA, Auto-Regressive Moving Average; ARMAX, ARMA-exogenous; DR, Demand response; BP, back propagation; CPV, concentrated PV; DHI, diffuse
horizontal irradiance; DNI, direct normal irradiance; GA, genetic algorithm; GHI, global horizontal irradiance; HS, hybrid system; IEA, International Energy Agency; ISO,
independent system operator; LMS, least means square; MA, moving average; MAE, Mean Absolute Error; MAPE, mean absolute percent error; MBE, Mean Bias Error; MLP,
multi-layer perceptron; NAR, non-linear AR; NARMAX, non-linear ARMA exogenous; NARX, non-linear AR exogenous; NWP, numerical weather prediction; PV, Photovoltaic.
⇑ Corresponding author.
E-mail addresses: Qamar.raza@uq.edu.au (M.Q. Raza), mithulan@itee.uq.edu.au (M. Nadarajah), chandima@itee.uq.edu.au (C. Ekanayake).
Solar Energy 136 (2016) 125–144
Contents lists available at ScienceDirect
Solar Energy
journal homepage: www.elsevier.com/locate/solener

4.5. Artificial intelligence techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6. Significance of ANN approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6.1. Artificial neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6.2. Artificial neural network architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6.3. Activation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.6.4. Multi layer perceptrons neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.6.5. Radial basis function network (RBFNN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.6.6. Recurrent neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.6.7. Feed forward neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.6.8. Feedback neural network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.7. ANN and classical time series models comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.8. Hybrid models for PV output forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5. Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6. Forecast model performance evaluations matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7. Conclusions and future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
1. Introduction
In last decades, the global energy demand increased steadily
with rapid growth in world population. The energy demand is at
the higher level ever before and most of the fossil resources are
the edge of depletion due to excess usage. Therefore, ‘‘how to
meet the 21 century energy demand” is the hot topic of discussion
among the governments, researcher, scientists and energy policy
makers in developed and developing countries. In addition, other
concern is rapid changes in environmental and climatic conditions
(i.e. global warming, depletion of ozone layer, etc.). Keep in view
the energy issue, International Energy Agency (IEA) raised the
concerned namely energy security, economic efficiency, and envi-
ronmental protection, which are known as ‘‘3Es” ((IEA), 2007).
Therefore, concentrated efforts have made to reduce the emission
of CO2 and minimum reliance on fossil fuels in order to achieve
the 3Es objectives. Serval countries have been made efforts to meet
the 3E objectives which are align with IEA guidelines and their
national energy targets.
European union (EU) was decided to meet the energy targets by
2020 (Council, 2010). First target is to reduce the EU Green House
Gas (GHG) emission by 20% below the level of 1990. Secondly, the
contribution of renewable energy resources (RES) raise up to 20%.
Thirdly, reduction of energy usage by 20% in contrast with pro-
jected levels through energy efficiency measures. European Union
renewable energy directive set the RES production targets. It states
that, 30% total energy will be produced from RES generation by
2030. The target of RES generation contribution will be climbed
up to 100% by 2050 (Zervos et al., 2010). In addition, a high RES
contribution in existing power grid network is also expected by
the energy regulators of USA, Canada, Australia, China and India.
Among number of RES resources, solar and wind power generation
are more promising sources. They have higher potential for pene-
tration in energy market with greater degree of success. However,
solar generation get much more attention by the energy player,
investors and Government funding agencies in the last decade
because of its economic and environmental benefits.
Solar energy is feasible solution in order to meet the world
energy demand. A research study highlights that, earth received
approximately 1.8 ⁄ 1011
MW power from solar radiation at instant
(B.M. Shah et al., 2015). However, the present world energy con-
sumption requirement is less than the amount of energy received
from solar (Wengenmayr and Bührke, 2011). Fig. 1 depicts the
world solar energy map with solar hotspots. A huge potential for
solar power generation in different countries can be observed
those are above 45°N or below latitude 45°S. It can also
be observed, the Middle East, Mojave Desert (USA), the Chilean
Atacama Desert, the Sahara and Kalahari Deserts (Africa) and
North-western Australia are potential locations for large power
generation from solar PV technology.
Another research study (R. Shah et al., 2015) highlights that, the
electricity demand of Mediterranean, North African region and
entire Europe can be fulfilled by developing solar plants in Sahara
Desert. The red sea including different areas of Saudi Arabia and
Egypt are also among the highest potential sources for solar
energy. In addition, United States and Australia also have greater
potential to get benefit form solar energy than the world average.
Due to potential of solar energy, large penetration of solar PV is
expected in Australian energy sector in terms of rooftop PV, large
and small scale solar PV units. In last decade, the higher penetra-
tion of PV technology in energy market of different countries is
observed due its environmental and economic benefits
(Photovoltaics, 2012). These benefits are reduction in CO2 emis-
sion, minimum refinance of fossil fuel resources and Solar Photo-
voltaic (PV) plants consist of solar panels, which directly convert
the sunlight into electricity unlike power generation using rotating
generators. PV becomes more popular due to different promising
features such as modularity, low maintenance and operational
cost, longer lifetime, CO2 reduction and environmental cleanliness.
The energy generation capacity of solar plant varies due different
factors such as PV plant site, meteorological variables, solar tech-
nology and installation capacity.
Fig. 2 highlights the growth of world solar PV capacity in the
last decade. An exponential growth can be observed in global solar
PV capacity from 2004 to 2014. Global capacity was increased from
3.7 GW to 7 GW in three years (2004–2007). In contrast, it was
increased from 7 to 40 GW in next three years. In addition, a huge
growth in global solar PV capacity was observed in next couple of
years. For example, global was more than double in 2010 as com-
pared to 2008. Overall, global PV energy capacity was increased
from 3.7 to 177 GW in the last decade. A research study reports
that, the PV module have individual capacity from 100 W to
320 W (Omran). The PV technology still facing lot of challenges
for large penetration, in which intermittent and uncertain nature
of solar PV is more prominent. The PV output power is variable
mainly due to variations in solar radiations and amount received
solar by the solar panels.
With a remarkable growth of PV in last decade, the integration
of photovoltaic plants in current power network raise the different
technical and stability issues for the power system directly or indi-
rectly. These distress arises due to continuous change in solar
resource, temperature, PV output power, high energy storage cost,
grid reliability, seasonal and environmental changes (Denholm and
Margolis, 2007; Dixon et al., 2010). The implementation of PV
126 M.Q. Raza et al. / Solar Energy 136 (2016) 125–144

power network as back up supply without storage devices is not a
technical viable solution as it affects the grid stability due variable
output power. It is due to large variations in meteorological condi-
tions, which increase the uncertainty of PV output power.
Therefore, an accurate PV output forecast over the spectrum of
forecast horizon is required for independent power producing (IPP)
and managing companies or equivalent grid balancing authorities.
The accurate PV forecast will help IPP or power authorities for bet-
ter energy planning and management. In addition, accurate fore-
cast will be beneficial in terms of smart integration the PV
generation with current grid with higher system reliability
(Dixon et al., 2010; Rodriguez, 2010; Helman et al., 2010). There-
fore, the importance of PV output forecast is vital in order to
achieve higher penetration of solar power technology. It will also
contribute to minimize the reliance on fossil fuels resources. In
addition, grid regulation, power scheduling, unit commitment
and energy management system can be designed in effective
manner with accurate PV forecast. The PV output forecast can be
divided into different categories based on forecast horizon such
as very short term, short term, medium term and long term PV out-
put forecast.
Short term PV output forecast can be utilized for automatic gen-
eration control (AGC), better unit dispatching, load balancing and
power plant operational management. ISO’s and utilities are more
interested in relatively longer forecast horizons for unit commit-
ment, load balancing and scheduling. The distribution and trans-
mission grids operational planning and balancing require the
spectrum of solar forecast for efficient management. It helps to grid
to reduce the ancillary costs associated with weather dependency
and deliver quality of energy. In addition, power gird stability of PV
integrated can be ensured with accurate PV forecast. It will
increase PV penetration in existing power grid network and help
to reduce of CO2 emission. From the grid prospective, reduction
of the power system operational costs is a main factor to design
accurate PV forecast models. PV output power forecast may also
part of smart grid (future generation power grids) energy manage-
ment system along with wind and load forecast.
A number of factors affecting on PV output power, which leads
to uncertain and unpredictable PV output pattern. Therefore, this is
essential to design a robust, intelligent and adaptive forecast
model which can accommodate the factors affecting on PV output
for higher forecast accuracy. The complexity of forecast model will
be increased by accommodating the different factors affecting on
the output such wind speed, irradiance, temperature, cloud cover,
and seasonal variations. Therefore, there is always need to trade off
the number of forecast model inputs and complexity by keeping in
view of forecast accuracy.
As a reminder the organization of the paper as fellows: Section 2
describes fundamental considerations for solar power generation.
Section 3 briefly illustrate the, solar output power profile of The
University of Queensland (UQ), Australia St. Lucia campus center
array. The preprocessing of input data and forecast model
performance evaluation matrices are elaborated in Sections 4 and
5. Section 6 reviews the regressive and artificial intelligence based
Year
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Power(GW)
0
20
40
60
80
100
120
140
160
180
200
Fig. 2. Global solar PV capacity from 2004 to 2014 (Zervos, 2015).
Fig. 1. The world solar energy map (Zhang et al., 2013).
M.Q. Raza et al. / Solar Energy 136 (2016) 125–144 127

forecasting techniques with help of comprehensive tables. The
potential benefits of hybrid system for PV forecast application
are discussed in Section 7.
2. Factors affecting PV output power forecast
A number of variable are affecting on the output of PV forecast
model such as forecast horizon, forecast model input, performance
of prediction and data preprocessing applied as forecast model
input data. The forecast accuracy can be enhanced by accommo-
dating the factors affecting on the PV output as forecast model
inputs. These factors are described below.
2.1. Forecast horizon
The span of time into the future for which forecasts are to be
prepared called forecast horizon. There are no well-defined criteria
to classify the forecasting in different categories based on forecast
horizon. However, some researcher reports that, forecast can be
divided in three based on time horizon. According to Raza and
Khosravi (2015), electrical load forecasting can be divided into
three categories by most of researchers but some of them divided
it into four categories (Amral et al., 2007). Broadly, forecasting can
be divided in four major’s categories/types based on forecast hori-
zon as given below:
I. Long term forecast (1–10 year ahead).
II. Medium term forecast (1 month to 1 year ahead).
III. Short term forecast (1 h or several hours ahead to 1 day or
1 week ahead).
IV. Very short term forecast (1 min to several min ahead).
Some of the researcher consider the few seconds or 1 min to 1 h
or several hours (maximum 6 h) ahead forecast as very short term
forecast. However, some researcher considers as subclass of short
term forecast. However, majority of them enlist the very short
forecast as a separate class. In case of PV output forecast, short
term or very short term forecast is useful in order to design PV
integrated better energy management system, unit commitment,
power scheduling and dispatching. It is reported that for PV output
forecast, the prediction accuracy of the model varies by changing
the forecast horizon even with identical forecast model parame-
ters. In Lipperheide et al. (2015), research study analyze the perfor-
mance of PV output forecast model over the different forecast
horizon time such as 20, 40, and 60 . . . up to 180 s. The proposed
forecast model produce prediction error (rRMSE) in the range of
3.2–15.5% for forecast horizon from 20 to 180 s. In Lonij et al.
(2013) authors design a forecast model which produces the error
4.6% and 2.4% for 15 and 30 min forecast horizons, respectively.
It can be observed from above reported that the forecast error var-
ies with change in forecast horizon.
2.2. Forecast model performance
The PV output forecast accuracy is dependent on prediction
model performance. It is due to capability of individual forecast
model to handle the meteorological uncertainties. A number of sta-
tistical and artificial intelligence based forecast models are
designed to accurately forecast the PV output. Several research
studies have been reported to compare the performance of conven-
tional, statistical and ANN based forecast models. In Almonacid
et al. (2010) authors designed three different conventional mathe-
matical models for PV output forecast and compare with artificial
neural network (ANN). According to their findings, ANN based
model outperform than the conventional mathematical models in
terms of forecast accuracy and adaptability in uncertain meteoro-
logical conditions. A research study (Oudjana et al., 2013), purpose
a methodology to compare the ANN and regression model perfor-
mance for PV plant in the Ghardaia province of Algeria. ANN model
demonstrate higher forecast accuracy than the regression model
with solar radiation and temperature as independent variables.
In Almeida et al. (2015), authors analyze the PV output
forecast performance of five different models named as the
k-Nearest-Neighbour, Persistent model, the Autoregressive
Integrated Moving Average (ARIMA), ANNs and the hybrid Genetic
algorithm based ANN model for 1 MW PV plant in California. ANN
model produces less forecast error up to RMSE of 11.42 for 1-h ahead
forecast. However, the forecast accuracy further can be enhanced by
optimizing the ANN parameters using population based optimiza-
tion techniques. It can be concluded that, the forecast accuracy of
PV output forecast model varies by changing the forecast model. It
is due to performance of individual forecast model.
2.3. Preprocessing of input data
A number of PV output forecast model utilized the historical PV
output data as forecast model input. The historical PV output data
may contain different spikes and non-stationary components due
to uncertain and variable meteorological conditions. As a result,
these non-stationary and spikes in data will leads to higher fore-
cast error due to improper training. The historical PV output data
can be processed for smoothing. In addition, missing input data
points in historical data will also play a role to increase the forecast
error. Therefore, the forecast accuracy of model can be consider-
ably improved by input preprocessing. A number of techniques
were applied to preprocess the inputs of forecast model. The pre-
processed input data will significantly reduce computational cost
of forecast model by learning the historical pattern in better way.
Stationary, trend free time series, historical lag identification and
normalization are useful techniques to preprocess the input data
for accurate PV output forecast. Time series of the clearness or
clear-sky index are used in different research studies for prepro-
cessing as reported in Bacher et al. (2009) and Kemmoku et al.
(1999).
However, some of research doesn’t agree with huge impact of
clearness or clear-sky index in enhancement of forecast accuracy
(Sfetsos and Coonick, 2000). This study reports that, time series
of the clearness or clear-sky index is random in nature and varies
due to different meteorological factors. Therefore, it does not pro-
vide strong learning basis to prediction model. It may lead to poor
forecast accuracy along with increased computational cost. The
forecast results of this study demonstrates that, the preprocessed
solar irradiance data is more effective to use as forecast model.
In Cao and Cao (2006), Wavelets transform (WT) technique was
used for preprocessing of input data. The inputs of forecast model
are split in different frequency components. These components
were used forecast model inputs. In Reikard (2009), solar irradi-
ance was used as input of model due to its impact on the PV out-
put. In addition, statistical tool was used to remove the seasonality
trend in input data and it helps to increase the learning perfor-
mance of the model. However, it is difficult to find the accurate
trend of daily solar irradiance data series due unpredictable noise.
Some other research studies, analyze the performance of forecast
model by applying a trend and de trend techniques for solar irradi-
ance data (Baig et al., 1991; Kaplanis, 2006). Generally, the PV out-
put power follow the solar irradiance patter up to certain extent.
Cyclic behavior of solar radiation can be predicted with high
degree of accuracy by using Fourier series as predictor. This tech-
nique is able predict the solar irradiance by combing the different
significant frequencies. According to Boland (1995, 2008), the daily
time series profile of solar irradiance can be constructed effectively
constructed by capturing the yearly and intraday cycles. In order to

analyze the performance of de trend model, Artificial Intelligence
based techniques were utilized in literature. Augmented Dickey–
Fuller (ADF) test is used to measure the performance of de trend
series which can be utilized as input to the forecast model. For time
series data, ADF is treated as test. In realization process, time series
data contains unit root which is tested using ADF technique as
given in Eq. (1).
Xt ¼ aXt þ Zt ð1Þ
where a = 1 and Zt $ WN 0; r2
Z
À Á
, WN represents the time series
white noise. Preprocessing techniques were also applied to different
other forecast application such as load, electricity price and wind
forecast. These results demonstrate the potential benefits of prepro-
cessing in terms of forecast accuracy.
2.4. Forecast model inputs
Forecast model inputs also play a vital in order to enhance the
predication accuracy and model performance in terms of computa-
tional complexity and cost. Predication error of forecast model is
increased due to improper selection of forecast model inputs.
Therefore, PV output forecast model unable to correctly map the
all input variables as a forecast output due to poor selection of
essential influential variables. In De Giorgi et al. (2014), authors
design a PV output forecast model with different input vectors
and analyze the impact of these input vectors on the output perfor-
mance of the model. In this study, three types of vectors are
designed i.e. vector 1 contains the historical PV output data, vector
2 comprises the values of solar irradiance and module temperature
in vector 3. The output forecast results highlights that, the predic-
tion error (NRMSE) is 12.57%, 12.60% and 10.91% with input vector
1, 2 and 3 respectively. A another research study (Liu et al., 2015)
proposed that, a PV output forecast model with historical PV out-
put data, weather data of current day, historical aerosol index
(AI), historical wind speed, weather and humidity data are as fore-
cast model input. Different case studies were designed for cloudy
and sunny day forecast with different set of inputs for the perfor-
mance analysis. The prediction results demonstrate that, forecast
error is 7.34% and 7.04% without AI and with AI as forecast input
respectively for sunny day forecast case study. The results demon-
strate that; the PV output forecast model performance varies with
change in input variables.
3. Solar output power profile
The University of Queensland (UQ), Australia install the PV
arrays at different location. These PV sites are UQ St. Lucia campus,
UQ Gatton campus, Heron Island and North Stradbroke Island with
installation capacity of 1.22 MW, 3.525 MW, 54 kW and 40 kW
respectively. UQ center is the largest PV array installed at UQ St.
Lucia campus as shown in Fig. 3.
The technical parameters details of PV UQ center is given in
Table 1. The characteristics of other UQ solar facility is given in
Table 2. Online solar data management system record reading of
every minute for different parameters. These recorded parameters
are PV output power, humidity, air temperature, wind speed and
direction.
3.1. UQ center array PV output profile
The PV output power pattern can be analyzed using minutely
recorded time series data of a full year 2014. The PV output data
series of year 2014 contains N = 525,600 values of different param-
eters. The recorded parameters of UQ center PV array are solar
output power, humidity, air temperature, wind speed and direction
at any time instant t as given in Eq. (2).
fpt; t ¼ 1; 2; 3; . . . ; Ng ð2Þ
where N represents the number of data points. Fig. 4 depicts the
yearly PV output power profile of UQ center array. The months of
the year are on x axis and y axis denotes generated output power
in watts. A variation in generated PV power graphs can be observed
over different months of the year 2014. The generated output power
is higher in first four months of the year and lower in next months.
However, the generated output power remains at medium form
September to December 2014. There are number of factors affecting
the solar output power. It is mainly due to meteorological related
variables which are affecting the output.
The recorded 1 min data contains humidity, air temperature,
wind speed and direction for complete cycle of 24 h and have
1440 data samples. However, the solar data is available from
5 AM to 7 PM. The rest of solar data is not available in solar data
management system due to unavailability solar output. Therefore,
solar time series data contains 841 data points and rest of values
solar power output values considers zero in order to synchronize
the with meteorological data. Meteorological data contains the
1440 sample for 24 h of the day and 525,600 for full year.
A one day PV output profile of UQ center array is shown in
Fig. 5. The graph represents the 841 data samples of solar output
power from 5 AM to 7 PM. The data samples are not recorded by
PV data base management for rest of the day hours. It is due to
unavailability of solar output power for remaining hours of the
day. However, there might small amount of power generated by
PV array for rest day hours. But it is not significant PV output
Table 1
UQ center solar array specification.
Parameters Specification
Site longitude 153°000
54.800
E
Site latitude 27°290
4500
S
Height above sea level Height above sea level: 28 m
Type of installation Rooftop installation (elevated)
Tracking system No tracking system
Orientation & Tilt 110° & 3° (Lower/South Roof)
Orientation & Tilt 20° & À3° (Perimeter)
Orientation & Tilt 20° & 6° (Core)
Module technology Polycrystalline silicon
Module size 1650 Â 992 mm
Number of modules 1806
Number of inverters 32 (31 Â 12.5 and 1 Â 5000)
Fig. 3. PV center array at UQ St. Lucia campus.

power to use. It is observed that, the value of PV output power
increases significantly as time increases. Graphs shows that, the
value of PV output varies from 5 am to 7 am. However, with
increasing PV output power, large fluctuations can be observed
from 7 am to 11 am due meteorological factors. The PV output
power was increased with passage of day time. It reaches to max-
imum level during the middle of the day. The PV output power
start decreasing after 2 pm due decrease in temperature.
Fig. 6 represents the UQ center array solar profile of year 2014.
In this graph number of days on X axis, data points of on the Y axis
and magnitude of power on Z axis. As discussed earlier the solar
output data is from 5 AM to 7 PM is available and it can be
observed for PV output pattern of UQ center array is similar to
yearly plot in 2D. The PV output power varies thought the year
2014. Similar output pattern can observe from 3D PV output
profile.
Fig. 7 highlights the relative change in PV output power with air
temperature. It can be observed that, the PV output power varies
with change in air temperature.
Table 2
Characteristics of Selected UQ PV sites.
Sites Longitude Latitude Height above sea level (M) Module area (M2) Modules Inverters Nominal output (kWp)
GCI 153°000
5200
E 27°290
5100
S 27+ BH 941.2 575 9 138
LEB 153°290
4400
E 27°000
4900
S 43 612 374 7 89.76
CP1 153°000
3700
E 27°290
4200
S 23 2305 1412 26 338.9
CP2 153°000
3500
E 27°290
4200
S 23 2305 1412 26 338.9
UQC 153°000
54.800
E 27°290
4500
S 28 2956 1806 32 433.44
AEB 153°000
5300
E 27°290
5800
S 18 + BH 640 383 10 95.75
GSRFDA 152°200
14.100
E 27°330
41.500
S 88 5784 7200 – 684
UQ Centre (UQC), Sir Llew Edwards Building (LEB), Car Park 1 (CP1), Car Park 2 (CP2), Global Change Institute (GCI), Building, Advanced Engineering Building (AEB) and Gatton
Solar Research Facility Dual Axis (GSRFDA), BH = Building Height.
Yearly Solar Power Data Points
Jan. Feb. March April May June July Aug. Sep. Oct. Nov. Dec.
Power(W)
10
5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5 Solar Output Power
Higher PV Ouput Power
Medium PV Ouput Power
Lower PV Ouput Power
Fig. 4. Yearly (2014) solar output plot of minute data.
Fig. 5. Solar PV output profile of the day 01-01-2014.
Fig. 6. Solar output power profile of year 2014.
Fig. 7. The per unit curves of PV output power and air temperature.

The amount of generated power is increased with raise in air
temperature and vice versa. This indicates the correlation between
PV output power and air temperature. Some other research studies
also reported that, there is strong correlation between temperature
and PV output power (Chen et al., 2011). Therefore, Air tempera-
ture can be applied as forecast model input in order to predict
the PV output correctly.
Fig. 8 depicts the variations in PV output power with change in
wind speed, which is recorded data in solar data management sys-
tem. The wind speed plays a role in heat dissipation and as result it
leads to reduction in PV cell temperature. Therefore, PV output
power will be reduced with lower the cell temperature. Fig. 8 indi-
cates, the PV output power pattern does not follow the exactly the
wind speed pattern. In day, the PV output power is at higher level
as compare the wind speed. After that, the per unit PV output
power was reduced with increase in wind speed. However, similar
PV output power pattern with wind speed was not observed for
reset of year. Therefore, relatively a weak correlation is observed
between PV output power and wind speed in comparison of
temperature.
Figs. 9–11 show the relationship between PV output power and
solar irradiance during clear day (CD), partially cloudy (PCLD) and
cloudy day (CLD), which are selected from year 2014. It can be
observed that in clear day graph, the PV output power fairly follow
the solar irradiance curve. It can be observed that, solar irradiance
fluctuates with high ramp rate. As a results, similar pattern is
observed for PV output power profile. A similar trend is observed
during the partially cloudy day as shown in Fig. 9. The solar irradi-
ance is less than the 400 W/m2
during the major portion of day
time except to hour 10–13. The solar irradiance goes up to
1250 W/m2
during the hour 10–13 and PV output power also fol-
low the same pattern. The sharp changes in PV output power is
observed during the hour 10–13 and solar irradiance pattern is fol-
lowed by the PV output power, which indicates the strong positive
correlation among them. It can be observed from Fig. 11 that, the
solar irradiance peak goes up to maximum 400 W/m2
in cloudy
day, which is less half of clear day. Therefore, average solar PV out-
put power is quite lower than the clear and cloudy day. In addition,
higher level fluctuations in solar irradiance are observed during the
cloudy day than the clear and partially cloudy day. As a result, solar
PV output power is also variable throughout the day.
It can be concluded that from the above figures, PV output
power have very strong correlation with solar irradiation as com-
pared to air temperature and wind speed. Therefore, these influen-
tial variables are recommended as forecast model to accurately
forecast the PV output power in variable meteorological condition.
In addition, these variables add more uncertainty in PV output
power, which may create some critical issue directly or indirectly
in PV integrated power grid.
Some other meteorological related parameters are also affected
the PV output power such as air sole index, cloud cover, shading,
humidity and wind speed. The forecast accuracy PV output forecast
model may be enhanced using large number of inputs. However,
forecast model computational cost and complexity will be also
Fig. 8. The per unit curves of PV output power and wind speed.
Fig. 9. Relationship between PV output and solar radiation for clear day.
Fig. 10. Relationship between PV output and solar radiation for partially cloudy
day.
Fig. 11. Relationship between PV power and solar radiation for cloudy day.

increased due to aggregating the large number of input parame-
ters. Therefore, it is utmost important to design a forecast model
with optimal number of forecast model inputs to deal with com-
plexity issue.
4. Classification of forecast techniques
Solar forecasting methods can be classify into different cate-
gories named as persistence method, physical techniques, statisti-
cal techniques, hybrid models and some forecast methods as
shown in Fig. 12 (Soman et al., 2010). Majority of forecast tech-
niques utilized the historical meteorological data and other exoge-
nous variables as forecast model input (Pelland et al., 2013). There
is some other solar irradiance and PV output forecast, which use
satellite imaging for data acquisition (Rezk et al., 2015). These
methods are not listed in following below classification.
4.1. Persistence forecast
Persistence forecast model is useful tool to analyze the perfor-
mance of other prediction model as reference model. The main
objective of designing a complex forecast model is to achieve the
better forecast accuracy than the subsequent prediction models
with less computational cost. However, persistence model is com-
mon reference method with less computational cost and to com-
pare with other short term solar output power forecast models.
The value of PV output power at time t + 1 is highly correlated to
the value at t. The future value PV output power can be predicted
output power at t. Similarly, persistence model can also be applied
to other forecast applications.
The persistence model can be utilized as benchmark for differ-
ent forecast models. The forecast accuracy of persistence based
model is largely affected due to change in forecast horizon. It is
also varies with change in meteorological condition such as tem-
perature, irradiance, wind speed and humidity level. Therefore,
persistence based forecast model shows higher forecast error and
it is used to compare with proposed in order to analyze the perfor-
mance. In Perez et al. (2010) research study, authors proposed
forecast model is evaluated with comparison of persistence model
results.
4.2. Physical models
The popular physical model is numeric weather predictor
(NWP). This predictor is based on mathematical set of equations,
which describe physical state and dynamic motion of the atmo-
sphere. These models are based on the PV plant characteristic such
as location, orientation historical data, and meteorological vari-
ables. It is also relay on the different forecasted weather variables
such as PV system characteristics, global horizontal irradiance
(GHI), global horizontal irradiance (GHI), relative humidity, wind
speed and direction along with PV models (Lorenz et al., 2011;
Mathiesen and Kleissl, 2011; Pelland et al., 2013). The forecast per-
formance of physical model is higher, when the weather conditions
are stable (Soman et al., 2010). However, the forecast accuracy is
largely affected due to sharp changes in meteorological variables.
4.3. Statistical techniques
Statistical techniques are based on the learning process of the
forecast model with historical influential variables. The forecast
model tries to reduce the network learning error by using the dif-
ference between network predicted PV output power and actual
measured values. Therefore, statistical models are based on histor-
ical patterns. Therefore, forecast accuracy of statistical model is
depend on the length and quality of historical input data. Statistical
techniques can be further segregated into two sub groups named
as time series and artificial intelligence (AI) based forecast models.
The time series forecast models are multiple linear regressions,
support vector machines (SVM), autoregressive moving average
(ARMA), autoregressive integrated moving average (ARIMA) for
Forecast
Techniques
Persistence/
Naive method
Physical
Approach
StaƟsƟcal
Approaches
New Techniques
Hybrid
Structures
ArƟficial
Neural
network
Time Series
Numeric
Weather
PredicƟon
MM5
HIRM
LAM
GFS FNN BPNN RBF ARX ARIMA ARMA
NWP
+NN
ANFIS
NN+
T.SEns. Fuzzy WT
Fig. 12. Classification of forecast techniques.

non-stationary time-series and autoregressive (integrated) moving
average with exogenous inputs (ARIMAX), etc. (Mohamed and
Bodger, 2004; Bacher et al., 2009; Alfares and Nazeeruddin,
2002). The different tine series for forecast models are discussed
below.
4.4. Linear models or time series models
It is observed that the, time series forecasting has been applied
for different applications with higher degree of success since the
last decade. In statistical techniques, variables are used as model
input having correlation with output and predictors. Several stud-
ies has been published for time series modeling (Rodriguez, 2010).
In this research study, the comparison of time series techniques is
presented. In Kasten and Young (1989), AR model is used to inves-
tigate the forecasting performance of PV power with other predic-
tion techniques.
4.4.1. ARMA model
ARMA model is combination of two basic models which are
autoregressive (AR) and moving average (MA) model as given in
Eq. (3).
XðtÞ ¼
Xp
i¼1
aiXðt À 1Þ þ
Xq
j¼1
bYðt À jÞ ð3Þ
Eq. (3) represents the forecasted PV output as it is represented
in form of function XðtÞ. P represent the number of AR process in
the model and ai is ith AR coefficient of the forecasting model.
Where second part of the equation eðtÞ represents the jth coefficient
of MA model. Y(t) represents the white noise and it is not corre-
lated forecast model output variable (Hamilton, 1994). Auto cor-
rected time series data can be treated by Autoregressive Moving
Average (ARMA) model. ARMA is considered as good prediction
model to forecast the future values of provided time series with
stable input variables. ARMA model refer as (p, q), where p repre-
sent the order of AR model and q denotes the order of MA model.
The ability to extract the statistical properties and Box Jenkins
adoption are the main reasons to the popularity of ARMA model
(Boland, 2008). In addition, several types of time series can be
characterized by using ARMA model with set of equations of differ-
ent order. The ARMA model more suitable for stationary time ser-
ies data (Hansen, 1995).
4.4.2. ARIMA techniques
Auto-Regressive Integrated Moving Average (ARIMA) time ser-
ies model an extension to ARMA model. It is widely used for differ-
ent modeling and forecasting application with acceptable level of
forecast accuracy (Box et al., 2011). ARIMA for (p, q) for the time
ðX1X2; X3; . . .Þ can be defined as given in Eqs. (4)–(6).
UpðZÞDd
Xt ¼ UðZÞat ð4Þ
UpðZÞ ¼ 1 À /1Z À /2Z2
À Á Á Á À /pZp
ð5Þ
HqðZÞ ¼ 1 À h1Z À h2Z2
À Á Á Á À hpZq
ð6Þ
where Z is backward shift operator. Therefore, back difference oper-
ators are ZXy ¼ ZXyÀ1, D ¼ 1 À Z. Up and Hq are the polynomials of
degree p and q. As mention earlier, ARIMA is product of AR model,
integrating part I and MA model. Therefore, ARIMA (p, q, q) model is
the combination of AR (p), integrating part IðdÞ ¼ DÀd
and moving
average MA (q). In order to avoid the unbounded process, the poly-
nomials parameters such as U and H are chosen in such a way that,
the both polynomials lies outside the unit circle. The variation from
the fixed distribution with zero mean and variance ra is called
white noise. Some of the inherent features of time series can be
extracted by using backshift operator and white noise process.
The backshift operator and the white noise process describe the
intrinsic features of the time series. In addition, the adjacent obser-
vations are dependent to independent time step t of the white
noise process. In Hansen (1995), describes the working of ARIMA
(Auto-Regressive Integrated Moving Average) methods can used
as reference in prediction models domain. In research study
(Reikard, 2009), ARIMA model is used to predict the solar irradi-
ance and forecast results are compared ANN based forecast model.
The results highlights that, the ARIMA based forecast model trace
the Sharpe changes of solar irradiance pattern and produces higher
forecast accuracy than the benchmark techniques. There is poten-
tial to apply the ARIMA model stand along or hybridize with other
models for PV output power forecast.
4.4.3. CARDS model
Autoregressive (AR) and dynamical system (DS) models are
coupled together. It is used to predict to time series data called
CARDS model. This model is also used to forecast the time series
solar irradiance (Huang et al., 2013). The dynamical system equa-
tion can be derived using Lucheroni model as given in Eqs. (7)
and (8).
_R ¼ x ð7Þ
e_x ¼ kðx þ RÞ À kð3R2
x þ R3
Þ À ex À cR À b À f ð8Þ
where f is noise term and k; k; c; e; b are tunable parameters. In
above equation _R represents the derivative of R with respect to time.
Where x denotes the double derivative of R w.r.t. time as given in
Eqs. (9) and (10).
Rtþ1 ¼ Rt þ XtDt þ xt ð9Þ
Xtþ1 ¼ Xt þ kðXt þ RtÞ À k 3R2
t Xt þ R3
t

À eXt À cRt À b
h i
Ã
Dt
e
þ at ð10Þ
where Dt represents the time step change and by using ordinary
least square method other parameter can be determined such as
k; k; e; c; b. In Boland (1995), authors utilized the Fourier series tech-
niques to de-seasoned the time series data. It is due to partial
inability of autoregressive process that it cannot model it alone.
Therefore, Fourier series is subtracted to from original series in
order to get the residual series. However, at the peak reversion,
the AR model is efficient enough to capture the series peaks. In
Lucheroni (2009), first who apply resonating model on power sector
application. Therefore, a good level of fitting is achieved for residual
series by using curvature’s proxy. The CARDS model shows good
results in comparison evaluated techniques in Kostylev and
Pavlovski (2011). The results of this study highlights that, CARDS
model produce RMSE 16.5% as compared to other implemented
model with RMSE 17% in clear day and 32% in cloudy at 1 h time
step.
Number of time series techniques are applied to different fore-
casting application along with different model inputs and forecast
horizons. There is potential to utilize the other time series tech-
niques for PV output power forecast such as stochastic time series
(Chakhchoukh et al., 2011), autoregressive moving average (Chen
et al., 1995), linear regression (Amral et al., 2007), general expo-
nential technique (Christiaanse, 1971; Marín and Sandoval,
1997). Generally, statistical techniques provide higher forecast
accuracy. Majority of time techniques provides the higher forecast
accuracy, if the forecast model input pattern is smooth. However,
sharp or abrupt changes in meteorological variables such as

temperature, irradiance, wind speed and humidity leads to
increase in forecast error.
4.5. Artificial intelligence techniques
Artificial intelligence (AI) based techniques popular among the
researcher since three decades for forecast applications. Among
the AI techniques, neural network (NN) is more poplar and used
as power computational tool for different predication applications
with higher degree of success since 1980. Generally, NN models
produces higher forecast accuracy. It is due to its ability to capture
the sharp changes in the output with help of intelligent training
process of the network. An adaptive and robust NN training meth-
ods can further improve the capability of the network to learn the
complex relationship between input and output variable
(Patterson, 1998).
A number of learning techniques are designed to train the NN
effectively such gradient and population based techniques. NN
model tries to predict the future output pattern using the different
set of input data. The forecast accuracy of the model is calculated
with real time data and predicted values. The forecast accuracy
of model can be further enhanced by carefully selecting the differ-
ent influential parameters. These parameters are the normalized
and suitable number of forecast model inputs, appropriate training
algorithm, optimized network structure, appropriate learning algo-
rithm, suitable training data and optimized network structure may
increase the overall performance of network and reduce the com-
plexity (Ho et al., 1992). The primary steps ANN based load forecast
model are provided in Fig. 13.
Input selection of PV output forecast model is one of most crit-
ical part in the design process. The forecast accuracy varies with
change in type and number of model inputs. It is due to large
dependence of PV output power on meteorological variables. Sec-
ondly, the real time meteorological and PV output recorded data
is used to train the forecast model and compare the model perfor-
mance. This data may contains several missing data points, sharp
peaks and variations. Therefore, input preprocessing technique is
need to be apply on data for smoothing before applying the data
as forecast model input. After that, the historical PV output power
data is divided in two groups named as training and testing data.
The training data of forecast model is used for learning of the net-
work to forecast the future values. Testing data is used to analyze
the performance of forecast model by comparing the actual and
predicted values. After that, neural network is initialized with dif-
ferent layers based on the type and complexity of the problem. The
network is trained using training data, which is applied as forecast
model inputs. A post processing techniques can be used before cal-
culating and analyzing the performance of prediction model.
4.6. Significance of ANN approach
Artificial Neural network based model has better capability to
map the input as model output without formulating the complex
relationship between input and output (Fausett, 2006). McCulloh
and Pitts conduct a research to model the nets based bio-system
for simple logical operation in 1942 (McCulloch and Pitts, 1943).
They attempt to model the simplest form of nonlinear model of a
neurons. This research come up with new world of computational
calculations. ANN models are robust in nature due to dynamically
respond to rapid changes with help of interconnected neurons and
learning methods. Several neural network learning techniques of
NN are available with different computational complexity and con-
vergence rate for global optimum solution. The computational
complexity of the network, convergence rate and training time
can be reduced by optimizing the different parameters (Shekhar
and Amin, 1992). These parameters are correlated forecast model
inputs, preprocessed training data of the network, optimal NN
structure and robust NN training techniques, etc. ANN based mod-
els have been implemented on several fields of life such as aero-
space, Bio-medical, research and development of socio economic
applications, automotive industry, electronics industry, stock mar-
ket and finance industry (Lai, 1998).
4.6.1. Artificial neural network
In the last decade, ANN models are utilized as power full tool for
different real life and computational applications. ANN have ability
to draw complex relationship between input and output using
learning mechanism of the network. Through learning algorithm
of neural network, ANN model can map the complex input output
relationship by using feedback error system. ANN based models
are robust and adaptive in nature and performed well up to certain
level even under the noisy environment. The summary of early
stages developments of ANN model are given below in Table 3.
4.6.2. Artificial neural network architecture
The artificial neural network (ANN) is network of connected
artificial neurons in different layers such as input, hidden and out-
put layers. The basic artificial neural network as shown in Fig. 14.
The neurons are connected in different layers with synaptic
weights values. The learning algorithm of neural network tries to
map the input and output relationship by updating the synaptic
weights values. The network generated output is compared with
desired output and then error is calculated. Therefore, the weights
and biases values of NN are updated based on the error. The acti-
vation function is applied to weighted input for output of the
network.
This cycle will continue until the desired output achieved.
The weighted sum of inputs can express in the form mathemat-
ical relationship as given below:
Ai ¼ g
Xn
i¼0
Wij Ã ai
!
ð11Þ
where Ai; Wij and aj are network output, connection weight of Ith
neuron to Jth layer neuron and network input respectively. A neural
network may have multiple inputs and single output. There are two
basic operation of neural network such as training and testing. At
training stage network is trained using learning the algorithm to
learn the basic relationship between input and output. The network
output is compared with desired output at testing stage. The output
Selection Of Forecast Model Inputs
Pre-processing of Input Data for
Forecast Models
Split Data Into Testing And Training
Sets
Initialize and Train ANN Model
Post-processing of Output Data
Calculate And Compare Forecast Error
Of Different Models
Fig. 13. Neural network based forecast model steps.

of the network varies with change in activation function, architec-
ture and inputs of neural network. Different types of activation
functions are discussed in next section.
4.6.3. Activation function
The output of the network is generated by using activation
function by summing of weighted inputs. Therefore, activation
function of network acts as squeezing function to transfer the input
in the form of output. Different activation functions are available
for neural network and output of the network also varies with
change of activation function (Zhang et al., 2007). There are num-
ber of transfer functions are available such as Gaussian radial basis,
uni and bipolar polar step function, linear function and sigmoid
function respectively. Table 4 summaries the different types of
activation function along with derivative and diagrams. There are
hard and fast rules for transfer function selection. The activation
function of neural network can be selected based on nature of
application (Mellit and Kalogirou, 2008).
4.6.4. Multi layer perceptrons neural network
A number of complex problems from different research
domains, which cannot be solved by using single layer neural net-
work. It is due to complex input and output relationship between
different variables. Multilayer perceptron’s neural network
(MLPNN) have the ability to map the input output relationship
using proper training of network. There are one or more than hid-
den layers between input and output layer of the network. These
layers are connected with each other. The multilayer perceptrons
neural network (MLPNN) was for different forecast applications
such as load and electricity price forecasting (STLF) (Tasre et al.,
2011; Raza et al., 2014). A typical MLPNN architecture for PV fore-
cast is represent in Fig. 15.
4.6.5. Radial basis function network (RBFNN)
The radial basis function neural network (RBFNN) is considered
as two-layer neural network. The learning process of RBFNN can be
divided in two different stages (Madan et al., 2003; Jain and Martin,
1998). The first and second layer of the network can be differenti-
ate on the basis of synaptic weights. The first layer synaptic
weights can be determined by using input data set. The weight val-
ues of input layer are fixed at first stage and the second layer
weights are determined. The RBFNN network is trained using
unsupervised learning method as only input data is provided to
the network. The supervised learning method is utilized for second
layer weights determination. Classic least mean squares is used for
optimization. The basic form RBFNN mapping is given in Eq. (11).
The RBFNN architecture is shown in Fig. 16.
YkðxÞ ¼
XM
j¼1
Wkj/jðxÞ þ Wko ð12Þ
4.6.6. Recurrent neural network
Recurrent neural network (RNN) demonstrate the higher capa-
bility to learn different complex relationships and computational
structures. A real-time recurrent learning network (RTRL) contains
input layers, processing layers (feed forward and connections lay-
ers) and some additional node elements. The successful application
of RNN model is discussed comprehensively in Hertz et al. (1991).
In Elman (1990), authors proposed RNN architecture with feedback
back loop. It is taken from hidden layer of the network to input
layer. However, another research studies the proposed the feed-
back from output layer to input layer of the network (Jordan,
1997). These feedback loops are used to minimize the network
learning error using training process.
In fully connected recurrent neural network (RNN) every pro-
cessing node is connected with other processing node and with
itself as well. Therefore, the output of RNN at any time is depends
on the two parameters, which are feedback signal at previous time
step and input signals. In Williams and Zipser (1989), authors ana-
lyze and perform experiments on the learning of real time of RNN.
The network was trained in every processing cycle. The activation
function of the network is weighted sum of feedback and current
input signals. Therefore, the activation function is given in Eq. (13).
Fig. 14. Basic ANN architecture (Khotanzad et al., 2002).
Table 3
Summary of major ANN developments.
Number Year Authors References ANN developments
1 1942 McCulloch Pitts McCulloch and Pitts (1943) Proposed the concept of first artificial neurons
2 1946 Hebb Pitts Morris (1999) Proposed first learning algorithm to memorize the adapting weight values
3 1958 Rosenblatt Rosenblatt (1962) Developed a first form of artificial network with Perceptron
4 1959 Lee Nilsson (1965) Proposed the Artron
5 1960 Widrow and Hoff Widrow and Hoff (1960) Proposed LMS training method and Adaline (Adaptive Linear Neuron)
6 1982 Hopfield Hopfield (1982) Design Hopfield neural network
7 1988 Widrow and Winter Widrow and Winter (1988) Design a network using Adeline neurons which is called Madaline
8 1988 Rumelhart et al. Widrow and Winter (1988) Proposed multilayer perceptron base neural network with backpropagation algorithm
9 1987 Hecht-Nielsen Hecht-Nielsen (1987) Proposed the concept of self-organizing mapping using counter propagation network
10 1988 Chua Yang Chua and Yang (1988) Design cellular neural network

SkðtÞ ¼
Xpþ1
p¼1
ðWikXpðtÞÞ
Xq
q¼1
ðVkqYqðtÞÞ ð13Þ
where SkðtÞ is activation function at the time of processing node k
and Vkq is the connection weight of the node q which is connected
with node k. Wpþ1 is the value of the bias. The output of node k is
given below in Eq. (14).
Ykðt ¼ 1Þ ¼ fkðSkðtÞÞ ð14Þ
where f is sigmoid activation function. The Recurrent neural net-
work (RNN) architecture is shown in Fig. 17.
4.6.7. Feed forward neural network
Feed forward neural network (FFNN) is relatively less complex
NN architecture. In FNN, the information moves from input to out-
put layer in forward direction. Network can be single layer or
multi-layer but information moves only on one direction. There
is no feedback loop or cycle for information to process. In feed for-
ward neural network, the information reach at output layer
through input and hidden layer of the network. Fig. 18 highlight
the neural network having input, hidden and output layer with 3,
2, 3 neurons respectively. Feed forward neural network was also
applied for several forecasting and pattern recognition application
(Ahmad et al., 2009; Malki et al., 2004).
Table 4
Artiﬁcial neural network transfer functions.
Class Function Derivative Diagram
Unipolar step function
fðxÞ ¼ HðxÞ ¼
1 if; x 0
0 if; x 0

dðxÞ ¼
1 if; x – 0
1 if; x ¼ 0

Bipolar step function fðxÞ ¼ sinðxÞ ¼ 2HðxÞ À 1
dðxÞ ¼
1 if; x – 0
1 if; x ¼ 0

Unipolar linear function
fðxÞ ¼ HðxÞ ¼
0 if x À1
1=2ðx þ 1Þ if jxj 1
1 if x 1
8

:
dðxÞ ¼ 1=2½Hðx þ 1Þ À Hðx À 1ÞŠ
Bipolar linear function
fðxÞ ¼ HðxÞ ¼
1 if x À1
y if jxj 1
1 if x 1
8

:
dðxÞ ¼ ½Hðx þ 1Þ À Hðx À 1ÞŠ
Unipolar sigmoid function fðxÞ ¼ ð1=1 þ eÀx
Þ dðxÞ ¼ f ðxÞð1 þ fðxÞÞ
Bipolar sigmoid(hyperbolic tangent) fðxÞ ¼ tanhðxÞ dðxÞ ¼ ð1 þ jfðxÞ2
jÞ
Gaussian radial basis fðxÞ ¼ exp Àkx À mk2
=r2

À2ðx À mÞfðxÞ=r2

4.6.8. Feedback neural network
Feedback neural network allows the information to move one
layer to previous layer by using feedback system. The output of
network inﬂuences the input as the output information feed into
the network. The feedback information is the error function, which
can be calculated by using desire and network output. The network
tries to achieve the desire level by back propagating the network
error. Feedback neural network is dynamic in nature as the error
function feedback to network and network tries to achieve the
equilibrium state. It is reported that, feedback neural network is
suitable for dynamic, complex and time lagged pattern recognition
problem (Hahn et al., 2009). A feedback neural network having 3
input, 2 hidden and 3 output layers neurons shows in Fig. 19.
The systematic and comprehensive literature review of
reported solar PV output power and irradiance techniques are pro-
vided in three tables. Majority of the forecast techniques have
potential to apply on other predictions problems. However, fore-
cast accuracy may vary due to different performance affecting
parameters. The forecast literature is segregated based on the fore-
cast horizon. The twenty-four hours or one day ahead forecast
methods are provided in Table 5. Tables 6 and 7 describe the fore-
casting techniques for 1 min to less one day ahead and more than
one day ahead forecast respectively. This table provides the author
details, year of publication, and name of the country (where PV
plant is installed and real time PV output data used as model
inputs). In addition, it also provides the forecast horizon, forecast
error, forecast method and benchmark techniques. Several data
basis have been studied for literature such Elsevier, IEEE, Hindawi,
Taylor Francis and Springer using different search engines.
4.7. ANN and classical time series models comparison
In Reikard (2009) and Sfetsos and Coonick (2000), the compar-
ison of artiﬁcial neural network and time series is investigated
under different scenarios. Both research studies suggest that, the
error of advance regression model is reduced by the factor of
0.6–0.8 to comparison of simple regression techniques. In
1
2
3
4
38
1
2
20
1
1
2
3
4
8
Input
Layer
Hidden
Layer
Output
Layer
Neural Network
ArchitectureHistorical PV
Output Data
Temperature
Humidity
Wind Speed
Cloud Cover
PV
Forecast
Fig. 15. Multilayer perceptron neural network.
Fig. 16. Radial basis function network (RBFNN) architecture (Rivas et al., 2004).
Fig. 17. Recurrent neural network (RNN) architecture (Smith and Jin, 2014).
Fig. 18. Feed forward NN structure.
Fig. 19. Feed back NN structure.

Table 5
A review of one day ahead solar and PV output power forecasting techniques.
Ref. Year Country of
PV data set
Journal/conference Forecast horizon Forecast error Forecast model Comments
Chen et al. (2011) 2011 China Solar Energy 24 h ahead MAPE 9.28% Self-organizing map (SOM)
trained ANN model
The performance of different test case studies on sunny, cloudy day and
rainy day. However, forecast model performance varies with day type
Ding et al. (2011) 2011 Ashland,
USA
Procedia
Environmental
Sciences
24 Hours ahead MAPE 10.06% Artificial Neural Network (ANN) Backpropagation learning algorithm based ANN is used to forecast the 24 h
PV output
Cococcioni et al.
(2011)
2011 Italy IEEE conference 24 h ahead MAPE 5% Artificial neural networks (ANN) Time-series analysis model NARX with feedforward neural network is used
to predict 24 h PV output with varying number of hidden layer, number of
neurons and training window
Kang et al. (2011) 2011 Korea IEEE conference 24 h ahead Approximately
MAPE 11%
k-means clustering method K means clustering technique is used at first stage and five years historical
data was analyzed to classify them based on cloudiness
Mori and Takahashi
(2012)
2012 Japan IEEE conference 24 h ahead Error 0.228 pu
[error is
quantized in
standard method]
Generalized Radial Basis
Function Network (GRBFN)
based Neural Netwrok
Generalized Radial Basis Function Network (GRBFN), Deterministic
Annealing (DA), and Evolutionary Particle Swarm Optimization (EPSO)
Haque et al. (2013) 2013 USA IEEE conference Seasonal one day
ahead
MAPE 12.11% Wavelet transform (WT) and
fuzzy ARTMAP (FA)
Wavelet transform (WT) is used to remove the unexpected spiks and sharp
changes in input data. Furthermore, fuzzy ARTMAP (FA) was employed to
forecast the PV output
De Giorgi et al.
(2014)
2014 Italy IET Journal 1–24 h ahead NAME 6.50% Multi regression analysis and the
Elmann artificial neural network
(ANN)
Multiple regression analysis have be employed and Elman artificial neural
network (ANN) model is used to predict the load demand
Sansa et al. (2014) 2014 Barcelona,
Spain
IEEE conference 24 h ahead Error 0.027 pu Artificial Neural Networks (ANN) Nonlinear Auto Regressive models with neural network was used. However,
the forecast model performance varies over the different forecast horizons
B.M. Shah et al.
(2015)
2014 China Signal Processing
for
Communications
24 h ahead 9.13–9.30 BP (Back Propagation) neural
network (NN)
A combination of particle swarm optimization and Back Propagation based
neural network was used to predict the PV output
Yang et al. (2014) 2014 Taiwan IEEE Transactions
On Sustainable
Energy
24 h ahead MRE 3.295% Self-organizing map (SOM) and
learning vector quantization
(LVQ)
Self-organizing map (SOM) and learning vector quantization (LVQ)
techniques used for classification of historical data and support vector
regression (SVR) was used for train Fuzzy inference system
Tao and Chen (2014) 2014 China IEEE conference 24 h ahead Error 8% Genetic Algorithm based neural
network
The proposed Genetic Algorithm (GA) based PV forecast model results
compared with back propagation NN based forecast model
Junior et al. (2014) 2014 Hokkaido,
Japan
Energy Procedia 24 h ahead Minimum RMSE
2.4%
Principal Component Analysis Principal Component Analysis (PCS) technique gives lower forecast error
than without PCA model
Ramsami and Oree
(2015)
2015 USA Energy Conversion
and Management
24 h ahead RMSE 2.74% Generalized regression neural
network, feedforward Neural
network and multiple linear
regression
Stepwise regression model use to select the input and hybrid model of
Generalized regression neural network, feedforward neural network and
multiple linear regression
Liu et al. (2015) 2015 China IEEE Transactions
On Sustainable
Energy
24 h ahead MAPE 7.65% Back propagation (BP) based
ANN model
Aerosol index (AI) was used along seasonal classification and back
propagation (BP) based ANN model for cloudy day forecast
Leva et al. 2015 Italy Mathematics and
Computers in
Simulation
24 Hours ahead NAME 11% Artificial Neural Network (ANN) ANN based model is applied to analyze the performance during sunny,
partially cloudy and cloudy day
Zhang et al. (2015) 2015 USA Solar Energy 1 h and 1 day
ahead
Minimum RMSE
0.995%
Ramp forecasting method Uniform forecasting method without ramp, ramp forecast and ramp
forecasting threshold changes
B.M. Shah et al.
(2015)
2015 Japan IEEE Transactions
On Sustainable
Energy
24 h ahead RMSE 2.74% Grid Point Value (GPV) Grid Point Value (GPV) was employed to forecast the cloudy/rainy/snowy
days
Dolara et al. (2015) 2015 Italy Solar Energy 24 h NAME and WAME
between 0.5% and
10%
Physical model There Physical models are designed for desi monocrystalline and
polycrystalline PV panels
138M.Q.Razaetal./SolarEnergy136(2016)125–144

Table 6
A review of one minute to day ahead solar and PV output power forecasting techniques.
Ref. Year Country of
PV data set
Journal/conference Forecast horizon Forecast error Forecast model Comments
Chupong and Plangklang
(2011)
2011 Thailand Energy Procedia 11 h MAPE 16.83% Elman neural network The proposed Elman neural network based forecast model
than Recurrent Neural Network based model
Pedro and Coimbra (2012) 2012 California,
USA
Solar Energy 1 and 2 h-ahead 35.1%
Improvement in
forecast results
Auto-Regressive Integrated Moving
Average (ARIMA), and ANN Genetic
Algorithm (GAs/ANN)
GA optimized Artificial Neural Networks (ANNs) outperform
than the other forecast models
Mandal et al. (2012) 2012 USA Procedia
Computer Science
1 h ahead MAPE from
2.38% to 4.08%
Wavelet transform (WT) and artificial
intelligence (AI)
Radial basis function neural network (EBFNN) forecast model
is used with wavelet transform was tested for spring,
summer, winter and autumn’s sunny and cloudy day
Lonij et al. (2013) 2013 USA Solar Energy 30–90 min RMSE
improvement
23%
Persistence model Forecast results show that, the prediction performance
increased by numerical weather Model
Marquez and Coimbra
(2013)
2013 USA Solar Energy 30, 60, 90, 120 min RMSE 2.95% Artificial neural network (ANN) ANN model inputs are satellite image analysis including
velocimetry and cloud indexing to enhance the forecast
accuracy
Kaur et al. (2013) 2013 USA Energy Conversion
and Management
15 min and 1 h Error 9% and 3%s Persistence, machine learning and
regression-based forecasting models
Forecast results show that, the auto regression is best suited
model for 1 h ahead forecast. Furthermore, the forecast
accuracy decreases with decrement forecast horizon from 1 h
to 15 min
Tuyishimire et al. (2013) 2013 USA IEEE conference 15 min to 12 h
ahead
Not available Kalman Predictor Two methods was designed to forecast the PV generation
Yona et al. (2013) 2013 Japan IEEE Transactions
On Sustainable
Energy
1 h ahead Max. RMSE
1.68%
Fuzzy theory and Neural Network Fuzzy theory was used for insulation and better training of
neural network
Yang et al. (2014) 2014 Taiwan IEEE transactions
on sustainable
energy
1 day ahead MRE 3.295% Self-organizing map (SOM) and learning
vector quantization (LVQ)
Self-organizing map (SOM) and learning vector quantization
(LVQ) techniques used for classification of historical data and
support vector regression (SVR) was used for train Fuzzy
inference system
Gohari et al. (2014) 2014 San Diego,
USA
Energy Procedia 10 min and more
than 10 min
0.70 and 0.82 San Diego Sky Imager (USI) San Diego Sky Imager (USI) compared with Total Sky Imager
(TSI) based forecast model and USI model demonstrate better
results
Yang et al. (2015) 2015 USA IEEE transactions
on sustainable
energy
1–2 h ahead Min MAE 145.6
for 2 h ahead
forecast
Spatial and temporal correlations Proposed spatial and temporal Correlation model along BPNN
is used to forecast the PV output and compare with
persistence model
Almeida et al. (2015) 2015 Northern
Spain
(latitude
42.2)
Solar Energy Up to 15 min MBE 1.3% Non-parametric model Non-Parametric forecast model use Numerical Weather
Prediction (NWP) model and spatial and temporal as input
Zagouras et al. (2015) 2015 California,
USA
Renewable Energy 1 h and 3 h hours
ahead
MAPE 8.458–
40.419%
Linear models, Artificial Neural
Networks, Support Vector Regression
Global optimization based linear model outperform than the
other benchmark models
Chu et al. (2015) 2015 USA Solar Energy 5, 10 and 15 min
ahead
Minimum MAE
21.02%
Artificial neural network (ANN) with GA
optimization
Genetic algorithm optimized ANN outperform than the other
3 models
Mori and Takahashi
(2012)
2015 Évora,
Portugal
Electrical Power
and Energy
Systems
6 Hours ahead MAPE 8–12% Vector auto regression framework Adoption of multivariate (spatial–temporal) model with
vector auto regression framework enhance the forecasting
accuracy. However, the forecast accuracy may increase by
using better data mining and optimization techniques
Lipperheide et al. (2015) 2015 USA Solar Energy Few Minutes RMSE 3.2% Endogenous method Proposed model shows better forecast results than
Persistence and ramp persistence including other benchmark
models
M.Q.Razaetal./SolarEnergy136(2016)125–144139

Reikard (2009), the comparison of different models are provided
such as UCMA model, ARIMA, UCM model, a transfer function
model, hybrid model and neural network based model. The perfor-
mance comparison analysis highlights that, ARIMA model gives
better results over the 60, 30 and 15 min window. However, other
studies reports that neural network based model outperform than
other comparative models (Mueller et al., 2004). It is reported that,
there is potential to improve forecast accuracy using robust fore-
cast techniques as PV (Reikard, 2009). It can be conclude that from
time series forecast techniques, it provides higher forecast accu-
racy under relatively smooth meteorological conditions. However,
the forecast error is increased under uncertain and sharp meteoro-
logical changes. NN models also not fully generalize over input
data of model inputs. Therefore, there is potential to apply the
hybrid techniques for PV output power forecast for precise
forecast.
4.8. Hybrid models for PV output forecast
Hybrid models are designed with the combination of two or
more techniques having superior attributes. It is reported that,
the hybridization of two or more techniques show better results
than the stand alone technique for forecasting problem. One of
main motivation of hybrid system is to explore the possibilities
of different algorithm combinations in order to enhance the fore-
cast accuracy. Hybrid models can produce better forecast results
by taking the advantage of each technique. Hybrid models were
used for several forecasting applications in order to achieve the
higher forecast accuracy. Another motivation hybrid system of
reduce the computational complexity and time for online forecast-
ing application. Therefore, forecast output can be used for real time
energy management and other applications.
Some of the research studies have been reported that, the
hybrid models are effective for different forecast application such
as global horizontal irradiance, solar irradiance and electrical load
forecasting. In Sfetsos and Coonick (2000), authors proposed a
hybrid forecast model for mean global horizontal irradiance
(GHI) forecasting using artificial-intelligence techniques, tradi-
tional linear stochastic methods and adaptive neuro-fuzzy infer-
ence technique. The proposed hybrid forecast model gives higher
forecast accuracy than the comparative single forecast models.
Another research studies (Mellit and Kalogirou, 2008), proposed
a hybrid forecast model for GHI prediction using artificial neural
network and Markov transition matrices method. In Chaabene
and Ben Ammar (2008) develop a neuro fuzzy estimator based
medium term dynamic forecast model for ambient temperature
and irradiance with meteorological parameters. In addition,
stochastic models and Kalman filtering based 5 min ahead short
term was employed for meteorological parameters.
In another research study investigate the performance of differ-
ent forecast models such as unobserved components models,
regressions in lags, ARIMA, neural networks and hybrid models
(Reikard, 2009; Photovoltaics, 2012; Baharudin et al., 2014). The
finding of this study highlights that, hybrid prediction model out-
performs the comparative forecast models in some of the case
studies. In addition, hybrid model provides better forecast than
the single forecast in different case studies. In Martín et al.
(2010), authors design a forecast model using hybrid model ARMA
and TDNN technique for hourly solar radiation forecast.
In Ji and Chee (2011), authors designed a forecast model for
hourly solar radiation series prediction model. The proposed was
developed in two phases. In first phase, non-stationary trend lying
in the solar radiation series was removed using preprocessing tech-
nique. In second phase, ARMA based forecast model was used to
predict stationary residual series with a time delayed neural net-
work. The proposed hybrid model gives higher forecast accuracy
Table7
AreviewofmorethanonedayaheadsolarandPVoutputpowerforecastingtechniques.
Ref.YearCountryof
PVdataset
Journal/conferenceForecasthorizonForecast
error
ForecastmodelComments
Paolietal.(2010)2010FranceSolarEnergySeasonal
forecast
4monthsahead
nRMSE2%Artificialneuralnetwork
(ANN)
ANNbasedmodelprovideslowerforecasterrorbyusingpre-processingtechniques
Huangetal.(2010)2010ChinaIEEEconferenceOneweekaheadnRMSE10%
and13%
NeuralNetworkand
statisticalmethod
Solarirradiance,Airtemperature,cloud,humidityandsunpositionisusedforboth
forecastmodels.However,theforecastaccuracyofbothmodelareclosetoeachother
Shietal.(2012)2012ChinaIEEEtransactionson
industryapplications
120and160h
aheadforecast
MRE8.64%Weatherclassificationand
supportvectormachines
(SVM)
Historicalpowerandweatherdataisappliedtosupportvectormachines(SVM)model
topredictthePVoutputpowerforsunny,foggy,rainyandcloudyday

than the comparative forecast model. In Voyant et al. (2011),
hybrid forecast model was proposed by using optimized MLP net-
work architecture. The exogenous and meteorological variable are
applied as model input. Hybrid forecast models were also utilized
for electrical load forecasting in order to enhance the prediction
performance. In Raza and Khosravi (2015) and Raza and
Baharudin (2012) provide the detailed analysis of hybrid models
for electrical load forecast. These hybrids forecast models have a
potential to apply on PV output forecasting. There are several
hybrid techniques reported for load forecasting as given below.
ANN with genetic Algorithms
ANN with wavelet and time series
ANN with fuzzy and genetic algorithm
ANN with Gradient Based Learning Techniques
ANN with expert system and regression technique
ANN with support vector machine and artificial immune system
Some hybrid models are also applied to solar output load fore-
cast in order to improve the accuracy of the model over the spec-
trum of forecast horizon. In Hernández et al. (2012), authors
designed a hybrid model which is based on weather classification
method and support vector machine. Different days are classified
into clear sky, cloudy day, foggy day, and rainy day. Therefore, sup-
port vector machine based forecast model was designed to predict
the 24 h ahead load forecast. In Yona et al. (2013), authors purpose
a 24 h ahead PV output power forecasting model using fuzzy the-
ory and neural networks (NN). Therefore, NN based forecast model
is trained using power output data of fuzzy system and meteoro-
logical variables. In Yang et al. (2014) authors designed a hybrid
model using fuzzy system, self-organizing map (SOM), Support
vector machine (SVM) and learning vector quantization (LVQ) to
forecast the PV output power. Therefore, self-organizing map
(SOM) and learning vector quantization (LVQ) used for classifica-
tion of PV output data. Support vector regression (SVM) used to
train the model and fuzzy inference system is used to select the
better trained forecast model for higher accuracy. Therefore, there
is need to design hybrid models using superior attributes of two or
more model will provide opportunity to enhance the forecast accu-
racy over the spectrum of forecast horizon for different geological
PV sites.
In literature, several techniques have been applied for wind
power forecast, load demand and price forecast in power and
energy systems. There is potential to apply these techniques for
PV output power forecast to increase accuracy over the spectrum
of horizon. However, the meteorological factors such as humidity,
wind speed, air temperature, cloud cover, global solar irradiance,
direct normal irradiance (DNI), and diffuse horizontal irradiance
(DHI) at solar panels add more uncertainty in PV output power.
In addition, physical characteristics of solar plant, solar technology
and other exogenous also affect the output power. Therefore, fore-
cast performance of prediction models applied on above mention
application may produce lower forecast results as compared other
application. It is difficult to declare that, a single class of prediction
model will suitable for PV output forecast problem. In reference
Yang et al. (2014) days are classified in groups due to variable out-
put power named as sunny and cloudy day, sunny day, cloudy day,
cloudy and sunny day, and rainy day, cloudy and rainy day.
Authors designed six sub models with the combination of self-
organizing map (SOM), learning vector quantization (LVQ) and
support vector regression (SVR). In Haque et al. (2013) forecasted
days are divided into three groups based on solar irradiation
named as sunny day (SD), cloudy day (CD) and rainy day (RD).
There is possibility to design a multiple sub models to forecast
the PV output power with higher accuracy. In previously reported
research, hybrid model based on the combination of two or more
models tries to forecast PV output power accurately. Due to bad
performance single model in hybrid architecture may leads may
to higher forecast error. Therefore, there is a need to design model,
in which each predictor doesn’t affect the performance of each
other. It is reported that, the multi predictor based forecast frame-
work organized in ensemble network and combined the output of
each predictor in intelligent way can enhance the overall forecast
output (Li et al., 2011). In conclusion, there is potential to apply
the ensemble based forecast framework to accurately predict to
PV output power.
5. Discussion
A major challenge for higher penetration (20%) of solar energy
in the grid’s ability to manage with the intrinsic variability of solar
renewable source. Therefore, accurate PV output power forecast
will assist design efficient control to deal with variability. To accu-
rately forecast the PV output power, availability of sufficient his-
torical training data and meteorological variables are very
important. Several models were developed, which use the histori-
cal PV output data to train the model for accurate prediction i.e.
neural network and fuzzy logic. However, the performance of these
forecast models is affected due to high PV output power ramp rate.
This due to uncertain meteorological condition, Sharpe changes in
solar irradiances and cloud cover. In literature, research studies
highlight that cloud cover affect the PV output power and this
makes forecasting task more challenging. Several research studies
classified days into different categories to mitigate the impact of
cloud cover on PV output power forecast. In Yang et al. (2014),
author design a methodology by classifying the days using self-
organizing map NNs. After that, Radial Basis Function NN (RBFNN)
is used to predict the 24 ahead PV output power. In Chen et al.
(2011), days are divided into four classes named as cloudy, clear-
sky, foggy and rainy. Separate forecast model based on support
vector machine is used to predict the PV output power during each
class of days. In another research study, a hybrid technique was
proposed with combination of NN and fuzzy logic. At first, fuzzy
model was applied to estimate hourly insolation using clouds,
humidity and temperature. Then recurrent NN applied to forecast
the hourly PV output power. In literature, serval techniques were
designed to forecast PV output power during the cloudy days. As
mention earlier, some of research designed sub models or multi
model based approaches to forecast the cloudy days. However, it
is observed that, the forecast error relatively higher than for cloudy
days than the sunny days. This indicates the inability of prediction
models not to fully capture PV output power pattern. For example,
if training data of neural network based forecast model doesn’t
contain sufficient data samples of cloudy day then, it leads to
higher prediction error. In addition, persistence model will also
higher error if historical pattern doesn’t contain similar PV output
power due to high ramp rate of solar irradiation and cloud cover.
Some research studies also design the experimental photovoltaic
solar radiation monitoring system, which could helpful for accu-
rate PV output power forecast.
6. Forecast model performance evaluations matrix
Generally, the steady power output is generated by the power
generation sources in a stable power grid condition. However, with
the variation of power demand it is also affect the power output. It
leads to unbalance in demand and supply (Marquez and Coimbra,
2013; Energy, 2010). On the other side, the large variation in PV
output is observed as several factors are affecting on the output
such as solar irradiance, temperature, wind speed and humidity.
A research study in Hoff et al. (2013) suggests that, accurate PV

output forecast for different forecast horizon is required for higher
penetration of solar plants, which is able facilitate grid, ISOs and to
achieve high grid stability.
As discussed earlier, output of PV unit is largely dependent on
the solar irradiance. In addition, a variation in solar irradiance
can be observed as it is fundamentally dependent several factors
such as time of the day and year, climatic conditions, geographic
location and elevation techniques. In order to measure the quality
of forecasted data, correlation coefficient is measured which mea-
sure the error variance to the variance of modeled data as given in
Eq. (15).
R2
¼ 1 À
varðZ À 1Þ
varðZÞ

ð15Þ
Different parameters are used to analyze and compare the fore-
cast model accuracy. Some of these parameters are discussed in
this study.
The absolute of value of the error is called Mean Absolute Error
(MAE) which be measured by using given in Eq. (16).
MAE ¼
1
N
XN
t¼1
jZt À Zj ð16Þ
where Zt is forecasted and Z is actual PV output power. A similar
notation is used later equations for forecasted and actual value.
The Mean Absolute Percentage Error (MAPE) can be calculated by
using this formula in Eq. (17).
MAPE ¼
100%
N
XN
t¼1
Zt À Z
Z

ð17Þ
The Average spread and average bias of error can be measured
by using Root mean square error (RMSE) and Mean Bias Error for-
mula as given in Eqs. (18) and (19) respectively.
RMSE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N
XN
t¼1
ðZt À ZtÞ2
r
ð18Þ
MBE ¼
1
N
XN
t¼1
ðZt À ZtÞ ð19Þ
Correction coefficient can be calculated according to Eq. (20).
qx;y ¼
Covðx; yÞ
rðxÞrðyÞ
ð20Þ
where Cov is covariance and r indicates the standard deviation.
Statistical distributions observation ability of a model is known as
Kolmogorov Smirnov Integral (KSI) (Hoyer-Klick et al., 2009;
Espinar et al., 2009). KSI can calculated as given in Eq. (21).
KSI ¼
Z Ymax
Ymin
Dndy ð21Þ
The cumulative distribution function difference can be repre-
sented by Dn. In addition, Trapezoidal integration can used for dis-
crete value of Dn. Frequency distribution reproduction can be
provided by using KSI (Hoff et al., 2013; Hansen, 1995). In Perez
et al. (2011), also utilized KSI method to analyze the performance.
A research study (Hoff et al., 2013) reports that, better relative dis-
persion error can be measured by using normalized Mean Absolute
Error by using Eq. (22).
MAE=Avg ¼
1
N
PN
t¼1jZt À Ztj
1
N
PN
t¼1Zt
ð22Þ
This above mentioned research study also suggests that the nor-
malization of forecast RMSE over the maximum nominal irradiance
cane calculated as provided in Eqs. (23) and (24).
RMSE=Capacity ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N
PN
t¼1ðZt À ZtÞ2
q
C
ð23Þ
RMSE=Capacity ¼
1
C
ffiffiffiffi
N
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N
XN
t¼1
ðZt À ZtÞ2
r
ð24Þ
7. Conclusions and future work
In this paper global solar PV status and potential has been ana-
lyzed to meet the current global energy requirements. In the last
decade, large pentation of PV was observed due to tremendous
potential of solar energy in the different regions of the world in
terms of rooftop PV, large, medium and small scale solar plants.
However, solar PV energy is can create different issues for modern
power systems directly or indirectly due to uncertain and intermit-
tent nature. Therefore, it is utmost important to accurately forecast
the PV output power.
This study provides systematic and comprehensive literature of
different solar forecasting technique. In addition, the factors affect-
ing on solar output were identified, which could be applied as fore-
cast model inputs for higher accuracy. Literature indicates that, a
certain level of forecast accuracy can be achieved by applying dif-
ferent stand alone and hybrid models for PV output forecast appli-
cation. It is identified that, solar irradiance, temperature, wind
speed and direction, humidity cloud cover and aerosol index are
major parameters to change of PV output power. It is also con-
cluded that, solar irradiance is highly correlated with PV output
power and follows the similar pattern. Therefore, the forecast accu-
racy of prediction models can be enhanced by optimizing and bet-
ter selection of these correlated variables.
Several attempts have been made to precisely forecast the out-
put power using different techniques in past few years. Among
these techniques, regressive methods take the advantage of corre-
lated nature of meteorological variables, which are used prediction
model as inputs. It is concluded that, endogenous stochastic meth-
ods such as AR, MA, ARMA and/or ARIMA can be used where less
number of meteorological parameters are available as model input.
In addition, different classification and clustering methods can be
applied for improved training the forecasting model to enhance
the forecast model performance. Intelligent Leaning techniques
such as artificial neural network (ANN) and fuzzy logic can applied
in dynamic environment to forecast the PV output, if adequate his-
torical patterns are available to train the network. ANN based
model offer improved nonlinear approximation performance and
better capability to handle the uncertainty using better training
data and algorithm. In order to achieve the higher prediction accu-
racy of PV output power forecast model, it is required to removed
sharp changes and fluctuations in data of meteorological variables
and historical PV output power. The forecast accuracy of prediction
models can be enhanced by pre-processing and post processing of
historical and forecasted PV output power. There is also a need to
investigate the performance of forecast models during different
days such as clear day, cloudy day and rainy day for further appli-
cation use. It is concluded that, the forecast performance of
stochastic models also affected due to individual poor perfor-
mance, model learning capability for certain PV system data, nat-
ure of meteorological events and their ramp rates. Therefore,
there is a need to design multi predictor based forecast model to
mitigate the above mentions factors up to certain level. Therefore,
it is recommended to explore more on ensemble forecast models
with various combination of predictors to achieve the higher pre-
diction accuracy. In future, accurate PV output forecast has a
potential to utilized for different power system applications such

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