Solar Radiation Forecasting Using Artificial Neural ...

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2HEI, 13 Rue de Toul, 59800, Lille. E-mail: ..... [12] Stanley K.H.Chow, Eric W.M.Lee, Danny H.W. Li, “Short-term prediction of photovoltaic energy ... [13] C. Monteiro, L. A. Fernandez-Jimenez, A. Ramirez-Rosado, I. J. ans. Munoz-Jimenez, and ...
Solar Radiation Forecasting Using Artificial Neural Network for Local Power Reserve Xingyu YAN1

Dhaker ABBES2

Bruno FRANCOIS1

1

L2EP, EC de Lille, Cité Scientifique, 59651, Villeneuve d'Ascq, France 2 HEI, 13 Rue de Toul, 59800, Lille E-mail: [email protected]

Abstract— Renewable energy sources have a variable nature and are greatly depending on weather conditions. The load is also uncertain. Hence, it is necessary to use power reserve equipment to compensate unforeseen imbalances between production and load. However, this power reserve must be ideally minimized in order to reduce the system cost with a satisfying security level. The quantification of power reserve could be calculated through analysis of forecasting uncertainty errors of both generation and load. Therefore, in this paper, a back propagation artificial neural network approaches is derived to forecast solar radiations. Predictions have been analyzed according to weather classification. Some error indexes have been introduced to evaluate forecasting models performances and calculate the prediction accuracy. Forecasting results can be used for decision making of power reserve for renewable energy sources system with some probability or possibility methods. Keywords--- photovoltaic power; power reserve; solar radiation forecasting; Artificial Neural Network

I.

INTRODUCTION

As energy prices get more and more high and emissions should be limited, new electrical generators supply options based on distributed resources are required. Thus, thanks to technological advancement and government policies, electricity produced by renewable energy sources (RES) is constantly increasing in the world. This development of RES contributes to energy supply portfolio diversity and greatly reducing the risks of expanded usage of fossil fuels. And also, it’s the most environmentally benign energy supply option available in current and near-term market [1]. However, energy productions of the RES, such as PV and wind power, are characterized by uncertainty and intermittence. They are greatly influenced by meteorological conditions. Facing the problem, power reserve is needed to cover unforeseen events caused by sudden decrease or/and increase of generators or/and in demand and unexpected loss of generators/lines. It can help to provide ancillary services in a local electrical network for frequency regulation and voltage regulation, etc. [2] However, power reserve equipment is greatly increasing overall cost of power generation system. Thus, the

balance between the amount of power reserve and the resulting cost needs to be considered and power reserve needs to be minimized while satisfying system security. Decision making approaches of power reserve can be computed by forecasting error uncertainty analysis [3, 4]. Technical and economic power forecasting models for wind farms or grid-connected PV plants are also advanced. In recent decades, several PV power forecasting models have been published. Some of these works were specifically dedicated to the PV power forecasting of power generation [6, 9-11], while some of these works were oriented to obtain solar radiation predictions [7]. Although some forecasting model have been done by using simple physical methods, the more universally applied technique is a specific soft-computing technique and is known as Artificial Neural Network (ANN). Since there are many factors, such as irradiation, air/panels temperature, humidity, pressure, cloud cover percentage, wind speed and other ones that can affect the PV power generation, different parameters have been used in each paper. As example, in paper [10], aerosol index was used with hourly PV output power, humidity, temperature, and wind speed while in paper [9], atmospheric pressure and cloud coverage were used. In addition, some error indexes are introduced to evaluate the performances of the forecasting models too. This paper uses a model of ANN for next 24-hours solar radiation prediction, based on last 24-hours radiation and multiple meteorological data. Firstly back propagation (BP) neural network is trained with historical meteorological data, and then weather data of the objective day are used as input variables of the designed BP neural network to get hourly irradiation output prediction. The efficiency of the proposed method is validated by analyzing the maximum error and mean absolute percentage error between predicted values and measured values and standard deviation. The paper is organized as follows. In section 2 a brief review of the PV power forecasting methods is presented. In section 3 the applied method is described giving emphasis to the BP neural network. In the section 4 a case study is presented and results are analyzed by using an error metric previously presented. To conclude, some conclusions are stated and several perspectives are proposed for future study.

II.

PV POWER FORECASTING METHODS

According to the literature, power production forecasting methods of RES are commonly classified into three categories: physical models, statistical models and hybrid models [10]. Physical models are based on mathematical equations and are used to describe the ability of PV system to convert the introduced meteorological resources into electrical power [1112]. These models are based only on solar radiation or some more additional parameters, so they are not complicated. However, the major disadvantage is that they have to be designed specifically for a particular energy system and location due to sensitization of weather prediction error. Statistical methods, for example ANN, are depending on the theory of persistence or stochastic time series. According to studied literature, ANN has been effectively used in prediction of hourly irradiation output [7, 14]. The main drawback of this method is that historical data of real power productions as well as weather forecast are necessary to train the ANN to get the appropriate weights among neurons in order to minimize the error during iteration. Moreover, the randomly setting of original weights can induce slightly differences in results for each time. Any combination of two or more of the previously described methods is a hybrid model. As for the combining models, the basic idea is to combine the unique features of each method to improve the forecasting accuracy. In addition, according to literatures there are two kinds of outputs for PV forecasting: PV power and global solar radiation (GSR). If we consider the electrical energy extracted from the physical models based on global solar radiation , which is received by a PV panel, the equation for a simplified model is as follows [5]: (1) where α is the conversion efficiency of the solar panel, A is its surface size, and is the outside air temperature. Since the parameters α and A can be easily found from datasheet of the PV panel and they are constant, the essential of this two methods are the same. III.

BACK-PROPAGATION ANN STRUCTURE

Based on the operating of the brain, artificial neural network is aiming to imitate neural network capabilities by using a large number of artificial neurons. In brief, neural network can learn, memorize and establish a system model through handling external information to get the capabilities of prediction and selfdiagnosing. Nowadays, ANN has been succeeded in several power system problems, such as planning, control, analysis, protection, design, forecasting, security analysis, and fault diagnosis [12]. Back-Propagation Network (BPN) is one of the most widespread and representative learning rules in the ANN [13-15]. Many ANN structures can be designed according to the application issues and implement generally mathematical approximations [8]. In our study, a basic structure of a three-layer BPN is shown in Fig 1. Fig 1 can be explained by mathematical equations to illustrate the relationships between inputs and outputs of artificial neurons.

Neuron input variables are X= [ ] T, hidden layer units are U = [ ] T, output variables are Y = [ ] T. The interconnection weights are . Input layer

Hidden layer Output layer

ij

x1

y1

u2

x2

xn

ij

u1

y2

u3 . . .

. . .

. . .

yl

um bias1

bias2

Fig. 1. The structure of a three-layer BP network

For the hidden layer, ∑

, j=1, 2, …, m , j=1, 2, …, m

(2) (3)

For the neuron output, ∑

, j=1, 2, …, l , j=1, 2, …, l

(4) (5)

where the transfer function of the neurons f(z) is the sigmoid function and can be expressed as follows: (6) The interconnection weights in the neural network are randomly settled before its training and they are gradually adjusted with an increasing number of training times in order to minimize the errors between the target values and output values of neural network. For that reason, an appropriate training method for the neural network is obligatory needed to learn iteratively until each input properly corresponds to the desirable output. Based on a multilayered, feed-forward topology, with supervised learning, back-propagation network is one of the most widespread and representative learning rules in the neural network. The algorithm of a typical BPN can be divided into two parts: feed-forward and back-propagation stages. In the first stage, the BPN starts out with randomly settled weights on each synapsis. Then a training set of input data is imported and transmitted to output layer, and the output should go along with every input. In the second back-propagation stage, the weights are incrementally adjusted and errors between target values and output values are propagated back to the network. At this stage,

the back-propagation algorithm is based on the gradient descent method to modify the weights.

Input paramaters

The training procedure of a BPN method can be explained as follows:

Temperature Humidity Pressure Cloud cover …

A) Setting the neuron input: ∑

)

(7)



(8)

Starting with random , the goal is to choose the suitable so that is close to the output of the training examples to get . D) Gradient descent algorithm (9) is used to reduce through constantly changing until we hopefully end up at a minimum. (9)

10 8 6 4 2 2009 0

0

200

2010 400 600 800 Observe Time (day)

2011 1000

Fig. 3. Daily mean global solar radiation at NREL AVG Specific Humidity (g/Kg)

ANN and its training with combination of other computational intelligence techniques are nowadays very well established. Nevertheless the paper does not aim to present a pure theoretical contribution, but introduces a BP-ANN method for GSR prediction with some meteorological parameters. By using the prediction process, next 24-hour GSR forecasted data can be obtained. By comparing them with the real GSR data in the same day, forecast errors can be used for uncertainty analysis, as shown in Fig. 2.

Uncertainty Analysis

In this paper, real data measured by the National Renewable Energy Laboratory (NREL) (latitude: 39°54' 38.34" North; longitude: 105°14' 5.28" West; elevation: 1855 meters) are used for the neuron network training and validation. Hourly data on GSR, specific humidity, and air temperature from 2009/01/01 to 2011/12/30 are shown in Figs. 3-5, respectively. Daily total values of GSR fluctuate approximately between 0 to 9 kWh/m2/ day, as shown on Fig.3. Fig.4 shows daily average specific humidity values which are variable between 400 to 1400 g/Kg (expressed as grams of water vapor per kilogram of air). The daily average values of temperature, as shown in the Fig. 6, to vary approximately between -10 to 25°C, with some peaks reaching -18°C in the winter.

E) If the convergence of target values reaches limit, the training procedure can be stopped; otherwise, go back to the step B and repeat until it converge.

IV. CASE STUDY A. Prediction structure and data description

Error

Fig. 2. Prediction flow process

where is the learning rate. If is too small, gradient descent can be slow to convergence. Whereas if is too large, gradient descent can overshoot the minimum and may fail to converge, or even diverge.

After the training stage, a set of validation data are used to validate the parameters, which have been obtained with training data.

Measured GSR data

2

B) Set up network’s related parameters, such as size of hidden layer and learning rate, and randomly initialize weights and biases, then input training data ( , ). C) Output and error calculation of hidden and output layers with a cost function:

Forecasted GSR data

Training Validation Forecasting

Measured Solar radiation

is the input variable, the interconnected weights and bias .

TotGlobal PSP (kW-hr/m)

where

(

Prediction Process

1500

1000

500 2009 0

0

200

2010 400 600 800 Observe Time (day)

Fig. 4. Daily mean specific humidity at NREL

2011 1000

Also there are many ways to assess the prediction model; the most commonly used are Root Mean Square Error (RMSE) and Mean Absolute Error (MAE).

AVG Temperature (°C)

30 20 10

-10 2009 -20

0

200

2010 400 600 800 Observe Time (day)

One year’s historical data of GSR, humidity, and temperature (from 2009/01/01 to 2009/12/31) are used as inputs for training the model. Next 60 days of data are used for the validation and another 30 days of data are used for the test. Input layer

Input data are 24 points of GSR in the last day in each hour; 24 points of specific humidity and average temperature in each hour of the predicted day. Hidden layer

There is only one hidden layer in this model. A trial-and-error method [13] has been used to determine the appropriate number of hidden neurons in this paper. c)



(15)

C. Forecasted results and discussion

1000

B. Data training and validation

b)

(14)

2011

Fig. 5. Daily mean air temperature at NREL

a)

√ ∑

0

In order to validate the accuracy of the obtained prediction model of GSR output, the GSR output of a clear sky day, a cloudy day, and a partly cloudy day were forecasted by using historical solar radiation data and weather data, the curves of the measured data and forecasted data are shown in Fig.6, Fig.7, and Fig.8, respectively. The

of the clear sky day is 1.4% (Fig. 6) and of a cloudy day is 3.0% (Fig. 7). However, the of a partly cloudy day is as high as 6.6%. The prediction of a clear sky day and cloudy day is much more accurate. In fact, in the clear sky and cloudy days the solar radiation is relatively stable and not always fluctuates, while in the partly cloudy day, the solar radiation is greatly affected by cloud changes. In particular, these results can be seen much clearly in table 1, where the predicted output based on the three kinds of weather conditions are summarized and compared by considering errors definitions previously introduced. 1000

Output layer

Real Predicted

900

d)

Assessment method

2

Since the objective of this paper is to forecast GSR one dayahead, a total of 24 points of GSR output in forecast day are taken as output for all hourly every day.

Avg Global PSP (W/m )

800

is the absolute value of (10): (11) , based on the

Hourly absolute percentage error hourly predicted GSR: ⁄ Daily Mean Absolute Prediction Error hourly output measured GSR ( : ∑

(12) , based on

500 400 300

100 0

0

5

10 15 Time (Hour)

20

25

(a) 1 predict errors in cleary sky day

Percentage Error (%)

Absolute hourly error

600

200

In order to correctly define prediction accuracy and relative error, it is necessary to analyze different error definitions. The starting point reference is the hourly error , defined as the difference between the measured GSR in the hour and the given prediction provided by the neural model: (10)

700

0.8 0.6 0.4 0.2 0

0

5

10 15 Time (Hour)

20

25

(b) Figure 6 Clear sky day: (a) Comparisons of real measured and predicted GSR (b) Percentage error of

(13)

In table 1, the results which have been given above are shown.

1000 Real Predicted

900

Table 1. Production results and error calculation for three-day examples

2

Avg Global PSP (W/m )

800 700

Physical quantities

600 500

Real daily GSR (W/m2) Predicted daily GSR (W/m2)

400 300

Daily absolute error (W/m2)

200 100 0

0

5

10 15 Time (Hour)

20

25

(a) 1

Percentage Error (%)

predict errors in cloudy day

(%) Standard deviation (std)

Clear sky day 7045.3 7142.6 97.3 1.4 0.019

Cloudy day 2814.2 2729.5 84.7 3.0 0.064

Partly cloudy day 4266.0 4546.5 280.5 6.6 0.084

Table 2 shows the RMSE and MAE of the GSR prediction neural network for training data, validation data and test data respectively.

0.8

Table 2. RMSE and MAE for the GSR prediction neural network 0.6 0.4 0.2 0

0

5

10 15 Time (Hour)

20

V.

Figure 7 Cloudy day: (a) Comparisons of real measured and predicted GSR (b) Percentage error of 1000 Real Predicted

900 800 2

700 600 500 400 300 200 100 0

0

5

10 15 Time (Hour)

20

MAE[%] 4.964 6.714 5.057

25

(b)

Avg Global PSP (W/m )

RMSE[%] 9.359 11.849 9.811

Training set Validation set Test set

25

(a) 1

CONCLUSION

Due to renewable energy penetration increase in the electric grid, it is quite important to estimate the amount of energy from such non-controllable sources. A BP neural network is presented for the day-ahead GSR forecasting by using some meteorological data. Errors between predicted outputs and real measured data of three different weather conditions are discussed. The benefit of the proposed approach is that it does not need complex modeling and calculation. The results show that the predicted accuracy is enough. In the future study, normal probability density function (pdf) will be used for presenting the probability and possibilities of error distribution for uncertainty analysis. After assessing the uncertainty, the power reserve can be quantified by taking into account the associated reliability risk index. Fig. 9 shows the steps necessary to be taken in order to assess the required power reserve.

Percentage Error (%)

predict errors in partly cloudy day

Assessing the uncertainty

0.8 0.6

Net forecasted demand uncertainty

0.4

Reliability assessment

0.2 0

0

5

10 15 Time (Hour)

20

25

(b) Figure 8 Party cloudy day: (a) Comparisons of real measured and predicted GSR (b) Percentage error of

Setting an ancceptable level for risk indexes Selection of power reserve Figure 9 Quantification of power reserve steps

VI. [1]

[2]

[3] [4]

[5]

[6]

[7]

[8]

[9]

[10]

[11] [12]

[13]

[14]

[15]

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