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Journal of International Council on Electrical Engineering Vol. 2, No. 4, pp.351~357, 2012http://dx.doi.org/10.5370/JICEE.2012.2.4.351

351

The Analysis of Output from PV Power Station to Estimate

Generation Reserve for Frequency Regulation

Motoki Akatsuka, Ryoichi Hara*, Hiroyuki Kita*

Katsuyuki Takitani** and Koji Yamaguchi**

Abstract As a solution for the global environmental issues and energy resource depletion issue,photovoltaic generation (PV) has been installed rapidly. However, PV generation output heavily dependson climatic conditions and it would give negative impacts on balancing between supply and demand inpower systems. In order to secure the power quality, the unstable output from the natural energy resource

driven generators should be considered directly in usual power system operations such as supply anddemand balancing. The solar radiation forecast would take a key role in the future operation of power

system; therefore, investigation of performance and its characteristics of the forecast accuracy is

important. In this paper, standard deviation and time series characteristics of solar radiation forecast errorare statistically estimated. This paper also develops a First-order Markov process model for solarradiation forecast error.

Keywords:PV power station, Solar radiation forecast, Statistical estimation, Time series analysis

1. Introduction

Recently, renewable energy driven generations have

received great attentions from the viewpoint of CO2

emission mitigation and energy security enhancement.Photovoltaic generation (PV) is one of major renewable

energy resources and its installed capacity has been rapidly

growing due to financial supports by governments [1]. In

Japan, the installation target of PV in 2030 is set to 40 times

of which in 2005. This challenging target accelerates

further installations in Japan. The penetration of PV brings

some advantages; however, unstable and intermittent

generation output may give some negative impacts on

stable power system operation such as voltage variation,

frequency variation and energy surplus. Therefore,

assessment of those impacts is essential to maintain stable

system operation in the near future. For the undesired

assessment results, precautions must be considered.

The authors have focused on the impact of PV

installations on frequency regulation. As well known,

frequency variation is caused by imbalance of total supply

and total demand across the power system and is kept

within the admissible level by controlling generations

output to follow total demand power momentarily. In detail,

the balancing control is achieved in two stages; demand

forecast based generation scheduling such as unit

commitment (UC) and economic load dispatch (ELD) andreal-time regulation so-called load frequency control (LFC)

and governor free control (GF) for forecast error and short-

term fluctuation. When large amount of PVs are installed to

the power system, solar radiation forecast should be also

considered in UC and/or ELD process. Consequently, LFC

and GF should compensate the solar radiation forecast error,

too. That is, importance of forecast accuracy improvement

is needless to say, forecast error estimation is also important

to allocate adequate regulation reserve. This paper analyzes

the actual solar radiation forecast error observed in the

demonstration project named Verification of Grid

Stabilization with Large-scale PV Power Generation

promoted by NEDO in Wakkanai, Japan [2]. More

specifically, static characteristic of the forecast error is

analyzed and discussed in terms of standard deviation.

Dynamic characteristic of forecast error is also modeled by

means of the first-order Markov process in this paper.

2. Preprocess of Solar Radiation

Trend of solar radiation forecast error depends on season,

time of day and weather condition. Therefore, the forecast

error should be investigated and modeled with being

Corresponding Author: Graduate School of Information Science andTechnology, Hokkaido University, Japan ([email protected]

udai.ac.jp)

* Graduate School of Information Science and Technology, Hokkaido

University, Japan** Japan Weather Association, Japan ([email protected])

Received: July 17, 2012; Accepted: September 15, 2012

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The Analysis of Output from PV Power Station to Estimate Generation Reserve for Frequency Regulation352

classified by these factors. Fig. 1 shows the solar radiation

forecast (If) predicted at around noon in FY2009 and thecorresponding extraterrestrial solar radiation (IET) [3]. Here,

the forecast was made for 30 minutes average of solar

radiation at the Wakkanai PV power station. IET can be

calculated by the following equation.

cosET oI I i= (1)

where, Io is the solar constant [kW/m2], i is the incidence

angle of direct solar radiation which can be calculated

theoretically from the date, time, latitude and longitude of

measuring point. Fig. 1 implies the similarity of seasonaltrends of If and IET; therefore, it is expected that

normalization of solar radiation data based on IET can

effectively eliminate the seasonal trend ofIf. For this reason,

the observed solar radiation data were analyzed after

normalization in this paper. The normalization was

performed by the following equations [3];

Tf f ET K I I= (2)

KT I ETe e I= (3)

I fe I I= (4)

/T ETK I I= (5)

where, KTf and eKT are the normalized solar radiation

forecast and forecast error, eIis the solar radiation forecast

error [kW/m2] defined as equation (4), I is 30 minutes

average of the actual solar radiation observed [kW/m2].KT

is the normalized solar radiation observed, and is so-called

clearness index.

As an example,If,I, eIfandIETin a certain day are shown

in Fig. 2. Corresponding normalized values,KTf,KTand eKT

are also shown in Fig. 3. As shown in Fig. 2, solar radiation

forecast in the example day smoothly varies according to

the diurnal motion. In Fig. 3, on the other hand, normalized

forecast is almost flat from 8 to 16 oclock. This

observation implies that the normalization process can

eliminate both of seasonal and temporal trends in forecast

error.

4 8 12 16 20-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

Time [h]

Solarradiation[kW/m

2]

If

Ie

If

IET

Fig. 2.Actual and forecasted solar radiation, forecast errorand extraterrestrial solar radiation.

4 8 12 16 20

-0.2

0

0.2

0.4

0.6

0.8

Time [h]

Clearnessindex

KTf

KT

eKTf

Fig. 3.Actual and forecasted clearness index and normalized

forecast error.

3. Static Characteristic

The mean value and standard deviation of clearness

index forecast error (eKT), represented as KTand KTin this

paper, were statistically estimated in the following

procedure. First, past annual eKT data were classified by

time of day (30 minutes interval was considered) and KTfsince statistical characteristic of eKT depends on these

factors. Then, KTand KTwere evaluated for each classified

group containing more than 20 samples (groups with less

than 20 samples were ignored from the credibility

perspective). Fig. 4 shows the estimated KT and KT. As

shown in Fig. 4(a), absolute values of KTare smaller than

0.05 and negligible in almost all groups; therefore, KT is

approximated by 0 in this paper. As shown in Fig. 4(b), KT

from 8 to 16 oclock tends to small when KTf is small

(cloudy sky) or large (clear sky). On the other hand, for the

mediumKTf(fine), KTbecomes larger. For example, KTis

0.11 (KTf: 0.2), 0.19 (KTf: 0.4) and 0.07 (KTf: 0.8) at from

11:00 to 11:30. Since the largest KTis 0.20 in Fig. 4(b), the

Jan. 1st Dec. 310

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Date

Solarradiation[kW/

m2]

If

IET

Fig. 1.30-minutes solar radiation and extraterrestrial

solar radiation at around noon in FY2009.

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Motoki Akatsuka, Ryoichi Hara, Hiroyuki Kita, Katsuyuki Takitani and Koji Yamaguchi 353

possible largest I is estimated as 0.24[kW/m2]

(multiplying 0.20 and maximum annual IET at Wakkanai

(1.21[kW/m2])). This value provides an important criterion

for discussion on regulation margin allocation, etc.

Bias

offorecasterror

Time [h]

Clearnessindexforecast

4 8 12 16 200

0.2

0.4

0.6

0.8

1.0

-0.10

-0.05

0

0.05

0.10

(a) Bias

Time [h]

Clearnessindexforecast

4 8 12 16 200

0.2

0.4

0.6

0.8

1.0

0

0.05

0.10

0.15

0.20

(b) Standard deviation

Fig. 4.Statistics of clearness index forecast error.

4. Autocorrelation Function

In this chapter, time sequential characteristic of solar

radiation forecast error is discussed in terms of

autocorrelation function. Fig. 4(b) indicates that the forecast

error from 9 to 15 oclock show similar static characteristic,

therefore, the authors have estimate the autocorrelationfunctions and autocorrelation coefficients of eKT from 9 to

15 oclock classified by the daily average of KTf. Here, the

autocorrelation function C() and the autocorrelation

coefficientR() are defined as follows.

( ) ( ) ( ) ( )

( ) ( )1 1

1 1

KT KT

D N md d

KT KT

d k

C C m t E e k e k m

e k e k mD N m

= =

= = +

= +

(6)

( ) ( ) ( )0R C C = (7)

where, t is the length of forecast interval (=0.5[h]), k

(=1, 2, ... , N) represents the forecast target period (9:00 -

9:30, 9:30 - 10:00, , 14:30 - 15:00),Nis the total number

of forecast intervals (=12), d represents the date having

same averageKTf,Dis the total number of days which havesame averageKTf. Estimated C() andR() are illustrated in

Fig. 5. As shown in Fig. 5, C() and R() exponentially

decrease with the increase in . Fig. 5(b) also reveals that

the autocorrelation coefficients for different average KTf

become similar and can be approximated by exp(-0.46).

SinceR(0.5) is close to 0.8, correlation coefficient between

successive two eKTcan be estimated at about 0.8 (value of

R(0.5) shown in Fig. 5(b)), that is, we can say that forecast

errors appeared in two successive time intervals are

strongly associated.

0 2 4 6-0.01

0

0.01

0.02

0.03

0.04

Lag [h]

AutocorrelationFunctionC()

KTf

=0.0-0.3

KTf

=0.3-0.4

KTf

=0.4-0.5

KTf

=0.5-0.6

KTf

=0.6-0.7

KTf

=0.7-1.0

(a) Autocorrelation function

0 2 4 6-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1.0

Lag [h]

AutocorrelationcoeffieicntR()

KTf

=0.0-0.3

KTf

=0.3-0.4

KTf

=0.4-0.5

KTf

=0.5-0.6

KTf

=0.6-0.7

KTf

=0.7-1.0

(b) Autocorrelation coefficient

Fig. 5. Autocorrelation function and autocorrelation coefficientof clearness index forecast error.

5. Markov Process Model

5.1 Modeling

As well known, an autocorrelation coefficient of the first-

order Markov process can be represented as an exponential

function. Therefore, we can assume from Fig. 5 that the

forecast error might be expressed as the first-order Markovprocess. Markov process representation of forecast error

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brings some useful applications such as a time-domain

frequency excursion analysis. The first-order Markov

process is expressed by equation (8) [4] whose parameters

are related to the autocorrelation function and coefficient asshown in equations (9) and (10).

( ) ( ) ( )1KT KTe k e k n k + = + (8)

1 t = (9)

( ) ( )2 21 0C = (10)

Here, n(k) is the white noise which follows the normal

distribution N(0,). Designed is 0.77 (coefficient 0.46 in

the approximation function for R() is substituted to ) and

designed 2

are shown in Table 1. The above Markovprocess model of forecast error is expressed in terms of

clearness index, however, we can easily convert to the solar

radiation forecast error by equation (11).

( ) ( ) ( )I KT ETe k e k I k = (11)

Table 1. Variance of random number for each average of

clearness index forecastaverage of KTf

2

0.0 - 0.3 0.008

0.3 - 0.4 0.013

0.4 - 0.5 0.0140.5 - 0.6 0.012

0.6 - 0.7 0.007

0.7 - 1.0 0.003

5.2 Residual Analysis

n(k) in equation (8) is assumed to be a normal random

number. For the validity of this assumption, the residual of

observed eKThas to distribute normally. Here, the residual

r(k) is defined as equation (12).

( ) ( ) ( )1KT KTr k e k e k = +

(12)

In order to validate the assumption on n(k), distribution

of the observed r(k) was investigated. In our investigation,

r(k) observed from 9 to 15 oclock are classified by the

daily averageKTf, as we did for eKTin the previous chapter.

After the classification, we count the relative frequencies of

r(k). The obtained relative frequencies are normalized by

the standard deviation of classified r(k) and plotted in Fig. 6.

Relative frequency of the normal distribution N(0,1) is also

shown in Fig. 6 for comparison. As shown in Fig. 6, relative

frequency of r(k) is close to the normal distribution whenthe daily average KTf is from 0.4 to 0.5. However, for the

daily average larger then 0.7, the relative frequency differs

from the normal distribution. Autocorrelation coefficients

of r(k) are also shown in Fig. 7. As shown in Fig. 7,

autocorrelation coefficient for lags longer than zero is

almost zero; this means that r(k) is independent from thepast ones. Here, the irregularity observed at 5[h] lag andKTf

>0.7 is a result of few samples.

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

normalized residual

relativefrequency

KTf

=0.0-0.3

KTf

=0.4-0.5

KTf

=0.7-1.0

normaldistribution

Fig. 6.Relative frequency of residual from equation (9).

0 1 2 3 4 5-0.5

0

0.5

1.0

Lag [h]

Aut

ocorrelationcoefficient

KTf

=0.0-0.3

KTf

=0.4-0.5

KTf

=0.7-1.0

Fig. 7.Autocorrelation coefficient of residual from equation (9).

5.3 Evaluation of Generated Forecast Error

Validity of the developed Markov process model is

ascertained through computational comparisons in this

section. In our investigation, time sequential solar radiation

forecast errors were generated by the developed Markovprocess model with initial value set by the normal random

number following N(0,2). The actual daily average of KTf

was applied in the error generation process for convenience

of comparison.

Fig. 8 shows generated eIfrom 9 to 15 oclock with the

actual observed eI. As shown in Fig. 8, instantaneous values

of observed and generated error are different due to random

factor in the Markov model.

For stochastic discussions, we have evaluated and

compared the relative frequencies of generated and

observed eIalong a year. Fig. 9 shows the obtained relative

frequencies and cumulative relative frequencies. From the

static viewpoint, relative frequencies at around maximum

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and minimum eIbecome one of main interests. From Fig.

9(b), we can find that 95% of forecast errors become larger

than -0.21[kW/m2] and smaller than 0.21[kW/m2] in case of

the generated errors. Likewise, 95% of observed forecasterrors are larger than -0.23[kW/m

2] and smaller than

0.23[kW/m2]. This result indicates that the developed

Markov model can provide good estimations of possible

forecast error magnitude.

9 10 11 12 13 14 15-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time [h]Solarradiationforecasterror[kW/m

2]

observed

simulated

Fig. 8.Example of observed and simulated solar radiation

forecast error.

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.05

0.10

0.15

0.20

0.25

Solar radiation forecast error [kW/m2]

Relativefreque

ncy

observed

simulated

(a) Relative frequency

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

1.0


Cumurativerelative

frequency

observed

simulated

(b) Cumulative relative frequency

Fig. 9.Relative frequency distribution and cumulative relativefrequency of observed and simulated solar radiationforecast error.

Fig. 10 shows the relative frequencies of generated and

observed eIclassified by the daily averageKTf. Comparison

of subfigures in Fig. 10 indicates that the developed

Markov model results in relatively worse accuracy against

large daily average KTf. The developed Markov processunderestimates the possible magnitude estimation by about

0.09[kW/m2] against the 95% threshold.

6. Conclusion

The static and dynamic characteristic of solar radiation

were analyzed in this paper. In the analysis, the solar

radiation forecast error was normalized based on the

extraterrestrial solar radiation to eliminate both seasonal

and temporal trends.Our static analysis revealed that possible largest standard

deviation of solar radiation forecast error is 0.24[kW/m2]

which is equivalent to about 24% of rate capacity of PV. In

the dynamic characteristics analysis, autocorrelation

functions and autocorrelation coefficients of the solar

radiation forecast error were calculated. Furthermore, this

paper also developed the Markov process model for solar

radiation forecast error.

The future work is more detailed verification of the

developed Markov process model, especially from the

viewpoint of long-term accumulation of forecast error

which provides an important insight for the energy required

to compensate the forecast error.

AcknowledgementsThis work employed the data acquired in demonstration

project Verification of Grid Stabilization with Large-

scale PV Power Generation by NEDO, Japan.

This work was supported in part by Global COE Pr

ogram Center for Next-Generation Information Technol

ogy based on Knowledge Discovery and Knowledge Fe

deration, MEXT, Japan.

References[1] IEA-PVPS, Trends in Photovoltaic Applications

Survey report of selected IEA countries between 1992

and 2008, Report IEA-PVPS T1-18, 2009

[2] R. Hara, H. Kita, T. Tanabe, H. Sugihara, A.

Kuwayama, S. Miwa, Testing the technologies

Demonstration Grid-Connected Photovoltaic Projectsin Japan, IEEE Power and Energy Magazine, Vol.7,

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No.3, pp.77-85, 2009[3] T. Muneer, Solar Radiation and Daylight Models,

ELSEVIER, 2004

[4] G. E. P. Box, G. M. Jenkins, G. C. Reinsel, Time

Series Analysis Forecasting and Control, WILEY,

2008

Motoki Akatsuka received the B.E. degree and M.E.

degree from Hokkaido University, Hokkaido, Japan in 2007

and 2009, respectively. He is currently a Ph.D. candidate at

Hokkaido University. He is interested in analysis andoperation of PV system.

Ryoichi Hara received the Ph.D degree from HokkaidoUniversity, Sapporo, Japan, in 2003. He has been an

associate professor at Hokkaido University. His research

interests are analysis, operation and control of electric

power system. He is particularly interested in technological

and economical harmonization of the bulk power system

and distributed energy resources.

Hiroyuki Kita received the Ph.D degree from Hokkaido

University, Sapporo, Japan, in 1994. He has been a

professor at Hokkaido University. His research interestsinclude the planning, analysis and control of electric power

system.

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4


Relativefreque

ncy

observed

simulated

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2

0.3


Relativefreque

ncy

observed

simulated

(a) Average of clearness index forecast: 0.0 - 0.3 (b) Average of clearness index forecast: 0.3 - 0.4

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2


Relative

frequency

observed

simulated

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2


Relativefrequency

observed

simulated

(c) Average of clearness index forecast: 0.4 - 0.5 (d) Average of clearness index forecast: 0.5 - 0.6

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4


Relativefrequ

ency

observed

simulated

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5


Relative

frequ

ency

observed

simulated

(e) Average of clearness index forecast: 0.6 - 0.7 (f) Average of clearness index forecast: 0.7 - 1.0.

Fig. 10.Relative Frequency of Observed and Generated Solar Radiation Forecast Error for Each Daily Average ClearnessIndex Forecast.

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Katsuyuki Takitani received the B.E. degree from

Hirosaki University, Aomori, Japan in 1981. He joined

Japan Weather Association in April 1981. His research

interest includes the meteorological information andmeteorological forecast.

Koji Yamaguchi received the M.E. degree from Osaka

Prefecture University, Osaka, Japan, in 1999. He joined

Japan Weather Association in April 1999 and has engaged

in development & research of the solar radiation forecast

method.

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