The location of PV systems in distribution system has been increased as one of countermeasure for global environmental issues. As the operation efficiency of PV systems is getting decreased year by year due to the aging phenomenon and maintenance problems, the optimal algorithm for state diagnosis in PV systems is required in order to improve operation performance in PV systems. The existing output prediction algorithms considering various parameters and conditions of PV modules could have complicated calculation process and then their results may have a possibility of significant prediction error. To solve these problems, this paper proposes an optimal prediction algorithm of PV system by using least square methods of linear regression analysis. And also, this paper presents a performance evaluation algorithm in PV modules based on the proposed optimal prediction algorithm of PV system. The simulation results show that the proposed algorithm is a practical tool of the state diagnosis for performance improvement in PV systems.
1. Introduction
The renewable energy sources such as wind power generation and photovoltaic (PV) system are being energetically interconnected with distribution system with the worldwide support of each government, as one of the solution to the energy and environment issues. And also, it has been actively promoted to expand the proportion of renewable energy up to 11% of total energy by 2030 under the green growth policy of Korea government. However, it is reported that the operation efficiency of PV system is getting decreased in a severe manner year by year with the aging phenomenon and maintenance problems. Therefore the optimal algorithm of output prediction and state diagnosis of PV system is getting required in order to improve operation performance of PV system.
[1

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But the conventional output prediction algorithms such as AMPP (Approximate maximum power point), FFv (Variable fill factor with constant series resistance) and Osterwald’s, which should consider various parameters and several conditions of PV system, may have complicated computation procedure and then their results may have possibility of large prediction error. Further, existing state diagnosis systems are difficult to find abnormal state of PV modules like aging and damage because it has simple monitoring system by only measuring output data of inverter of PV system.
[5
,
6]
Under these backgrounds, this paper proposes an optimal prediction algorithm of PV system by using least square methods of linear regression analysis in order to reduce the prediction error and avoid complicated computation process. And also, this paper presents a performance evaluation algorithm using the proposed prediction algorithm of PV system and then implements the performance improvement system based on the monitoring system of each PV modules. From the simulation results, it is clear that the proposed algorithms are useful method of the state diagnosis for performance improvement in PV systems.
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2. Degradation Characteristic of PV System
Existing state diagnosis systems are difficult to find abnormal state of PV modules such as aging and damage because it has simple monitoring system only measuring output data of inverter of PV system and monitoring PV module by web camera as shown in
Fig. 1
.
Existing monitoring systems
Although life span of PV modules may be more than 20 years, the degradation of performance due to the aging phenomena in PV modules with the exposal to the outdoor environment has caused the huge power loss and decreased the total efficiency of PV system. The aging test results of 50kW class PV system are performed by Korea Electric Power Research Institute (KEPRI) as shown in
Fig. 2
and
Table 1
. From the report, there is around 34% of cumulative power loss during 11 years after initial installation of the PV module. Namely, it is about 3.7% of cumulative power loss every year.
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,
11]
Aging test result of KEPRI
Cumulative power loss with aging (unit : %)
Cumulative power loss with aging (unit : %)
3. Performance Evaluation algorithm of PV System
 3.1 Conventional prediction method of output power
Many kinds of conventional output prediction methods of PV module such as AMPP, FFv, and Osterwald’s have been developed. AMPP algorithm among these method, considering short circuit current (I
_{sc}
) and open circuit voltage (V
_{oc}
) based on the standard test conditions (STC) and the solar radiation amount as shown in Eq. (1) and Eq. (2) has been widely used in the prediction method. And also, the maximum current (I
_{M}
) and the maximum voltage (V
_{M}
) of Eq. (5) and Eq. (6) can be calculated by relationship between short circuit current and open circuit voltage of Eq. (1) and Eq. (2) and the coefficient equation of Eq. (3) and Eq. (4). Finally, the output prediction of AMPP algorithm can be obtained as shown in Eq. (7).
where, G
_{i}
is solar radiation measured,
is solar radiation at STC,
is short circuit current at STC,
is open circuit voltage at STC, β is voltage factor by temperature condition, T
_{c}
is back sheet temperature of PV module, v
_{oc}
is normalized open circuit voltage and r
_{s}
is series internal resistance.
 3.2 New prediction algorithm of output power
As mentioned earlier, the conventional output prediction algorithms which should deal with various parameters of PV modules and weather conditions may have complicated process and then their prediction results may have possibility of large computation error. To overcome these problems, this paper proposes the idea of relationship between output characteristic of PV modules and weather conditions based on the measured data of real PV site.
[12]
Furthermore, this paper proposes optimal prediction algorithm of PV system by using least square methods of linear regression analysis in order to avoid complex computation procedure and reduce the prediction error.
 3.2.1 Operation characteristics of PV system
The relationship between the output of PV modules and weather conditions such as temperature and solar radiation can be analyzed as shown in
Fig. 3
and
Fig. 4
, which show the distribution characteristics measured at every 15 minutes during one month (April, 2013) in real PV site of Korea Conformity Laboratories system. It is clear that
Fig. 3
shows very weak relationship between output of PV modules and temperature, but
Fig. 4
shows strong relationship between output of PV modules and solar radiation. Therefore this paper will concentrate on the latter idea, relationship between output of PV module and solar radiation characteristics.
Distribution characteristics of output and temperature
Distribution characteristics of output and solar radiation
 3.2.2 Novel prediction algorithm of output power
In order to improve the accuracy of output prediction at PV system, a concept of standard temperature conversion equation considering coefficient of temperature efficiency (γ) and the temperature measured at time interval of t(T
_{t}
) is introduced by Eq. (8),
where,
is output of PV module at standard temperature (25℃) and P
_{(t)}
is measured output of PV module.
By combining the distribution characteristics of PV module in
Fig. 3
and
Fig. 4
and the standard temperature conversion equation of Eq. (8), output prediction equation using the quadratic linear regression method can be formulated by
where, X
_{(t)}
is solar radiation, α and β are linear coefficients and e
_{(t)}
is error.
To solve the linear coefficients of α, β in Eq. (9), the least square method to minimize error is introduced by
and then, obtaining the derivatives for α, β,
Solving the equation for α and β in Eq. (9) cannot provide a linear equation. Therefore, the least square method is introduced in order to find out linear coefficients of α and β, it can be obtained as follows.
 3.3 Performance evaluation algorithm of PV system
Based on the proposed output prediction algorithm of PV system as mentioned earlier, the performance evaluation procedure of PV modules can be expressed as shown in
Fig. 5
. Firstly, the output prediction value (P
_{p}
) of PV module is calculated by using the linear regression analysis method like Eq. (9). And then, the criteria value (P
_{s}
) of abnormal state for PV modules is defined as 0.8pu of the prediction value (P
_{p}
), which is derived from the experience value of abnormal PV modules. In next process, the measured output of n
^{th}
PV module (P
_{(n)}
) is compared with the criteria value (P
_{s}
) in order to evaluate the state of PV modules. If P
_{(n)}
is bigger than P
_{s}
, n
^{th}
PV module is evaluated as normal state. However, if P
_{(n)}
is smaller than Ps, n
^{th}
PV module is evaluated as temporarily abnormal state and also the iteration value (Ec
_{(n)}
) is getting increased. By repeating the process at each time interval, the PV modules are evaluated as abnormal state if the accumulated iteration values exceed the reference setting value (S
_{c}
), which is decided by the weather conditions like shading of cloud.
Performance evaluation algorithm of PV modules
4. Implementation of Performance Evaluation System for PV System
 4.1 Configuration of performance evaluation system
In order to evaluate state of module in PV system, the performance evaluation system for PV system is implemented by the proposed method as shown in
Fig. 6
. Firstly, the data which was measured from sensor at PV module including voltage, current, temperature and radiation is transmitted to datalogger using the communication device. And then, transmitted data are stored at specified table of database server which is divided by each date type like voltage, current, temperature and radiation. Based on the stored date at table of database, output prediction of PV system and performance evaluation of PV module is analyzed by performance evaluation system for PV system which adopts the proposed method. Additionally, state diagnosis evaluation system can offer various function such as alert, trend analysis, event and report writing.
Performance evaluation system of PV system
 4.2 Database design
In order to carry out performance evaluation of PV modules, the stored data in database through the datalogger are categorized into operation and maintenance data as demonstrated in
Table 2
. The former includes surrounding climate data, power conditioning system data and PV module data and the latter is malfunction information data, output prediction data and temporary storage data.
Table item of database
Based on the proposed algorithm mentioned earlier, this paper has implemented performance evaluation system for PV system using the Autobase software. And also, in order to provide various functions to operator, it is designed to carry out state diagnosis of PV modules by using data transferred in remote PV sites and to store evaluation results of state diagnosis at database. The normal monitoring and control menu of performance evaluation system is designed for operator to easily access the operation and maintenance information as shown in
Fig. 7
.
Monitoring function of state diagnosis system
Furthermore, abnormal menu as shown in
Fig. 8
is designed to promptly find out abnormal PV modules by adapting popup function like red warning light and warning window, at array configuration of PV system.
Warning function for abnormal state
5. Case studies
 5.1 Output prediction analysis
Table 3
shows the measurement data of 250W PV module installed in Korea Conformity Laboratories during one month on April, 2013. “Where, P
_{MAX}
is maximum power of PV module, V
_{mp}
is voltage of maximum power point, I
_{mp}
is current of maximum power point, FF is fill factor, Solar45 is vertical solar radiation and Solar00 is horizontal solar radiation”. By using
Table 3
, the comparison results between the proposed output prediction algorithm and the conventional output prediction algorithms are shown in
Table 4
and
Fig. 9
. It is clear that the conventional output prediction algorithms such as FFv, Osterwald’s and AMPP considering various parameters of PV modules and weather conditions have big prediction error of 9.5% to 27.08%, however the proposed method (LRM: liner regression method) considering the relationship between the recent solar radiation and output of PV modules only has small prediction error of 2.3%. Where, error rate is obtained by comparing real measurement data with each calculated prediction data. Therefore, it is confirmed that the proposed method has an excellent performance for output prediction of PV system.
Measured data of PV module
Measured data of PV module
Comparison results of prediction algorithm
Comparison results of prediction algorithm
Error characteristic of each prediction algorithm
 5.2. Performance evaluation algorithm analysis
By using the proposed method, this paper performed the simulation for the 12.5kW PV system located at Korea University of Technology and Education, which has a total of 50 modules and consists of 5 strings with 10 modules. It is assumed that
Table 5
shows potential abnormal modules at each time interval, meaning that the measured output of PV module is less than criteria value as shown in
Fig 5
. Therefore, if a PV module is potential abnormal module in series three times, it is finally evaluated as an abnormal module. For example,
[1

3]
module can be evaluated as abnormal module because it is potential abnormal module from first time interval to third time interval consecutively, but
[1

5]
module is not abnormal module because it is potential abnormal module from first time interval to second time interval.
Potential abnormal PV modules
*[ab] : a is string number and b is module number
The state diagnosis system implemented by the proposed method as shown in
Fig 10
, can successfully find out the five abnormal PV modules of
[1

3]
,
[2

5]
,
[3

8]
,
[4

6]
and
[5

4]
, which is bigger than counting number (3 iterations), and also show abnormal information to the operator with a popup alert menu. And also, the abnormal state module can be stored at the table in database server as shown in
Fig. 11
. Therefore, it is clear that the proposed method is a useful tool of the state diagnosis for performance improvement in PV systems.
Menu of performance evaluation system
Abnormal information in database
6. Conclusions
This paper has proposed the optimal output prediction algorithm of PV system by using least square methods of linear regression analysis, and the performance evaluation algorithm of PV modules based on the proposed optimal prediction algorithm of PV system. The main results are summarized as follows.

(1) It is clear that the conventional output prediction algorithms such as FFv, Osterwald’s and AMPP considering various parameters of PV modules and weather conditions have big prediction error of 9.5% to 27.08%, however the proposed method considering the relationship between the recent solar radiation and output of PV modules only has small prediction error of 2.3%. Therefore, it is confirmed that the proposed method has an excellent performance for output prediction of PV module.

(2) From the simulation result of the performance evaluation system, the proposed method can successfully find out the abnormal PV modules, and also show abnormal information to the operator with a popup alert menu. Therefore, it is clear that the proposed method is a useful tool of the state diagnosis for performance improvement in PV systems.
Acknowledgements
This work was supported by the Power Generation & Electricity Delivery Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20131020400720)
BIO
ByungKi Kim He received the B.S. degree and M.S. degree in KOREATECH, CheonAn, South Korea, in 2008 and 2012. And he is currently pursuing the Ph.D. degree at KOREATECH, CheonAn, South Korea. He is interested in renewable energy resources and new power distribution systems.
Sungsik Choi He received the B.S. degree and M.S. degree in KOREATECH, CheonAn, South Korea, in 2010 and 2014. And he is currently pursuing the Ph.D. degree at KOREATECH, CheonAn, South Korea. He is interested in renewable energy resources.
JongYong Wang He received the B.S. degree in Electrical Engineering from Korea University of Technology and Education, CheonAn, South Korea, in 2012. And he is currently pursuing the M.S degree at KUT, CheonAn, South Korea. He is interested in power distribution system
SeungTaek Oh He received the B.S. degree in KOREATECH, CheonAn, South Korea, in 2013. And he is currently pursuing the M.S degree at KOREATECH, CheonAn, South Korea. He is interested in renewable energy resources.
DaeSeok Rho He received the B.S. degree and M.S. degree in Electrical Engineering from Korea University, Seoul, South Korea, in 1985 and 1987, respectively. He earned a Ph.D. degree in Electrical Engineering from Hokkaido University, Sapporo, Japan in 1997. He has been working as a professor at Korea University of Technology and Education since 1999. His research interests include operation of power distribution systems, dispersed storage and generation systems and power quality.
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