1. bookVolumen 7 (2022): Heft 1 (January 2022)
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Zeitschrift
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2444-8656
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01 Jan 2016
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Visualized calculation of regional power grid power data based on multiple linear regression equation

Online veröffentlicht: 15 Dec 2021
Volumen & Heft: Volumen 7 (2022) - Heft 1 (January 2022)
Seitenbereich: 93 - 102
Eingereicht: 16 Jun 2021
Akzeptiert: 24 Sep 2021
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
2444-8656
Erstveröffentlichung
01 Jan 2016
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
Abstract

The power generation of distributed power generation systems in regional power grids is mainly affected by external environmental factors, and there are volatility and intermittent power generation issues. This paper establishes a relatively simple multiple linear regression prediction model to predict grid-connected photovoltaic power generation systems. The article uses a hybrid modelling method to filter more important weather forecast input variables through a step-by-step linear regression method to realize the visual calculation of power data. The research results show that the multiple linear regression equation methods proposed in the article have pervasive application value in the actual application of solar photovoltaic power consumption data.

MSC 2010

Introduction

The rapid development of society and the economy has led to a sharp increase in energy consumption, increasingly depleted fossil energy sources, and increased environmental pollution. This poses a severe threat to the ecological balance of the earth and the survival of humankind. Large-scale photovoltaic power plants are an effective way to meet human demand for energy. Because photovoltaic power generation is affected by solar radiation intensity, battery component temperature, weather, cloud cover, and some random factors, the system operation process is an unbalanced random process. Its power generation and power output are highly random, fluctuating, and uncontrollable. This is particularly prominent when the weather changes suddenly. This kind of power generation inevitably brings a series of problems to the safety and management of the power grid after it is connected to the power grid [1]. Therefore, it is imperative to predict the output of the photovoltaic system accurately. At present, there are several types of prediction models for the power generation of photovoltaic power generation systems, such as neural network models, radial basis function models, and multi-layer perception models. In addition, the photovoltaic system is a typical grey system with partly clear and partly unknown information [2]. Grey theory forecasting models have a wide range of applications in power planning and load forecasting. Because these models are relatively complex, this paper establishes a relatively simple multiple linear regression prediction model to predict the power generation of grid-connected photovoltaic power generation systems.

Theoretical calculation of power generation of solar cell modules

Photovoltaic power generation uses the photovoltaic effect of the P–N junction to convert light energy into electrical energy. The equivalent circuit of its components and system under ideal conditions is shown in Figure 1. The maximum output power is represented as follows: Pm=UmIm=UocIscFF {P_m} = {U_m}{I_m} = {U_{oc}}{I_{sc}}FF

Fig. 1

Equivalent circuit diagram of an ideal DC model of a photovoltaic module.DC, direct current.

Here, Uoc,Isc,FF are the open-circuit voltage, short-circuit current, and fill factor of the battery. Silicon solar cells are n = 1,Rs → 0,Rsh → ∞ under ideal conditions [3]. Therefore, the open-circuit voltage, short-circuit current, and fill factor can be expressed as follows: {Uoc=nsnkTqln(ILID+1)I=ILIscFF=uocln(uoc+0.72)uoc+1(1RsIscUoc) \left\{{\matrix{{{U_{oc}} = {{{n_s}nkT} \over q}\ln \left({{{{I_L}} \over {{I_D}}} + 1} \right)} \hfill \cr {I = {I_L} \approx {I_{sc}}} \hfill \cr {FF = {{{u_{oc}} - \ln ({u_{oc}} + 0.72)} \over {{u_{oc}} + 1}}\left({1 - {{{R_s}{I_{sc}}} \over {{U_{oc}}}}} \right)} \hfill \cr}} \right.

Here, ns,n are the number of batteries in series in the module and the ideality factor of the diode, respectively; B is the normalized open-circuit voltage; uoc = qUoc/nkT ; are the load current, photogenerated current, and diode response saturation current.

The performance of monolithic silicon solar cell modules is mainly affected by radiation intensity and temperature. Battery’s output power and power generation also strongly depend on both these factors. The short-circuit current is proportional to the radiation intensity within several orders of magnitude and is proportional to the light-receiving area of the battery [4]. The open-circuit voltage tends to saturate quickly with radiation, regardless of the battery area. The fill factor does not have a simple, functional relationship with the radiation amount. The open-circuit voltage, fill factor, and output power all decrease with an increase of component temperature. The temperature coefficients are −2.3 mV/°C, −0.0015/°C and −(0.004–0.005) W/°C, respectively. As the temperature of the components increases, the short-circuit current also increases slightly. The temperature coefficient is +0.107 mA/°C. Therefore, the output power of the photovoltaic system can be expressed as a function of the radiation intensity and temperature: Pm = Pm(G,T). The relationship between the short-circuit current on the one hand and the photogenerated current, the incident light intensity and the temperature is shown as follows: IscIL=IscR(GGR)+KT(ttR) {I_{sc}} \approx {I_L} = {I_{scR}}\left({{G \over {{G_R}}}} \right) + {K_T}(t - {t_R})

Here, IscR is the component’s short-circuit current obtained under standard testing conditions; is the radiation intensity under the standard test (1000 W/m2); KT is the temperature coefficient of the short-circuit current (amperes per degree Celsius [A/°C]); t,tR are the temperatures of the battery under arbitrary conditions and standard conditions (25 °C), respectively. Because the temperature has less influence on the short-circuit current, Eq. (3) can be rewritten as follows: IscIL=IscR(GGR)=γG {I_{sc}} \approx {I_L} = {I_{scR}}\left({{G \over {{G_R}}}} \right) = \gamma G

In the equation, γ is a constant, which is related to the battery area. We substitute Eq. (4) into Eq. (2) to obtain the open-circuit voltage: Uoc=nsnkTqln(γG/ID+1)nsnkTqln(γG/ID)=nsnkTq[ln(γ/ID)+lnG]=a+blnG {U_{oc}} = {{{n_s}nkT} \over q}\ln (\gamma G/{I_D} + 1) \approx {{{n_s}nkT} \over q}\ln (\gamma G/{I_D}) = {{{n_s}nkT} \over q}[\ln (\gamma /{I_D}) + \ln G] = a + b\ln G

Among them, a=nsnkTqln(γID) a = {{{n_s}nkT} \over q}\ln \left({{\gamma \over {{I_D}}}} \right) , b=nsnkTq b = {{{n_s}nkT} \over q} . We substitute Eqs (4) and (5) into Eq. (2) to get the fill factor, as follows: FFuocln(uoc+0.72)uoc+1(1RsγGa+blnG)=Uocns/bln[(Uocns/b)+0.72](Uocns/b)+1×[1RsγGa(1+(lnγlnID)1×lnG]Uocbln(Uoc/b)Uoc×(1RsγGa) \matrix{{FF \approx {{{u_{oc}} - \ln ({u_{oc}} + 0.72)} \over {{u_{oc}} + 1}}\left({1 - {{{R_s}\gamma G} \over {a + b\ln G}}} \right) = {{{U_{oc}}{n_s}/b - \ln [({U_{oc}}{n_s}/b) + 0.72]} \over {({U_{oc}}{n_s}/b) + 1}}} \hfill \cr {\times \left[ {1 - {{{R_s}\gamma G} \over {a(1 + {{(\ln \gamma - \ln {I_D})}^{- 1}} \times \ln G}}} \right] \approx {{{U_{oc}} - b\ln ({U_{oc}}/b)} \over {{U_{oc}}}} \times \left({1 - {{{R_s}{\gamma _G}} \over a}} \right)} \hfill \cr}

Therefore, the output power can be expressed as Pm=Uoc×Isc×FF×KT,P {P_m} = {U_{oc}} \times {I_{sc}} \times FF \times {K_{T,P}}

Here, KT,P = 1 + ε(t − tR) is the weight of the relationship between output power and temperature; ε is the temperature coefficient of output power [5]. The output power on the silicon solar cell monolithic module can be obtained by actually measuring the radiation intensity on the solar cell surface and the temperature of the module. The hourly power generation capacity of the solar cell can be calculated by adding up within hours.

Multiple linear regression model

The general form of the multiple linear regression model is yi=β0+β1x1i+β2x2i++βjxjii=1,2,,n;j=1,2,,k \matrix{{{y_i} = {\beta _0} + {\beta _1}{x_{1i}} + {\beta _2}{x_{2i}} + \cdots + {\beta _j}{x_{ji}}} \hfill \cr {i = 1,2, \cdots ,n;j = 1,2, \cdots ,k} \hfill \cr} , where j is the number of explanatory variables, βj is the regression coefficient, and xji is a variable. In the photovoltaic power generation system, the radiation amount and temperature greatly influence the battery output [6]. Therefore, the article builds a multiple linear regression model of a photovoltaic power generation system around these two factors. We substitute Eqs (4)(6) into Eq. (7) to obtain the following expressions: Pm=γG(a+blnG)KT,P{(1cG)a+blnGbln[(a+blnG)/b])a+blnG {P_m} = \gamma G(a + b\ln G){K_{T,P}}\{(1 - cG){{a + b\ln G - b\ln [(a + b\ln G)/b])} \over {a + b\ln G}}

c = Rsγ/a. We can simplify the above formula to get Pm=(γGγcG2)[abln(a/b)+blnGbln(1+balnG)]KT,P {P_m} = (\gamma G - \gamma c{G^2})[a - b\ln (a/b) + b\ln G - b\ln \left({1 + {b \over a}\ln G} \right)]{K_{T,P}}

We perform Taylor series expansion on the term ln(1+balnG) \ln \left({1 + {b \over a}\ln G} \right) in Eq. (9) and take the first three terms to obtain ln(1+balnG)c0+c1lnG+c2(lnG)2 \ln \left({1 + {b \over a}\ln G} \right) \approx {c^0} + {c^1}\ln G + {c^2}{(\ln G)^2}

In this expression, c0,c1.c2 are the expanded constant terms respectively. Eq. (10) is inserted into Eq. (9), and after finishing, we get Pm={[γaγbln(a/b)γbc0]G+(γbγbc1)GlnG+(γbc2)[G(lnG)2]{N1=γaγbln(a/b)γbc0N2=γbγbc1N4=γbcln(a/b)γac+γbcc0N3=γbc2N5=γbcc1γbcN6=γbcc2{x1=KT,PGx4=KT,PG2x2=KT,PGlnGx5=KT,PG2lnGx3=KT,PG(lnG)2x6=KT,PG2(lnG)2 \matrix{{{P_m} = \{[\gamma a - \gamma b\ln (a/b) - \gamma b{c^0}]} \hfill \cr {G + (\gamma b - \gamma b{c^1})G\ln G + (- \gamma b{c^2})[G{{(\ln G)}^2}]} \hfill \cr {\left\{{\matrix{{{N_1} = \gamma a - \gamma b\ln (a/b) - \gamma b{c_0}} & {{N_2} = \gamma b - \gamma b{c^1}} \cr {{N_4} = \gamma bc\ln (a/b) - \gamma ac + \gamma bc{c_0}} & {{N_3} = \gamma b{c^2}} \cr {{N_5} = \gamma bc{c_1} - \gamma bc} & {{N_6} = \gamma bc{c^2}} \cr}} \right.} \hfill \cr {\left\{{\matrix{{{x_1} = {K_{T,P}}G} & {{x_4} = {K_{T,P}}{G^2}} \cr {{x_2} = {K_{T,P}}G\ln G} & {{x_5} = {K_{T,P}}{G^2}\ln G} \cr {{x_3} = {K_{T,P}}G{{(\ln G)}^2}} & {{x_6} = {K_{T,P}}{G^2}{{(\ln G)}^2}} \cr}} \right.} \hfill \cr}

Then, Eq. (11) can be changed to Pm=N1x1+N2x2+N3x3+N4x4+N5x5+N6x6 {P_m} = {N_1}{x_1} + {N_2}{x_2} + {N_3}{x_3} + {N_4}{x_4} + {N_5}{x_5} + {N_6}{x_6}

Here, N1N6 are constants, x1x6 are six unknowns about temperature and radiation intensity. In the grid-connected photovoltaic system, the photovoltaic array is composed of many photovoltaic modules connected in series (Ns) and parallel (NP). The conversion efficiency of each part of the entire system is not 100%. The overall efficiency of the system η is η = η1η2η3, where η1,η2,η3 are the photovoltaic array efficiency, inverter efficiency, and alternating current (AC) grid-connected efficiency [7]. Then, the output power of the photovoltaic array is PA=PmNsNPη {P_A} = {P_m}{N_s}{N_P}\eta

We substitute Eq. (12) into Eq. (13) to get PA=N1x1+N2x2+N3x3+N4x4+N5x5+N6x6 {P_A} = N{{'}_1}{x_1} + N{{'}_2}{x_2} + N{{'}_3}{x_3} + N{{'}_4}{x_4} + N{{'}_5}{x_5} + N{{'}_6}{x_6}

Here, – N1N6 \mathop N\nolimits_1^{'} \,\mathop N\nolimits_6^{'} are constants. It can be seen that there is a multivariate linear relationship between the output power and the unknown variables. They can collect a lot of radiation intensity and temperature data. We use regression methods to obtain the six constants in Eq. (14). The predictive regression equation can be obtained. In a short period, we consider the test volume to be approximately constant [8]. At the same time, we can predict the power and output of the photovoltaic system by using the radiation and temperature measured at the last moment.

Data testing and regression analysis
Theoretical calculation of components

The photovoltaic system consists of 18 Kyocera KC130GH-2P polysilicon solar cell modules connected in series. The parameters of the single-piece components are shown in Table 1.

Kyocera KC130GH-2P polysilicon module parameters

Component Pmax, W Um, V Im, A Uoc, V Isc, A Area, m2
Polysilicon 130 17.6 7.39 21.9 8.02 0.81

We calculate the relationship between the open-circuit voltage Uoc and short-circuit current Ise with the radiation amount G under the standard condition of a single module. Figure 2 shows the relationship between output power and radiation and the component temperature.

Fig. 2

The relationship between the output power of the module and the amount of radiation.PV, photovoltaic system.

When the component’s temperature does not change, there is a logarithmic relationship between the open-circuit voltage and the amount of radiation. When the radiation becomes >500 W/m2, the open-circuit voltage tends to a particular value. There is a linear relationship between the short-circuit current and the amount of radiation, and there is also a linear relationship between output power and radiation [9]. When the temperature of the component gradually increases, the output power decreases significantly. Therefore, photovoltaic modules should be kept in as low-temperature working environments as possible.

Test system design and method

We tested the 2 kW grid-connected photovoltaic system for several months. The test system is shown in Figure 3. We collected data after installing the test equipment according to the requirements of the instrument. The test parameters are as follows: radiation intensity (G), ambient temperature (Ta), component back panel temperature (Tb), wind speed (v), power generation (PA), and hourly power generation (Q). Among them, G,Ta,Tb,v and PA are collected every 3 minutes and Q is recorded every hour. {PA,I=1.522x1+0.549x20.083x3+0.0135x40.0028x5+1.49×104x6PA,II=0.672x1+0.339x20.056x3+0.011x40.0023x5+1.5×104x6PA,III=0.802x1+0.404x20.067x3+0.013x40.003x5+1.3×105x6PA,IV=0.47x1+0.237x20.039x3+0.0076x40.0016x5+8.6×105x6 \left\{{\matrix{{{P_{A,I}} = - 1.522{x_1} + 0.549{x_2} - 0.083{x_3} + 0.0135{x_4} - 0.0028{x_5} + 1.49 \times {{10}^{- 4}}{x_6}} \hfill \cr {{P_{A,II}} = - 0.672{x_1} + 0.339{x_2} - 0.056{x_3} + 0.011{x_4} - 0.0023{x_5} + 1.5 \times {{10}^{- 4}}{x_6}} \hfill \cr {{P_{A,III}} = - 0.802{x_1} + 0.404{x_2} - 0.067{x_3} + 0.013{x_4} - 0.003{x_5} + 1.3 \times {{10}^{- 5}}{x_6}} \hfill \cr {{P_{A,IV}} = - 0.47{x_1} + 0.237{x_2} - 0.039{x_3} + 0.0076{x_4} - 0.0016{x_5} + 8.6 \times {{10}^{- 5}}{x_6}} \hfill \cr}} \right.

Fig. 3

Test system.AC, alternating current; DC, direct current; PV, photovoltaic system; Vdc

Regression analysis

We process classified and unclassified (IV) test data. The weather is classified into three categories: sunny (I), cloudy (II) and sunny to cloudy (or overcast to cloudy) (III). Then, we perform linear regression on the classified and unclassified test data. The regression results are shown in Tables 24.

Regression statistics

Weather type Sunny (I) Cloudy (II) Partly cloudy/overcast to cloudy (III) Uncategorized (IV)
R 0.997415 0.99715 0.99652 0.99667
R2 0.994838 0.99431 0.99314 0.99336
R-adjusted 0.98404 0.98545 0.98373 0.99026
Standard error, % 10.61 9.11 9.99 10.34
F-value 3051.26 3379.02 2,652.47 8,301.23
Significance value 0 0 0 0
Observation point 101 122 117 340

Note: R is the precision of regression coefficient; R2 is the precision of model fitting coefficient; R-adjusted is the precision of the fitting coefficient after correction.

Analysis of variance

Weather type Regression analysis Residual Sum
Sunny (I) Df 6 95 101
SS 205.93 1.068 206.998
MS 34.32 0.0112
Cloudy (II) Df 6 116 122
SS 166.97 0.955 167.9272
MS 27.828 0.0082
Partly cloudy/overcast to cloudy (III) Df 6 110 116
SS 160.17 1.107 161.2801
MS 26.69 0.0101
Unclassified (IV) Df 6 333 339
SS 532.81 3.562 536.38
MS 88.8 0.0106

The output results of the coefficients of each equation in the regression calculation

Weather type N1 \mathop N\nolimits_1^{'} N2 \mathop N\nolimits_2^{'} N3 \mathop N\nolimits_3^{'}
N4N5N6 \mathop N\nolimits_4^{'} \,\mathop N\nolimits_5^{'} \,\mathop N\nolimits_6^{'} Sunny (I) X −1.15 0.55 −0.08 0.01 0.00 1.49 × 10−4
Standard deviation, % 24.14 113.67 16.85 2.57 0.52 0.03
T −0.48 0.48 −0.49 0.52 −0.53 0.53
Cloudy (II) X −0.80 0.40 −0.07 0.01 0.00 1.5 × 10−4
Standard deviation, % 63.56 31.45 5.05 0.94 0.20 0.01
T −1.26 1.29 −1.33 1.42 −1.43 1.44
Partly cloudy/overcast to cloudy (III) X −0.68 0.34 −0.06 0.01 0.00 1.3×10−5
Standard deviation, % 53.43 26.59 4.31 0.82 0.17 0.01
T −1.28 1.29 −1.32 1.38 −1.38 1.39
Unclassified (IV) X −0.47 0.24 −0.04 0.01 0.00 8.6 × 10−5
Standard deviation, % 34.72 17.13 2.73 0.50 0.10 5.6 × 10−3
T −1.35 1.38 −1.43 1.51 −1.52 1.53

From Tables 24, the following conclusions can be drawn:

The linear regression equation for the three weather types and unclassified conditions is shown in Eq. (15). That is the photovoltaic system generating the power prediction equation.

The complex correlation coefficient between the six independent variables and the dependent variable in the linear regression model is R>0.996 or more [10]. The better the weather, the greater is the R-value, and the corresponding significance values are all zero. This means that the result is significant at the 0.01 level. After adjustment, R2>0.993, which shows that the established model fits better.

The constant term in the regression Eq. (15) is zero. The regression coefficients are within the range of 95% confidence. The corresponding significance values are all zero. This shows that the results are significant.

In sunny and cloudy weather, the classified regression equation PA,I, can be used to predict the power generation of the photovoltaic system. Its prediction accuracy is higher than that obtained by directly using the unclassified regression equation. For sunny to cloudy (or overcast to cloudy), we use the unclassified regression equation PA,IV to predict the accuracy.

It can also be seen from the data (Table x) that the regression coefficient and T-statistic of the unknown quantity X1X6 in the regression equation are also significant. This shows that the six established unknowns have a significant linear effect on the photovoltaic power generation system [11]. At the same time, the F-detection method is used to detect the significance of the regression equation. This also shows that the established model has an excellent fitting effect.

Analysis and discussion of forecasted results

We apply the prediction model to the 2 kW grid-connected photovoltaic system. Among them, the weather of sunny (I), cloudy (II), sunny to cloudy (or overcast to cloudy) (III) adopts the PA,I,PA,II,PA,IV forecast models, respectively [12]. We predict the average power generation (in kilowatts [kW]) and power generation (in kilowatt hour [kWh]) per hour for 2 consecutive days under different weather types. The forecasted values for sunny days (I) are higher than the measured values, the forecasted values for sunny to cloudy (or overcast to cloudy) (III) days are lower than the measured values, and cloudy days (II) have a better forecasting effect. The average residuals under sunny (I), cloudy (II), and sunny to cloudy (or overcast to cloudy) (III) weather are about 0.095, 0.066, and 0.126, respectively. The comparison result of the prediction residuals is shown in Figure 4.

Fig. 4

Comparison of three types of weather prediction residuals.

Conclusion

We have carried out theoretical calculations on the monolithic components of silicon crystal cells. On this basis, we establish a multiple linear regression model of photovoltaic system power generation and power generation with radiation and module working temperature as variables. Multiple linear regression analyses were conducted on the data under weather classification (I, II, and III) and unclassified conditions. The model has a good fit, and its accuracy is high.

Fig. 1

Equivalent circuit diagram of an ideal DC model of a photovoltaic module.DC, direct current.
Equivalent circuit diagram of an ideal DC model of a photovoltaic module.DC, direct current.

Fig. 2

The relationship between the output power of the module and the amount of radiation.PV, photovoltaic system.
The relationship between the output power of the module and the amount of radiation.PV, photovoltaic system.

Fig. 3

Test system.AC, alternating current; DC, direct current; PV, photovoltaic system; Vdc
Test system.AC, alternating current; DC, direct current; PV, photovoltaic system; Vdc

Fig. 4

Comparison of three types of weather prediction residuals.
Comparison of three types of weather prediction residuals.

Fig. 1

Equivalent circuit diagram of an ideal DC model of a photovoltaic module.DC, direct current.
Equivalent circuit diagram of an ideal DC model of a photovoltaic module.DC, direct current.

Fig. 2

The relationship between the output power of the module and the amount of radiation.PV, photovoltaic system.
The relationship between the output power of the module and the amount of radiation.PV, photovoltaic system.

Fig. 3

Test system.AC, alternating current; DC, direct current; PV, photovoltaic system; Vdc
Test system.AC, alternating current; DC, direct current; PV, photovoltaic system; Vdc

Fig. 4

Comparison of three types of weather prediction residuals.
Comparison of three types of weather prediction residuals.

Regression statistics

Weather type Sunny (I) Cloudy (II) Partly cloudy/overcast to cloudy (III) Uncategorized (IV)
R 0.997415 0.99715 0.99652 0.99667
R2 0.994838 0.99431 0.99314 0.99336
R-adjusted 0.98404 0.98545 0.98373 0.99026
Standard error, % 10.61 9.11 9.99 10.34
F-value 3051.26 3379.02 2,652.47 8,301.23
Significance value 0 0 0 0
Observation point 101 122 117 340

The output results of the coefficients of each equation in the regression calculation

Weather type N1 \mathop N\nolimits_1^{'} N2 \mathop N\nolimits_2^{'} N3 \mathop N\nolimits_3^{'}
N4N5N6 \mathop N\nolimits_4^{'} \,\mathop N\nolimits_5^{'} \,\mathop N\nolimits_6^{'} Sunny (I) X −1.15 0.55 −0.08 0.01 0.00 1.49 × 10−4
Standard deviation, % 24.14 113.67 16.85 2.57 0.52 0.03
T −0.48 0.48 −0.49 0.52 −0.53 0.53
Cloudy (II) X −0.80 0.40 −0.07 0.01 0.00 1.5 × 10−4
Standard deviation, % 63.56 31.45 5.05 0.94 0.20 0.01
T −1.26 1.29 −1.33 1.42 −1.43 1.44
Partly cloudy/overcast to cloudy (III) X −0.68 0.34 −0.06 0.01 0.00 1.3×10−5
Standard deviation, % 53.43 26.59 4.31 0.82 0.17 0.01
T −1.28 1.29 −1.32 1.38 −1.38 1.39
Unclassified (IV) X −0.47 0.24 −0.04 0.01 0.00 8.6 × 10−5
Standard deviation, % 34.72 17.13 2.73 0.50 0.10 5.6 × 10−3
T −1.35 1.38 −1.43 1.51 −1.52 1.53

Kyocera KC130GH-2P polysilicon module parameters

Component Pmax, W Um, V Im, A Uoc, V Isc, A Area, m2
Polysilicon 130 17.6 7.39 21.9 8.02 0.81

Analysis of variance

Weather type Regression analysis Residual Sum
Sunny (I) Df 6 95 101
SS 205.93 1.068 206.998
MS 34.32 0.0112
Cloudy (II) Df 6 116 122
SS 166.97 0.955 167.9272
MS 27.828 0.0082
Partly cloudy/overcast to cloudy (III) Df 6 110 116
SS 160.17 1.107 161.2801
MS 26.69 0.0101
Unclassified (IV) Df 6 333 339
SS 532.81 3.562 536.38
MS 88.8 0.0106

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