3.1.4 maximum MPP voltage U MPPmax maximum voltage at which the inverter can convert its rated power under MPPT conditions NOTE If the specified value of the manufacturer for U MPPmax
Inverter input (PV generator)
3.1.1 maximum input voltage (U DCmax ) allowed maximum voltage at the inverter input
NOTE Exceeding of U DCmax may destroy the equipment under test
3.1.2 minimum input voltage (U DCmin ) minimum input voltage for the inverter to energize the utility grid, independent of mode of operation
3.1.3 rated input voltage (U DC,r ) input voltage specified by the manufacturer, to which other data sheet information refers
NOTE If this value is not specified by the manufacturer, V dc,r = (V mppmax + V mppmin )/2 shall be used
3.1.4 maximum MPP voltage (U MPPmax ) maximum voltage at which the inverter can convert its rated power under MPPT conditions
NOTE If the specified value of the manufacturer for U MPPmax is higher than 0,8 × U DCmax , the measurement must be performed with
3.1.5 minimum MPP voltage (U MPPmin ) minimum voltage at which the inverter can convert its rated power under MPPT conditions
NOTE The actual minimum MPP voltage may depend on the grid voltage level
3.1.6 rated input power (P DC,r ) rated input power of the inverter, which can be converted under continuous operating conditions
If the manufacturer does not specify the value, it can be calculated using the formula \$P_{DC,r} = \frac{P_{AC,r}}{\eta_{conv,r}}\$ where \$\eta_{conv,r}\$ represents the conversion efficiency at the rated DC voltage In cases where the rated conversion efficiency is not provided, it must be measured.
3.1.7 maximum input current (I DC,max ) maximum input current of the inverter under continuous operating conditions
NOTE At inverters with several independent inputs, this value may depend on the chosen input configuration.
Inverter output (grid)
3.2.1 rated grid voltage (U AC,r ) utility grid voltage to which other data sheet information refers
3.2.2 rated power (P AC,r ) active power the inverter can deliver in continuous operation
Measured quantities
PV simulator MPP-Power (P MPP, PVS )
MPP power provided by the PV simulator
3.3.2 input power (P DC ) measured input power of the device under test
PV simulator MPP voltage (U MPP, PVS )
MPP voltage provided by the PV simulator
3.3.4 input voltage (U DC ) measured input voltage of the device under test
PV simulator MPP current (I MPP, PVS )
MPP current provided by the PV simulator
3.3.6 input current (I DC ) measured input current of the device under test
3.3.7 output power (P AC ) measured AC output power of the device under test
3.3.8 output voltage (U AC ) measured AC voltage
3.3.9 output current (I AC ) measured AC output current of the device under test
Calculated quantities
MPPT efficiency, denoted as η MPPT, is the ratio of the energy extracted by the device under test during a specified measurement period TM to the theoretically available energy from the PV simulator at the maximum power point (MPP).
(1) where pDC(t) instantaneous value of the power drawn by the device under test; pMPP(t) instantaneous value of the MPP power provided theoretically by the PV simulator
The conversion efficiency, denoted as energetic (\(η_{conv}\)), is defined as the ratio of the energy output from the device under test at the AC terminal during a specified measurement period (\(T_M\)) to the energy input received at the DC terminal.
The instantaneous value of the delivered power at the AC terminal of the device under test is represented as \$p_{AC}(t)\$, while the instantaneous value of the accepted power at the DC terminal is denoted as \$p_{DC}(t)\$.
The overall efficiency, denoted as energetic (\(η_t\)), is the ratio of the energy output from the device under test at the AC terminals during a specified measurement period (\(T_M\)) to the theoretically provided energy from the PV simulator.
Other definitions
3.5.1 photovoltaic array simulator current source emulating the static and dynamic behaviour of a PV array, in particular the current-voltage characteristic (cf IEC/TS 61836) The requirements are outlined in Clause A.1
General description
The static and dynamic MPPT efficiencies are calculated using the sampled instantaneous voltage and current values at the inverter's input, reflecting the actual power utilized by the inverter from the theoretically available PV generator power.
The static MPPT efficiency is determined by means of measurement as follows:
U DC,i sampled value of the inverter’s input voltage;
IDC,i sampled value of the inverter’s input current;
∆T period between two subsequent sample values
The static MPPT efficiency describes the accuracy of an inverter to regulate on the maximum power point on a given static characteristic curve of a PV generator
NOTE U DC,i and I DC,i must be sampled at the same time b) Dynamic MPPT efficiency
The static MPPT efficiency does not account for variations in irradiation intensity and the inverter's transition to a new operating point To evaluate this transient characteristic, the dynamic MPPT efficiency is introduced, which is defined as follows:
MPPT efficiency measures how effectively an inverter adjusts its operating conditions to align with the maximum power point on a PV generator's characteristic curve This efficiency can be categorized into static and dynamic conditions.
Inverters with subpar MPPT performance lead to discrepancies between the DC input voltage and the MPP voltage, affecting conversion efficiency Therefore, it is essential to conduct simultaneous measurements of static MPPT efficiency and static power conversion efficiency as outlined in section 4.3.
(detailed explanation in the informative Annex F)
Test set-up
The generic test setup for single-phase grid-connected inverters is illustrated in Figure 1, which can also serve as a single-phase representation of a test circuit for multi-phase inverters.
Figure 1 – Exemplary test set-up for MPPT efficiency measurements Key
EUT Equipment under test (inverter);
The DC source connected to the PV input of the inverter shall be a PV simulator in accordance to the specifications in Clause A.1
The AC supply of the inverter must be in accordance to the specifications in Clause A.2
4.3 Conversion and static MPPT efficiency
The measurement of the conversion and static MPPT efficiency shall be performed simultaneously with test specifications as defined in Table 1
For the conversion efficiency, the DC and AC voltages shall be measured as close as possible to the inverter terminals.
For MPPT efficiency, the DC voltage shall be measured as close as possible to the PV simulator For combined conversion and
To ensure accurate MPPT efficiency measurements, it is essential to take two voltage readings: one at the output of the PVS and another at the DC input of the EUT This approach helps prevent measurement errors caused by voltage drops occurring between the PVS and the EUT.
∆Tj period in which the power PMPP,PVS,j is provided;
∆Ti period in which the power UDC,i and IDC,i are sampled
Table 1 – Test specifications for the conversion and static MPPT efficiency
MPP voltage of the simulated I/U characteristic of the PV generator
MPP power of the simulated I/U characteristic normalised to rated DC power d , P MPP,PVS /P DC,r
The lower value between UMPPmin and UMPPmax will be utilized to ensure proper MPPT operation without being hindered by voltage limits For devices not designed for thin-film technologies, certain measuring points may be excluded Additionally, for other cell technologies, the maximum MPP voltage (UMPPmax) must be adjusted to match the maximum DC voltage (UDCmax) To determine the static MPPT efficiency based on normalized rated AC power, the procedure outlined in Annex E should be followed.
Measurements should be conducted at the nominal grid voltage UAC,r to prevent any influence of grid voltage levels on the results Any deviations from this standard must be recorded in the measurement report.
For each of the above specified test conditions a corresponding I/U characteristic has to be defined which must be emulated by means of the PV simulator
NOTE 1 The requirements on the accuracy of the defined characteristic are outlined in Annex C
After commissioning the device under test the stabilization of the MPP tracking must be awaited firstly
The measurement should be performed at an ambient temperature of 25 °C ± 5 °C Other ambient temperatures can be mutually agreed The actual ambient temperature shall be specified in the test report
Each test condition, as outlined in Table 1, requires a measurement duration of 10 minutes For the initial power level at each MPP voltage setting, it is essential to wait for the MPPT tracker to stabilize If stabilization is not observed, a minimum stabilization time of 5 minutes is mandated.
After adjusting the power level, it is essential to allow a general stabilization period of 2 minutes Data collected during this stabilization phase should not be included in the calculations for static MPPT and conversion efficiency.
After the stabilisation of the MPP tracking the following parameters have to be logged:
The MPP voltages at the different test conditions (U , U DC,r , U MPPmin ) shall be kept constant during the test for each power level.
For test devices featuring multiple independent input terminals, it is essential to conduct measurements for all input configurations specified by the manufacturer In the absence of specific instructions from the manufacturer, the total power should be evenly distributed across the individual input terminals.
4.3.3 Evaluation – Calculation of conversion and static MPPT efficiency
For each MPP voltage and each simulated I/U characteristic respectively the following particulars are to be calculated and documented in the measuring report:
– the weighted European MPPT efficiency according to Annex D.1
– as well as the weighted CEC MPPT efficiency (California Energy Commission) according to Annex D.2.
Furthermore, modifications of the internal setting of the device under test, conspicuous behaviour during the measurement as well as variations from the defined procedure are to be documented
NOTE Alternative test procedures are in discussion
Dynamic MPPT efficiency tests should be conducted at the rated DC voltage For devices with multiple independent input terminals, measurements must be taken for all configurations specified by the manufacturer Unless stated otherwise, the total power should be evenly distributed across the individual input terminals.
For each test condition outlined in Annex B, a corresponding I/V characteristic must be established and emulated using the PV simulator A radiation intensity of 1,000 W/m² is associated with the rated DC power PDC, r of the device being tested Prior to each test sequence, an initial set-up time is required to allow the device to stabilize, and measurements taken during this period are excluded from the calculation of dynamic MPPT efficiency as specified in section 4.4.3.
For each power level measured as outlined in Table 1, the conversion efficiency (\$η_{conv}\$) and static Maximum Power Point Tracking (MPPT) efficiency (\$η_{MPPT}\$) will be calculated as energetic averages based on definitions 3.4.2 and 3.4.1 The findings will be recorded in the measurement report corresponding to each test condition specified in Table 1.
The test sequences are influenced by variations in solar irradiance, with measurements primarily conducted using a c-Si PV model, and additional assessments possible with a TF model (refer to Table C.1) The selected PV technology model must be documented in the report.
The measurement should be performed at an ambient temperature of 25 °C ± 5 °C Other ambient temperatures can be mutually agreed The actual ambient temperature shall be specified in the test report
The measurement of the dynamic MPPT efficiency has to be performed according to the test conditions as outlined in the tables in Annex B
The sampling and recording rates are not explicitly stated, but they need to be sufficiently high to accurately capture the specific Maximum Power Point (MPP) tracking behavior of the tested device This is especially important for monitoring the fluctuations in input voltage that occur at photovoltaic (PV) inverters, which are influenced by multiples of the grid frequency.
The standard does not specify a defined waiting period for various MPPT methods and their parameters, as stabilization time varies based on the characteristics of the device under test This time must be documented in the test report If stabilization of the MPPT is not observed due to the device's behavior, a minimum latency of 5 minutes is required.
For the evaluation and the determination of the dynamic MPPT efficiency the following parameters are to be recorded during the measurement:
– PMPPPVS MPP power provided by the PV simulator;
– PDC measured input power of the device under test;
– U MPPPVS MPP voltage provided by the PV simulator;
– UDC measured input voltage of the device under test;
– IMPPPVS MPP current provided by the PV simulator;
– IDC measured input current of the device under test
The sampling and recording rates are unspecified but must be sufficiently high to accurately capture the specific Maximum Power Point (MPP) tracking behavior of the device under test, particularly the fluctuations in input voltage at PV inverters that occur at multiples of the grid frequency It is essential that U DC and I DC are sampled simultaneously.
NOTE 4 P DC may be calculated from U DC and I DC
4.4.3 Evaluation – Calculation of the dynamic MPPT efficiency
The overall dynamic MPPT efficiency is the mean value of the single dynamic MPPT efficiencies of the test sequences according to tables B.1 and B.2 It is calculated by:
– ηMPPTdyn,t averaged dynamic MPPT efficiency
– ηMPPTdyn,I dynamic MPPT efficiency for each test sequence
NOTE Unless other values are defined the weighting factor is assumed to be a i =1, i=1 N
The dynamic MPPT efficiency, denoted as \$\eta_{MPPT,dyn}\$, must be calculated for each test sequence as outlined in Annex B, using the recorded data in accordance with the specified definition The findings should be documented in the measurement report.
For each test sequence the calculated MPPT efficiency is to be documented tabularly in the measuring report
Furthermore, modifications of the internal setting of the device under test, conspicuous behaviour during the measurement as well as variations from the defined procedure are to be documented
NOTE 1 The requirements on the accuracy of the defined characteristic are outlined in Annex C
Dynamic MPPT efficiency
NOTE Alternative test procedures are in discussion
Dynamic MPPT efficiency tests should be conducted at the rated DC voltage For devices featuring multiple independent input terminals, measurements must be taken for all configurations specified by the manufacturer In the absence of specific instructions from the manufacturer, the total power should be evenly distributed across the individual input terminals.
For each test condition outlined in Annex B, a corresponding I/V characteristic must be defined and emulated using the PV simulator A radiation intensity of 1,000 W/m² is associated with the rated DC power PDC, r of the device being tested Prior to each test sequence, an initial set-up time is required to allow the device to stabilize, and the values measured during this period are excluded from the calculation of dynamic MPPT efficiency as per section 4.4.3.
For each power level measured as outlined in Table 1, the conversion efficiency (\$η_{conv}\$) and static Maximum Power Point Tracking (MPPT) efficiency (\$η_{MPPT}\$) will be calculated as energetic averages based on definitions 3.4.2 and 3.4.1 The findings will be recorded in the measurement report corresponding to each test condition specified in Table 1.
The test sequences are influenced by variations in solar irradiance, with measurements primarily based on a c-Si PV model, and additional assessments possible using a TF model (refer to Table C.1) The selected PV technology model must be clearly documented in the report.
The measurement should be performed at an ambient temperature of 25 °C ± 5 °C Other ambient temperatures can be mutually agreed The actual ambient temperature shall be specified in the test report
The measurement of the dynamic MPPT efficiency has to be performed according to the test conditions as outlined in the tables in Annex B
The sampling and recording rates are unspecified but must be sufficiently high to accurately capture the specific Maximum Power Point (MPP) tracking behavior of the device under test This is particularly important for monitoring the fluctuations of the input voltage at photovoltaic (PV) inverters, which occur at multiples of the grid frequency.
The standard does not specify a defined waiting period for various MPPT methods and their parameters, as the stabilization time is contingent upon the specific characteristics of the device under test This time must be appropriately set and documented in the test report If stabilization of the MPPT is not observable due to the device's behavior, a minimum latency of 5 minutes is required.
For the evaluation and the determination of the dynamic MPPT efficiency the following parameters are to be recorded during the measurement:
– PMPPPVS MPP power provided by the PV simulator;
– PDC measured input power of the device under test;
– U MPPPVS MPP voltage provided by the PV simulator;
– UDC measured input voltage of the device under test;
– IMPPPVS MPP current provided by the PV simulator;
– IDC measured input current of the device under test
The sampling and recording rates are not explicitly stated, but they need to be sufficiently high to accurately capture the specific Maximum Power Point (MPP) tracking behavior of the device being tested This is especially important for monitoring the fluctuations in input voltage at PV inverters, which occur at multiples of the grid frequency Additionally, it is crucial that U DC and I DC are sampled simultaneously.
NOTE 4 P DC may be calculated from U DC and I DC
4.4.3 Evaluation – Calculation of the dynamic MPPT efficiency
The overall dynamic MPPT efficiency is the mean value of the single dynamic MPPT efficiencies of the test sequences according to tables B.1 and B.2 It is calculated by:
– ηMPPTdyn,t averaged dynamic MPPT efficiency
– ηMPPTdyn,I dynamic MPPT efficiency for each test sequence
NOTE Unless other values are defined the weighting factor is assumed to be a i =1, i=1 N
The dynamic MPPT efficiency, denoted as \$\eta_{MPPT,dyn}\$, for each test sequence outlined in Annex B, must be calculated using the recorded data as per the defined criteria The findings should be included in the measurement report.
For each test sequence the calculated MPPT efficiency is to be documented tabularly in the measuring report
Furthermore, modifications of the internal setting of the device under test, conspicuous behaviour during the measurement as well as variations from the defined procedure are to be documented
NOTE 1 The requirements on the accuracy of the defined characteristic are outlined in Annex C
The standard does not specify a defined waiting period for various MPPT methods and their parameters, as stabilization time varies based on the individual characteristics of the device under test This time must be appropriately set and documented in the test report If stabilization of the MPPT is not observed due to the device's behavior, a minimum latency of 5 minutes is required.
5 Calculation of the overall efficiency
The DC power is converted to the AC power PAC by means of the conversion efficiency ηconv The actual
DC power PDC of the device under test is the product from the static MPPT efficiency ηMPPTstat and the MPP power provided by the PV simulator PMPP, PVS:
PAC = ηconv⋅PDC = ηconv⋅ηMPPTstat⋅PMPP,PVS = ηt⋅PMPP, PVS (7) The overall efficiency ηt can also be considered as
Formula (8) should be utilized for every power and voltage level listed in Table 1 By applying the weighting factors of EUR and CEC as outlined in sections D.1 and D.2, the efficiencies can be summarized for each voltage level (U MPPmax, U DC,r, U MPPmin) Consequently, the overall weighted efficiencies, denoted as η t,EUR and η t,CEC, are derived.
Requirements on the measuring apparatus
PV generator simulator 1 4
To accurately assess the MPPT efficiency as outlined in Clause 4, it is essential to utilize a PV simulator that precisely replicates both the stationary and dynamic characteristics of a PV generator.
In the following the minimal requirements are defined, which must be met by the used PV simulator
The requirements outlined in Table A.1 specify the dependency of the maximum power point (MPP) voltage on irradiation, the relationship between MPP voltage and open circuit voltage, and the correlation between MPP current and short circuit current Additional requirements for both static and dynamic scenarios are detailed in the subsequent sections.
Table A.1 – General requirements on the simulated I/V characteristic of the PV generator cSi- technology Thin film technology Tolerance
A.1.2 Requirements on the static characteristic
The current/voltage characteristics of the PV simulator must align with the specified models of the PV generator outlined in Annex C Key parameters for the partial tests, including UOC, UMPP, PMPP, FFU, and FFI, are critical for compliance Additionally, the actual current/voltage characteristics of the PV simulator should not deviate more than 1% in power within the voltage range of 0.9 * UMPP, PVS to 1.1 * UMPP, PVS, compared to the predetermined characteristics under rated conditions.
The PV simulator must accurately replicate the current and voltage characteristics of the PV generator model as outlined in Annex C, even during transient changes in parameters such as UOC, UMPP, and PMPP Any variations in these parameters, particularly during specified ramps, should be minimized to less than 1% of the corresponding output value.
The PV simulator must accurately emulate the PV characteristics as outlined in Annex C for devices operating at voltages below 0.9 times the maximum power point voltage (U MPP, PVS).
A.1.3 Requirement on the transient stability
During the measurement time the MPP power must not change more the 0,1 % related to the specified I/U characteristic at rated conditions
A.1.4 Requirements on the dynamic characteristic
A PV simulator must be designed to ensure optimal operation of the device under test, particularly in relation to Maximum Power Point (MPP) tracking To achieve this, the simulator needs to exhibit sufficient dynamic response to accurately follow the voltage fluctuations that arise during measurements, such as the typical ripple produced by single-phase inverters at twice the grid frequency.
The dynamic characteristics required for a PV simulator can significantly differ based on the specific properties of the device being tested Consequently, some test devices may necessitate higher performance standards Insufficient dynamic response can adversely impact the Maximum Power Point Tracking (MPPT) behavior of the device, particularly for MPPT methods that rely on the relationship between input current and input voltage To ensure that the MPPT tracking is not negatively influenced by the PV simulator, it may be essential to conduct comparative measurements with a real PV generator prior to the MPPT test.
For devices under test lacking galvanic isolation between the DC and AC sides, the PV simulator's output must be ungrounded and compatible with the voltages present between the device's DC input and protective earth (PE) To minimize any adverse effects on the electromagnetic compatibility (EMC) characteristics of the device under test, the capacitance between the PV simulator's output and ground should be kept to a minimum.
The discrepancies between the emulated current and voltage characteristics of the PV simulator and its default settings can significantly impact measurement outcomes Therefore, it is essential to perform proper calibration prior to measurements to ensure that the PV simulator operates correctly with the device under test and that the actual parameters generated by the simulator, such as open-circuit voltage (UOC), maximum power point voltage (UMPP), and maximum power point (PMPP), are accurate.
AC power supply 1 5
As AC source for the measurements a grid simulator should be used preferably, which provides a stable and interference-free AC voltage according to EN 50160
To ensure accurate testing, it is crucial to verify that the device under test is not adversely influenced by grid conditions, such as voltage levels and distortions, in the absence of a grid simulator.
Generally all measurements shall be performed at the rated grid voltage UAC,r (- 3 % to + 3 %) and rated grid frequency fAC,r ± 0,1 Hz as specified by the manufacturer of the device under test
NOTE Compliance with these limits assures that abnormal effects on the behaviour of the device under test due to the grid voltage are avoided
Test conditions for dynamic MPPT efficiency
Test profiles
Dynamic MPPT efficiency tests will be conducted following specific sequences The percentage specification of radiation intensity is linked to standard test conditions (STC), where 100% corresponds to 1.
Test time Irr ad ian ce ( W /m 2 )
Ramp tests (low - medium irradiance)
Time considered for evaluation Simulated irradiance
Ramp down x W/m²/s Dwell time n Repetitions
Dwell time Initial waiting time
Figure B.1 – Test sequence for fluctuations between low and medium irradiance
Test time Irr ad ian ce ( W /m 2 )
Ramp tests (medium - high irradiance)
Time considered for evaluation Simulated Irradiance
Ramp down x W/m²/s Dwell time n Repetitions
Figure B.2 – Test sequence for fluctuations between medium and high irradiance
Descriptive code: n repetitions, in brackets the rise time t1, the dwell time t2 on high level (value +H), the fall time t3 and finally the dwell time on low level (value +L).
Test sequence with ramps 10 % - 50 %
Table B.1 – Dynamic MPPT-Test 10 % 50 % G STC (valid for the evaluation of η MPPTdyn )
# Slope Ramp UP Dwell time Ramp DN Dwell time Duration
NOTE Ramp and dwell times are given as rounded values
Start-up and shut-down test with slow ramps .1 8
Table B.2 – Dynamic MPPT-Test 30 % 100 % G STC (valid for the evaluation of η MPPTdyn )
From-to Delta Dwell time setting Waiting time setting
# Slope Ramp UP Dwell time Ramp DN Dwell time Duration
NOTE Ramp and dwell times are given as rounded values
Total test duration
The total test duration is the sum of the test sequences according to Clauses B.2, B.3 and B.4
Test time Irr ad ian ce ( W /m 2 )
Time period of measurement Simulated irradiance
Figure B.3 – Test sequence for the start-up and shut-down test of grid connected inverters
Models of current/voltage characteristic of PV generator
C.1 PV generator model for MPPT performance tests
Table C.1 – Technology-dependent parameters cSi- technology Thin film technology Tolerance
The final definition of the parameters is in process
For the measurements of the static and dynamic MPPT efficiency, changes of module temperature shall be neglected
MPP to open circuit voltage ratio:
MPP to short circuit current ratio:
Formula for the PV current as a function of PV voltage:
TPV computed PV generator temperature;
T0 correction temperature (T0 = -3 °C); k irradiance gain (k = 0,03 km 2 /W); τ time constant (τ = 5 min); α temperature coefficient of the current; β temperature coefficient of the voltage;
CR, CV, CG technology depending correction factor
Voltage ratio from UMPP at an irradiance of 200 W/m 2 to UMPP at an irradiance of 1 000 W/m 2
In order to fulfil the requirements of Table 1 (constant U MPP at each power step), for U oc in
Formula (C.5) U oc,STC should be used rather than C.7
Irradiance G and temperature T dependent short circuit current in Formula (C.3):
Irradiance and temperature dependent open circuit voltage in Formula (C.3):
OC OC STC PV STC V R
The parameter of the PV generator model must be set as follows:
Table C.2 – Technology-dependent parameters cSi- technology Thin film technology Tolerance
Objective: PMPP,STC = 1 000 W, VMPP,STC = 100 V, cSi –Technology, TPV = 25 °C
Table C.3 – MPP-values obtained with the cSi PV model
Figure C.1 – Irradiation-dependent U-I- and U-P characteristic of a c-Si PV generator
Objective: PMPP,STC = 1 000 W, UMPP,STC = 100 V, TF–Technology, TPV = 25 °C
Figure C.2 – Irradiation-dependent U-I- and U-P characteristic of a thin-film PV generator
Table C.4 – MPP-values obtained with the TF-PV mode
C.2 Alternative PV generator model for MPPT performance tests”
Alternative models for PV generator characteristics, such as the 1-diode and 2-diode models, can also be utilized It is essential that these models meet the technology-dependent parameters outlined in Table C.1 If a model fails to satisfy the requirements of Table C.1, the resulting technology-dependent parameters must be documented, along with the specific model used and its associated parameters.
Example: cSi-PV generator with 1-diode model
I ph photo current (source current) in A;
G irradiance in W/m 2 ; c constant for the linear temperature model in K;
C 0 coefficient of diode saturation current in A/K 3 ; m diode factor; e 0 elementary charge in C; k Boltzmann constant in J/K
For the application of the 1-diode model for the crystalline technology, the following parameters can be applied:
– the photo current at GSTC amounts to I ph = 1 A;
– the band gap amounts to 1,1 eV
With these parameters, a standard PV cell is obtained that fulfils the requirements of Table C.1
By parallel or serial interconnections of the standard cell, PV generators of arbitrary size can be configured
For the calculation of a weighted European MPPT and conversion efficiency the following formula and factors are to be applied:
MPPTstat EUR MPP MPP MPP MPP
+ ⋅η + ⋅η (D.1) aEU_i weighting factor ηMPP_i static MPPT efficiency at partial MPP power MPP_i
Table D.1 – Weighting factors and partial MPP power levels for the calculation of the European efficiency
Factor aEU_1 aEU_2 aEU_3 aEU_4 aEU_5 aEU_6
MPP_1 MPP_2 MPP_3 MPP_4 MPP_5 MPP_6 0.05 0.1 0.2 0.3 0.5 1
For the calculation of a weighted CEC MPPT and conversion efficiency the following formula and factors are to be applied:
MPPTstat CEC MPP MPP MPP MPP
+ ⋅η + ⋅η (D.2) aCEC_i weighting factor ηMPP_i static MPPT efficiency at partial MPP power MPP_i
Table D.2 – Weighting factors and partial MPP power levels for the calculation of the CEC efficiency
Factor aCEC_1 aCEC_2 aCEC_3 aCEC_4 aCEC_5 aCEC_6
MPP_1 MPP_2 MPP_3 MPP_4 MPP_5 MPP_6 0.1 0.2 0.3 0.5 0.75 1
Specification of the static MPPT and conversion efficiency in terms of normalised rated AC power
NOTE The procedure in this Annex is exemplified for the case of conversion efficiency measurements It can be applied to MPPT efficiency measurements in the same way
As a result from the static MPPT and conversion efficiency measurement the following data are available
- Output power of the inverter PAC
- Input power of the inverter PDC
- by PAC and PDC calculated efficiency η
A normalisation of PDC and PAC to the rated dc power PDC,r leads to the values in Table E.1 The values in brackets are for exemplary clarification only
Table E.1 – Measured quantities at the conversion efficiency test
P DC /P DC,r P AC /P DC,r Efficiency η pDC_1 = 1 pAC_1 =(0.9740) η1 = (0.9740) pDC_0.75 = 0.75 pAC_0.75 = (0.7370) η0.75 = (0.9827) pDC_0.5 = 0.5 pAC_0.5 = (0.4940) η0.5 = (0.9880) pDC_0.3 = 0.3 pAC_0.3 = (0.2960) η0.5 = (0.9867) pDC_0.25 = 0.25 pAC_0.25 = (0.2460) η0.25 = (0.9840) pDC_0.2 = 0.2 pAC_0.2 = (0.1950) η0.2 = (0.9750) pDC_0.1 = 0.1 pAC_0.1 = (0.0930) η0.1 = (0.9300) pDC_0.05 = 0.05 pAC_0.05 = (0.0420) η0.05 = (0.8400)
Based on these results an approximation for the specification of the efficiency in term of normalised rated
AC power is given in the following steps
Re-normalisation of output power P AC to the rated output power P AC,r
The inverter's output power, denoted as PAC,r, is considered to be equal to its rated output when it operates at the rated input power, PDC,r, on the DC side This relationship highlights the efficiency and performance of the inverter under optimal conditions.
PDC,r is the rated efficiency ηr, which is used to calculate the normalised output power pAC
Representation of the conversion efficiency in terms of normalised rated output power
The efficiency can be expressed in terms of normalized rated output power, as indicated in (E.1) However, the power values \( p'_{AC} \) vary across the nodes, as detailed in section 4.5.1 and illustrated in Table E.2.
Table E.2 – Conversion efficiency in term of rated AC power p′ AC = P AC /P AC,r η p′AC_1 = 1,000000 η1 = 0,9740 p′AC_0.75 = (0,756674) η0.75 =0,9827 p′AC_0.5 = (0,507187) η0.5 =0,9880 p′AC_0.3 = (0,303901) η0.3 =0,9867 p′AC_0.25 = (0,252567) η0.25 =0,9840 p′AC_0.2 = (0,200205) η0.2 =0,9750 p′AC_0.1 = (0,095483) η0.1 =0,9300 p′AC_0.05 = (0,043121) η0.05 =0,8400
If the calculated values of p′AC fall within ±5% of the normative nodes specified in section 4.5.1, sufficient accuracy is assumed, and no further interpolation is necessary The limits are detailed in Table E.3.
Table E.3 – Allowed limits for the nodes of the normalised AC power
If the calculated values of p′AC fall outside the limits specified in Table E.3, interpolation on the normative values is necessary This interpolation utilizes the average slope of the measured efficiency values New efficiency values are derived using a linear equation, aiming to determine the efficiency values η ′′ i precisely at the normative nodes p″AC, as illustrated in Table E.4.
Table E.4 – Seeked values by means of interpolation
It is assumed that at rated DC power on the input side the inverter delivers rated AC power at the output Therefore η 1 ′′ is always η = η 1 ′′ 1
The average slope in the point ( p AC _ 0.75 , η 0.75 ) is
The linear equation with slope m0.75 through the point ( p AC _ 0.75 , η 0.75 ) is
′′ ′′ η = η + ⋅ + , where η ′′is the new efficiency at the power node p″AC
If p′′ AC is set to p AC ′′ = p AC ′′ _ 0.75 = 0.75, the new interpolated efficiency value is found:
According to the explanations above the interpolated efficiency value η ′′ 0.75 is found by
Based on the measured values in Table E.3 the interpolated conversion efficiency values in terms of rated AC power are shown in Table E.5
Recent advancements in PV module specifications now include not only power ratings at Standard Test Conditions (STC) and lower irradiance levels but also energy yields measured over specific time periods under real weather conditions This enhancement allows for more accurate calculations of the DC energy yield of a PV array However, neglecting energy losses due to inadequate Maximum Power Point (MPP) tracking by inverters introduces significant uncertainty in determining the energy yield of grid-connected PV systems The implementation of overall or total efficiency, denoted as ηt, as outlined in the standard, addresses this issue effectively.
The standard aims to establish a comprehensive measure of overall efficiency (\(\eta_t\)) that encompasses both conversion efficiency and maximum power point tracking (MPP-tracking) characteristics This approach provides a more precise representation of the performance of grid-connected photovoltaic (PV) inverters compared to relying solely on conversion efficiency (\(\eta_{conv}\)).
A grid-connected inverter comprises two essential components: the Maximum Power Point (MPP) tracker, which continuously extracts the maximum available power (P MPP) from the solar array, influenced by factors such as irradiance (G) and module temperature (T), and the DC-AC converter, responsible for transforming the available direct current (DC) power (PDC) into alternating current (AC) power.
PAC as efficiently as possible
Ensuring optimal static performance of the inverter is crucial, which is why a significant portion of the standard focuses on this aspect Additionally, due to varying weather conditions based on location, the standard includes tests for dynamic performance that assess the inverter's sensitivity to fluctuating irradiance levels.
Definition: DC-AC conversion efficiency
The conversion efficiency (\( \eta_{\text{conv}} \)) of an inverter is influenced by both the DC power and the DC voltage, expressed as \( \eta_{\text{conv}} = f(P_{\text{DC}}, U_{\text{DC}}) \) To accurately indicate the conversion efficiency, it is essential to specify the DC-input voltage at which this efficiency is measured, in accordance with EN 50524 standards.
As conversion efficiencies improve, the importance of accurately measuring MPP-tracking efficiency in PV inverters increases Currently, assessing the actual MPPT performance of these inverters is challenging and necessitates advanced measuring equipment Many manufacturers, plant designers, and simulation programs mistakenly assume that grid-connected PV inverters consistently operate at the maximum power point (MPP), which is often not true, making this assumption misleading.
MPP-tracking efficiency can be defined as follows:
The I-U-curve and the maximum available power (PMPP) of a photovoltaic (PV) array are influenced by the actual in-plane irradiance and module temperature A PV array operates along a specific I-U-curve and corresponding PV-curve, reaching its peak power at the maximum power point (MPP), where the available power is maximized at the related MPP voltage (UMPP) To ensure optimal performance, a grid-connected inverter is equipped with a maximum power point tracker (MPPT) that maintains the inverter's operating point at the MPP, even as changes in irradiance and module temperature affect PMPP and UMPP.
The performance of an inverter can vary based on the MPP-tracking algorithm it employs, leading to notable deviations from the Maximum Power Point (MPP) at specific power and voltage levels Consequently, this can result in a lower average value of P DC.
PMPP, which can reduce energy yield of the whole PV plant up to a few %:
In scenarios where the maximum power point tracking efficiency (ηMPPT) is less than 100%, the inverter's operating voltage (U DC) will differ from the maximum power point voltage (U MPP) This deviation is crucial when calculating the resulting AC output power (P AC) from the DC input power (P DC), as the conversion efficiency (η conv) is influenced by U DC, expressed as η conv = f(P DC, U DC).
The overall efficiency, denoted as \$\eta_t\$, can be determined by multiplying the conversion efficiency \$\eta_{conv}\$ with the maximum power point tracking efficiency \$\eta_{MPPT}\$ Subsequently, the direct current power \$P_{DC}\$ is calculated using Equation (D.3) and is then transformed into alternating current power \$P_{AC}\$ through the conversion efficiency \$\eta_{conv}\$, as outlined in Equation (D.1).
P AC = η conv ⋅P DC = η conv ⋅η MPPT ⋅P MPP = η t ⋅P MPP (F.4)
The overall efficiency ηt can also be considered as