Harmonic assessment on two photovoltaic inverter modes and mathematical models on low voltage network power quality

ABSTRACT


INTRODUCTION
An interconnected or grid-tied photovoltaics (PV) system must fulfill specific criteria like voltage level, phase sequence, and frequency, as stated in the IEEE standard of distributed energy resources (DER) [1].In order to satisfy those standards, power electronics technology is needed to increase energy conversion efficiency and reliability and to reduce cost.An inverted-connected PV system has several essential features, such as maximum power point tracking, anti-islanding, grid fault detection, and many others [2].An inverter controls its switch using sequential sinusoidal control voltage to change the DC voltage from renewable energy sources to the 3-phase AC voltage needed by the electricity network [3].An inverter can be operated as power electronics equipment for renewable energy sources such as grid-connected PV [4].Inverter is categorized as a non-linear load if its output value is not proportional to the input voltage [5].However, the intermittent nature of solar energy and the operation characteristics of inverters in PV systems can cause adverse effects such as protection coordination failure, high conductor losses, voltage fluctuation, harmonic distortion, and grid disturbance [6].The inverter's output voltage should be a sine wave.In practice, the output voltage is non-sinusoidal and contains harmonics [7].The assessment of the non-sinusoidal waveform can be done using Fourier transformation [8].So, harmonic distortion became a severe issue in new renewable energy utilization.If the harmonic distortion problem is not solved, further renewable energy penetration cannot reach its full potential [9].Harmonics affects the distribution networks by increasing the heating losses and decreasing the operation life of insulations [10].Based on Germany's standard of voltage regulation VDE-AR-N 4105, inverters must supply their load with reactive power [11].The inverter's capability to generate reactive power depends on the active power supplied by the PV arrays.Grady and Gilleskie [12] in Elkholy's [2] paper also researched the effect of harmonics on power factors (PFs).They created a mathematical model called true power factor (TPF) [2].TPF can be implemented in harmonics analysis to limit the harmonics caused by nonlinear load using the widely accepted concept of power factor.
Past research has discussed photovoltaics' operation on low voltage networks and quality assessment on inverter power output.Elkholy's research [2] on harmonics assessment on low voltage networks in Electronic Research Institute Building, Cairo, is the primary reference for our research.The data used in that research was extracted directly from the building's electrical system within a specified time range, then compared using mathematical analysis of power factor and total harmonic distortion (THD) [2].Another relevant research was done by Rampinelli et al. [13] using direct measurement in the Solar Energy Laboratory of Federal University Rio Grande do Sul and mathematical model simulation using ten models of inverters [13].Both of those researchers analyzed the characteristics of THD of on-field inverters with power factor setting as the treatment variables.However, they have yet to discuss the effect of different power factor setting on the system.
Our research adds a new perspective by simulating the system using electrical transient analyzer program (ETAP) 20.5.0 software.This software analyzes the effect of irradiance on the inverter's power quality while operating at 85% and 100% power factor.From the simulation result, we look into the total current and voltage harmonic distortion (THDi and THDv), then compare them with values based on mathematical analysis.We also analyze the effect of PV penetration at every inverter power level on harmonics-induced transformer and system losses.This research can predict the condition and effect of harmonics in PV-integrated systems on 100% or 85% power factor under every irradiance level.

METHOD
This research is conducted by performing simulations in ETAP Power Station 20.5.0 software to analyze harmonics.ETAP 20.5.0 is widely used for power system simulation since it is commercial software for simulating and designing electrical power systems in industries and academics.Moreover, ETAP Power Station has a comprehensive interface and can be run on Windows operating system, making it an excellent analysis tool for designing and testing the power system.ETAP can be used in offline mode for real-time monitoring, simulation, optimization, energy management system, and high-speed intelligent loading with realtime data operation [14].Our research follows a workflow, as shown in Figure 1.

System
The power system network used for the simulation came from Bhatt's [15] research, with several adjustments.In this system, there are six individual PV arrays, four lump load, and two static load that is supplied by the grid as shown in Figure 2.However, the irradiance data is only simulated on 0.4 kV PVs: PV A1, PV A2, PV A3, and PV A4.The rest of the PV arrays, PV A5 and PV A6, are connected to 6.3 kV busses and supply Load 1 and Load 2 with constant power.The PV and inverter ratings in every PV array are shown in Table 1.Simulation is performed on PV A1 through PV A4 by using irradiance data of Surabaya city, as shown in Table 2.The data given below can be fully accessed from the Global Solar Atlas website.Each average irradiance data will be applied to every low-voltage PV inverter on two different power factor levels, 100% and 85%.

Harmonics simulation using ETAP
Simulation using ETAP is divided into fundamental power flow simulation and harmonic power flow.In the fundamental simulation, the system will be tested for every change in irradiance as shown in Table 2 for each power factor change of 1 and 0.85.The observed results are changes in power flow, current in each line, and voltage at each busbar.Meanwhile, harmonic load flow analysis will be conducted to observe changes in each fundamental condition, such as changes in current and voltage under harmonic conditions.These current and voltage values are represented in root mean square (RMS) values.The RMS values depend on the characteristics of harmonic distortion at each measurement point.As shown in (1) and (2) represent the relationship between RMS values of current and voltage with harmonics [16].
The magnitude of total harmonic distortion of current (THDi) and total harmonic distortion of voltage (THDv) is determined through (3) to (4) [17].THDi value is a primary characteristic used to analyze the level of harmonics in an inverter.On the other hand, THDv represents the distortion caused by the injection of distorted current through an impedance [18].
Harmonic load flow analysis is also performed to obtain changes in power factor due to harmonic distortion, known as the TPF.TPF is the ratio of real power output to the apparent power output of the circuit.It is typically viewed as the amount of power that could be consumed by the load [12].The TPF is modeled as (5): where, is a displacement power factor (DPF) that also represented as   .So, the value of TPF can also be expressed as (6) [12].

Modelling true power factor and THDi using MATLAB
Simulation results from ETAP Power Station will give us each inverter's characteristics and power quality at a given irradiance level.Then, those data will be processed in MATLAB R2021B to find all variables in the mathematical model for power factor and THDi parameters.Those equations are needed to find the characteristic of each inverter.
Equations ( 1) to (6) show the modeled calculation for TPF and THDi but neglected the effect of irradiance on the true power factor, whereas irradiance and the output of the inverter affect the TPF.Hence, a mathematical model is needed to calculate the true power factor on an inverter's varying output power towards its irradiance (through the ratio of PAC and PNOM) [13].Equation suitable for the mathematical model for calculating the average value of power factor on different load conditions are expressed by (7).
Coefficients C0, C1, C2, and C3 are obtained by applying the measured curve in MATLAB.The ratio of PAC and PNOM indicates the output efficiency of the inverter.Equation suitable for the mathematical model for calculating the average value of power factor on different load conditions are expressed by (8).5955 Coefficients T0, T1, T2, and T3 are obtained by applying the measured curve.The ratio of PAC and PNOM indicates the output efficiency of the inverter.

Harmonics impact analysis
After the condition in the previous analysis, we will continue by doing a harmonics analysis to determine the amount of harmonics-induced transformer and system power losses.These losses are calculated for 100% and 85% power factor for every irradiance level.The rating of each transformer in the system is shown in Table 3.The IEC-60076 standard is used as a reference for the calculation of no-load and on-load losses.The rating for the electric lines is shown in Table 4. Transformer power loss caused by harmonics can be classified into on-load loss and no-load loss.The total power loss in transformers can be modeled as shown in (9).In the equation,   is the transformer's total losses,   is the no-load transformer losses, and   is the on-load transformer losses.In a no-load transformer, the losses produced by the transformer are not affected by harmonics.The total losses caused by the harmonics can be calculated using (10) (using per-unit system).
where   is the total losses of an on-load transformer caused by harmonics,   2 − is the DC I2 R harmonics losses,   is the harmonics factor for eddy current losses on the transformer's winding,   is the eddy current losses on the transformer's winding.The eddy current losses will cause excessive core losses and abnormal temperature changes in the transformer [4]. − is the loss factor caused by harmonics current on other stray losses, and   is the stray losses.Loss analysis in transformers and lines requires calculations to determine the impedance values.This is because the available ratings are still in per-unit values with a base of 100 kVA.To determine the ohmic value of resistance (R), reactance (X), and impedance (Z) of the transformer, equations (11) to (12) are used [19].

. Effect of harmonics
The simulation was done in ETAP Power Station to determine the effect of solar power plant installation with the different inverter operation modes.The result of the simulation will give the power and harmonics data in a distribution network.Each of the average irradiance levels in Table 2 is used as the independent variable, with the inverters' power output and quality as the dependent variable.The database used for harmonics simulation can be seen in Table 5.
The result of the simulation in Table 5 is processed using line charts to understand better the effect of irradiance on the change of active and reactive power in each inverter operation mode.As shown in Figure 3, it can be inferred that the higher the irradiance, the higher the active power generated by the inverter while working under 100% power factor in Figure 3(a) and 85% power factor in Figure 3(b).Inverters working in power factors produce the same active power because the inverter's type stays the same.Reactive power produced by the inverters is proportional to the irradiance received by the PV arrays [20].Inverters with a 100% power factor produce no reactive power because they only generate active power.Inverters with an 85% power factor produce reactive power proportional to their active power, with an active-reactive ratio dictated by the power factor.In past research, active and reactive power generated by inverters can be controlled to match the demand.One of the methods to achieve such control is by controlling the reactive power output to mitigate voltage sag in the system [21].Irradiance's effect on the system's harmonics can be observed by looking at the magnitude of THDi and THDv.THDi and THDv data are extracted when the inverter works below its nominal power.This is done because THDi data is difficult to observe when inverters are operating at their nominal power [22].From Figure 4, it can be inferred that the larger the irradiance, the smaller the THDi in the system, regardless of whether the inverter is working on 100% PF in Figure 4(a) or 85% PF in Figure 4(b).Therefore, it can be concluded that the value of THDi is affected by the active power output of the inverters.The value of THDi is very large at an irradiance level below 330 W/m 2 .This is caused by the high harmonics current when inverters work less than 20% of their nominal power [23].In this case, the inverter's nominal power is 714.5957 means 330 W/m 2 is the threshold where they generate more than 20% of the nominal active power.Inverters in 100% power factor have a slightly smaller THDi value than those in 85% power factor.Analysis of the effect of irradiance on THDv shows that both parameters are proportional to each other, as shown in Figure 5.That applies to both 100% power factor shown in Figure 5(a) and 85% power factor shown in Figure 5(b).This characteristic is opposite to THDi, where irradiance is inversely proportional to THDi [24].Inverters will try to match their generation power factor with the setting power factor.If it is set at 100% power factor, then the generation power factor will not necessarily be exactly 100%, but there will be a slight deviation.The same thing applies to the 85% power factor.As shown in Figure 6, when irradiance is at 330 W/m 2 , there is a drastic increase in power generated compared to when irradiance is at 300 W/m 2 at 100% PF as shown in Figure 6(a) and 85% PF as shown in Figure 6(b).This happens because, at an irradiance level of 300 W/m 2 and below, PV arrays' output current and voltage do not fulfill the minimum voltage level for MPPT in inverters to activate.Therefore, the output power will be minimal.If compared between both operation modes, inverters working at 85% generate smaller THDi or harmonics current compared to ones working at 100%.Inverters with a 100% power factor tend to absorb reactive power, making the THDi value slightly larger [22].

Simulation result of ETAP Power Station
Figure 7 shows a comparison between output active power characteristics and relative power characteristics (PAC/PNOM) with the inverter's generation power factor at 100% PF and 85% PF for inverter PV A1 as shown in Figure 7(a), PV A2 as shown in Figure 7(b), PV A3 as shown in Figure 7(c), and PV A4 as shown in Figure 7(d).In order to obtain a viable result, this research compared the mathematical calculation result with the ETAP Simulation. Figure 7 also represents the difference between ETAP Power Station simulation and mathematical calculation.The coefficient used to model the inverter's characteristics using mathematical calculation is acquired using (4) and the result is shown in Table 6.The generation power factor is relatively constant when the inverters are working at around 5% of relative power and above.That pattern applies to both 85% and 100% power factors.The data trends acquired from ETAP Simulation and mathematical calculation have the same pattern.If Figure 7 is compared with Figure 8 for inverter PV A1 as shown in Figure 8 8(d), it will show that the higher the relative power, the closer the power factor to 100% with a smaller THDi [23].Therefore, we can analyze the relative power of past research.Rampinelli et al. [13] analyzed the characteristics of IG 30 inverters with 100% and 95% power factors.The comparison of the power factor in this research and past research is shown in Table 7.The coefficient that determines the inverters' characteristics from the relation between PAC/PNOM and THDi is shown in Table 8.Based on the coefficients in Table 8, we can compare the PAC/PNOM data acquired from ETAP and mathematical calculation to identify the characteristics of an inverter when connected to the system.While Figure 7 shows the relation between PAC/PNOM and THDi, Figure 8 compares the THDi characteristic curve of each inverter in the system.
Figure 8 shows that THDi at 100% power factor is more prominent than at 85%.This confirms the true power factor principle, where THDi is affected by the power factor [25].The relationship between THDi and the power factor is proportional: the more significant the power factor, the bigger the THDi.Therefore, THDi is bigger when inverters are operating at 100%.When relative power is less than 5%, the magnitude of THDi is enormous.When the relative power is above 5%, inverters operating on 85% power factor tend to increase, while ones on 100% power factor decrease.The increase and decrease in THDi are not significant.
The THDi value at several relative power can be seen in Table 9.Those data are acquired from the mathematical calculation, with coefficients achieved using the curve fitting method in Table 8.The result of this calculation is compared with the data acquired from the research done by Rampinelli et al. [13] on IG 30 inverters.It is worth noting that Rampinelli did an on-field measurement on inverters operating at 10% of relative power with 100% and 95% power factors.Based on Table 9, the magnitude of THDi is very high when the inverter is working under the nominal operation value of relative power.A low relative power means a low irradiance level.Therefore, the inverters absorb a significant amount of reactive power, which affects the magnitude of the harmonics current [26].The result of past research shows that when inverters are working on high relative power, the magnitude of THDi tends to get smaller both in 100% and 95% power factors.However, our research results show a different pattern, where inverters operating on 85% power factor tend to have increasing THDi.In comparison, ones on 100% power factor tend to have decreasing THDi.This discrepancy is caused by differences between the inverter's manufacturer or characteristics.The tendency of THDi to increase when relative power rises is caused by the high irradiance level, which makes the inverters generate high reactive power.A high reactive power injected into the system means the amount of switching inside the components of the inverter is also high [20].The higher the relative power of a non-unity power factor inverter, the magnitude of individual harmonic distortion (IHD) on low orders will also increase [22].Figure 9 shows the harmonics order spectrum at 5% relative power and 100% PF as shown in Figure 9(a) 50% relative power and 100% PF as shown in Figure 9(b), 5% relative power and 85% PF as shown in Figure 9(c), 50% relative power 85% and PF Figure 9(d).

The effect of harmonics on system losses
Harmonics have a negative impact on the grid.The effect of harmonics on a distribution feeder can cause a power loss of up to 18% of the power absorbed by the load.In such a case, the THD in the current greatly influences the harmonics-induced losses.Figure 10 shows that power losses in cable B as shown in Figure 10(a) and cable F as shown in Figure 10(b) are greater at 100% power factor than at 85% power factor.This happens because inverters working at 85% power factor produce reactive power that acts as a reactive power compensator in the system [27].Based on the modified grid code IEEE 1547a-2014, reactive power compensation by PV injection can regulate the voltage in the system and reduce system losses.This means that power losses in the cables can be reduced by injecting reactive power generated by the inverters, which also confirms the result of past research [28].Harmonics-induced and fundamental power losses on both cable at 85% and 100% power factor can be seen in Table 10.
Irradiance received by the PV has a significant effect on cable power loss.Irradiance level is proportional to the active and reactive power generated.Past research has explained that a low irradiance level will affect the generation power factor, affecting the power losses in the cables.Therefore, the lower the irradiance level, the higher the power losses in the system or cables [29].
ISSN: 2088-8708  Harmonic assessment on two photovoltaic inverter modes and mathematical … (Ontoseno Penangsang) 5961 In the system used for our simulation, the power grid acts as a swing or reference to supply the demand that the distributed energy resources cannot.If the irradiance is low, the PV arrays' power output is reduced, meaning the grid has to supply more active and reactive power to meet the power demand.If the grid provides more power, there will be more power losses in the transformers and transmission lines, which means the overall system losses will also increase.

The effect of harmonics on transformer losses
High harmonics content in the system is unwanted because it is considered a disturbance.The distortion caused by high harmonic orders could lead to higher system losses, one of which is due to copper losses in transformers.Distribution transformers with nonlinear loads will increase the harmonics-induced power losses.Figure 11 shows that power losses in transformers 6 as shown in Figure 11(a) and transformers 4 as shown in Figure 11(b) are more significant at 100% power factor than at 85% power factor.This happens because inverters working at 85% power factor produce reactive power that acts as a reactive power compensator in the system [30].Harmonics-induced and fundamental power losses on both transformers at 85% and 100% power factor can be seen in Table 11.

CONCLUSION
On-grid PV systems with inverters working at 85% power factor cause a lower THDi value than the system with a unity power factor.However, with the system set on 85% power factor, the THDi value increases slowly as the irradiance increases.This differs from the system that runs at 100% power factor, in which the value of THDi will decrease gradually.This is caused by the increasing number of switching of the inverters' components.In turn, this will cause the distortion to be bigger as irradiance increases in 85% power factor, which significantly increases IHDi on the 5 th order.Meanwhile, the THDv value increases with 85% power factor and unity power factor as the irradiance increases.However, the THDv value is higher at 85% power factor system than those at 100% power factor since there is more reactive power compensation if the irradiance increases.Relative power changes in the on-grid PV system cause the magnitude of the harmonic in the system to be dynamic, which will cause the losses to fluctuate on both electric lines and transformers.When the irradiance increases, the losses on lines decrease.This is caused by less energy supplied from the grid, reducing the system losses and transformers losses.This condition applies when inverters operate on 85% power factor in which the network and transformers have smaller losses value than the unity power factor.Therefore, inverters with an 85% power factor have increased harmonics proportional to their irradiance level, so losses will slightly increase.From the case above, designing a system with power quality in mind is vital, especially to anticipate harmonics conditions and their effects on network losses.Furthermore, active or passive filters could be useful in a system with a high level of harmonics distortion.This research can describe harmonics conditions and their effects on network losses on the on-grid PV-integrated system when irradiance varies.

Figure 2 .
Figure 2. Single line diagram of system Int J Elec & Comp Eng ISSN: 2088-8708  Harmonic assessment on two photovoltaic inverter modes and mathematical … (Ontoseno Penangsang)

Figure 3 .
Figure 3.Comparison of active and reactive power at all irradiance levels (a) 100% PF and (b) 85% PF 4 kW, which Int J Elec & Comp Eng ISSN: 2088-8708  Harmonic assessment on two photovoltaic inverter modes and mathematical … (Ontoseno Penangsang)

Figure 8
Figure 8(c), and PV A4 as shown in Figure8(d), it will show that the higher the relative power, the closer the power factor to 100% with a smaller THDi[23].Therefore, we can analyze the relative power of past research.Rampinelli et al.[13] analyzed the characteristics of IG 30 inverters with 100% and 95% power factors.The comparison of the power factor in this research and past research is shown in Table7.

Figure 11 .
Figure 11.The effect of harmonics on losses at (a) transformer 6 and (b) transformer 4 Harmonic assessment on two photovoltaic inverter modes and mathematical … (Ontoseno Penangsang) 5963

Table 2 .
. PV and inverter rating Solar irradiance data

Table 4 .
Cable rating

Table 5 .
Harmonics simulation data at each irradiance level

Table 6 .
Mathematical power factor coefficient

Table 7 .
Actual power factor at several relative power operations

Table 9 .
THDi magnitude at several relative power operations

Table 11 .
The effect of harmonics on transformer losses in kW