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Unregulated utilization of renewable generation including residential photovoltaic (PV) systems can have a significant impact on load characteristics in distribution networks. For improving PV generation capabilities, power quality aspects have to be coordinated with present load characteristics. This paper discusses the harmonic content of PV generation and the influence to power quality indicators in residential distribution networks. PV generation measurement results including current harmonic amplitude and phase angle values are presented. Results of different modelling scenarios are analysed and a simplified model of harmonics in PVs is offered. The results of the study showed a moderate additional harmonic distortion in residential load current and voltage distortion at the substation’s busbar when PVs were added. Novelty of the paper is that harmonic current values at higher orders are presented and analysed. The results pointed out in this paper could be further used for modelling the actual harmonic loads of the PVs in distribution networks.

Harmonic voltage levels in low-voltage networks represent an important aspect of power quality. From the point of view of electromagnetic compatibility, they must be kept within the compatibility levels to enable satisfactory operation of all the equipment supplied by the network. Furthermore, since electricity is also defined as a product, utility companies could be held responsible for excessively high harmonic levels and any resulting damage to customers’ property [

Distorted voltage and current in the distribution system may result in undesirable effects, such as overloading, over-voltages, mechanical stress, malfunction of critical control and protection equipment, and lower the efficiency of appliances. Distortion affects all customers fed through the point of common coupling (PCC).

The development of electronics for the general public as well as industrial applications has led to a rapid increase in the number of non-linear loads. In addition to the increased number of electronic devices, also resistive devices such as incandescent lamps are ever more frequently replaced by energy saving lamps utilizing non- linear elements. For example, depending on type and brand, switching power supplies absorb distorted currents which flow through the impedances of the power distribution system and result in distortion of system bus voltage [

Residential photovoltaic (PV) generators are the dominant renewable energy source in urban and metropolitan areas. This technology is enjoying rapid growth due to a combination of subsidies, the abundance of sunshine, and the low impact of the technology on the urban landscape [

Distributed generation (DG) impacts the network. This impact is dependent on the location, characteristics of the distributed energy source, related power electronic device, network configurations, voltage level at the connection point, and the capacity of DG relative to load consumption [

Over the past decade, power quality (PQ) issues have become increasingly important in the distribution grid with the widespread use of non-linear electronic equipment. The most cited PQ problems that may arise due to grid connected PV generation are voltage dips and fluctuations, harmonic distortion, transient phenomena and reverse power flow. These effects result in potential damaging of sensitive electronic equipment and capacitor banks, overheating of transformers and neutral conductors and additional losses in the power system. Degraded power quality entails additional costs for both the electricity distributor and its customers [

The purpose of the present study is to demonstrate and analyse possible power quality situations in a residential distribution network by examining the impact of nonlinear domestic loads and PV inverters. For the analysis, measured power consumption and current waveforms of different home appliances and PV inverters have been used. Novelty is that magnitudes and phase angles of each harmonic up to the 50th order were applied for all modelled loads. The main purpose of this paper is to present the use of actual measurement data from different devices for modelling the effects on the residential distribution network and give an estimation of the important values for further modelling.

In electrical power networks, a distorted sine wave can be divided into numerous components, each having an integer-multiple frequency of the main frequency. Different waveforms have different harmonic content referring to individual harmonic magnitudes and phase shift relative to the main frequency component. Hereafter in this paper, the presented measurements of loads are all indicated as magnitudes and phase shift of each individual harmonic up to the 50th order.

Distortions can be observed individually by comparing different harmonic components and calculating harmonic distortion (HD). A more general approach to quantifying the distortions is using the total harmonic distortion level (THD). Total harmonic distortion can be expressed separately for current harmonic distortion as THD_{I} and for voltage distortion as THD_{U}. The harmonic distortion indicators can be calculated using corresponding Equations (1), (2), (3) and (4),

where i_{i} is current of order i, i_{1} is current of 1^{st} order, u_{i} is voltage of order i and u_{1} is voltage of 1^{st} order.

It has to be pointed out that THD_{I} (total harmonic distortion of current) does not reveal the magnitudes of individual harmonics, which could still exceed the limits for specific harmonics regardless of THD_{I} value. For the correct estimation of the harmonic levels, phase angle values of individual harmonics are also required in addition to magnitudes. It is reported that 10% smaller harmonic current magnitudes can be seen when phase angle information is included compared to the simple summing of magnitudes without phase angle values [

Harmonic currents in a network largely depend on the harmonic characteristics of the connected devices, their phase angles and the background distortion level of the supply voltage. Harmonic current emission spectrum information of a device (or a group of devices connected at a PCC) under different supply voltage conditions is very useful for analysing the device’s influence in the network. This can be further utilised to determine the probability density profile of each order harmonic currents in the network considering their “time-varying” behaviour [

Some loads draw current with total harmonic distortion over 100%, but their active power consumption is not as significant when compared to other harmonic generating devices [

The harmonic generation of a PV system depends on the inverter technology, solar irradiance, temperature, loads, and the supply system characteristics. The harmonic distortion generated in PV plants can occur as a result of intrinsic and extrinsic effects. Intrinsic harmonic distortions are related to inverter deficiencies, e.g. com- ponents and control loop nonlinearities, measurement inaccuracies, and limited pulse-width modulation (PWM) resolution. Connection to a weak and distorted electrical grid can be considered an extrinsic effect on the output waveform of a PV plant. A distorted voltage acts like a disturbance in the inverter control system, causing distortion of the current waveform generated by the inverter [

Several factors affect the power quality characteristics of the PV inverter output current. Both the current THD and the output reactive power are related to the output active power levels, which in turn are strongly dependent on solar irradiance levels. Most of the inverters consume or feed reactive power into the network depending on their output active power and their technology. During operation at low solar irradiance levels (e.g. sunrise, sunset, cloudy days), current THD values can increase rapidly, since the THD factor is inversely proportional to the output active power of the PV inverters. Nevertheless, THD is notably reduced as the output active power of the PV Inverters increases and reaches its nominal value. The intrinsic characteristics of the control circuit and nonlinear components of PV inverters may explain the current distortion behaviour in the low power generation stages [

Varying power density of renewable energy resources (i.e. irradiance level and temperature in PV conversion) potentially cause voltage and frequency variation or sag/swell patterns in the grid. Also, application of power converters as interfaces between energy sources and the grid and their interaction with other system components may cause high harmonics distortion [

In small and distributed or decentralized PV controlled systems, the CSIs (current source inverters) can generate highly distorted current waveforms so that their cumulative effect in high penetration PV systems can create hot spots within transformers; ultimately generating excessive eddy or copper loss [

The differing influences of harmonics in distribution networks are not necessarily visible/evident initially. However, harmonics can have serious long-term consequences, of which the most important ones are [

Overloading of consumer’s electrical installations and power system elements by higher order frequencies of currents and voltages;

Increased heating of neutral conductors caused by triple current harmonics (frequency multiplier of number 3). The increased level of the triple harmonics in the neutral conductor can cause serious damage and even lead to fires because the neutral conductor is not usually overload protected;

Increased transformer heating caused by higher (order and magnitude) harmonics, as well as saturation effects in the core;

Higher harmonics the power system can cause interference to telecommunication lines;

Overstressing and resonant condition on the capacitors bank.

The residential distribution network and loads for assessing load flow were modelled using DIgSILENT Power Factory software. The model consisted of a three-phase residential load at 0.4 kV voltage level composed of different single phase loads. The schematic of the residential load model is presented in

The compiled residential load was connected to the distribution network substation via a 1.4 km long overhead line (OHL) as depicted on

nominal power 25 kVA;

relative short circuit voltage 4.5%;

magnetizing impedance/ short circuit impedance ratio 3;

vector group Yyn.

Implemented parameters in the simulation were selected based on power quality problematic issues identified in Elektrilevi’s network (Estonia’s main distribution grid operator) for July 1, 2013. The length of the OHL between substation and customer’s PCC was defined as an average of all the lines between substations and customers with power quality problems. Similarly, the selected diameter of the line and nominal power of the transformer are the most common values for the identified problematic components.

Harmonic voltage amplitudes and phase angles up to the 50th order were obtained from measurements conducted by Elektrilevi at one of the sites where power quality issues were identified. Harmonic voltage distortion at the 10 kV bus was measured and modelled around 2%, which is a common value for this grid.

For modelling PV generation, three different commercially available PVs were measured for one week. The first measured system was single phase while the remaining were three phase systems. For all three systems, harmonic current amplitudes and angles up to 50th order were measured and used in the models in DIgSILENT. A mean load model of averaged values was composed for the single phase system and it was compared with other models composed of actual measurement results. PV inverters were connected to residential load’s busbar as was described in

In order to model the network response of nonlinear loads, 14 different home appliances were measured. The results of the corresponding measured active and reactive power, harmonic current magnitudes and harmonic current phase shift angles of measured devices are presented in [

First, modelling results are given for the case where one single phase PV system was integrated to the existing grid. In the second and third case, different three phase systems were installed. All three scenarios were examined at three different power levels (stage 1―near 30%, stage 2―near 60%, stage 3―near 100%). Exact power level ratios depended on the availability of measurement data. Initial values of voltage THD in the grid before adding PV generations are presented in

1) First case―single phase PV

A single phase PV inverter is connected to the residential busbar at phase C. Measurement results for the three different power levels are given at

Phase A | Phase B | Phase C |
---|---|---|

6.4 | 6.2 | 7.7 |

Stage | Urms [V] | Irms [A] | P [W] | Q [var] | S [VA] |
---|---|---|---|---|---|

1―30% | 233.6 | 3.45 | 739 | 322 | 807 |

2―60% | 238.8 | 9.08 | 2125 | −425 | 2168 |

3―100% | 239.1 | 11.73 | 2783 | −257 | 2805 |

Stage | cos(fi) | PF | THD_U [%] | THD_I [%] |
---|---|---|---|---|

1―30% | 1 | 0.92 | 1.01 | 4.27 |

2―60% | 1 | 0.98 | 0.82 | 1.98 |

3―100% | 1 | 0.99 | 1 | 1.67 |

Voltage and current distortion during a 15 h period is shown in

Active power P, reactive power Q, and apparent power S are displayed in

As is evident in

For modelling mean PV generation, average values of the presented current harmonic amplitudes and angles (^{rd} order harmonic.

In the case where one single phase PV was added to the grid, voltage THD was observed to increase in all phases. Voltage distortion increased more as PV power level increased. Voltage THD for all power output stages and modelled mean PV are presented in

2) Second case―first three phase PV

In this case, a three phase PV inverter is connected to the existing network. Measurement results for three different power levels are given in

Harmonic currents up to 21^{st} order of first three phase PV inverter are given in ^{th} which exhibited values in the proximity of 2% in all phases, even at highest power level. Also the 13^{th} harmonic had prominent values in phases B and C at highest power level. At the lower power level, most of the harmonics had significantly high values, even exceeding 6% at times.

Phase angles of harmonic current amplitudes displayed in

Voltage and current distortion of the first three phase PV inverter over a 15 hour period is shown in

Order | I_1 | Angle_1 | I_2 | Angle_2 | I_3 | Angle_3 | I_mean | Angle_mean |
---|---|---|---|---|---|---|---|---|

1 | 100 | 0 | 100 | 0 | 100 | 0 | 100 | 0 |

3 | 1.92 | 28 | 1.20 | 62 | 1.01 | 52 | 1.38 | 47 |

5 | 0.48 | 97 | 0.31 | 146 | 0.26 | 139 | 0.35 | 127 |

7 | 1.08 | 175 | 0.27 | 159 | 0.27 | 164 | 0.54 | 166 |

9 | 0.88 | 116 | 0.33 | 145 | 0.35 | 146 | 0.52 | 135 |

11 | 0.89 | 104 | 0.38 | 60 | 0.32 | 52 | 0.53 | 72 |

13 | 0.69 | 75 | 0.21 | 73 | 0.20 | 77 | 0.37 | 75 |

15 | 0.23 | 109 | 0.08 | 104 | 0.10 | 107 | 0.14 | 107 |

17 | 0.35 | 88 | 0.07 | 145 | 0.06 | 190 | 0.16 | 141 |

19 | 0.29 | 287 | 0.10 | 259 | 0.10 | 271 | 0.16 | 272 |

21 | 0.63 | 209 | 0.20 | 205 | 0.17 | 209 | 0.33 | 208 |

Stages | THD_U_a | THD_U_b | THD_U_c |
---|---|---|---|

1―30% | 3.5 | 2.9 | 2.9 |

2―60% | 12.9 | 10.2 | 9.7 |

3―100% | 15.7 | 11.9 | 13.8 |

Mean | 11.2 | 7.2 | 7.5 |

Stage | 1―30% | 2―60% | 3―100% |
---|---|---|---|

THD_U_avg [%] | 2.33 | 1.98 | 2.03 |

THD_I_avg [%] | 11.29 | 4.38 | 3.3 |

P_tot [kW] | 1.06 | 2.78 | 3.88 |

Q_tot [kvar] | 0.28 | 0.43 | 0.47 |

S_tot [kVA] | 1.62 | 3.01 | 4.04 |

cos(fi)_avg | 0.99 | 1 | 1 |

PF_avg | 0.65 | 0.92 | 0.96 |

Stage | 1―30% | 2―60% | 3―100% |
---|---|---|---|

Q_a [Var] | −335 | −207 | −104 |

Q_b [Var] | −104 | −61 | −98 |

Q_c [Var] | 718 | 695 | 669 |

PF_a | 0.68 | 0.97 | 1 |

PF_b | 0.94 | 1 | 1 |

PF_c | 0.52 | 0.84 | 0.9 |

Order | Stage 1―30% | Stage 2―60% | Stage 3―100% | ||||||
---|---|---|---|---|---|---|---|---|---|

I_a | I_b | I_c | I_a | I_b | I_c | I_a | I_b | I_c | |

1 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

3 | 5.01 | 4.19 | 2.56 | 0.87 | 1.09 | 1.43 | 0.7 | 0.87 | 1.03 |

5 | 6.68 | 5.7 | 3.66 | 0.62 | 0.58 | 0.45 | 0.94 | 0.92 | 1.05 |

7 | 2.72 | 4.85 | 3.95 | 1.31 | 1.62 | 1.34 | 0.14 | 0.31 | 0.8 |

9 | 3.81 | 4.28 | 3.43 | 3.07 | 3.27 | 3.07 | 2.07 | 1.96 | 1.97 |

11 | 5.14 | 6.69 | 5.07 | 0.96 | 1.12 | 1.09 | 0.61 | 0.83 | 0.43 |

13 | 0.54 | 2.66 | 1.09 | 0.34 | 0.91 | 0.93 | 0.4 | 1.52 | 1.5 |

15 | 2.79 | 2.55 | 1.69 | 0.66 | 0.91 | 0.61 | 0.78 | 0.86 | 0.59 |

17 | 0.66 | 1.45 | 0.99 | 0.98 | 0.31 | 1.1 | 0.35 | 0.7 | 0.18 |

19 | 0.65 | 0.49 | 0.42 | 0.9 | 0.16 | 0.94 | 0.25 | 0.11 | 0.17 |

21 | 1.11 | 0.71 | 0.95 | 0.26 | 0.44 | 0.37 | 0.59 | 0.45 | 0.34 |

Stage 1―30% | Stage 2―60% | Stage 3―100% | |||||||
---|---|---|---|---|---|---|---|---|---|

Order | Angle_a | Angle_b | Angle_c | Angle_a | Angle_b | Angle_c | Angle_a | Angle_b | Angle_c |

1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 275 | 170 | 262 | 38 | 26 | 57 | 281 | 17 | 271 |

5 | 214 | 35 | 220 | 85 | 303 | 227 | 278 | 182 | 340 |

7 | 11 | 202 | 344 | 196 | 226 | 288 | 91 | 285 | 17 |

9 | 143 | 320 | 139 | 19 | 31 | 75 | 166 | 29 | 171 |

11 | 181 | 147 | 219 | 100 | 145 | 219 | 124 | 234 | 51 |

13 | 39 | 201 | 76 | 262 | 326 | 74 | 42 | 147 | 110 |

15 | 314 | 132 | 286 | 336 | 18 | 98 | 205 | 96 | 218 |

17 | 227 | 161 | 43 | 195 | 254 | 335 | 118 | 310 | 98 |

19 | 65 | 229 | 58 | 23 | 233 | 88 | 23 | 241 | 27 |

21 | 268 | 307 | 255 | 204 | 98 | 171 | 264 | 108 | 243 |

Voltage distortion at the measurement point remained at a moderate level (around 2.25%) throughout most of the time period. Correlation with current distortion was not detected.

Reactive power generation is shown in

Power indices over the 15 hour period are presented in

Results of having the first three phase PV in the grid are presented in

Stages | THD_U_a | THD_U_b | THD_U_c |
---|---|---|---|

1―30% | 4.4 | 4.2 | 4.5 |

2―60% | −1.4 | 0.6 | −1.7 |

3―100% | 6.0 | 6.7 | 5.0 |

3) Third case―second three phase PV

In this case, the three phase PV inverter is replaced with another inverter. Measurement results for three different power levels are given at

Reactive power and PF values for each phase are given in

Phase angles presented harmonic current amplitudes in

Voltage and current distortion of second three phase PV inverter throughout the 15 h time period is shown in

Reactive power generation is shown in

Power (P, Q, and S) during the investigated time period is shown in

The impact of the second three phase PV is presented in

4) Comparison of results

It could be concluded that changes in voltage THD values increase as power output of PVs grows. For the one phase PV installation, it was clear that voltage harmonics increased in all three phases. For the three phase PV installations, the two cases showed different outcomes. With the first three phase PV, notable degradation was observed. However, a conclusive assessment could not be done with second three phase PV installation. Voltage THD results at the highest power level for all three cases are depicted in

Stage | THD_U_avg [%] | THD_I_avg [%] | P_tot [kW] | Q_tot [kVAr] | S_tot [kVA] | cos(fi)_avg | PF_avg |
---|---|---|---|---|---|---|---|

1―30% | 1.18 | 5.34 | 1.9 | 0.17 | 2.20 | 1.00 | 0.84 |

2―60% | 1.18 | 1.77 | 5.82 | −0.75 | 5.95 | 1.00 | 0.98 |

3―100% | 1.07 | 1.19 | 10.19 | −0.16 | 10.26 | 1.00 | 0.99 |

Stage | Q_a [Var] | Q_b [Var] | Q_c [Var] | PF_a | PF_b | PF_c |
---|---|---|---|---|---|---|

1―30% | 52 | −431 | 544 | 1.00 | 0.79 | 0.77 |

2―60% | 66 | −459 | −360 | 1.00 | 0.97 | 0.96 |

3―100% | 123 | −434 | 149 | 1.00 | 0.99 | 0.99 |

Order | Stage 1―30% | Stage 2―60% | Stage 3―100% | ||||||
---|---|---|---|---|---|---|---|---|---|

I_a | I_b | I_c | I_a | I_b | I_c | I_a | I_b | I_c | |

1 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

3 | 4.12 | 3.03 | 3.30 | 1.02 | 0.85 | 0.93 | 0.84 | 0.68 | 0.71 |

5 | 1.53 | 1.74 | 1.98 | 0.24 | 0.36 | 0.36 | 0.60 | 0.59 | 0.61 |

7 | 1.60 | 1.32 | 1.31 | 0.69 | 0.59 | 0.64 | 0.32 | 0.42 | 0.39 |

9 | 1.56 | 1.56 | 1.60 | 0.49 | 0.42 | 0.48 | 0.18 | 0.19 | 0.21 |

11 | 0.80 | 0.32 | 0.43 | 0.66 | 0.71 | 0.68 | 0.19 | 0.21 | 0.19 |

13 | 1.04 | 1.10 | 1.17 | 0.28 | 0.41 | 0.39 | 0.27 | 0.19 | 0.20 |

15 | 1.46 | 1.00 | 1.24 | 0.53 | 0.46 | 0.49 | 0.26 | 0.23 | 0.26 |

17 | 0.74 | 0.93 | 0.74 | 0.26 | 0.21 | 0.13 | 0.22 | 0.18 | 0.20 |

19 | 0.31 | 0.28 | 0.23 | 0.27 | 0.23 | 0.29 | 0.06 | 0.05 | 0.08 |

21 | 0.34 | 0.45 | 0.49 | 0.13 | 0.09 | 0.15 | 0.15 | 0.13 | 0.14 |

Order | Stage 1―30% | Stage 2―60% | Stage 3―100% | ||||||
---|---|---|---|---|---|---|---|---|---|

angle_a | angle_b | angle_c | angle_a | angle_b | angle_c | angle_a | angle_b | angle_c | |

1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 205 | 193 | 198 | 16 | 16 | 16 | 19 | 247 | 17 |

5 | 53 | 32 | 38 | 219 | 212 | 208 | 202 | 324 | 198 |

7 | 80 | 330 | 334 | 245 | 259 | 248 | 346 | 60 | 341 |

9 | 191 | 172 | 178 | 68 | 49 | 45 | 148 | 66 | 135 |

11 | 201 | 252 | 111 | 213 | 194 | 200 | 207 | 300 | 197 |

13 | 326 | 331 | 323 | 328 | 320 | 328 | 175 | 73 | 342 |

15 | 98 | 71 | 82 | 101 | 87 | 88 | 141 | 83 | 115 |

17 | 303 | 233 | 255 | 304 | 286 | 311 | 20 | 135 | 157 |

19 | 286 | 283 | 235 | 25 | 325 | 205 | 186 | 113 | 183 |

21 | 101 | 60 | 45 | 98 | 67 | 96 | 327 | 296 | 317 |

Stages | THD_U_a | THD_U_b | THD_U_c |
---|---|---|---|

1―30% | 1.2 | −3.2 | −2.3 |

2―60% | −0.6 | 3.5 | 1.2 |

3―100% | −3.1 | 2.5 | −1.6 |

While the discreet disturbances of harmonic distortion may not cause immediate and easily-observed impacts, it can cause some equipment to malfunction, and result in additional power losses in both customer and network equipment [

Harmonic current angles of small generators such as PVs are seldom considered. One aim of this paper is to draw attention to this topic which could lead to advances in modelling PV inverters with different topologies. To help mitigate harmonic distortion problems, models with appropriate harmonic current amplitudes and phase angles could be used to select most suitable devices.

This study only examines one household and one PV at time. The described effects may escalate when a larger number of devices are considered. Special attention is need in situations where devices have similar harmonic patterns and the harmonic cancellation effect is minimal. Additional measurements should be performed to obtain unified values for modelling PV generators more accurately. It would be necessary to have measurement data extending over entire years in order to acquire results independent of any disturbance. Furthermore, flicker and voltage level issues should be accounted for as they may have a significant influence in real applications.

Firstly, it can be concluded that current harmonic distortion of the PV’s output is correlated with current. Distortion decreases when the PV is operating at a higher loading level. PVs function accurately under ideal conditions. Due to unstable energy availability (i.e., variable solar radiation), continuous variation in power quality parameters is to be expected. In the presented research, two PVs showed considerable harmonic current distortion (average THD over 5%) even at full loading. Only one PV had average current THD under 2% which was considered a very good achievement.

All of the measured PV systems had quite different harmonic patterns when compared with each other throughout their loading range. As such, it is difficult to propose simplified values for modelling without measuring and analysing a greater number of devices. Also, for more reliable harmonic current phase angle data, laboratory tests should be performed.

Secondly, contrary to theory, reactive power generation of PVs was not observed to be correlated to active power. Measured devices showed different levels and variation of reactive power in different phases. These differences may be hazardous in cases where high reactive power values and variations in one phase and zero reactive power in other another phase are not considered. It was also observed that main order reactive power was compensated more efficiently than higher order reactive power which was evident when comparing cos(φ) and PF.

Relative to the initial conditions where no PVs were installed, modelling one PV results in voltage distortion exceeding 10%. The influence is dependent on grid structure and topology of the PV. In case of PV with less distorted current working at high power level, minor improvement of voltage distortion was observed.