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Harmonics distortion is a crucial problem in microgrid. Harmonic sources can be categorized as two main factors: renewable energy integration and nonlinear loads. Both factors are investigated in this paper. For renewbale energy, photovoltaic (PV) power is one of the most effective solutions for energy crisis and it is showing great potential for serving customers in microgrid. A three- phase PV source model is establised and integrated at different locations in order to observe the impact of harmonics on a microgrid and power quality (PQ). A composite load is modeled using Crossed Frequency Admittance Matrix theory. A practicdal microgrid loacated at GA, USA is used as a study system. The microgrid, PV model and nonlinear load model are simulated in MATLAB/ Simulink environment. The results show the impact of installing PV sources at two types of locations considering linear and composite nonlinear loads. In addition, three PQ indices are discussed to show the numerical impacts with various perspectives.

Apart from conventional sources of power generation, photovoltaic (PV) is a promising zero-pollution renewable energy resource. PV transforms solar energy into electrical power. Investments are more willing to focus on PV energy especially with the fast developments in PV cell technology. As expected, inverters and intermittent characteristic of PV bring negative impacts on micrigrid [

In addition to the PV sources of microgrid, house appliances or small scale of business buildings are the majority of customers, which are considered as nonlinear loads. Therefore, nonlinear loads is another source of harmonics that should be investigated with PV injection. In [

Power quality (PQ) indices are used to quantify the quality of the system and comparing the negative impacts of different disturbances/modeling on power networks [

This paper studies the impact of PV sources on a microgrid system considering composite linear/nonlinear loads. The crossed frequency admittance matrix method is used for nonlinear load modeling. In addition to the study of harmonic distortion, three PQ indices are applied and compared in order to give a clear view about the power distortion, waveform distortion and system unbalance. The paper is organized as follows: Section 2 describes the PV source and its control scheme, Section 3 describes the composite nonlinear load model based on cross-frequency admittance matrix method, Section 4 introduces the harmonic distortion method and PQ indices, Section 5 presents a description for the microgird study system and the corresponding data, Section 6 presents the simulation results, and Section 7 concludes the study and future direction.

PV source consists of PV panel (a set of PV cells), DC-DC boost converter with MPPT, coupling capacitor, three phase inverter and its control and filter. In this paper, KC200GT is chosen as a model of PV cell [_{a}, i_{b}, i_{c}) of AC currents into two components (i_{d}, i_{q}). Active and reactive power signals (P_{ref}, Q_{ref}) are used to obtain the reference signal (i_{dref}, i_{qref}) using the matrix solver in (1) [

where L and R represent inductance and resistance of the impedance Z_{a}, Z_{b} and Z_{c} between three phase inverter and voltage feedback in _{d} and u_{q} are the output control signals of the current control block.

The crossed frequency admittance matrix model [

where voltages and currents are represented as complex numbers. The subscript m stands for the harmonic order. For pure fundamental frequency voltage sources, voltage vector elements are zeros except V_{1}. But currents flowing into loads still have harmonic distortion due to the fact that Y_{21}, Y_{31} and Y_{m1} are not all zeros for nonlinear load. On contrary, for linear load, the crossed frequency admittance matrix becomes a diagonal matrix and the off diagonal elements are zeros. The crossed frequency matrix models the load as a harmonic currents source. In this paper, a composite load consists of a linear load and three types of nonlinear loads. Linear load is very clearly built in software platform. Three different crossed frequency admittance matrixes are built for the three nonlinear load models, which are DBR, CFL and PAVC loads. DBR, CFL and PAVC cover major appliances for both residential and commercial building in microgrid system. Circuit diagrams used in this research are given in

For the purpose of composite load simulation, with given voltages, output currents can be monitored. When monitoring output currents, time domain current waveform is analyzed by the Fast Fourier Transformation (FFT) so that it can be expressed as a complex number matrix. Each row of this matrix stands for a current on a distinct harmonic order. With only fundamental voltage, 60 Hz, first column elements in crossed frequency admittance matrix can be calculated. Then by superimposing 3^{rd}, 5^{th}, 7^{th}, 9^{th}, 11^{th} and 13^{th} order harmonic voltage sources, each one at a time, the other columns can be calculated likewise. Therefore, three 7 × 7 admittance matrixes are built for the three types of nonlinear loads.

THD is the measure of the harmonic distortion at each bus in the system. In order to look at the harmonic distortion in the whole system, whole system harmonics distortion level (WSHDL) is defined as:

where n is the number of nodes; h represents the harmonic order; m is the considered maximum harmonic order. I_{1} is the absolute value of fundamental (60 Hz) current.

In addition to the WSHDL, there are three types of PQ indices are introduced and discussed along with simulation results. Distortion power DP index is defined in (5) [

where the total apparent power

fundamental active power

fundamental reactive power

By normalizing DP to unity, normalized DP^{norm} index can be obtained. DP index has the ability to show contributions of distortion power from individual customers to PCC. Waveform distortion WD index is defined as [

where I_{1} is the rated current magnitude and I_{m}_{1} is the measured fundamental current magnitude. I_{integ−h}_{,i} is the i_{th} integer harmonic component and I_{inter−h}_{,j} is the j_{th }inter-harmonic component. WD index expresses how much a component, AC current, is distorted or deviated from ideal sinusoidal waveform. WD index includes inter-harmonic components, which can take a large part of harmonics when different types of inverters involved. Also inter-harmonics cannot be presented by THD which only include integer order of harmonics. Instead of an average value, WD index gives an instantaneous distortion ratio and it can be depicted along with time axis to be monitored. Symmetrical components deviation SCD index is defined as [

where I_{mp}, I_{mn}, I_{mz} are the measured currents at positive, negative and zero sequences. SCD index has a significant meaning for microgrid because it can give the level of unbalance on currents. SCD index can help staff who work in substations to recognize the unbalance in each node and its impact on the whole system.

Study system shown in _{a}, e_{b}, e_{c}, i_{a}, i_{b}, i_{c} are obtained from monitoring the integration point in microgrid. If these values are away from ideal balanced condition and changing along with time, then PV sources will provide more harmonics than running under ideal balanced condition.

The system in Section 5 is simulated in MATLAB/Simulink and analyzed considering the PV model in Section 2 and the composite load model in Section 3 to study the harmonic distortion and PQ indices described in Section 4. The PV data are set as in

Bus | Load Data for the System | ||
---|---|---|---|

Note | Active Power (kW) | Reactive Power (kVar) | |

10 | ― | ― | ― |

20 | Three phase | 630^{ } | 212 |

30 | Three phase | 412 | 112 |

31 | ―^{ } | ― | ― |

32 | One phase | 37 | 12 |

33 | One phase | 24 | 8 |

34 | Three phase | 343 | 122 |

40 | Three phase | 175 | 100 |

41 | Three phase | 133 | 51 |

50 | Three phase | 298 | 151 |

51_{ } | Two phase | 68 | 12_{ } |

60 | Three phase | 200 | 70 |

61 | Three phase | 74 | 28 |

62 | One Phase | 32 | 11 |

Two cases are studied based on PV locations. In case I, PV locations shown in _{sc}/I_{L} is smaller than 20, THD of current is regulated under 5% by standards.

Element | Data |
---|---|

PV array | 600 kW maximum power at 1000 W/m^{2} irradiance |

DC-DC boost converter | 1 kHz, 300 V boost converter with MPPT controller. |

DC filter | 0.001 F, 100 µH for output of the PV array. 0.003 F capacitor for inverter input. |

3-PHASE INVERTER system | 1 MW, 720 V DC/300V AC with active power control |

AC filter | 600 µH inductor |

Coupling transformer | 1 MVA, 60 Hz, 300 V/4.16kV. |

So the THD values above 5% represent nodes that negatively influenced by PV integration. In case II, the PV sources are integrated at buses 20, 40 and 60.

This section investigates the effect of nonlinear loads. According to experiences from Grainger Industrial Supply [

For the purpose of PQ indices investigation, the microgrid system in

Bus Number | Phase | DBR | CFL | PAVC | Linear Load |
---|---|---|---|---|---|

51 | A&B | 15% | 15% | 30% | 40% |

60 | ABC | 20% | 20% | 10% | 50% |

61 | ABC | 25% | 25% | 10% | 40% |

62 | C | 15% | 10% | 15% | 60% |

large amount of motors and heating pumps) is a PAVC type of nonlinear loads. Buses 60 and 61 (two business buildings which contain many devices like computers) are classified as DBR. Load of bus 62 is considered residential. PQ indices section 4 are applied on the simplified system. Harmonics distortion ranking (HDR) can be found through descending sorting of DP and WD indices. The simulation results are shown in

This paper discussed the impact of two harmonic sources in a microgrid. First, the PV source integration is studied using linear loads. Then PV sources are combined with nonlinear loads. While considering only linear loads, this study provides a comparison between two types of PV integrating locations. Then the whole system

Bus Number | Phase | DP^{norm } | HDR |
---|---|---|---|

51 | A | 0.0791 | 7 |

51 | B | 0.0787 | 8 |

60 | A | 0.1417 | 3 |

60 | B | 0.1798 | 1 |

60 | C | 0.1645 | 2 |

61 | A | 0.0793 | 6 |

61 | B | 0.1072 | 4 |

61 | C | 0.0977 | 5 |

62 | C | 0.0720 | 9 |

Bus Number | Phase | WD^{ } | HDR |
---|---|---|---|

51 | A | 0.482 | 2 |

51 | B | 0.511 | 1 |

60 | A | 0.301 | 9 |

60 | B | 0.336 | 7 |

60 | C | 0.324 | 8 |

61 | A | 0.382 | 6 |

61 | B | 0.453 | 3 |

61 | C | 0.419 | 5 |

62 | C | 0.437 | 4 |

harmonics distortion level as well as the THD are considered as the main measures to evaluate the PQ and impact of PV integrations. Instead of single PV source, this study investigates mutual influences with multiple PV sources. A composite load model helps to analyze the harmonic distortion compared to linear loads. An actual microgrid with historical-based weather conditions is used as a study system. Simulation results can indicate a discernible look at these negative impacts on the microgrid PQ. In order to make numerical comparison and ranking PQ indices are used to estimate the current distortion from several different perspectives. Three PQ indices are applied and compared to investigate the power distortion, waveform distortion and system unbalance. Further research may develop an algorithm to find the optimized integration plan for unbalanced microgrid system, with multiple PV sources and nonlinear loads.