P Three-Phase Active Power Vφ Phase-to-Phase Voltage
φ Angle of the Phase Impedance
µ Base Energy Tax
EG Consumed Active Energy
P Fref Threshold Value for the Power Factor p Total of Hours for Measurement QC Capacitive Reactive Power
QL Inductive Reactive Power Consumed by the Load PL Active Power Consumed by the Load
P F∗ Reference Power Factor vdc dc-link Voltage
vgabc Grid Voltage in abc Reference igabc Grid Current in abc Reference
Q∗ Reactive Power Reference for the Control PIN V∗ Active Power Reference for the Inverter Q∗IN V Reactive Power Reference for the Inverter PIN V∗0 Saturated Active Power for the Inverter Q∗IN V0 Saturated Reactive Power for the Inverter vgd Grid Voltage in the Direct Axis
vgq Grid Voltage in the Quadrature Axis igd Grid Current in the Direct Axis igq Grid Current in the Quadrature Axis
ω Grid Angular Frequency L LCL Filter Total Inductance ρ Phase Angle of the Grid Voltage P W Minv PWM Reference for the Inverter
PIN V Active Power Delivered by the Inverter QIN V Reactive Power Delivered by the Inverter Sn Inverter Rated Power
PG Active Power Drawn from the Grid
P FP V Power Factor with the Installation of a PV Plant Ntap Number of Taps for the Capacitor Bank
QC,T Capacitive Reactive Power Rounded to a Number of Taps
∆QC Step Size of One Tap
k Oversizing Factor for the Inverter
P FCAP Power Factor Corrected by the Tapped Capacitor Bank P FIN V Power Factor Corrected by the Inverter
P Fi Instantaneous Power Factor at Time i Cdc Dc-Link Capacitor
Si Gate Signal to the IGBT i in the Inverter Lf Inverter Side Filter Inductance
Lg Grid Side Filter Inductance
Rf Internal Resistance of the Inverter Side Inductance Rg Internal Resistance of the Grid Side Inductance Cf Filter Capacitance
rd Filter Damping Resistor Vg Grid Phase-to-Phase Voltage
Ig Grid Current
vα Alpha-Coordinate Grid Voltage vβ Beta-Coordinate Grid Voltage
vα0 Filtered Alpha-Coordinate Grid Voltage
qvα0 Quadrature Filtered Alpha-Coordinate Grid Voltage vβ0 Filtered Beta-Coordinate Grid Voltage
qvβ0 Quadrature Filtered Beta-Coordinate Grid Voltage vα+ Positive Sequence Alpha-Coordinate Grid Voltage vβ+ Positive Sequence Beta-Coordinate Grid Voltage Tαβ Transformation Matrix from abc to αβ Coordinates Tdq Transformation Matrix from αβ to dq Coordinates vq+ Positive Sequence Q-Coordinate Grid Voltage θ0 Phase Angle of the Grid Voltage
∆pl Strain Difference Between Elastic and Plastic Behavior σyield Limit Stress to Achieve Plastic Behavior
G Solar Irradiance
Ta Ambient Temperature Tj Junction Temperature
Ploss Conduction plus Switching Losses for Semiconductors Ic(h) h-harmonic Capacitor Current
idc(t) Dc-Link Current
f(x) Probability Density Function (PDF)
F(x) Cumulative Density Function (CDF) / Unreliability Bx Time which x % of the Samples Fail
Pco Conduction Losses Psw Switching Losses Pc Capacitor Losses
Tc Case Temperature
Rc−h Case-to-Heatsink Thermal Resistance Rh−a Heatsink-to-Ambient Thermal Resistance Th Hotspot Temperature
Rthc Hotspot-to-Case Thermal Resistance Cthc Hotspot-to-Case Thermal Capacitance
ton Heating Time
∆Tj Junction Temperature Fluctuation Tjm Average Junction Temperature
Rc Hotspot-to-Ambient Equivalent Thermal Resistance fn Fundamental Frequency
Nf Number of Cycles to Failure fd Semiconductor Parameter
L Capacitor Lifetime Under Operating Conditions L0 Capacitor Lifetime Under Testing Conditions V0 Capacitor Voltage Under Testing Condition T0 Capacitor Temperature Under Testing Condition n Voltage Stress Exponent
Nf(l)k Number of Cycles to Failure for Each k Sample of the Long Cycle Nf(s)k Number of Cycles to Failure for Each k Sample of the Short Cycle Ts Sample Time of the Mission Profile
t0on Static Heating Time
∆Tj0 Static Junction Temperature Fluctuation Tjm0 Static Average Junction Temperature
Nf,i Number of Cycles to Failure for the i Monte Carlo Simulation Fi(x) Unreliability of the IGBTs
Fd(x) Unreliability of the Diodes Fc(x) Unreliability of the Capacitors
ni Number of IGBTs
nd Number of Diodes
nc Number of Capacitors Fsys System Unreliability
B10 Time when 10 % of the Samples Fail
G Average Irradiance
Ap Area of the Solar Panel η Efficiency of the Panel
N Number of Panels
Eindustry Daily Energy Demanded by the Industry Epanel Daily Energy Produced by the PV Panel Pmax PV Panel Rated Maximum Power
Vmp PV Panel Maximum Power Voltage Imp PV Panel Maximum Power Current Voc PV Panel Open Circuit Voltage Isc PV Panel Short Circuit Current Ns PV Panel Number of Cells Kp,cur Current Proportional Gain Ki,cur Current Integral Gain
Kp,bus Bus Control Proportional Gain Ki,bus Bus Control Integral Gain
Kp,rea Reactive Control Proportional Gain Ki,rea Reactive Control Integral Gain
Rthi Foster Thermal Resistance for the i Layer
τi Foster Thermal Time Constant for the i Layer Cthi Foster Thermal Capacitance for the i Layer
Contents
2.3 Theoretical Analysis of PF Reduction with PV Plants Installation . 39 2.4 Solutions for dynamic PF correction . . . 42 2.4.1 Solution based on tapped capacitor banks . . . 42 2.4.2 Solution based on the multifunctional PV inverter . . . 43 2.5 Chapter Conclusions . . . 44 3 PV INVERTER LIFETIME EVALUATION . . . . 47 3.1 Physics of Failure of Semiconductors and Capacitors . . . 47 3.1.1 PoF for Semiconductor Switches . . . 475.3 Lifetime Results . . . 70 5.3.1 Temperature analysis of the devices . . . 70 5.3.2 Multifunctional PV inverter reliability evaluation . . . 72 5.4 Chapter Conclusions . . . 75 6 CLOSURE . . . . 77 6.1 Conclusions . . . 77 6.2 Future Works . . . 77
REFERENCES . . . . 79
27
1 Introduction
1.1 Context and Relevance
Small, medium and large industries consider that the reduction of the energy provided by the electric utility is determining for the reduction of their fixed costs. Hence, investment in local photovoltaic (PV) solar generation has increased rapidly in recent decades, mainly in the industrial sector. Associated with reduced energy bill, PV systems attract great interest due to the production of sustainable energy with low environmental impact and reduced maintenance costs (Yang; Sangwongwanich; Blaabjerg,2016). However, the increasing penetration of PV systems into the grid has made it more vulnerable, which has led the need for studies to assess their impacts (Wandhare; Agarwal, 2014).
Fig. 1 shows the increasing total installed capacity of PV power plants in Brazil.
The growth of this type of energy has become more evident in the recent years, in a large scale for industrial applications. In the recent 4 years, the total increase on the installed PV power has grown higher than 320 %.
Year
2012 2013 2014 2015 2016 2017 2018 2019 2020
Installed Power (MW)
Figure 1 – Total installed capacity of PV power plants in Brazil. (Absolar,2020)
The industry draws a certain amount of active and reactive power from the grid to supply the power demanded by its load. However, the introduction of a photovoltaic plant reduces the liquid active power demand from the grid due to local generation. According to the power triangle, reduction of active power results in an increased power factor (PF) angle. Therefore, it can reduce the PF to below the acceptable limit, according to the grid standards (ANEEL, 2010). The industry power factor must be corrected to above the threshold allowed by the standards, or else there will be extra fees over the exceeding reactive power (ANEEL,2010). In this scenario, reactive power support to avoid paying fees due to low PF is essential to make the investment in the PV system attractive