Abstract: Photovoltaic power generation has gained popularity among enterprises and businesses of all sizes in recent years. The government's strong advocacy and support for the photovoltaic industry has also fostered a diversity of power structures for photovoltaic inverters. Currently, grid-connected photovoltaic inverters can achieve parallel connection of individual inverter units or parallel connection of multiple inverter devices based on photovoltaic units, depending on the needs of the power station or user. This design focuses on the DC bus capacitor capacity of a 100kW photovoltaic inverter. The capacitor capacity is calculated based on maximum power and extreme IGBT operating conditions. The feasibility of the capacitor value is calculated and verified according to the manufacturer's capacitor manual parameters. Finally, a suitable capacitor specification is selected for the 100kW photovoltaic inverter.
1 Introduction
The capacity of photovoltaic inverters varies depending on the application. From the perspective of procurement consistency and bulk cost, we hope that the components used in the device remain as consistent as possible across different power levels; of course, this is difficult to achieve for most power devices. However, since the device may be a single integrated unit or have multiple power units connected in parallel, consistency in the selection of the DC bus capacitor becomes possible. This article mainly explains the calculation and selection criteria for the DC bus capacitor from the following aspects.
(1) Selection of DC bus capacitor: The DC bus capacitor value is calculated by considering the maximum power (considering the inverter conversion rate) and the IGBT direct-through extreme conditions.
(2) Calculate and compare the peak-to-peak value of the DC bus voltage fluctuation. Calculate the peak-to-peak value of the DC bus according to the formula, and compare it with the DC bus voltage fluctuation in the MALTAB simulation of the photovoltaic inverter. Find the maximum value as the basis for subsequent calculations.
(3) The peak current and effective value within the period of the capacitor are calculated using the parameters in the manual of the farad capacitor manufacturer, Ih and Irms, so as to obtain the periodic average current Irms1 on a capacitor.
(4) Verify the rationality of the capacitor parameters based on the thermal power and ambient temperature.
2. Selection of the maximum power DC bus capacitor
The topology of a single-stage three-phase grid-connected photovoltaic power generation system consists of a 100kW photovoltaic module, a DC bus capacitor Cdc, a three-phase voltage source inverter, an LCL filter, and a three-phase three-wire power grid. Here, Linv is the inverter-side inductance value; Lg is the grid-side inductance value; and Cf is the filter capacitor. The DC energy generated by the photovoltaic module is converted into three-phase AC power by the inverter and fed into the grid. The three-phase photovoltaic inverter is shown in Figure 1.
Figure 1. Main circuit topology of a three-phase photovoltaic inverter
When a grid fault causes a voltage drop at the grid connection point, following the conventional grid-connected control approach for photovoltaic inverters, the inverter maintains maximum power output. Assuming constant power, the current relationship on the DC side is as follows:
(1)
According to the power balance relationship, the grid-side power is equal to the DC-side power, therefore the power relationship is:
(2)
According to the law of conservation of energy, then we have
(3)
The time required for a grid fault to cause a voltage drop at the grid connection point is extremely short. Therefore, the voltage drop at the grid connection point, Uabc, occurs almost instantaneously, leading to a sudden decrease in the output power Pg of the photovoltaic inverter. If the original MPPT control algorithm is maintained, the output power of the photovoltaic module will stabilize at the maximum power point.
Without considering energy transmission losses, during a voltage dip in the grid, the grid-connected output power will remain consistent with the DC input power, thus the grid-connected current will continuously increase. Considering the regulating effect of the regulator in the control system, the current undergoes a regulation process during the voltage dip; therefore, the transient response during the output power drop will be an oscillating regulation process. Due to the power balance relationship, energy will instantly accumulate on the DC bus, causing the bus voltage to rise. For minor voltage dips at the grid connection point, as long as the grid-connected current does not exceed the inverter's safety range, the grid fault will not affect the control and operation of the photovoltaic grid-connected power generation system.
In the event of a deep voltage dip, faults such as instantaneous overcurrent in the inverter and overvoltage on the DC bus may occur. Without appropriate measures, the inverter will disconnect from the grid due to self-protection. In regions with high photovoltaic (PV) renewable energy penetration, large-scale grid disconnection of PV power plants will significantly reduce the active power output of the grid, increasing the difficulty of restoring the entire power system and potentially exacerbating faults, causing other power plants to disconnect, and leading to large-scale power outages. To address these issues, in-depth research is needed on low-voltage ride-through control technology for high-power grid-connected inverters.
Here, we only consider the selection of the voltage and capacity of the DC bus capacitor.
Considering the DC bus voltage fluctuations, this design option can use film capacitors; however, polarized capacitors are also acceptable if the ripple voltage fluctuates within a relatively small range.
1) Rated voltage; typically 1.2-1.5 times the DC side overvoltage capacity.
2) Capacitor capacity Q; The Q value is related to the carrier frequency (i.e., the switching cycle) of the charging and discharging of the DC bus capacitor during the IGBT switching period; that is, during one PWM switching cycle, when the IGBT is turned on, the capacitor provides the output energy of the inverter; when the IGBT is turned off, the grid charges the DC side capacitor through the body diodes of the three-phase IGBT of the inverter.
The energy required by the DC bus during one switching cycle is:
(4)
In the formula, η is the inverter efficiency; fs is the switching frequency; and w is the sum of the energy released by the capacitor and the energy output by the solar panel during the IGBT turn-on cycle.
Assuming the DC bus capacitor is a lossless device, its charging and discharging are balanced during IGBT turn-on and turn-off. Therefore, its charging energy is Q, calculated using the following formula.
(5)
In the formula, U is the DC bus voltage, and ΔU is the bus ripple voltage. Therefore, we can consider that during the switching cycle, the inverter output energy is twice the capacitor charging energy, i.e.
W=2Q （6）
In this design, the inverter's DC-side active power is 100kW, efficiency ρ is 98.6%, fs is 8kHz, and bus voltage is 550V, while simulation results show it to be 2V. Note that our design parameters must be within a sufficiently large range so that even if the debugging environment or inertial factors change, we can adjust them to suitable and stable target values via software.
Based on the above formula, the bus capacitance of this design is calculated as follows:
(7)
3. Selection of bus capacitor capacity when reactive power supports the power grid under extreme conditions (IGBT shoot-through)
Inverter output current:
If the output power P is 100KW, the AC output voltage Uout is 315V, and the angular frequency ω is 314, C is calculated to be 1853uF using formulas (6) and (7).
4. Calculation and Simulation Comparison of Peak-to-Peak Value Δu of DC Bus Fluctuation Voltage
Based on the charging and discharging process of the DC bus capacitor, the energy required by the bus in one switching cycle is Win. The energy released by the capacitor in one switching cycle is Q.
From equation (3), we can deduce
(10)
Based on the design parameters above, the theoretical peak-to-peak ripple (Δu) of the DC bus is 3V; however, in the MATLAB photovoltaic inverter system simulation, the observed peak-to-peak ripple (Δu) of the DC bus waveform is 10V. To meet the combined design requirements of both, a Δu value of 10V is chosen here.
5. Calculation of peak current Ih
The peak current of one cycle is calculated by combining equations (4), (10), and (11):
It can be determined that: Ih = 76.8A
RMS current value Irms over 6 cycles
Because of the inrush current, the temperature coefficient is unacceptable when calculating losses, so multiple capacitors need to be connected in parallel here. After using four 500uF power capacitors in parallel to shunt the current, the Irms1 value can be obtained.
If the highest frequency of DC bus ripple fluctuation is 4kHz, then Irms is 54.3A according to equation (12).
Therefore, the effective value of the current through a capacitor can be calculated;
The capacitor uses the specifications from the farad capacitor manufacturer. Based on its ESR (Equivalent Series Resistance) and Rth (thermal resistance between the winding hot spot and the external environment (natural cooling)), the following calculations were performed at an ambient temperature limit of 85 degrees Celsius:
From equation (13), we can obtain: Pt = 0.295; H = 1.3K; Qu = 356.7K.
7. Conclusion
Based on the parameters calculated by Farad, the final ambient temperature margin of the capacitor is 83.7°C. Compared with an ambient temperature of 40°C in summer, the temperature margin is more than 40°C.
When selecting capacitors, we generally refer to the capacitance range of major manufacturers. Here, we take Farad's product parameters as an example. From the manufacturer's selection manual, find a capacitor with a capacitance of 420uF. That is, in a 100KW unit, four 420uF capacitors connected in parallel are sufficient.
