The loss calculation formula for solar inverters is not uniform, but varies depending on the type of loss. It needs to be determined based on the specific loss generation mechanism (such as power devices, transformers, lines, etc.) and device parameters (such as conduction resistance, switch energy, etc.). Mastering the calculation formulas for different losses is the foundation for accurately evaluating inverter efficiency and optimizing design.
Main loss types and calculation formulas of inverters
The losses of inverters can be divided into power device losses (with the largest proportion), magnetic component losses (such as transformers and inductors), line and auxiliary losses, etc. The specific formula is as follows:
Calculation formula for subdivision types of loss types, key parameters applicable scenarios
Power device loss, conduction loss - MOSFET：\(P_{\text{cond}} = I_{\text{rms}}^2 \times R_{\text{ds(on)}}\)- IGBT：\(P_{\text{cond}} = V_{\text{ce(sat)}} \times I_{\text{avg}}\) \(I_{\text{rms}}\)： Effective current value\ (R_ {\ text {ds (on)}} \): MOSFET on resistance\ (V_ {\ text {ce (sat)}} \): IGBT saturation voltage drop\ (I2 {\ text {avg}} \): Energy loss when the average current device is conducting
Switching Loss \(P_{\text{sw}} = (E_{\text{on}} + E_{\text{off}}) \times f_{\text{sw}}\) \(E_{\text{on}}\)： Activate energy (provided in the device manual)\ (E {\ text {off}} \): Turn off energy\ (f_ {\ text {sw}} \): Energy loss during the on/off process of switching frequency devices
Reverse recovery loss \ (P_ {\ text {rr}}=E {\ text {rr}} \ times f_ {\ text {sw} \) \ (E {\ text {rr} \): Reverse recovery energy (diode parameters, provided in the manual)\ (f_ {\ text {sw}} \): Loss during reverse recovery of switching frequency freewheeling diode
Magnetic component loss and iron loss (magnetic core) \(P_{\text{fe}} = K_f \times f^\alpha \times B_m^\beta \times V_{\text{core}}\) \(K_f\)： Material coefficient; f: Working frequency\ (Bm \): maximum magnetic flux density\ (\ alpha, \ beta): Experience index (usually \ (\ alpha ≈ 1.2-2 \), \ (\ beta ≈ 2-3 \))\ (V_ {\ text {core}} \): Core loss of magnetic core volume transformers and inductors
Copper loss (winding) \(P_{\text{cu}} = I_{\text{rms}}^2 \times R_{\text{winding}}\) \(I_{\text{rms}}\)： Effective value of winding current\ (R_ {\ text {winding}} \): Winding DC resistance (including skin effect) of transformer and inductor winding resistance loss
Other line losses \ (P_ {\ text {line}}=I ^ 2 \ times R_ {\ text {line}} \) I: Line current\ (R_ {\ text {line}} \): Line resistance (including wire and connection point resistance) DC bus, AC output line
Auxiliary power loss \(P_{\text{aux}} = P_{\text{control}} + P_{\text{driver}}\) \(P_{\text{control}}\)： Control circuit power consumption\ (P_ {\ text {driver}} \): Power consumption of driving circuit, inverter control board, driving chip, etc
Analysis and Application of Key Formulas
Power device losses: The core power devices (MOSFET or IGBT) that cause inverter losses are the main source of losses, accounting for 60% -80% of the total losses.
Conduction loss: It is proportional to the resistance of the device during conduction (MOSFET's \ (R_ {\ text_ ds (on)} \)) or the voltage drop (IGBT's \ (V_ {\ text_ ce (sat)} \)), and is affected by the effective current value. For example, when the MOSFET has a current of 10m Ω and an effective operating current of 10A, the conduction loss is 1W (10 ^ 2 times 0.01).
Switching loss: It is directly related to the switching frequency \ (f_ {\ text {sw}} \) (the higher the frequency, the greater the loss). It is necessary to check the turn-on energy \ (E {\ text {on} \) and turn off energy \ (E {\ text {off} \) through the device manual. For example, if the switching frequency of an IGBT is 50kHz with \ (E {\ text {on}}=100 μ J \), \ (E {\ text {off}}=80 μ J \), the single tube switching loss is \ ((100+80) × 10 ^ {-6} × 50 × 10 ^ 3=9W \).
Magnetic component loss: The difficulty of high-frequency design is that iron loss (core loss) increases exponentially with frequency (in the formula \ (f ^ \ alpha \)), so high-frequency inverters need to use low loss core materials (such as nanocrystals and ferrites); Copper loss is related to the winding diameter and current density, and needs to be reduced by optimizing the winding method (such as multi strand parallel winding).
Total loss and efficiency calculation
Total loss: Sum up the above types of losses, that is, \ (P_ {\ text {loss (total)}=P_ {\ text {cond}}+P_ {\ text {sw}}+P_ {\ text {fe}}+P_ {\ text {cu}}+P_ {\ text {line}}+P_ {\ text {aux}} \)
Efficiency calculation: The inverter efficiency \ (\ eta \) is the ratio of output power to input power, i.e. \ (\ eta=\ frac {P_ {\ text {out}} {P_ {\ text {out}}}+P_ {\ text {loss (total)}} \ times 100 \% \)
Common Misconceptions and Precautions
Neglecting the influence of temperature on parameters: for example, the \ (R_ {\ text {ds (on)} \) of MOSFET increases with temperature (usually, \ (R_ {\ text {ds (on)} \) increases by 10% -15% for every 10 ℃ increase in temperature), and the actual operating temperature parameters need to be substituted into the calculation.
Simplified calculation of switch losses: Actual switch losses are affected by voltage and current waveforms (such as differences between hard and soft switches). The values of \ (E {\ text {on}}, E {\ text {off} \) in the manual are usually values under specific conditions (such as rated voltage and current) and need to be adjusted according to actual operating conditions.
Missed stray losses: such as parasitic inductance losses and capacitor ESR losses caused by unreasonable PCB layout, although accounting for a small proportion, need to be considered in high-precision design.
Summary: The core of accurate calculation of losses
The loss calculation formula for solar inverters needs to be selected based on specific loss types, with the core being the combination of device manual parameters (such as \ (R_ {\ text {ds (on)}}, E {\ text {on} \)) and actual operating conditions (such as current, frequency, temperature). By performing sub item calculations and comprehensive summation, the efficiency of the inverter can be accurately evaluated, providing a basis for circuit optimization (such as selecting low loss devices and optimizing switching frequencies), ultimately improving the energy conversion efficiency of the photovoltaic system.
