Why is there a discrepancy between the power displayed by the inverter and that shown on the electricity meter?

After users install a photovoltaic power generation system, they can see from the mobile phone monitoring APP or the inverter how many kilowatt-hours of electricity are generated every day and calculate how much money can be earned every day. But at the end of the month, when settling electricity bills with the power supply bureau, there will be some differences. Some users have less and some users have more. What’s going on here?
In fact, the power read from the inverter may be different from that read from the electricity meter. Generally, there will inevitably be losses between the inverter and the electricity meter. According to the law of conservation of energy, the power generation of the electricity meter is lower than the power generation displayed by the inverter.
In practical applications, due to the measurement error of the inverter and the measurement error of electric energy, the power displayed by the electricity meter may be higher or lower than that shown by the inverter. This is all a normal state.

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1. Power calculation principle

To understand the reason for this, first we need to figure out how power is actually calculated.
The power calculation formula is:
W = UIT = I²RT
In the formula:
W – power generation of the photovoltaic system, in KWH.
U – mains voltage, in V.
I – output current, in A.
T – daily power consumption time of the load, in h.
R – impedance of the output cable, in Ω.

No matter what kind of instrument or equipment it is, the rule for calculating power is the same. Based on the data acquisition of three physical variables of voltage, current, and time, power is calculated through different algorithms.
2. Inverter power calculation

In the entire photovoltaic power generation system, in addition to performing the DC-to-AC conversion work, all dynamic operation data of the power station is completed on the inverter side, and power calculation is also a part of it. The inverter collects voltage and current data through the built-in current sensor and voltage sampling circuit, and calculates the power generation through software algorithms and displays it on the inverter screen and monitoring platform.
The calculation of inverter power generation involves the detection of voltage and current. From the current sensor to the computing chip, there is also a hardware sampling processing circuit. The accuracy of the current sensor is about ±0.5%. Combined with the hardware sampling circuit and software calculation, the overall accuracy is about ±1%.

3. Electricity meter power calculation

At present, there are many types of electric energy meters, but the principles of measuring power are essentially the same. Taking electronic energy meters as an example, the current and voltage sensors connected to the measured circuit convert the data through the module converter and input it to the microprocessor for analysis and processing. The positive and negative active and reactive power consumption in time-sharing measurement is displayed through the display screen.

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Like the inverter, the measurement of the electricity meter also has errors. For single-phase or three-phase electricity meters, the accuracy class will be marked on the nameplate, such as 0.2S, 0.5S, 1.0S, 2.0S level, etc., which means that an error within ±0.2%, ±0.5%, ±1.0%, ±2.0% is allowed. At present, the accuracy class of the electricity meters commonly used by residents is 1.0S, so there is an error of ±1%.

Case analysis
Knowing the basic measurement rules of power, let’s take an actual case and establish a mathematical model to see the differences in the power displayed by the inverter and the power displayed by the electricity meter under different circumstances.

Case: A 10KW photovoltaic power station with three-phase 380V grid connection, using one AiFu inverter. The output side of the inverter is connected with 6 square copper wires. The distance from the output side of the inverter to the electricity meter is 30 meters. The daily power generation is calculated based on full load for 4 hours. The daily power generation is: 10KW * 4h = 40KWH.
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Cable loss calculation formula:
△W = I²RT (1)
R = ρL/S (2)
Through the formula and the length and size of the cable, the loss of the three output phase lines can be calculated as 0.16KWH.
Situation 1: The inverter current measurement accuracy is -1%, and the electricity meter measurement error is +1%.
The output current detected by the inverter I = 15.2A * (1 – 1%) = 15.05A.
Inverter displayed power generation:
W1 = UIT = 380V * √3 * 15.05A * 4h = 39.62 degrees.
Electricity meter displayed power generation:
W2 = 40KWH * (1 + 1%) – 0.16KWH = 40.24 degrees.
Conclusion: W1 < W2.
Situation 2: The inverter current measurement accuracy is +1%, and the electricity meter measurement error is -1%.
Similar calculations as in Situation 1 can yield:
Inverter displayed power generation W1 = 40.41 degrees.
Electricity meter displayed power generation W2 = 39.44 degrees.
Conclusion: W1 > W2.
Situation 3: The inverter current measurement accuracy is -1%, and the electricity meter measurement error is -1%.
Similar calculations as in Situation 1 can yield:
Inverter displayed power generation W1 = 39.62 degrees.
Electricity meter displayed power generation W2 = 39.44 degrees.
Conclusion: W1 > W2.
Situation 4: The inverter current measurement accuracy is +1%, and the electricity meter measurement error is +1%.
Similar calculations as in Situation 1 can yield:
Inverter displayed power generation W1 = 40.2 degrees.
Electricity meter displayed power generation W2 = 40.2 degrees.
Conclusion: W1 = W2.
Summary

The four situations listed above are actually a mathematical model, just to let everyone understand the principle simply. The specific situation is much more complicated than the above four situations. Inverter voltage sampling error, temperature influence, uncertainty of sampling error, inverter and electricity meter calibration coefficient, material thickness and length of the cable, contact loss of wiring terminals, etc. will all affect the accuracy of power measurement. Therefore, there will always be more or less differences between the power displayed by the electricity meter and that shown by the inverter, which is a normal phenomenon. Under normal conditions, it is generally considered that when the distance between the connection cable from the inverter to the electricity meter is within 50 meters, a deviation within 2% between the power generation display values of the electricity meter and the inverter is acceptable.

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