PV Performance Guarantees (Part 1): Page 7 of 8
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While this complicates performance verification, expected PV system output power is directly proportional to solar irradiance, which is the input-power source. Therefore, as measured solar irradiance in the plane of the array changes, the output power of a PV plant should change proportionally. This means that the temperature- and irradiance- corrected expected PV system output power (PEXPECTED) can be derived from the temperature-corrected nominal plant power (PTC), as calculated in Equation 3, by multiplying the latter by the normalized solar irradiance, as shown in Equation 4:
PEXPECTED = PTC x (GPOA ÷ 1,000 W/m2) (4)
where GPOA equals the measured solar irradiance in the plane of the array.
When managing a large PV asset, verifying power instantaneously is generally less informative than verifying energy production over time. For example, one might want to characterize the daily, monthly or lifetime performance ratio for a PV power plant. As shown in Equation 2, this is a function of the actual energy measured at the revenue meter and the ideally expected amount of energy after temperature and irradiance compensation. This can be accomplished in two steps: determining the available irradiation and solving for the temperature- and irradiance-compensated ideally expected energy.
The first step is to determine the irradiation, the solar energy, available at the point of measurement. In Photovoltaic Systems Engineering, Robert Messenger and Jerry Ventre explain, “Since energy is power integrated over time, irradiation is the integral of irradiance.” In this context, the verb “to integrate” is just a fancy way of saying “to sum up.” In other words, available solar energy is the sum of all the little bits of solar energy, which might be measured in 1-second, 1-minute or 15-minute increments, added up over some interval (hour, day, month, year, etc.). While this can be expressed as a sum equation, the integral is shown in Equation 5:
H = ∫ GPOA dt (5)
In this formula, H equals the irradiation or solar energy at the point of measurement. As was the case in Equation 4, GPOA is the irradiance or solar power in the plane of the array. This needs to be multiplied by an increment of time in order for power to result in a unit of energy. This increment of time is shown in the equation as dt, which represents a change in time, the smallest increment being measured. It is most common for this to be a 15-minute interval, as this simplifies the math and data collection. The irradiance in the plane of the array is averaged over a 15-minute interval, and then all of these tiny 15-minute bits of energy are added together to determine the total irradiation in the plane of the array over a longer interval of time.
The second step is to use the solution from Equation 5 to solve for the temperature- and irradiance-compensated ideally expected energy (EIDEAL), which might look like Equation 6:
EIDEAL = (H ÷ 1,000 W/m2) x PTC (6)
Dividing the solution found in Equation 6 into the actual measured energy over an identical period of time determines a PV system’s performance ratio, as described in Equation 2 (above). This index allows for the comparison of PV plants across different sites, regardless of the PV technology. It is obviously important to choose units and metrics that match the measurement equipment and resolution of data.
These formulae help to give guidance as to who should hold the risk, the EPC contractor or the project sponsor. The key to using these equations is to know their limitations, which are a function of overall project design and measurement accuracy. The results are not intended to be exact, but rather to be very close approximations given the instrumentation options. Furthermore, accurately measuring and correcting for temperature and irradiance is a powerful tool for determining system health. When combined with other plant measurements, temperature and irradiance information are useful as both troubleshooting and revenue-estimating tools.
GUIDELINES FOR MEASUREMENT, ACCURANCY AND PROOF
Measurement is the backbone of a solid performance guarantee. Sometimes the performance of the meter and data acquisition system can be more important than the actual system performance. If it matters to the contract, and if it determines assessed damages, then it has to be measured and reported accurately and often. Good plant measurements lessen the challenges associated with verifying that performance guarantees are met or enforcing the contract terms when they are not.