Adding modules to a string on a cold Aberdeenshire roof
A 4.8 kWp domestic system is being designed using 12 x 400 W modules on a south-facing roof in Aberdeenshire. Module data: Voc 41.6 V, Vmp 34.2 V, Isc 12.4 A, Imp 11.6 A, Voc temperature coefficient -0.29 %/degC, Vmp coefficient -0.35 %/degC. Recorded minimum cell temperature on site is -10 degC and summer cell temperature reaches 70 degC. The selected single-phase transformerless inverter is rated 3.6 kW with a maximum DC input of 600 V, one MPPT with an operating window of 150-500 V and a start-up voltage of 120 V. After the quotation has been issued, the customer asks for two extra modules to be added to the same string and points out that a neighbour has a bigger array.
1. Determine whether the customer's request is technically acceptable, and state the maximum number of modules that may be connected in series on this inverter.
Read the worked answer
Work to the worst case, which is the coldest cell temperature, not STC.
Voltage multiplier at -10 degC: 1 + (-0.0029 x (-10 - 25)) = 1 + 0.1015 = 1.1015
Voc per module at -10 degC = 41.6 x 1.1015 = 45.82 V
- 14 modules: 14 x 45.82 = 641.5 V > 600 V maximum DC input. Not acceptable - the inverter would be overstressed or damaged on a cold, bright morning when there is no load to pull the voltage down.
- Maximum number = 600 / 45.82 = 13.09, so 13 modules.
Judgement: 13 is the calculation limit (13 x 45.82 = 595.7 V), but that leaves only 0.7 % margin and ignores measurement tolerance and the fact that the coefficient is a typical, not guaranteed, value. A prudent design uses 12 modules (550 V), giving roughly 8 % headroom, and that is what should be offered to the customer. The answer to the customer is therefore: two extra modules cannot be added to one string; the options are 12 on this inverter, or a different inverter with a higher maximum DC input if they want 14.
2. Check the 12-module string against the MPPT window at both temperature extremes and explain why the upper MPPT limit matters as well as the maximum DC input.
Read the worked answer
Minimum voltage (hot day): Vmp at 70 degC = 34.2 x (1 - 0.0035 x 45) = 34.2 x 0.8425 = 28.8 V 12 x 28.8 = 346 V - comfortably above the 150 V lower limit and above the 120 V start-up voltage, so the inverter will run and stay in MPPT on hot afternoons.
Maximum MPPT voltage (cold day): Vmp at -10 degC = 34.2 x (1 + 0.0035 x 35) = 34.2 x 1.1225 = 38.4 V 12 x 38.4 = 461 V - inside the 500 V window.
For comparison, 13 modules gives 13 x 38.4 = 499.1 V, sitting exactly on the MPPT ceiling, so on a cold morning the array would run above the tracking window and the inverter would move off the maximum power point, losing yield precisely when irradiance is good.
Why both checks are needed: exceeding the absolute maximum DC input is a safety/equipment failure; exceeding the MPPT upper window is a performance failure that is invisible on a warm commissioning day and shows up as unexplained underperformance in winter. The string must satisfy all four limits: max DC input, MPPT max, MPPT min and start-up voltage.
3. The 12-module array is 4.8 kWp on a 3.6 kW inverter. Explain whether this DC/AC ratio is acceptable and what limits apply to the AC side.
Read the worked answer
DC/AC ratio = 4.8 / 3.6 = 1.33. This is normal and generally beneficial: for most of the year the array never reaches STC output, so the inverter is worked harder for more hours and annual yield rises. Clipping only occurs around midday in spring on cool, clear days, and the lost energy is typically 1-2 % - far less than the gain.
Checks that must still be made:
- String current: Isc 12.4 A must not exceed the inverter's maximum input current per MPPT, and the maximum input short-circuit current. Both need confirming against the datasheet; if the inverter accepts, say, 13.5 A per MPPT the single string is fine.
- G98 limit: a single-phase inverter is a G98 (notifiable) connection only if the rated AC current is 16 A per phase or less. 3600 / 230 = 15.65 A, so it just fits - but the manufacturer's declared maximum output current must be used, and if it were declared at 16.5 A the connection would become a G99 application.
- Document it: the oversized array and resulting clipping should be recorded in the design and explained at handover so the customer does not treat summer clipping as a fault.