DC Wiring Power Loss

PV plants generate a considerable amount of energy. When a solar generator is operating at the MPP (as is the case, for example, with a grid-connected installation), it often pays to use a wire whose gauge is greater than the minimum required by the applicable standard, so as keep DC wiring loss to an acceptable level. The additional cost is a negligible factor in most such cases.

The ohmic resistance R of a wire with length I and gauge a is calculated as follows using specific resistance p of the wire material:

1

R – p ‘ A

(4.21)

For copper, p at 20 °C is around 0.0175 O mm2/m and at 85 °C is around 0.022 O mm2/m. To use the equation above correctly with these p values, I must be expressed in m and A in mm2, and for two-wire cables must be twice as large as the wire length.

To determine the ohmic loss in solar generator wiring, only one equivalent loss resistance RDc should be determined. For nSP strings wired in parallel with one resistance Rstr each and a main DC cable with resistance RH, the ohmic loss is determined as follows:

image491
Подпись: (4.22)

In calculating Rstr and RH, both pure line resistance as well as additional resistance stemming from any fuses such as diode fuses and terminals must also be factored in (e. g. 1 mQ per terminal if terminal resistance is taken into account).

Подпись: Ohmic loss PVR on the DC side: PVR — RDC ■ IDc (4.23)

In such a case, the total ohmic loss PVR on the DC side is as follows for current IDC:

Подпись: DC loss PVD at string diodes: PVD — VF ■ IDC (4.24) Total loss Pv on the DC side: PVDC — PVR + PVD (4.25)

The diode flow voltage at the string diodes is almost always Vf ~ 0.8 V for silicon diodes. Thus the total loss at the string diodes is as follows:

The value of interest is usually not absolute but rather relative loss, i. e. system loss that occurs in the presence of nominal direct current IDCn relative to nominal DC loss PDCn incurred by the inverter. If the solar generator is not oversized, IDCn will roughly equate to solar generator current at the MPP and PDCn will roughly equate to effective solar generator output PAo at STC power output (1 kW/m2, 25 °C), which is usually somewhat lower than nominal solar generator output PGo at STC. However, PDCn can also be defined as a value that is somewhat lower than PAo.

Подпись: PVDCn RDC ' IDCn + VF PDCn VDCn

With VDCn as the nominal voltage on the DC side (usually solar generator MPP voltage) PDCn — VDCn ■ IDCn, the following holds true for relative DC-side power loss under nominal voltage conditions:

In the case of stand-alone installations without solar trackers, relative DC power loss of up to around 5% has little impact on energy yield since the voltage of such solar generators is usually somewhat oversized (except in very hot locations). This scenario is clearly shown in Figure 4.39, as it basically makes no difference whether voltage loss occurs at shaded modules or at diodes and resistances. On the other hand, when it comes to installations with solar trackers – that is, primarily grid-connected installations and particularly at sites with PV system feed-in tariffs – efforts should be made to keep relative DC power loss to under 1%, and at the outside under 2%, so as to avoid needless power loss. A key factor in such cases is power loss in lengthy DC wire runs and at string diodes with low nominal voltages VDCn.

image496 image497 Подпись: (4.27)

If a PV system’s insolation and energy yield distribution across the various power stages is a known quantity, these data can be used to estimate annual DC power loss based on wiring power loss, as follows:

In Burgdorf (in the Swiss Mittelland region), with PDCn — PAo the energy loss coefficient kEV ~ 0.5 is obtained.

This value can also be applied to other flat areas in Europe. If PDCn < PAo, or for Southern European or high Alpine installations, a value higher than 0.5 (up to about 0.65) should be used for kEV.

Updated: August 7, 2015 — 3:17 pm