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Voltage drop is a common name for the electrical potential loss that inevitably occurs when current flows through a conductor between the source and the load. Conductor resistance and reactance combine to make a small heating load that draws power from the circuit whenever a normal load is attached. The amount of voltage drop—also known as voltage rise, resistive losses, or wire loss—is dependent on circuit voltage, current and length; conductor size and material; and other complicated factors, such as the type of raceway, the geometry of the conductors, the number of phases and the temperature.
Why Worry about Voltage Drop?
There are two problems with voltage drop in PV systems. First, it represents wasted energy. Transforming electrical energy into heat in circuit conductors is lost energy production. Second, voltage drop can cause PV inverters to stop working properly under certain conditions. For example, if the dc bus voltage drops below the inverter’s minimum MPPT voltage, then the inverter will operate in a limited state. If the ac bus voltage rises above the maximum grid voltage set point, then the inverter will stop operating completely.
What can you as a PV system designer do about voltage drop? You can optimize the schematic design and layout of equipment strategically to minimize voltage drop. You can also consider upsizing certain system conductors to further reduce voltage drop.
Quantifying Voltage Drop
To understand how you can reduce voltage drop, you have to quantify it. In its simplest form, a circuit conductor can be considered a long, lowresistance electric heater obeying Ohm’s Law. The voltage across the heater is the current multiplied by the resistance, or V = I x r. The resistance will depend on the size, material, temperature and length of the conductor. Typical values for standard conductors are given in tables as ohms per 1,000 feet of conductor length. Therefore, the basic equation for dc voltage drop is:
V_drop = I x r
= I x (2 x L x R) / 1,000
= (2 × L × R × I) / 1,000
where I is the circuit current, L is the one-way circuit length and R is the conductor resistance per 1,000 feet. The basic equation can be modified for single-phase or 3-phase ac circuits, different temperatures and different power factors.
A good place to start for manual voltage-drop calculations is provided by the NEC. Values for dc resistance per 1,000 feet can be found in Chapter 9, Table 8. Reactance and ac resistance per 1,000 feet can be found in Chapter 9, Table 9. The NEC Handbook lists some voltage-drop equations and gives example calculations following the Tables.
To be clear, however, the NEC does not require any particular amount of voltage drop. Instead, Article 210 on branch circuits and Article 215 on feeders both have a fine print note (FPN) suggesting that “reasonable efficiency of operation” occurs if voltage drop is limited to less than 3% each on feeders and branch circuits, and less than 5% overall (210.19(A) FPN No. 4 and 215.2(A)(3) FPN No. 2.) These FPNs are not binding and certainly were not written with PV in mind. Nevertheless, they provide useful reference points. One general requirement the Code does make in Article 250.122(B) is that if the current-carrying conductors are upsized for voltage drop, the equipment grounding conductor (EGC) must also be proportionally upsized. The 2008 NEC includes an exception to this rule in Article 690.45(A), stating that it is not necessary to upsize the dc EGC in a PV system to address voltage drop. As a result, the EGC in PV source and output circuits is generally sized according to Table 250.122.
Another option for performing voltage-drop calculations is to use one of the many available electrical calculator programs. Some programs can be used online, and some can be downloaded to your computer. Handheld calculators with special buttons for electrical functions are also available. Most of these calculators are reasonably accurate and good for standard situations. However, most will not show you exactly how the calculations are being done so that you can verify the answer you are getting. Most will not adapt very well to nonstandard applications like PV. For example, many allow dc voltages up to only 48 V, and few allow adjustment for temperature or power factor.
The best source for good voltagedrop calculations specific to your project is a licensed electrical engineer experienced in both PV and voltagedrop issues.
Principles for Minimizing Voltage DropAll other things being equal, designing with the following principles in mind will help minimize voltage drop:
1. Transmission at higher voltage will result in lower losses. In fact, for the same power, doubling the voltage decreases the voltage drop by a factor of four.
2. Shorter distances will have smaller voltage drops.
3. Transmission with 3-phases is more efficient than single-phase.
4. Larger conductors will have lower voltage drop.
5. Copper conductors will have lower voltage drop than aluminum conductors of the same size.
6. Transmission with two conductors in dc will result in lower losses than two-conductor, single-phase ac, especially with relatively large conductor sizes like 350-kcmil and larger. However, this effect is much smaller for inverter output circuits, in which the power factor is close to unity.
7. Use parallel conductors for large ac circuits.
8. Cooler conductor temperatures will reduce voltage drop.
9. Higher power factors are better.
10. Pay attention to the type of conduit used. For ac circuits with small conductor sizes (less than 3/0) and power factor of 0.85 to 1.0, the type of conduit makes almost no difference in the voltage drop; for power factor of 0.85 and larger wire sizes (3/0 and above) PVC is best, but aluminum is better than steel. However, for PV inverter-output circuits, with power factor close to 1.0 and larger wire sizes, PVC is still best, but steel is better than aluminum.
Schematic Design and Equipment Layout
An example of a PV system with possible voltage-drop challenges would be one where you want to transmit 100 kW of power from a PV array through a central inverter to a main switchgear that is 1,000 feet away from the final combiner box at the array. There are several possible ways of transmitting the power.
You could locate the inverter right next to the combiner box and plan to cover the long distance in 3-phase ac at the nominal voltage dictated by the electrical service and inverter output. Another option is locating the inverter next to the switchgear and covering the distance with the dc output from the combiner box. Of course, the inverter could also be located somewhere in between, with part of the long run in dc and part in ac. Other options include step-up and step-down transformers located at the inverter and at the interconnection location, allowing the use of higher voltage 3-phase ac for long-distance power transmission, although the inefficiencies and standby losses of the transformers must be taken into account.
Depending on the PV string voltage and the available ac voltages on site, it might make more sense to design the long-distance run in ac or dc, to minimize voltage drop and installation costs. Calculations for the various options will quickly show which one provides the lowest voltage drop with the least amount of copper. Assuming that you use parallel conductors when appropriate, in general the best option for long distance runs is 700–800 Vdc, which is the typical PV operating voltage where 1,000 Vdc systems are allowed. If the open-circuit voltage is limited to 600 Vdc, then 3-phase 480 Vac is the best option for long runs. The next best option is any dc voltage from about 300–500 Vdc. These PV operating voltages are preferable to 3-phase 240 Vac or single-phase 277 Vac, which are roughly equivalent depending on the range of wire sizes. 3-phase 208 Vac or single-phase 240 Vac are next best, depending again on the range of wire sizes, and are preferred over long runs at 120 Vac or 48 Vdc. In summary, if possible, design the longest distance run according to Table 1, which shows nominal operating voltage in descending order of preference.
For designers who are used to large ac loads, voltage drop can be much worse on an ac motor circuit than on a similar dc circuit. However, power factor is an important consideration, especially for larger conductor sizes. For the same voltage and current, a two-wire, single-phase ac circuit using 300-kcmil conductors will have 50% more voltage drop than the same two-wire dc circuit using 300-kcmil conductors, according to the standard tables (NEC Chapter 9, Tables 8 and 9) at 85% power factor. However, since the power factor in PV applications is very close to 100%, the ac circuit actually has only 5% more voltage drop than the dc circuit. In other words, factors such as voltage level and number of phases in PV applications are far more important than ac versus dc.
How Much Is too Much Voltage Drop?
After strategically designing the PV system layout to minimize voltage drop, you must make decisions about upsizing the various circuit conductors to reduce voltage drop further.
First, voltage drop must be low enough to allow the inverter to operate as intended. To that end, the dc input voltage to the inverter under worst-case normal operating conditions must be no lower than the bottom end of the MPPT window of the inverter. This means that at the highest expected ambient and cell temperatures, after the module has aged a decade or two, and with full sun and full current available, the string voltage—after voltage drop to the inverter is considered—must be within the MPPT window.
Second, the inverter ac output circuit must not have excessive voltage drop that would cause the inverter to reach the high voltage limit. This scenario can easily occur if the grid voltage is above its nominal value, which is a common occurrence during parts of the day and times of the year, though it is more frequent in some locations than others. For example, grid voltage at the interconnection might be 252 Vac line-to-line on a nominal 240 Vac system. If there is 5% voltage drop in the inverter output circuit, then the ac voltage at the inverter will be 265 Vac, which is higher than the typical 264 Vac high-voltage trip point, and the inverter will go offline with a “high grid voltage” error.
Third, voltage drop must be within the project specifications, if any exist. Typical blanket values called for in bid packages are less than 2% voltage drop on each of the dc and ac circuits, and less than 3% overall voltage drop from the modules through to the interconnection. These requirements protect the system owner’s investment and help to ensure that excessive energy is not wasted in wiring losses.
Rule of Thumb: PV Source-Circuit Homerun LengthFor installers who are wondering whether extra-long dc homeruns are acceptable on a particular project, consider this rule of thumb: For modules with maximum power current around 5 A and 12 AWG homerun wiring, the voltage drop will be less than 2% if the distance from the array to the inverter in feet is less than or equal to the string voltage. The same is true for maximum power current up to 8 A and 10 AWG homerun wiring.
For example, assume you have a 200 W module with the following operating characteristics: Imp = 5 A and Vmp = 40 V. With a 12 AWG copper homerun conductor, you can have 400-foot long homeruns if there are 10 modules (400 Vdc) in each string, or 280-foot homeruns if there are seven modules (280 Vdc) per string. To achieve a 1% voltage drop, the homerun length can be half of the string voltage.
This rule of thumb is handy for installers who are used to dealing with a handful of module types and know the corresponding Vmp values by heart.
Upsizing Wires to Increase Production
After meeting the inverter considerations, voltage drop can be further reduced, if cost effective, to increase system energy production. While voltage drop may result in a slight change in operating current—for example, when the MPPT algorithm in the inverter adjusts to the change in the load—a percent drop in voltage is essentially equivalent to a percent drop in a PV system’s power production at any instant.
With that in mind, there are two primary ways to consider the additional cost of larger-than-minimum conductor sizing. The first method is to compare the first costs of larger conductors versus the system lifetime costs of reduced production. Since this comparison requires investment assumptions about the time value of money, it is best captured using financial analysis spreadsheets or other software tools. An easier method is to compare the incremental cost to install larger conductors versus the incremental cost to install additional PV modules to produce the equivalent additional power. Consider the following two examples.
Example 1. Assume a 50 kW PV system at 400 Vdc with 1,000 feet from combiner box to inverter. The minimum dc output-circuit conductor is 4/0 for ampacity, resulting in 3.8% voltage drop, or 1,900 watts of lost power at full-power conditions. Upsizing to 300-kcmil conductors would result in 2.68% voltage drop, or 1,340 watts of lost power, which is a net gain of 560 watts. Is upsizing worth it? Table 2 illustrates the incremental cost per watt to reduce the voltage drop in Example 1, factoring in conductor, conduit and labor costs. Note that in this case, increasing the conductor size requires increasing the conduit diameter and purchasing larger fittings. According to the table, it appears that the net gain of 560 watts from upsizing the conductors from 4/0 to 300-kcmil costs about $12.50 per watt. This suggests that adding another string of modules, if possible, is a more cost effective way to increase energy harvest.
Example 2. Assume a 2 kW PV system at 400 Vdc with 1,000 feet from combiner box to inverter. In this case, as shown in Table 3, switching from 12 AWG to 8 AWG to reduce voltage drop by a few percentage points may well be worthwhile. This assumes that the same size conduit is used in both instances, meaning that upsizing from the smaller wire size does not increase conduit costs.
When considering the benefit of increased conductor sizing, remember that, on average, both dc and ac PV conductors will carry less than the maximum power current. This is because, most of the time, irradiance is less than 1,000 W/m2 and cell temperature is generally above 25°C. Therefore, annual production losses from voltage drop will be less than those calculated using Imp values. Conversely, when conductors are sized for voltage drop for long runs rather than for ampacity, conductors will not heat up as much. They are oversized for the current they are carrying, and voltage drop will be reduced by more than the amount calculated at the standard 75°C tables, because of the reduced conductor temperature. These facts make any return on increased conductor size investment slightly more complicated than the simple calculation implies.
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[SIZE=4][COLOR=Navy]مدرس بقسم الهندسه الكهربيه - كليه الهندسه - جامعه المنيا -ج. م. ع.
THANKS A LOT Mr. AHMED FOR THAT VALUABLE INFORMATION
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