THE BREAK EVEN DISTANCE BEVISITED

5. OPTIMUM USE OF

6.2 THE BREAK EVEN DISTANCE BEVISITED

For fair comparison with ac, the lower dc transmission line losses must be weighed against the dc converter losses, which do not exist for the ac There is a transmission length for which the lower dc transmission cost pays for the higher dc terminal (converter) cost. This distance is referred to as the break even distance. The break even distance, as illustrated in Figure 3.2 earlier, is a classical way of characterizing the viability of transmission compared to ac transmission. For longer distances is less costly; for shorter distance ac is less costly.

Using present worth analyses, the evaluated cost of losses can be combined with installation cost to calculate cost”. Since the line will not always be at peak load the load duration must also be considered. A loss factor of 0.4, (the ratio of average losses over a year to losses at peak load) is assumed for this analysis. The break even distances would be less for higher loss In Tables and of Appendix D.3, separate break even distances are shown for the installed cost., for the energy losses, and for the “total cost”. The break even distance for “total” cost will depend heavily upon the expected level of line loading losses will dominate cost at heavier load and installed cost will be more important for lighter loads.

Table 6.1 shows break even distances based upon “total cost” for selected ac and transmission options. That table combines the results in Tables D.3.1 and D.3.2 of Appendix D.

The present worth (of losses) analysis used to calculate the break even distance is based upon

For some conductors, which are used mostly for lower voltage circuits, the core losses increase dramatically at heavy loading. At 75% of rating, and a conductor temperature of 50 degrees Centigrade, the ac resistance for a single layer ACSR is 1.4 times the dc r&stance. Conductors]

an effective rate of return of 8% (the difference between the expected return on investment and inflation) and a expectancy of 30 years. With those assumed data, used through Section 6.4, the losses are worth $2,080 per Section 6.5 contains results with the value of losses varied from zero to

Appendix D.2 contains the equations used to calculate the present worth of losses. Tables D.3.3 and D.3.4 in Appendix D.3 show the, cost assumptions used for the analysis.

the converter, typical costs are assumed (see Section 4 or Appendix D).

Except for The converter costs are assumed to be 50% of todays costs, which are in Section 4.4.

Figures 6.2 and 6.3 show the sensitivity of the break even distance to converter costs for the ac and transmission options and loading levels indicated in Table 6.1 and depicted in Figure 6.1. In Figure 6.2 and 6.3, 1.0 cost equals today’s converter cost. To calculate the break even distances for Figure 6.2, the peak line loading assumed are at the high end of that typically experienced during normal operation today. The break even distances in Figure 6.3 were calculated for peak line loading at the ac thermal limit. The converter MVA ratings and substation equipment ratings were assumed to equal the peak line loadings in arriving at the results in Figures 6.2 and 6.3.

Table 6.1 gives two break even distances for each level of loading; labeled “Without and ‘With where corresponds to reactive compensation. The former is the break even distance computed without including the cost of additional var support which will be needed to reasonable voltages for heavy line loading. The “With break even distance was calculated including the cost of var support to compensate 100 % for the reactive power absorbed by the line at peak loading. The cost of var support was assumed at This cost falls between the costs of conventional series compensation and conventional shunt compensation. To permit loading up to thermal ratings some of the var support would most likely need to be augmented by devices. The added costs for FACTS controllers were not included.

The break even distance was calculated for seven cases. For each case two levels of load (unity power factor) were considered. For most cases the converter ratings and ac substation equipment ratings are assumed to equal the peak line loading. For Cases and 7 the break even distances were also calculated for converters and substation equipment rated to handle peak load with one circuit out. Table D.3.5 in Appendix the installed cost and losses for each transmission configuration. The results in Table 6.1 are valid for the

“reduced-cost converters 50% of today’s cost) while Figure 6.2 and 6.3 show results vary with converter costs.

Case 1. In this case, a 408 DC bipole is compared to a 500 single circuit ac line, as depicted in Figure 6.1 a. Presently 1000 is considered a heavy load for both transmission options. The peak voltage is the same for both options and the same conductor size was assumed. The thermal rating for the ac line, typical 2000 MW, is therefore almost the same as

for the HVDC bipole. The right-of-way width for the dc-bipole was assumed to be about 100 feet compared to 200 feet for the 500 ac line.

For 2000 loading the break even distance, based upon reduced-cost converter and substation installed cost, var support and losses, is 248 miles. At present day heavy loading levels, 1000 installed cost largely determines the break even distance of 266 miles.

Case 2. In this case, a 281 DC bipole is compared to a 345 single circuit ac line shown in Figure 6. lb. The thermal rating of a 345 single circuit ac line is normally around 1000 MVA. Again the alternative is chosen to have the same peak voltage as the ac alternative and the conductor sizes are assumed to be the same. The thermal rating for the bipole circuit is therefore almost the The right-of-way width for the Hvdc bipole was assumed to be 135 feet compared to 150 feet for the 345 ac line.

For a peak load of 1000 MW with reduced-cost converters rated for 1000 the “total cost” (installed cost + losses + var support) of the 345 line will exceed the total cost of the Hvdc bipole iftransmission distances exceed 193 miles. peak loading and converter ratings are 500 MW, 50% of the dc or ac lines thermal rating, the break even distance will be 196 miles.

Case 3. illustrated in Figure 6.1 c, a double circuit 230 ac line is compared to the 281 dc bipole considered in Case 2. A single phase ac line fault (the most common kind) will normally result in power interruption for all three phases. It may therefore be necessary to use two ac circuits instead of one ifreliability is important. One dc-bipole with ground return may however be since a line fault on one pole will not normally cause power interruption on the other pole. The double circuit ac line is selected to have approximately the same thermal capacity for both circuits) as the dc option. The ac and dc alternatives also have approximately the same (500 MVA) thermal capacity with a single contingency outage. The right-of-way requirements of the AC and DC options are also similar.

For transmission distances greater than 90 miles the total cost (installed cost losses var support) of the 2-230 circuits operated up to 1000 will exceed the total cost for the bipole (including reuced-cost converters rated for 1000 For peak transmission loading and converter ratings of 500 MW, the break even distance for Case 3 is 163 miles. For some applications, however, a may be designed so the system can transmit peak power with a single contingency outage. Depending upon the number of parallel lines, the dc converters or ac substation equipment might therefore be rated for as much as 1000 MW to accomplish this.

The break even distance with 500 peak loading and 1000 MW converters is 275 miles.

Case 4. In this case, a 408 dc with ground return is compared with 345 single circuit ac transmission as depicted in Figure 6.1 d. Outage of a dc would have approximately the same impact on the system as outage of a single circuit ac line.

The total cost of the 345 ac line (with var support) operated up to its thermal rating will exceed the cost of the dc (reduced-cost converters rated for 1000

9 0

when the transmission distance is greater than 140 miles. maximum loading is “only”

500 MW, and the converters and var support are sized accordingly, the break even distance will be 151 miles.

Case 5. To reduce transmission losses, a double circuit ac be converted into transmission circuits for 3 bipoles of Hvdc as noted in Figure This may only require changing the insulators and adding the converter stations. The conversion might be done while still operating with ac so the down-time could be minimal. In this case, the double circuit 230 ac line peak line to ground, 1000 MW thermal capacity) is compared to 3-188 dc bipoles. The 3 bipoles are assumed to use towers and conductors that were previously used by a double circuit 230 line.

For transmission distances greater that miles the savings in losses and ac var support will more than pay for reduced-cost converters rated for 1000 MW peak line

is 1000 MW. For peak loading and converter ratings of 500 MW the break even distance is 254 miles.

Case 6. This case is a variation of Case 5 in that an existing double circuit ac line is converted to three bipoles to increase transmission capacity with minimal impact on the transmission corridor. As illustrated in Figure 6. this case compares the described conversion to adding a third ac circuit is feasible) to the existing double circuit ac line. The thermal ratings of both options are about equal to 1500 MW and capacity will also be almost the same for both options with a first contingency outage. Case 6 compares the total cost of adding a single 230

ac circuit to the cost of converting an existing double circuit 230 ac line to three 188 dc bipoles.

For peak of 1500 MW (the approximate thermal limit of the ac dc lines) with reduced-cost converters rated for a total of 1500 MW at each terminal the dc alternative is less expensive if the line length is greater than 151 miles.

For peak loading of 1000 with converters rated for 1000 MW at each terminal, the dc alternative in this case is less expensive than that of the ac if the line length is greater than 192 miles.

For some applications, however, a line must be designed so the system can transmit peak power with a single contingency outage. If there are no other parallel lines, the dc converters or equipment may therefore be rated for as much as 1500 MW to accomplish this.

The break even distance with 1000 peak loading and three 500 MW converters at each terminal is 260 miles. Increasing the converter rating does not raise the distance in the same proportion because the costs are dominated by losses.

Case 7. This final compares ac and dc underground or underwater cables. As illustrated in Figure 6. lg, two three phase 345 ac circuits are compared with a dc bipole with a part-time ground or sea return. The thermal capacity of both options is 1000

With reduced-cost converters rated at 1000 MW and peak loading of 1000 MW the

“total cost” of the ac option exceeds the total cost of the dc option for distances greater than 28 miles. Since a 345 ac cable is technically impractical for uncompensated distances longer than

18 miles (30 km per Figure 7. the economic comparison in this case is moot for submarine cables. However, ifunderground ac cables are equipped with shunt reactors at strategic points along their length (the costs for which are not included herein), cables may be more economical than ac cables.

For peak transmission cable loading and converter ratings of 500 MW the break even distance for Case 7 is 17 miles. However, a cable system. probably would never be designed this way since the cables would be very underutilized. In some cases, however, a cable system might need to transmit peak power with a single contingency outage. If there are no other parallel cables the converters or ac substation equipment must then be rated for 1000 MW, not 500 MW.

The break even distance with 500 MW peak loading and 1000 Mw converters is 29 miles. The break even distance for cable does not increase when is lower because the ac cable dielectric losses, unlike most other losses, do not decrease with current loading.

0a

500 408

1000 , ac not at thermal limit

345 ac 281 dc

2-23Okvac 281 1000 MW , ac at thermal limit

Figure 6.1 Configurations Compared in Break Even Analysis

Case 4

a c 4 0 8 1000 , ac at thermal limit

0e

Cases 5 9

Convert

2-23Okvac to 3-188 1000 , ac at thermal limit

N W ’

230

Case 6

Add new ac circuit or convert

Figure 6.1 Configurations Compared in Break Even Analysis continued

2 345 3 phase ac cables -vs 2-400

ac line

TABLE 6.1. TRANSMISSION DISTANCE IN MILES FOR HVDC BECOMES LESS COSTLY THAN THE AC ALTERNATIVE

(CALULATED USING 50% OF PRESENT-DAY I

bipole

Converter Peak Loading

W i i

I I I I

miles 600

case2 case3 case4 case5 --A-- case6 case7

0.20 0.40 0.60

cost

0.80 1 .oo 1.20

Figure 6.2 Break Even Distance vs Converter Cost for Heavy Line Loading

Consistent With Today’s Practice 1 Equals Today’s Converter Costs

Legend for Figure 6.2 above

Case ac Line Voltage dc Line Voltage Loading

circuits Poles

408 bipole 1000

2 1-345kV 1 281 bipole 500

3 1 281 bipole 500

4 1-345kV 1 408 500

5 2 230 converted to 3 188 bipoles 500

6 3rd 230 convert to 3 bipoles 1000

7 2 345 3 ph cables, 2 400 bipole 500

cables

miles

600

100

0 0.20 0.40 0.60 0.80 1 .oo 1.20

cost

Figure 6.3 Break Even Distance vs Converter Cost for Peak Line Loading at Thermal Limits Equals Today’s Converter Costs Legend for Figure 6.3 above

3rd 230 convert to 3 188 bipoles

2 345 3 ph. cables 2 400 bipole cables 1000

6.3 VARIATION IN BREAK EVEN DISTANCE WITH LOADING

For each case shown in Table 6.1, Figure 6.4 shows the break even distance for

levels of peak load. In this figure, 1 .O per unit load equals the ac line’s thermal capacity. The cost of converters was assumed to be half of today’s typical cost.

The break even distance for low voltage lines loaded to their thermal limit is smaller than the break even distance for high voltage lines. This is true because:

Line losses as a percentage of loading decrease as the voltage increases.

The break even distance is largely determined by the cost of losses when the lines are loaded to thermal rating.

It is also noted that when lines are loaded near their thermal limits, the break even distance decreases as load increases. This is true because:

Losses increase as the square of loading.

2. Converter costs are proportional to peak loading.

Interestingly, when loading becomes low enough the break even distance can also decrease with decreasing load. This is noticed for the 500 and 345 lines and is true because:

1. Installed cost of a line largely determines the break even distance.

2. As loading decreases, converter costs also decline, but the line cost remains constant.

That is, the Hvdc line becomes more competitive if the line will be underutilized.. ,

miles

per unit loading

Figure 6.4 Break Even Distance vs Peak Line Loading

Assuming The Converter Rating Equals the Peak tine Loading 1 Loading Equals the tine’s Thermal Capacity

Legend for Figure 6.4 above Using “todays” converter costs = $1001

6.4 CONTINGENCIES AND THE VALUE OF LOST TRANSFER CAPACITY The import of economy power into some metropolitan areas and inter-regional transfers are limited even today by first contingency transfer capability. For multiple outages, it may be permissible to shed load but for more common occurrences such as single circuit outages load shedding is not a viable option Since the system must be designed to survive a first contingency outage, the power import capability during normal operation is often determined by the transmission capability with the worst single contingency outage.

The value of first contingency transfer is difficult to determine and is very situation-dependent. Iftransfer capability is not sufficient, it may be necessary to provide local peaking power even though sufficient generation is available elsewhere. A gas turbine is commonly used to provide peaking capacity, so first contingency transfer capacity might be worth as much as the cost of a gas turbine (approximately However, in most cases the cost that can be attributed to the transfer capacity lost for a particular outage is somewhat less. The gas turbine may provide peaking capacity for more than one equally critical outage so its cost may not always be associated only with one most critical outage. Measures that only increase transfer capacity for a specific contingency are therefore less valuable. A gas turbine may also provide benefits other than peaking which some of its cost or it may partially replace new generation outside the load area.

Nevertheless, capacity with a single contingency outage can have value.

With new right-of-way becoming scarce, the transfer capability remaining after a single contingency outage could become more valuable. Economy import during operation can be limited by the need to all contingency outages. Therefore, there may be an energy cost differential associated with a first contingency constraint as well as the costs associated with lost capacity as discussed above. For this analysis it was assumed that the present worth of the energy cost caused by a first contingency constraint is lumped into an average cost for lost transfer capacity.

Previous Sections 6.2 and 6.3 compared the installed costs and losses for several ac and HVDC alternatives and concludes that may be cost competitive with ac even for relatively short distances as many suggest, transmission is loaded close to thermal limits. This section extends the previous analysis to include the value of transfer capability during single contingency outages. The equipment cost and characteristics used for this analysis are documented in Section 4 and were discussed earlier in Section 6. Section sets the stage by first comparing two ac alternatives. Section 6.4.2 continues the comparison of ac and

with today’s converter costs about and then varies that cost as in previous sections to derive break-even distance values.

6.4.1 Single Circuit ac versus Double Circuit ac Lines

A comparison considers a single circuit 345 line and a double circuit.230 line.

During pm-contingency operation, the 345 line is assumed to be loaded to its thermal rating (approximately 1000 with the aid of reactive compensation to attain the appearance of surge impedance loading, conditions. Similarly, the double circuit 230 line is assumed to be loaded to 1000 MW, approximately its thermal capacity. Again, sufficient reactive compensation is assumed to attain equivalent SIL conditions. Figure illustrates the pre-contingency conditions where the subject line delivers 1000 to the load area and the parallel system, if any and the local generation serve the remainder of the demand.

Consider the contingency loss of one circuit of the subject line. Of course, the loss of the single circuit 345 line yields zero post-contingency transfer capacity. With one 230 circuit out of service the 230 circuit is assumed to be capable of 500 MW transfer.

Figure illustrates the post-contingency conditions following the loss of the single circuit 345 line. The replacement capacity is shared between a “peaking generator” serving fraction “f’

lost 1000 MW capacity and the parallel system picking up (l-f MW. Figure shows that only 500 must be shared by the parallel system and the “peaking generator?’ for loss of one 230 circuit. The cost of the replacement capacity will vary due to numerous conditions but is assumed to vary zero to for this example.

It would seem that double-circuit ac lines should be more competitive (compared against single circuit lines at a higher voltage levels) if the costs of replacing the lost transfer capacity

In document Hauth, R. L - HVDC Power Transmission Assesment.pdf (Page 108-143)