Question 9.13: Calculate the utility bills for a customer serviced under tw......
Calculate the utility bills for a customer serviced under two rates:
(i) Conventional rate with the following charges:
(a) Customer charge: $150.00
(b) Energy charge: $0.0264/kWh
(c) Demand charge: $13.1/kW
(ii) RTP rate structure with the hourly prices given in Table 9.11. In addition, a customer charge (referred to as an administrative charge) of $300 is incurred monthly by the customer under the RTP rate.
The hourly energy use and the contracted CBL profiles (for the RTP rate) are summarized in Table 9.12 for typical week and weekend days.
Assume that the month has 21 weekdays (including 2 curtailment days) and 9 weekends. In the utility bill calculations, do not account for any other charges such as taxes and credits.
| TABLE 9.11 Day-Ahead-Price Rates for Typical Curtailment and Noncurtailment Days | ||
| Curtailment Rate Price ($/kWh) | Noncurtailment Rate Price ($/kWh) | Hours |
| 0.01673 | 0.01673 | 0:00–1:00 |
| 0.01683 | 0.01683 | 1:00–2:00 |
| 0.01730 | 0.01730 | 2:00–3:00 |
| 0.01780 | 0.01780 | 3:00–4:00 |
| 0.01900 | 0.01900 | 4:00–5:00 |
| 0.02130 | 0.02130 | 5:00–6:00 |
| 0.02730 | 0.02730 | 6:00–7:00 |
| 0.02890 | 0.02890 | 7:00–8:00 |
| 0.02932 | 0.02932 | 8:00–9:00 |
| 0.03213 | 0.03213 | 9:00–10:00 |
| 0.03575 | 0.03575 | 10:00–11:00 |
| 0.03423 | 0.03423 | 11:00–12:00 |
| 0.03456 | 0.03456 | 12:00–13:00 |
| 0.03677 | 0.03677 | 13:00–14:00 |
| 0.03977 | 0.03977 | 14:00–15:00 |
| 1.06350 | 0.04254 | 15:00–16:00 |
| 1.08950 | 0.04354 | 16:00–17:00 |
| 0.89875 | 0.03595 | 17:00–18:00 |
| 0.64675 | 0.02587 | 18:00–19:00 |
| 0.48750 | 0.01950 | 19:00–20:00 |
| 0.01523 | 0.01523 | 20:00–21:00 |
| 0.01532 | 0.01532 | 21:00–22:00 |
| 0.01723 | 0.01723 | 22:00–23:00 |
| 0.01722 | 0.01722 | 23:00–24:00 |
(i) First, the utility bill is determined using the conventional rate structure based on the actual energy use (see Table 9.12):
(a) Customer charge=\$150.00
(b) Energy charge=\$0.0264 \ kWh ^*[21^*42,461 / \ kWh+9^*10,510 \ kWh]=\$26,037.55
(c) Demand charge=\$13.1/kW^*3,015 \ kW=\$39,496.50
Total monthly charges =(a)+(b)+(c)=\$65,684.05
The average cost of electricity for the month based on the conventional rate structure is then \$65,684.05/[21 ^* 42,461 \ kWh + 9 ^* 10,510 \ kWh] or \$0.06660/kWh.
(ii) The utility bill based on the RTP rate is described here:
(a) Customer charge=\$300.00
(b) Energy charge for week days (non-curtailment days) (see Table 9.13)=\$19^*55.99
(c) Energe charge for week days (curtailment days) (Table 9.14)=\$2^*8196.79
(d) Standard charge based on the CBL profile (see note below)
i. Customer charge =\$150.00
ii. Energe charge =\$0.0264/ kWh^*958,960 (see note)=\$26,037.55
iii. Demand charge = \$13.1/ kW^*2,765 \ kW=\$36,221.50
Total monthly charge =i. +ii. +iii. =\$62,409.05
Total monthly charge =(a)+ (b) +(c) +(d)=\$80,166.44
The average cost of electricity for the month based on the RTP rate structure is then \$80,166.44/[21 ^* 42,461 \ kWh + 9 ^* 10,510 \ kWh] = \$0.08128/kWh.
Therefore, the conventional rate structure is more cost-effective for the industrial facility considered in this example (at least during the month for which the utility bills were calculated).
NOTE: The total monthly energy use based on the CBL profiles is calculated as detailed here:
kWh(CBL)=19 \ days^*42,040 \ kWh/day+2 \ day^*32,805 \ kWh/day+9 \ day*10,510 \ kWh/dayor
kWh (CBL)=968,960 \ kWh| TABLE 9.12 Actual and CBL Hourly Energy Use Profiles for the Industrial Facility Assumed in Example 9.13 | ||||
| Curtailment Typical Day CBL Energy Use (kWh) | Noncurtailment Typical Day CBL Energy Use (kWh) | Typical Weekend day Actual Energy Use (kWh) | Typical Weekday Actual Energy Use (kWh) | Hours |
| 220 | 220 | 250 | 345 | 0:00–1:00 |
| 230 | 230 | 270 | 455 | 1:00–2:00 |
| 325 | 325 | 305 | 676 | 2:00–3:00 |
| 360 | 360 | 320 | 785 | 3:00–4:00 |
| 455 | 455 | 360 | 980 | 4:00–5:00 |
| 645 | 645 | 405 | 1,200 | 5:00–6:00 |
| 1,715 | 1,715 | 460 | 1,800 | 6:00–7:00 |
| 2,450 | 2,450 | 510 | 2,905 | 7:00–8:00 |
| 2,545 | 2,545 | 525 | 2,825 | 8:00–9:00 |
| 2,480 | 2,480 | 520 | 2,800 | 9:00–10:00 |
| 2,560 | 2,560 | 535 | 2,845 | 10:00–11:00 |
| 2,765 | 2,765 | 550 | 3,015 | 11:00–12:00 |
| 2,745 | 2,745 | 565 | 2,500 | 12:00–13:00 |
| 2,730 | 2,730 | 560 | 2,765 | 13:00–14:00 |
| 2,650 | 2,650 | 535 | 2,890 | 14:00–15:00 |
| 500 | 2,590 | 525 | 2,815 | 15:00–16:00 |
| 500 | 2,520 | 530 | 2,825 | 16:00–17:00 |
| 500 | 2,370 | 510 | 2,780 | 17:00–18:00 |
| 500 | 2,175 | 495 | 1,755 | 18:00–19:00 |
| 500 | 2,080 | 480 | 1,100 | 19:00–20:00 |
| 1,945 | 1,945 | 395 | 845 | 20:00–21:00 |
| 1,680 | 1,680 | 345 | 635 | 21:00–22:00 |
| 1,230 | 1,230 | 290 | 535 | 22:00–23:00 |
| 575 | 575 | 270 | 385 | 23:00–24:00 |
| 32,805 | 42,040 | 10,510 | 42,461 | Total |
| TABLE 9.13 RTP Hourly Energy Cost During a Typical Non-Curtailment Day for the Industrial Facility of Example 9.13 | ||||
| Non-Curtailment Typical Day Hourly Energy Cost ($) |
Non-Curtailment Typical Day Hourly Energy Price ($/kWh) |
Non-Curtailment Typical Day CBL Energy Use (kWh) |
Typical Weekday Actual Energy Use (kWh) |
Hours |
| 2.09 | 0.01673 | 220 | 345 | 0:00–1:00 |
| 3.79 | 0.01683 | 230 | 455 | 1:00–2:00 |
| 6.07 | 0.01730 | 325 | 676 | 2:00–3:00 |
| 7.57 | 0.01780 | 360 | 785 | 3:00–4:00 |
| 9.98 | 0.01900 | 455 | 980 | 4:00–5:00 |
| 11.82 | 0.02130 | 645 | 1,200 | 5:00–6:00 |
| 2.32 | 0.02730 | 1,715 | 1,800 | 6:00–7:00 |
| 13.15 | 0.02890 | 2,450 | 2,905 | 7:00–8:00 |
| 8.21 | 0.02932 | 2,545 | 2,825 | 8:00–9:00 |
| 10.28 | 0.03213 | 2,480 | 2,800 | 9:00–10:00 |
| 10.19 | 0.03575 | 2,560 | 2,845 | 10:00–11:00 |
| 8.56 | 0.03423 | 2,765 | 3,015 | 11:00–12:00 |
| −8.47 | 0.03456 | 2,745 | 2,500 | 12:00–13:00 |
| 1.29 | 0.03677 | 2,730 | 2,765 | 13:00–14:00 |
| 9.54 | 0.03977 | 2,650 | 2,890 | 14:00–15:00 |
| 9.57 | 0.04254 | 2,590 | 2,815 | 15:00–16:00 |
| 13.28 | 0.04354 | 2,520 | 2,825 | 16:00–17:00 |
| 14.74 | 0.03595 | 2,370 | 2,780 | 17:00–18:00 |
| −10.87 | 0.02587 | 2,175 | 1,755 | 18:00–19:00 |
| −19.11 | 0.01950 | 2,080 | 1,100 | 19:00–20:00 |
| −16.75 | 0.01523 | 1,945 | 845 | 20:00–21:00 |
| −16.01 | 0.01532 | 1,680 | 635 | 21:00–22:00 |
| −11.97 | 0.01723 | 1,230 | 535 | 22:00–23:00 |
| −3.27 | 0.01722 | 575 | 385 | 23:00–24:00 |
| 55.99 | 42,040 | 42,461 | Total | |
| TABLE 9.14 RTP Hourly Energy Cost during a Typical Curtailment Day for the Industrial Facility of Example 9.13 | ||||
| Curtailment Typical Day Hourly Energy Cost ($) |
Curtailment Typical Day Hourly Energy Price ($/kWh) |
Curtailment Typical Day CBL Energy Use (kWh) |
Typical Weekday Actual Energy Use (kWh) |
Hours |
| 2.09 | 0.01673 | 220 | 345 | 0:00–1:00 |
| 3.79 | 0.01683 | 230 | 455 | 1:00–2:00 |
| 6.07 | 0.01730 | 325 | 676 | 2:00–3:00 |
| 7.57 | 0.01780 | 360 | 785 | 3:00–4:00 |
| 9.98 | 0.01900 | 455 | 980 | 4:00–5:00 |
| 11.82 | 0.02130 | 645 | 1,200 | 5:00–6:00 |
| 2.32 | 0.02730 | 1,715 | 1,800 | 6:00–7:00 |
| 13.15 | 0.02890 | 2,450 | 2,905 | 7:00–8:00 |
| 8.21 | 0.02932 | 2,545 | 2,825 | 8:00–9:00 |
| 10.28 | 0.03213 | 2,480 | 2,800 | 9:00–10:00 |
| 10.19 | 0.03575 | 2,560 | 2,845 | 10:00–11:00 |
| 8.56 | 0.03423 | 2,765 | 3,015 | 11:00–12:00 |
| −8.47 | 0.03456 | 2,745 | 2,500 | 12:00–13:00 |
| 1.29 | 0.03677 | 2,730 | 2,765 | 13:00–14:00 |
| 9.54 | 0.03977 | 2,650 | 2,890 | 14:00–15:00 |
| 2,462.00 | 1.06350 | 500 | 2,815 | 15:00–16:00 |
| 2,533.09 | 1.08950 | 500 | 2,825 | 16:00–17:00 |
| 2,049.15 | 0.89875 | 500 | 2,780 | 17:00–18:00 |
| 811.67 | 0.64675 | 500 | 1,755 | 18:00–19:00 |
| 292.50 | 0.48750 | 500 | 1,100 | 19:00–20:00 |
| −16.75 | 0.01523 | 1,945 | 845 | 20:00–21:00 |
| −16.01 | 0.01532 | 1,680 | 635 | 21:00–22:00 |
| −11.97 | 0.01723 | 1,230 | 535 | 22:00–23:00 |
| −3.27 | 0.01722 | 575 | 385 | 23:00–24:00 |
| 8196.79 | 32,805 | 42,461 | Total | |