Utilities and Energy Suppliers: Bill Analysis

Abstract

Once the energy rate structures for a customer have been examined and been understood, the next step in understanding how utility costs are determined is to perform a utility bill analysis. Knowing how a customer is charged for the energy it uses each month is an important piece of the overall process of energy management at a facility. This article discusses how electric bills and gas bills for large commercial, industrial, and institutional customers are calculated. Average costs, peak load costs, and time-of-use (TOU) costs are presented and evaluated. Electric costs are found as demand costs per kilowatt per month, and energy costs per kilowatt hour. The utility cost data are used initially to analyze potential energy savings opportunities, and will ultimately influence which of these opportunities are recommended.

INTRODUCTION

The ability to calculate utility bill impacts is fundamental to the evaluation of any energy system. An effective method for determining the energy operating cost impact of a proposed option is to compare the calculated annual utility bills with and without the option in place. The difference represents the energy operating cost impact associated with the option. To do so, one must carefully identify not only the aggregate change in fuel or electricity usage associated with the proposed option, but when the changes occur with respect to the various time periods and other billing factors integral to the rate schedule.


The average unit cost for utilities defined as the total annual cost divided by the annual consumption, is a tempting simplification of utility rate structures. It allows easy calculation of energy cost impact from changes in energy usage patterns. In some cases, this simplistic approach yields accurate answers. More typically, however, application of average unit costs gives results that are inaccurate and can, at times, be very misleading.

For any proposed technology application that would change the number of fuel or electricity units consumed, the cost impact can rarely be accurately determined by merely multiplying the change in units by the average cost per unit for the total facility usage. This is because incremental costs are usually quite different from averagecosts. With most currently available utility rates, the addition or subtraction of usage during peak periods may have several times the cost impact as the addition or subtraction of the same amount of usage in off-peak periods. Therefore, one must consider the weighted average cost of the increase or decrease in consumption units associated with a proposed application.

CALCULATING UTILITY BILLS

Utility bills can typically be broken down into the following basic components:

• A customer or minimum service charge

• An energy or commodity charge

• A demand or maximum level of service charge

• Power factor penalties

• Adjustments such as taxes levied by state, county, and city authorities

• Surcharges or credits associated with specific orders established by various regulatory authorities

• Fuel cost adjustments that reconcile the actual cost of fuel used or delivered by the utility, with the estimated cost used in the most recent rate proceeding to set the energy or commodity charge.

These basic components are expressed and calculated in many ways using various units of measure. Combined, they comprise the total utility bill with each contributing in different ways to the weighted average cost. To calculate a utility bill, one must carefully read the rate tariff inclusive of all rate riders and adjustment clauses. One must also know the current values for items that vary such as fuel adjustment charges. Based on this information, one should be able to calculate the utility bill exactly. If such calculations do not equal the utility bill exactly, either a mistake has been made in the computation or a piece of information is missing.

Utility rate spreadsheets are useful in performing such computations. Once a spreadsheet is built, it can be used to calculate costs for any usage pattern under a given rate or set of rates. It can also be used to quickly calculate cost savings from energy efficiency improvements.

TYPICAL GAS BILL CALCULATION

The following is a sample utility bill calculation for a given natural gas usage profile for natural gas service. This is a typical declining block rate structure, where different levels of usage are billed at different unit costs. In this case, the billing unit is 100 cubic feet (Ccf) of natural gas. Hundred cubic feet is a commonly used volume of gas for billing purposes. Other commonly used billing units are 1000 cubic feet (Mcf), therm (100,000 Btu), and million Btu (MMBtu). The rate schedule is shown in Fig. 1. Refer to Chapter 5 for details on the energy or heat content of natural gas billing units. Assuming that the gas usage for the month was 47,500 Ccf, the bill would be calculated as follows:

The commodity rate is first adjusted to account for the purchased gas adjustment (PGA) and the demand side management (DSM) surcharge. To each rate block, $0.0097 is subtracted to account for the PGA and $0.0020 is added to the commodity rate to account for the DSM surcharge. The resulting net commodity rate is:

Block Ccf Per Ccf
First 10,000 $0.4297
Next 20,000 $0.4145
All over 30,000 $0.4023
Monthly service charge: $80.00
Minimum monthly charge = The service charge
Commodity rate:

Block Ccf

Per Ccf
First 10,000 Next 20,000 All Over 30,000 $0.4374 $0.4222 50.4100
Purchased gas adjustment (PGA): Demand-side management (DSM) charge: ($0.0097) $0.0020
State tax: 4.3% City tax: 1.5%

Fig. 1 Sample natural gas rate tariff.

Therefore,

tmp61-54

Note that if the customer used no gas during the billing month, the bill would have been only the service charge of $80.00 plus the state and city taxes for a total monthly bill of $84.64.

TYPICAL ELECTRIC BILL CALCULATION

Fig. 2 is a sample electric rate tariff for a seasonally differentiated electric rate. In this example, assume that the customer’s electricity usage in August was 200,000 kWh and the peak demand was 1655 kW. The energy rate is adjusted to account for the fuel adjustment charge (FAC) and the nuclear decommissioning surcharge. To the base rate of $0.05890/k Wh, $0.00123 is subtracted to account for the fuel adjustment and $0.00074/k Wh is added to account for the surcharge. The resulting net energy charge is $0.05841. Note that the FAC varies each month and can be either positive or negative.

The monthly charge for energy is therefore:

tmp61-55

If the customer had used no electricity during the billing month, and the highest demand in the previous 11 months is assumed to be 1890 kW, the pre-tax bill would be only the service charge of $71.29 plus a minimum (demand ratchet) charge of:

1890 kW X $4.57 per kW = $8637.30

for a total of $8708.59. Adding on the state and city tax of 5.8% results in a final bill of $9213.69 for the month. This extreme example illustrates the importance of accounting for all elements of the rate structure. Had the demand charge been ignored, the bill calculation would have been grossly underestimated.

Sample electric rate tariff.

Fig. 2 Sample electric rate tariff.

DETERMINING THE WEIGHTED AVERAGE COST OF POWER

In the following pages, three electric rate examples are discussed. To keep the analysis manageable, certain billing factors, such as customer charges, taxes, and power factor, have been excluded. These examples, which represent typical industrial, institutional, and large commercial electric rate structures and clearly demonstrate the relationship between varying consumption load profiles and electricity costs, are based on the following three rate structure types:

• Rate 1. A seasonal time-of-use rate

• Rate 2. A conventional seasonal (CONV) rate

• Rate 3. A four-tier seasonal real-time pricing (RTP)rate.

The three rates presented here are representative of current rates in many parts of the country (between $0.05 and $0.06/kWh for baseloaded usage, inclusive of demand charges). However, they should not be used to evaluate specific technology applications. One must always use the rates charged by the local utility. It must be noted that electric rates vary dramatically across the country. In fact, neighboring utilities in the same state often have significant differences between the types of rates offered and rate levels. These differences will likely increase as the utility industry continues to undergo restructuring. While all the three rates have fairly similar costs for baseloaded usage, they have very different structures.

Rate 2 is referred to as a conventional electric rate because it has historically been the most common type of rate. It is, however, being increasingly replaced by time-of-use (TOU)-differentiated rates designed to send market price signals that shape consumer usage patterns and better reflect the cost to serve. Because the usage charge per kilowatt hour does not vary with time of use and because peak demand charges are more moderate, Rate 2 price signals do not strongly drive usage away from peak periods or attract usage in off-peak periods to the extent TOU rates do.

In the two standard (i.e., Rate 1 and 2) rates, a demand charge combines generation, transmission, and distribution system capacity charges, although each is charged separately in many rate structures. Many TOU rate structures will use varying demand charges in each rate period. In addition to peak demand charges, this TOU rate charges for excess demand in off-peak periods. The peak usage charges also include some allocation for capacity costs. But, in many rate structures, costs between peak and off-peak usage are not nearly so differentiated. In those rate structures, a larger portion of the various capacity costs are embedded in demand charges. Rates 1 and 2 have demand ratchets, which can only be set in summer months, as part of their seasonal differentiation. Many rate structures do not have ratchets and some have ratchets that can be set in any month. The RTP rate combines all capacity and commodity costs into usage charges, differentiated by four rate periods.

WEIGHTED AVERAGE COST FOR REPRESENTATIVE OPERATING LOAD PROFILES

The simple average price of electricity or gas for a given facility can be calculated by dividing the annual cost by the annual usage in billing units (e.g., kilowatt hour or 100 cubic feet). This yields an average cost per kilowatt hour or 100 cubic feet. However, average cost calculations provide limited and often misleading information about the actual incremental cost of a particular end-use or load profile. The weighted average cost for specific usage profiles may vary dramatically. In fact, it could be several times greater with one rate structure compared with another.

To demonstrate this important concept, a table reflecting the price of purchasing electricity under various usage profiles is presented for each of the three example rates. Each of these tables lists ten different power usage profiles that might be associated with usage of a certain device or, perhaps, the usage of an entire facility.

The individual profiles in Tables 1-3 show the annual usage, in kilowatt hour, for each profile, the weighted average incremental cost of a kilowatt hour, and the annual cost of consuming power under specific load profiles for a theoretical kilowatt device. Explanation of how the various profiles in Tables 1-3 are calculated and how they relate to various types of usage follows the three electric rate examples.

While different rate designs result in widely varied costs under different usage profiles, the weighted average cost for the baseloaded kilowatt usually is fairly similar for a given utility’s cost structure. The rate structures and costs used in these three rate examples could all realistically be offered by one utility. The baseloaded cost per kilowatt of capacity requirement is based on continuous usage every hour of the year, with the total usage being 8760 kWh/kW of demand. This type of usage is shown for each rate example as Profile 8. This particular profile is illustrated graphically in Fig. 3. As shown, 1 full kilowatt hour is consumed in each of the 24 h in each day in each of the 12 months of the year, producing a volume of 100% of usage for one kilowatt of demand. Hence, the terms baseloaded kilowatt and 100% load factor (LF) are applied. A decrease in usage volume per kilowatt of demand corresponds to a decrease in LF. The weighted average cost per kilowatt hour for the baseloaded kilowatt is $0.0600 in the CONV rate, $0.056 in the TOU rate, and $0.056 in the RTP rate. Since the weighted average cost for baseloaded usage is close, comparison of these three rates clearly demonstrates the cost impact of rate design on various types of usage patterns.

Table 1 Billing effect of 1 kW, with usage under different usage profiles operating on electric Rate 1 time-of-use (TOU)

Profile number Period of use Annual kilowatt hour (kWh) Average

cost ($/kWh)

Annual cost ($) Annual load factor (LF) (%)
1 1 ratchet setting kilowatt hour per summer month 4 24.870 99 0.1
2 Baseload (BL) summer peak (no ratchet set) 700 0.137 96 8.0
3 50% LF summer peak (w/ratchet) 350 0.351 123 4.0
4 BL summer peak and shoulder (w/ratchet) 1400 0.134 187 16.0
5 6 month cooling profile (w/ratchet) 1870 0.103 193 21.3
6 12 month cooling profile 3379 0.077 260 38.6
7 50% LF 12 months peak 1043 0.169 176 11.9
8 BL 12 months all rate periods 8760 0.056 494 100.0
9 Mixed use (MU) 12 months all rate periods 4755 0.068 321 54.3
10 BL 12 months off-peak and shoulder (no peak demand) 6674 0.038 254 76.2

Notes: Load factor (LF): ratio of actual use vs. maximum potential use in all or certain rate periods; Baseload (BL): 100% LF, or the maximum use in rate period(s); Mixed use (MU): usage based on 80% peak; 60% shoulder and 40% off-peak usage; Cooling profile: demand based on 100% in 2 summer months, 85% in 2 summer months, and 60% in non-summer months. Summer usage based on 80% peak, 60% shoulder, and 30% off-peak. Non-summer usage based on 48% peak, 36% shoulder, and 18% off-peak.

Profile 4 in each of the rates is based on a total annual usage of only 1400 kWh for the 1 kW device. All of this usage is in the peak and shoulder rate periods during the four ratchet-setting summer months. As a result, in each of the three rates, the weighted average cost per kilowatt hour is significantly higher than the weighted average cost of the baseload (BL) usage associated with Profile 8, which also includes off-peak usage. The weighted average cost is so much higher, because it is more expensive to provide power during peak periods than off-peak periods. This is reflected in the rate structures, though to varying degrees. The BL usage profile of Profile 8 blends this high-cost peak usage with low-cost off-peak usage.

Table 2 Billing effect of 1 kW, with usage under different usage profiles operating on electric Rate 2 conventional (CONV)

Profile number Period of use Annual kilowatt hour (kWh) Average

cost ($/kWh)

Annual cost ($) Annual load factor (LF) (%)
1 1 ratchet setting kilowatt hour per summer month 4 22.850 91 0.1
2 Baseload (BL) summer peak (no ratchet set) 700 0.108 76 8.0
3 50% LF summer peak (w/ratchet) 350 0.312 109 4.0
4 BL summer peak and shoulder (w/ratchet) 1400 0.116 163 16.0
5 6 month cooling profile all rate periods (w/ratchet) 1870 0.097 181 21.3
6 12 month cooling profile all rate periods 3379 0.075 252 38.6
7 50% LF 12 months peak 1043 0.147 154 11.9
8 BL 12 months all rate periods 8760 0.060 522 100.0
9 Mixed use (MU) 12 months all rate periods 4755 0.066 315 54.3
10 BL 12 months off-peak 6674 0.048 318 76.2

Table 3 Billing effect of 1 kW, with usage under different usage profiles operating on electric Rate 3 real-time pricing (RTP)

Profile number Period of use Annual kilowatt hour (kWh) Average cost ($/kWh) Annual cost

($)

Annual load factor(LF)

(%)

1 1 kWh per summer month (peak) 4 0.750 3 0.1
2 Baseload (BL) summer (peak) 700 0.201 141 8.0
3 50% LF summer (peak) 350 0.234 82 4.0
4 BL summer (peak) 1400 0.152 213 16.0
5 6 month cooling profile 1870 0.102 190 21.3
6 12 month cooling profile 3379 0.074 249 38.6
7 50% LF 12 months (peak) 1043 0.142 148 11.9
8 BL 12 months 8760 0.056 493 100.0
9 Mixed use (MU) 12 months 4755 0.066 316 54.3
10 BL 12 months (base) 6674 0.039 259 76.2

Notes: Peak: indicates that kWh are first charged to the highest rate block and then successively to lower rate blocks; Base: indicates that kWh are first charged to the lowest rate block and then successively to higher rate blocks; Cooling: profile kWh are allocated between rate blocks to correspond to the allocations used in the time-of-use (TOU) rate examples; Mixed-use: profile kWh are allocated between rate blocks to correspond to the allocations used in the TOU rate example.

The annual usage for Profile 4 is illustrated graphically in Fig. 4. Note that usage is only shown during the four summer months and during hour 6-21 of each day, which correspond to the peak and shoulder periods (6 a.m.-9 p.m.) from Monday to Friday. Hence, this figure only represents the usage during the normal five-day workweek.

In comparison to Profile 8, which shows an annual consumption volume of 8760 kWh, Profile 4 only shows a volume of 1400 kWh for the same 1 kW of peak demand. As will be shown below in the computations provided in the detailed discussion of each rate profile, the LF for Profile 4 is only 16% since only 1400 of a possible 8760 kWh are consumed over the course of the year.

In contrast, Profile 10 is based on a total annual usage of 6674 kWh, with all usage in the off-peak and shoulder rate periods. As a result, in each of the rates, the weighted average cost per kilowatt hour is even lower than the weighted average cost of the BL usage profile (Profile 8). In this case, since it is far less costly to provide electricity in the off-peak period, the result is a very low weighted average cost. The utility now has this extra capacity available, during the peak periods, that it can sell at the much higher rate to balance the sale of this low-cost usage.

Rate structure Profile 8, the base loaded kilowatt.

Fig. 3 Rate structure Profile 8, the base loaded kilowatt.

Rate structure Profile 4, peak and shoulder summer usage Monday-Friday.

Fig. 4 Rate structure Profile 4, peak and shoulder summer usage Monday-Friday.

The ten profiles listed in each of the Tables 1-3 were created to match the hours in each of the rate periods specific to the TOU rate structure. To allow for a reasonable basis of comparison, the same rate periods have been imposed on the rate structure used in the RTP rate. While the RTP rate has been calibrated for this purpose, it would also be appropriate to view these rate structures with respect to their own natural rate blocks.

For example, the RTP rate has a total annual base period, or lowest cost rate block of 3020 h/year, while in the TOU rate there are 4588 annual hours in the off-peak rate block. To make the RTP rate compatible with this load profile, it was assumed that the 4588 annual hours would be composed of 3020 h from the base period, with the remaining 1568 h assigned to the intermediate, or next lowest, cost rate period. The rest of the profiles for the RTP rate were calibrated to the TOU rate structure in a similar manner.

Electric Rate 1 (TOU) Seasonal. TOU Electric Rate

Summer f> (4 months)

Demand Charges

Jan-summer (8 months)

($/kW)

Peak $12.00 $8.00
Shoulder Excess $6.00 $4.00
Off-Peak Excess $3.00 $3.00
Energy Charges ($/kWh)
Peak $0,068 $0,058
Shoulder $0,058 $0,048
Off-peak $0,032 $0,032

Fig. 5 Electric Rate 1 tariff summary.

The table (i.e., Tables 1-3) accompanying each rate provides a calculation of the annual electric bill that would result from each of the ten usage profiles under each of the rate structures. Following the three rate descriptions are explanations for each of the profiles.

ELECTRIC RATE 1 (TOU)

Electric Rate 1 is a seasonal TOU rate. The basic tariff is summarized in Fig. 5. Under this rate, shoulder and off-peak demand charges are assessed only for demand levels that exceed that of the peak periods. For example, if summer peak usage was 1000 kW and shoulder usage was 1500 kW, the demand charge would be:

tmpBE3_thumb

Ratchet Adjustment

Under this rate, if one month had a peak demand of 2000 kW and the next 11 months had a peak demand of 1000 kW, each of those next 11 months’ demand charges would be based on 80% of the 2000 kW figure, or 1600 kW The impact over the course of a year on the customer’s bills would be an additional 600 kW in monthly billable kilowatt charge over the actual demand. Over a period of one year, the customer would pay for

tmpBE4_thumb

Specific Hours of Operation Peak:

10:00 a.m.-6:00 p.m., Monday-Friday 4 summer months at 40 h/week (700 h)

8 non-summer months at 40 h/week (1386 h) Shoulder:

6:00 a.m.-10:00 a.m. and 6:00 p.m.-10:00 p.m., Monday-Friday 4 summer months at 40 h/week (700 h) 8 non-summer months at 40 h/week (1386 h) Off-peak:

10:00 p.m.-6:00 a.m., Monday-Friday, all day Saturday and Sunday

4 summer months at 88 h/week (1540 h) 8 non-summer months at 88 h/week (3048 h)

ELECTRIC RATE 2 (CONV)

Electric Rate 2 is a conventional seasonally differentiated Commercial, Industrial and Institutional (CI&I) rate. The basic tariff is summarized in Fig. 6. Specific hours of operation are:

Summer-4 months (17.50 weeks totaling 2940 h) Non-summer-8 months (34.64 weeks totaling 5820 h).

ELECTRIC RATE 3 (RTP)

Electric Rate 3 is a simplified real-time-pricing rate. There are several ways in which this developing rate is offered by electric utilities to customers. In one common approach, the pricing is established per rate block based on an analysis of the utility’s costs associated with the dispatch of various generation stations in the stack. Each day, the utility informs the customer of which hours will be applied to each rate block.

Electric Rate 2 (TOU)
Seasonal, TOU Electric Rate
Summer Non-summer
(4 months) (8 months)
Demand Charges |$AW|
$10.00 $8.00
Energy Charges <$/kwh]
$0,051 $0,046

Fig. 6 Electric Rate 2 tariff summary.

Unit Cost Summer Non-summer Total
Rate Block ($/kWh) Hours Hours Hours
1. Base $0.025 700 2,320 3,020
2. Intermediate $0.038 1,200 3,200 4,400
3. Peak $0.170 1,000 300 1,300
4. Power pool peak $0.740 40 0 40
Total 2,940 5,820 8,760

Fig. 7 Real-time pricing (RTP) rate pricing blocks.

In this case (Fig. 7), four blocks have been assigned: base, intermediate, peak, and power pool peak. The power pool peak refers to costs incurred as a result of the utility requiring peak power from the pool. Since each hour of the year is assigned to a rate block based on actual (real time) dynamic conditions, there is no established schedule. A good approximation can be made based on experience, however. For the purpose of demonstrating the workings of this rate, hours have been assigned for winter (36.64 weeks) and summer (17.50 weeks) to each of the four rate blocks.

Fig. 8 shows the maximum cost in each rate block for a baseloaded kilowatt Fig. 9 shows the annual hours of operating and cost per kilowatt hour for various combinations of rate blocks.

ELECTRIC RATE COMPARISONS AND CONCLUSIONS

The period during which power is used affects operating costs as much as, or more than, the amount of power used. This concept becomes critical in energy use planning as price differentiation by time of use increases.

While accountants may look at electric operating costs in terms of the average cost per kilowatt hour, energy use planners must look at the incremental costs of individual end uses and various consumption profiles to understand price impact. Energy planners audit facilities to develop incremental cost-usage profiles associated with individual equipment, systems, and activities. These audits are done in much the same manner as the ten profiles presented in the preceding pages.

Rate Block Summer Non-Summer Annual
1. Base $17.50 $58.00 $75.50
2. Intermediate $45.60 $121.60 $167.20
3. Peak $170.00 $51.00 $221.00
4. Power pool peak $29.60 $0.00 $29.60
Total $262.70 $230.60 $493.30

Fig. 8 Maximum cost per rate block.

Annual and Average Costs
Weighted
Rate Block Hours Ann. Cost Avg. Cost
($) ($ kWh)
3+4 Summer 1,040 $199.60 $0.1n’
2+3+4 Summer 2,240 $245.20 $0.109
1 +2+3+4 Summer 2,940 $262.70 $0.089
1 +2 Annual 7,420 $242.70 $0.033
1 +2+3 Annual 8,720 $463.70 $0.053
3+4 Annual 1,340 $250.60 $0.187
2+3+4 Annual 5,740 $417.80 $0.073
1+2+3+4 Annual 8,760 $493.30 $0.056

Fig. 9 Operating hours and cost per rate block combinations.

Planners look at seasonal end uses, such as cooling, and understand that the relevant weighted average cost per kilowatt hour may be several times greater than the facility’s overall average cost per kilowatt hour, especially if a ratchet adjustment is in effect. They look at base loaded operations and consumption blocks and understand that the costs may be lower than the facility’s average cost. They look at identical devices, in a multiple-unit system, that run the same amount of hours per year, and they understand that if they operate with different load profiles, their operating cost may be dramatically different.

Evolving RTP electric rate structures may extend this discrete differentiation to every hour of the year, or perhaps even every minute. An important benefit of RTP rates is that one peak hour of extraordinary usage might not have the dramatic cost impact that a rate with a high demand charge and ratchet adjustment would have. This type of rate flexibility is well suited for electricity purchase strategies that involve a mix of on-site power generation or purchase of non-utility-generated power along with the purchase of utility provided power. In the event of retail purchase of non-utility-generated electricity, traditional, TOU or RTP type rate structures may be applied to transmission and distribution services, while some type of RTP structure would be applied to the usage for the purpose of commodity transaction.

With this understanding, energy planners develop strategies to minimize operating costs and optimize productivity. Efficiency improvements and alternative energy source options are considered with respect to these incremental costs. Self-generation and electricity displacement strategies should be evaluated in the same manner. Electric cost savings opportunities should be considered on the basis of incremental cost per kilowatt hour, as well as the total usage. Elimination of 1 kW of low-LF usage should produce larger cost savings per kilowatt hour than the elimination of 1 kW of high-LF usage, even though it may not produce greater aggregate energy savings.

Annual operating cost for each load profile.

Fig. 10 Annual operating cost for each load profile.

Following are explanations for each of the profiles and a discussion of the type of equipment usage or facility characteristics that would result in each profile. Also included are examples of how LF, annual cost, and weighted average cost were calculated.

DETERMINING THE WEIGHTED AVERAGE COST FOR VARIOUS LOAD PROFILES

For individual equipment or an entire facility operating with anyone of the load profiles presented in Tables 1-3, the total annual usage and cost are based on the total input power (kilowatt) of the equipment (or the connected load of the facility) times the usage and cost of 1 kW as presented in each table entry. In all cases, it is assumed that the facility has only one billing meter that measures consumption and demand of all connected loads.

The annual and weighted average costs per kilowatt hour for the ten sample load profiles under each of the example utility rates are summarized in Figs. 10 and 11. Note that because of the extremely low LF for Profile 1, TOU and CONV average costs shown in Fig. 11 are off the scale (> $20/kWh).

 Weighted average cost ($/kWh) for each load profile.

Fig. 11 Weighted average cost ($/kWh) for each load profile.

EXPLANATION OF TEN SAMPLE LOAD PROFILES

Profile 1 is based on a device rated at 1 kW, operated only one hour during each summer month June, July, August, and September) when the entire facility is already operating at its highest peak demand level. This added load increases the peak demand level for the month by 1 kW Therefore, there is a peak demand charge for that 1 kW in each of the 4 summer months. It also adds 1 kW to any applicable peak demand ratchet level. Under Rate 1, for instance, the effect of this 1 kW is a monthly demand charge based on 0.8 kW in each of those 8 non-summer months.

Thus, the 4 kWh produce a total annual billable demand charge based on 10.4 kW. In addition, there is a usage charge for the 4 kWh totaling $0.27. Based on Electric Rate 1, the annual cost for using the 4 kWh is:

(1 kw x $12/kW x 4) + (0.8 kw x $8/kW x 8)

+ (4 kWh X $0.068/kWh)

= $99.47

The weighted average cost per kilowatt hour is: $99.47/4 kWh = $24.87/kWh

If that same 1 kW device is operated for 4 h in the off-peak rate period, then no demand charges apply and the consumption charges are lower. The total annual cost of the 4 kWh is only $0.13, and the weighted average cost of 1 kWh is $0.032/kWh. While the first profile is an extreme example, it demonstrates how significant the impact of demand charges and ratchet adjustments can be in a given rate structure.

A large chiller used for space cooling, for example, may operate at peak capacity only a few hours during the entire year. In many cases, peak cooling demand coincides with the facility’s maximum electric use period and establishes not only a demand peak for the month, but also an increased ratchet demand level for the year. If, at the hour of maximum monthly electric usage (the peak demand hour), the chiller consumes 1 extra kilowatt hour to satisfy load, that 1 kWh will increase the billing peak demand by 1 kW.

Taking the most extreme case of Profile 1 in Rate 1, the use of only 4 kWh at the peak demand period of the peak demand month would cost $99. This could actually be the case with a resting lab or a university that holds commencement in the summer and experiences an extraordinary peak load on only one day per year. If the facility is able to somehow shed these 4 kWh at the same time that the chiller or testing equipment consumes these ratchet-setting kilowatt hour, it would save $99.

At first glance, the idea of 4 kWh costing $99 might seem absurd. However, an understanding of how electric rate structures operate shows that the incremental cost per kilowatt hour can actually vary by several thousand percent. In fact, with a typical demand window of 15 min, this equipment need only set a peak for 15 min, consuming only 0.25 kWh to cause the facility to endure the full 10.4 kW of annual demand charge. Under the RTP rate, no such dramatic costs would be incurred. Since there is no demand charge impact, the costs only consist of the peak cost per kilowatt hour times the hours of use. In this example, the most expensive kilowatt hour of the year would cost $0.74 and the 4 kWh would, therefore, cost $2.96. However, it is important to note that in a real-time market, the cost for these 4 kWh could be quite a bit higher, conceivably as high as $99, though perhaps not likely.

Profile 2 is based on a device rated at 1 kW and operated as a BL in all 4 summer month peak hours. Under Rate 1 (the TOU example consisting of 700 h/year based on a 40-h/week rate period extending for 17.5 weeks), the annual cost for using those 700 kWh is:

(1 kw x $12/kW x 4) + (700 kWh x $0.068/kWh)

= $96

The weighted average cost per kilowatt hour is: $96/700 kWh = $0.137 /kWh The annual LF is: 700 h/8760 h = 8%

In this scenario, demand charges total $48, slightly more than half of the annual cost. It is assumed in this case that peak demand is sufficiently high in the winter months so that there is no ratchet in effect. Based on Rate 1, if, for example, an electric motor with an input power rating of 100 kW operates at full load in each of the 700 h in this profile (represented in Table 1, Profile 2), the annual cost would be $9600. This can also be calculated by multiplying the input power (100 kW) by the total full-load hours of operation (700 h) by the weighted average cost per kilowatt hour of $0.137.

Under the RTP rate, assuming that the 700 h corresponding to the TOU rate summer peak would be composed of the full 40 h of the power pool peak block and 660 h of the peak block, the total cost would be $141 and the weighted average cost would be $0.20/kWh. Based on this example, operating the same 100 kW electric motor during the same 700 h would result in an annual cost of $14,350.

In Profile 3 the 1 kW device operates with a 50% LF during the 40 h/week peak rate period over the 4 summer months rather than at a 100% LF. This results in a usage of 350 kWh over the 700 total hours in this rate period and a total annual LF of 4%, rather than 8% with Profile 2. Usage over the 17.5 week summer period and annual LF, respectively, are calculated as follows:

tmpBE7_thumb

Using the TOU rate, the total annual cost is reduced compared with Profile 2 due to reduced usage. Therefore, demand charges as a percent of the total cost increase. In Profile 3 (with ratchet adjustment), demand charges represent 84% of the total cost. The impact of reduced usage with constant demand charges is an increased weighted average cost per kilowatt hour. The weighted average cost per kilowatt hour for Profile 3 increases to $0.351.

For this profile with only summer peak usage, the traditional non-time-differentiated rate is less costly than the TOU rate, and the RTP rate is the lowest, with a weighted average cost of $0.234. The reason is that with such a low LF load of 4%, the impact of demand charges, inclusive of ratchets, drives up costs dramatically for the other rate structures.

Profiles 2 and 3 are realistic examples of the cost of cooling equipment operation during peak periods. In many cases, these operating profiles are only a portion of a cooling unit’s total energy usage. In other cases, they may represent the total operation. In facilities with multiple cooling units, one unit is often predominantly used as a peaking unit. Peak cooling loads often correspond to the TOU peak electric rate period (10:00 a.m.-6:00 p.m., Monday-Friday) due to ambient temperature profiles, increased productivity, and increased internal gains from people and equipment. In single shift C&I operations, the peak period coincides with most of the operating hours of the facility. In those cases, profiles such as Profiles 2 and 3 may also be representative.

Electric usage with profiles of the type listed in Profiles 1-3 are often targeted for elimination or reduction by various load shedding or alternative energy source technologies. Peak-shaving generators and fuel- or steam-powered cooling are two commonly applied technologies for eliminating these blocks of electric usage.

Profile 4 is similar to Profiles 2 and 3, in that it reflects the higher cost of power resulting from seasonal differentiation and significant demand charges. With 100% usage in Summer Peak and Shoulder periods, this profile has greater usage, with a LF of 16%, as compared with 4% in Profile 3. Under the TOU rate, this produces a weighted average cost per kilowatt hour of $0.134, as compared to $0.351 for the lower LF usage of Profile 3.

In this profile, demand charges represent a lower percentage of the total cost than in Profile 3 because each unit of demand is spread over a greater usage base. However, demand charges still represent a significant portion of the total cost. Profile 4 also includes the effect of demand ratchets. Extending usage to the shoulder periods in this profile partially integrates lower-cost power into the profiles and results in increased LF and decreased weighted average cost.

Under the RTP rate, assuming the 1400 h in Profile 4 would include 40 power pool peak hours, 1000 peak hours, and the balance of 360 h intermediate, the annual cost and weighted average cost, respectively, are:

tmpBE8_thumb

Profiles 5 and 6 refer to mixed use cooling season profiles. While Profiles 2-4 are all based on a 1 kW device running either all of the time or with a 50% LF in a given rate period, Profiles 5 and 6 are based on a 1 kW cooling device running with a load that varies between each month and rate period. These profiles were designed to represent typical space cooling loads served by an electric vapor compression system.

During the 4 summer months, it is assumed that the equipment operates with a LF of 80% peak, 60% shoulder, and 30% off-peak, based on the TOU rate structures. In July and August, it is assumed that the full 1 kW peak demand is set. In June and September, it is assumed that the peak demand impact of the 1 kW equipment is 0.85 kW In the non-summer months, it is assumed that the equipment operates with a LF of 48% peak, 36% shoulder, and 9% off-peak and the demand impact is 0.60 kW in each month. These profiles were then calibrated and applied to the CONV and RTP rate. The difference between the two profiles is that Profile 5 is based on 6 months of operation and profile 6 is based on year-round operation. Notice that profile 6 has a far lower weighted average cost per kilowatt hour than Profile 5 as more lower cost non-summer usage is blended in and there is no ratchet impact.

Profile 7 has peak usage every week of the year and demand charges in every month. This type of profile might be targeted for elimination with peak shaving power generation or replacement of base loaded electric-driven equipment with fuel- or steam-driven equipment operated in the peak periods.

Profile 7 is representative of a load profile that might result from electric-driven equipment operated with a 50% LF during the peak period only. Under the TOU rate, this corresponds to 20 h of operation per week. There is a significant increase in weighted average cost for Profile 7 for all rate types. This is due to the fact that demand charges remain the same, but are spread over only half the usage as the LF is only 11.9%. Under the RTP rate, the weighted average cost is relatively high because as LF is decreased, a greater percentage of the usage is assumed to fall in the highest cost rate block.

Profile 8 (BL 12 months, all rate periods) represents the baseloaded kilowatt, or 1 kW baseloaded every hour of the year. The annual usage of 8760 kWh has an annual LF of 100%.

With this profile, the fixed investment in electric generation and distribution capacity is spread over the maximum possible annual usage. As shown in Profiles 1-7, different rate structures result in widely varied costs under different usage profiles. However, the weighted average costs for the baseloaded kilowatt usually are fairly similar for different rates under a given utility’s cost structure. The rate structures and costs used in the TOU, CONV and RTP rates could realistically be offered by one utility.

While with the profiles with lower LF, peak usage produced much higher costs for the RTP rate, compared with the CONV rate, the higher LF off-peak usage produced much lower costs with the RTP rate. These opposing trends are roughly canceled out with continuous BL usage, though traditional rate structures, such as Rate 2, commonly produce slightly higher baseloaded kilowatt hour costs. Thus, a three-shift facility with a very high LF would choose the TOU or RTP rate structures.

The annually baseloaded kilowatt is the load profile most often targeted for prime mover-driven power generation and mechanical service applications that employ heat recovery (cogeneration cycles). The weighted average cost per kilowatt hour of the baseloaded kilowatt is often the benchmark for determining the feasibility of such applications. While the cost per kilowatt hour is lower than most of the other load profile entries, the total annual cost is the greatest.

Profile 9 represents a profile that might result from annual operation of individual electric motors or other process equipment. It might also result from the combined operation of multiple equipment in a facility. Facilities rarely have absolutely flat loads. Therefore, the BL, or 100% LF load profile, is not necessarily representative of the weighted average cost of power. Some type of mixed use profile, such as Profile 9, is generally more representative of the weighted average cost. This is an aggregate of varying individual components, such as lights and motors, each with a different load profile.

Sometimes, equipment does operate with a LF of 100%, either in a specific rate period or in all rate periods. More often, equipment operates under varying load or under full load for intermittent periods. Profile 9 is an example of such operation. The LF of this profile is about half that of Profile 8. The total annual cost is lower due to significantly lower use, but is greater than half the cost of Profile 8, because the weighted average cost per kilowatt hour is greater. This is due to the greater relative impact of demand charges (the dollar value of which remains the same as in Profile 8).

Profile 10 represents extensive off-peak non-demand setting usage. It has no demand charge at all. Notice that with no demand charges, the weighted average costs are lower for the TOU rate than the CONV rate. This is a result of the price signals of the TOU differentiated rates, which greatly emphasize usage in off-peak and shoulder periods—which the traditional rate does not do. Also note that only a lower cost excess demand charge can be assessed to these usage profiles in the TOU rate example, while a full demand peak can be set in the CONV rate. This would increase costs still further. Under the RTP rate, these average weighted costs are produced by blending the lowest cost rate block with the successively higher cost rate blocks.

As Profile 10 shows, TOU rates offer relatively low-cost power for about three quarters of the hours of the year. When an excess demand charge is assessed to shoulder usage, or if standard shoulder-period demand charges are in effect, the costs will be slightly greater, although still significantly lower than during the costly peak period.

The RTP rate offers relatively low-cost power for about 85% of the annual hours. The weighted average annual cost for the 3020 h of base block usage and 4400 h of intermediate block usage is only $0.033/kWh. This is balanced by a much higher unit cost in the peak and power pool peak blocks, which comprise about 15% of the total annual hours, but slightly more than half the total annual cost. The weighted average cost is only a usage cost, but it also reflects imbedded fixed costs, a large portion of which are included in the demand charges associated with the other two rates. Table 4 provides a comparison of Profiles 7, 8, and 10 for the CONV (2) and RTP (3) rates.

Notice that the sum of total costs for Profiles 7 and 10 approximately equal Profile 8, the annually baseloaded kilowatt The total annual costs of Profiles 7 and 10 are somewhat dose, compared with the stark contrast in usage. The weighted average cost per kilowatt hour for Profile 7 is about three times that of Profile 10.

MATCHING ENERGY TECHNOLOGY ALTERNATIVES WITH ELECTRIC RATES AND USAGE PROFILES

Following is a brief discussion of the fuel- and steam-powered technology applications that should be considered for use in eliminating electricity purchases associated with the 10 representative load profiles presented in Tables 1-3.

Table 4 Comparison of Profiles 7, 8, and 10 for conventional (CONV) and real-time pricing (RTP) rates

Rate number Profile number Usage (kWh) Annual load factor (LF) (%) Average cost per kWh ($) Total cost ($)
2 7 1043 12 0.147 154
2 10 6674 76 0.048 318
2 8 8760 100 0.060 522
3 7 1043 12 0.142 148
3 10 6674 76 0.039 259
3 8 8760 100 0.056 493

Electric Peak Shaving Generation Applications

The primary focus here is on peak demand and usage charge savings. Thus, the emphasis is on eliminating costly peak demand charges resulting from poor LF or, in the case of RTP rates, eliminating the usage in the highest cost rate blocks. As shown above in the RTP rate, the total annual cost is about the same for a load with a 15% LF occurring in the highest cost rate blocks as a load with an 85% LF occurring in the lowest cost rate blocks. Since peak shaving applications will have relatively low annual hours of operation, low capital cost is emphasized more heavily than optimum thermal efficiency and simple energy costs, and heat recovery is not commonly used. Representative load profiles that might be targeted for peak shaving generation include Profiles 1-3, and 7. Other potential technology applications include load shedding control, battery storage and thermal energy storage (TES).

Electric Cogeneration Applications

The primary focus of power generation applications that employ heat recovery is on overall system thermal fuel efficiency and durability, since equipment run times may range from several thousand hours to continuous operation. The object is to minimize the use of purchased electricity while simultaneously eliminating other internal fuel usage via heat recovery. The 8760 h load profile associated with Profile 8 is ideal for cogeneration in most cases. Other high LF load profiles, such as Profile 9, may also be targeted for elimination with on-site application of cogeneration technologies. In some cases, notably with highly stratified rate structures, it may not be economical to generate power on site in periods when the lowest cost power is available from the utility. In such cases, load profiles with somewhat less than 100% LF may be appropriately targeted for elimination. Other potential technology applications include combined cycles and steam injection cycles, along with a host of other standard BL energy conservation measures.

Single- Unit, Year-Round Mechanical Drive Applications

The primary focus here is on satisfying end use requirements with a single unit that has the lowest life cycle cost. Single-unit systems may operate several thousand hours or more annually. In some cases, prime mover-driven systems using heat recovery may be less costly to operate than electric-driven systems in all use periods. In other cases, prime mover-driven systems may be more costly in some periods (i.e., off-peak), but less costly to operate on the average (mixed use) due to significant savings in peak and shoulder periods. System efficiency and durability are particularly emphasized for applications with significant run-time requirement. Heat recovery will be increasingly cost-effective with increased hours of operation. In single or two-shift operations, the unit may operate only in costly peak periods or in peak and shoulder rate periods. Representative load profiles that might be targeted for elimination with single-unit prime-mover mechanical drive systems include Profiles 8 and 9. Other potential technology applications include building and process automation systems and variable volume distribution systems (i.e., air, water, steam, etc.).

Multiple-Unit Mechanical Drive Mixed (Hybrid) System Applications

The primary focus here is overall system optimization with use of electric units in off-peak periods and non-electric units during peak and shoulder periods, or a variation with some baseloading of equipment. Equipment may operate anywhere from several hundred hours to several thousand hours annually. Thermal fuel efficiency (and heat recovery potential) of non-baseloaded individual units may be sacrificed for lower capital costs.

A cogeneration cycle unit may be baseloaded and electric units used for the remaining off-peak load and non-electric units used for the remaining peak and shoulder loads. Alternatively, an electric unit may be baseloaded and non-electric units used for peaking duty only. In one- or two-shift, five-day operations, a single unit might experience a similar operating profile as would a peaking unit in a three-shift, seven-day operation. Profile 7 might be targeted for elimination with use of a prime mover-driven mechanical drive system. Other potential technology applications include building and process automation, peak shaving, load shedding control and variable volume distribution systems (i.e., air, water, steam, etc.).

Single-Unit Seasonal Cooling Applications

The primary focus here is satisfying cooling requirements with a single unit with the lowest life cycle cost. Equipment may operate anywhere from several hundred hours to a few thousand hours annually. Heat recovery is a viable option, but has less impact than in year-round, single-unit applications, because operating hours are typically lower. Heat recovery becomes more important with higher hours of operation and fuel costs. In single- or two-shift operations, the unit may operate predominantly in costly peak periods or peak and shoulder rate periods. Representative load profiles that might be targeted for elimination with use of a non-electric-driven cooling systems include Profiles 2-6. Other potential technology applications include peak shaving, load shedding control, battery storage and TES.

Multiple-Unit Cooling (Hybrid) Applications

The primary focus here is to minimize system operating costs with use of electric units in off-peak periods and nonelectric units in peak and shoulder periods, or a variation with some baseloading of equipment. Electric peak demand charges are a critical consideration. Equipment may operate anywhere from two hundred to several thousand hours annually. Thermal efficiency (and heat recovery potential) on non-baseloaded individual units may be sacrificed for lower capital costs. This is similar to strategies for year-round, multiple-unit mechanical drive systems. However, optimization strategies will differ somewhat due to the greater electric unit costs with seasonal pricing and ratchet potential. In one- or two-shift, five-day operations, a single unit might experience a similar operating profile as would a peaking unit in a three-shift, seven-day operation. Representative load profiles that might be targeted for elimination with use of non-electric-driven cooling equipment as part of a mixed system application include Profiles 2-4. Other potential technology applications include peak shaving, load shedding control, battery storage and TES.

CONCLUSION

As shown in this article, the weighted average cost of a kilowatt hour is highly variable. Different technology applications must be matched with different cost scenarios and electric load profiles. The aggregate energy cost for any particular application is the real determinant of operating cost savings potential. While savings of $0.30 or $0.60/kWh are attractive targets, savings must accrue over enough hours to provide sufficient payback on the investment in alternative energy equipment. Baseloaded cogeneration applications, for example, emphasize overall thermal fuel efficiency, effective heat recovery, and durability. These systems will save less per hour of operation than other technology applications in many cases, but will accrue savings over a greater number of operating hours. Conversely, peak shaving applications may run fewer hours, but target the most expensive electricity usage. In these applications, thermal fuel efficiency is generally less of a concern than low capital costs, because the key is elimination of low LF high-cost power purchases.

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