POWER FACTOR AND P.F. CORRECTION
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Figure 1 |
WHAT IS POWER FACTOR
Power factor is defined as the ratio of the actual power (Watts) to the apparent power (Volt-ampers). Power factor=Actual Power/Apparent Power
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Figure 2 |
From figure 2 above, it can be seen that the apparent power which is transmitted by the power plant is actually composed vectorially of the actual power and the reactive power. The active power is used by the motor and results in useful work. The reactive power is wasted and merely bounces energy back and forth between the motor and the generators at the power company's plant. If the power factor is corrected, figure (2) shows how the reaction power element decreases in size and the apparent power element approaches the size of the actual power used. This means that less power need be generated to obtain the same amount of useful energy for the motor. Power factor correction is discussed below. Power factor is also numerically equal to the cosine of the angle of the lag of the primary input current with respect to its voltage.
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Figure 3 |
From Figure (3) above, it can be seen that the current is lagging the voltage by an angle 0. An ideal power supply would have no lag on lead angle and the power transmitted to the motor would be an useful power. The equation for useful or actual power is:
P = El cos Ø
Or
Power = Volts x Current x Cosine of the lag angle 0
Where:
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Cos Ø = Power Factor El = KVA El cos Ø = KW |
If the lag Ø is zero then the cos Ø is equal to one, and the useful or actual power equals El and no power is lost due to reactance in the system.
LOW P.F. DISADVANTAGES
The disadvantages of low power factors are three. The first is that transmission lines and other power circuit elements are usually more reactive than resistive. Reactive components of current produce larger voltage drops than resistive components, and add to the total IZ = (I(R + LX)) drop, therefore, the system-voltage regulation suffers more and additional voltage- regulating equipment may be required for satisfactory operation of the equipment using power. The second disadvantage is the inefficient utilization of the transmission equipment since more current flow per unit of real power transmitted is necessary due to the reactive power also carried in the power lines. If the current necessary to satisfy reactive power could be reduced, more useful power could be transmitted through the present system. The third disadvantage is the cost of the increased power loss in transmission lines. The increased power loss is due to the unnecessary reactive power which is in the system. The reactive power losses vary as the square of the reactive current or as the inverse of the power factor squared.
POWER FACTOR CORRECTION
There are two common P.F. correction techniques used by industry to correct an unacceptable lagging power factor. The expensive fix is to use an overexcited synchronous motor or generator in the power system. The cheaper and quicker fix is to connect properly sized capacitors to the motor supply line.
A synchronous machine furnishes the opposite (leading) reactive power to the system to which it is connected. It can provide very economical P.F. correction in low-speed drive applications (less than 51 4 RPM) such as a compressor because the cost of a synchronous motor is less than the cost of an AC induction motor in situations where the ratio of HP to speed is greater than 1 . There are two standard power factor ratings which are unity and .8 power factor. The .8 P.F. is larger and more expensive, but provides a good deal more reactive power to the system throughout its entire speed range. The use of a synchronous motor in hp-speed ratings that favor induction motors to correct P.F. requires careful economic study. In most cases the use of induction motors with capacitors can provide lower first cost and reduced maintenance expense in comparison.
The use of static capacitors connected in the motor power supply is a simple means of P.F. connection. The capacitor causes the current to lead the voltage which tends to offset the lagging current caused by the motor inductance. The effect on the power system is an improvement of the power factor and a reduction in the total power supply line current as shown below.
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Figure 4 |
Two common methods of connecting capacitors to the supply line are shown below.
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Figure 5 |
Note on three phase sources (A) and (B) above represent each leg of the supply connection. Capacitors are usually connected in such a way that they are removed from the system as the power is removed. In connection (A) above, the lower current through the motor overload relay requires the selection of lower rated overload relay to protect the motor. The overload relay should be selected in the normal fashion, however, an adjusted full load motor current should be used. This adjusted full load motor current can be obtained from the following formula:
Adjusted full load motor current = (Nameplate Motor / Full Load Current) x (Uncorrect P.F. / Corrected P.F.)
In connection (B) the adjusted current need not be used so the overload relay is selected in the conventional manner using the motor nameplate full load current.
CAPACITOR SELECTION*
(See note at
bottom of page for above 95% P.F.)
For capacitor selection, the following steps must be observed:
| First: | |
Use the formula below to determine the capacitor KVAR rating. KVAR=(K1-K2) x HP x 0.746 / Efficiency KVAR is reactive kilovolt amperes required to correct the P.F. HP is motor nameplate horsepower Efficiency is motor full load efficiency expressed or a percentage. K1 and K2 are constants from the following tables (Tables 1 and 2). |
| % PF (1) | Constant K1 | % PF (1) | Constant K1 | % PF (1) | Constant K1 | % PF (1) | Constant K1 |
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| 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 |
1.333 1.316 1.299 1.282 1.266 1.249 1.233 1.217 1.201 1.185 1.169 1.154 1.138 1.123 1.108 1.093 1.078 1.064 |
69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 |
1.049 1.035 1.020 1.006 0.992 0.978 0.964 0.950 0.936 0.923 0.909 0.896 0.882 0.868 0.855 0.842 0.829 0.815 |
78.0 78.5 79.0 79.5 80.0 80.5 81.0 81.5 82.0 82.5 83.0 83.5 84.0 84.5 85.0 85.5 86.0 86.5 |
0.802 0.789 0.776 0.763 0.750 0.737 0.724 0.711 0.698 0.685 0.672 0.659 0.646 0.633 0.620 0.607 0.593 0.580 |
87.0 87.5 88.0 88.5 89.0 89.5 90.0 90.5 91.0 91.5 92.0 92.5 93.0 93.5 94.0 94.5 95.5 |
0.567 0.553 0.540 0.526 0.512 0.498 0.484 0.470 0.456 0.441 0.426 0.411 0.395 0.379 0.363 0.346 0.329 |
Table 1
*Avoid over correction of the power factor above 95% since excessive capacitance is dangerous to the driven equipment and motor.
- Refer to motor department for P.F. correction over 95%.
- Refer to motor department for P.F. correction of multispeed motors.
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Table 2 |
| Second: | |
Make sure that the capacity voltage rating is equal to or greater than the rated motor voltage. |
| Third: | |
Make sure the capacitor frequency and number of phases is the same as the motor. |
| Fourth: | |
Note that the capacitor ambient temperature must not exceed 40°C. |
MAXIMUM DEMAND
Basic Demand Control
BY THOMAS D. "DAN" MULL, PE, CEM, CDSM, CAROLINA CONSULTING GROUP, INC.
August 29, 2000
Every energy manager must develop a viable strategy to optimize energy efficiency while minimizing costs. For the plan to be effective, the energy manager must understand how each energy source is metered and billed and understand the facility's actual load and energy requirements.
Not fully understanding how a facility is billed for electricity can result in a failed energy strategy and a great deal of frustration for the energy manager. In some cases, parts of the load management program may actually increase energy expenditures. For this reason, it is essential that the various mechanisms for billing electricity be fully understood.
Billing Fundamentals
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Electricity billing can be quite complicated. A number of factors built into an electric rate, not directly based upon actual use, affect the price to the consumer. It is generally understood that customers are never charged for more energy (kilowatt-hours) than they use in a given billing period. Demand charges are a different story.
Electric demand is the rate at which electrical energy is consumed (kilowatt-hours per hour). Electric demand is measured in kilowatts or kilovolt-amperes on a demand meter by the supplying entity. Although demand is a rate, many think of it in terms of the power required to operate a piece of equipment, a system, or a facility. In other systems, gallons per minute or pounds of steam per hour would be analogous.
The electric demand for a facility usually varies hourly, daily, and seasonally. The supplier must have generating capacity, transformers, and distribution equipment installed to provide the maximum or peak demand at any time-even if that peak demand occurs for only one hour a month. The supplying utility recovers the cost of providing the equipment required for this maximum demand in commercial and industrial rates by a separate charge called the demand charge.
For a specific facility, the demand charge may be set by provisions of the rate rather than by the actual power requirement.
The Facility
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The optimum result of a successful demand control strategy is to have a flat load profile, without significant peaks and valleys. Flat end-user energy profiles enable electric generators and suppliers to maximize their use of their generation and distribution facilities. The higher the utilization a utility achieves, the more competitive it is. As a result, utilities can offer incentives in the form of lower rates to customers with consistent power requirements.
A completely flat profile is not usually achieved in actual practice, but load profiles can be used as an indicator of control potential which may be able to be improved through load management.
Variation in the load profile can be measured by the load factor. Load factor is calculated by a ratio of the actual energy (kWh) consumed during a given period and the maximum amount of energy that could have been used, based upon the recorded peak demand during the same period. For example, if a customer used 300,000 kWh in a 30-day period, with a peak demand of 1,000 kW, the load factor for that period would be:
Load Factor =
300,000 kWh/(1,000 kW x
30 days x 24 hr/day)
= 0.417 or 41.7% (normally
quoted as a percentage)
For facilities with a single-shift operation, a monthly (or annual) load factor in the range of 35 to 45% would be considered normal. For a two-shift operation, load factor should be in the 45 to 65% range. The range of load factors for a three-shift operation (24 hours/day, seven days/week) should be 65 to 80%. The higher a customer's load factor, the better the utilization of the purchased energy.
Most consumers cannot achieve a high load factor. Seasonal variations in use due to heating and cooling requirements are usually sufficient to cause significant variations in the load profile. However, an effective demand control strategy can minimize peaks, fill valleys, and result in a more consistent power requirement. Demand or load control reduces electrical expenditures and flattens the load profile. Most importantly, those utility customers with higher load factors become more attractive to the utility, establishing a better position for negotiations with suppliers.
The starting point for an effective demand control program is to understand the fundamentals of demand and billing. With this understanding comes the knowledge required to develop a meaningful and successful demand control strategy.
Fundamental No. 1-Understanding Electrical Pricing
State or local regulatory authorities normally set rates, but the design of these rates can take many forms. Unlike most market commodities, electricity is not sold at a fixed price. Even so-called fixed rates can incorporate a number of factors that may dramatically affect final cost. The manner (how) and time (when) that the end user uses electricity can have a significant impact on its final cost. The manner in which power is used can, under some rate designs, change its final cost by a factor of 50% or more.
What other commodities are purchased on a daily basis, where the final cost depends upon such factors as:
- Selected pricing schedule
- Total energy consumed
- Time of day or time of year of use
- Maximum (power) requirement in a given interval
- How efficiently the commodity is used
- How use impacts the supplier providing the service
- How use impacts other customers
The three factors that are most often used to determine the final cost are: the maximum power requirement (kW or kVA), the total energy consumed (kWh), and the resulting power factor (PF). How each of these influences the ultimate cost is determined by the basic rate philosophy of the selling utility.
How is Demand Billed?
Demand is usually measured over an integrated 15- or 30-minute interval. In many rate structures, demand charges account for 30 to 50% of the total billing. There are a number of different terms used throughout the industry to describe demand. They include contract demand, actual demand, coincident peak demand, non-coincident peak demand, billing demand, and minimum billing demand.
oContract demand (kW or kVA)-Anticipated customer peak demand specified in a contractual arrangement and the demand value on which installed transformer capacity (kVA) for a facility is usually based. If a customer uses less than a specified percentage (normally about 75%) of the contracted amount, then that customer may be billed for that percentage, regardless of actual use. For example, if a customer contracted for 4,000 kW and the actual use for a billing period was only 2,500 kW, then the customer could be held liable for 3,000 kW (4,000 kW x 75% = 3,000 kW).
If a load reduction is permanent and results from a demand control program, provisions may be made with the supplier to reduce the contracted amount.
- Actual demand (kW or kVa)-Maximum demand value recorded on the customer's meter during a billing period.
- Coincident peak demand (CP)-Demand that a facility incurs at the same time the supplying utility sustains its peak demand during a billing period. Many larger customers request rates based upon CP billing, since their actual contribution to the system peak is less than their recorded maximum demand.
- Non-coincident peak demand (NCP)-Maximum facility demand incurred during a billing period, regardless of the time.
- Billing demand-Demand on which monthly billing charges are calculated. This may be the actual demand incurred during the billing period, a percentage of the peak demand for the previous eleven months (ratchet), a percentage of the contracted demand, or based upon other contractual factors. Unless a ratchet is involved, the billing demand will usually be the actual demand.
- Minimum billing demand-The minimum demand value specified in the utility rate schedule. Variations depend on the rate selected, but seldom are a factor in the billing
Other Factors that Impact Demand Charges
- Ratchets are a pricing mechanism that allows a supplier to
recover a portion of its fixed cost in power generation and
distribution equipment when an end-user does not maintain a specified
level of use. Pricing is usually in the form of a percentage of the
peak demand that occurred in the previous eleven months. For example,
if a facility consistently used 2,000 kW during the summer months and
only 1,400 kW during the non-summer months, with a ratchet of 90% the
customer would be held to minimum of 1,800 kW of billing demand (2,000
kW x 90% = 1,800 kW).
The ratchet would only apply in months in which the demand was less than 1,800 kW. When a new peak demand was established, the ratchet value would then change. Ratchet percentages usually vary from 50 to 100% of the established peak use.
Ratchets are important factors in determining the payback periods associated with demand control. If a ratchet applies, it can delay much of the projected savings resulting from demand control for up to eleven months, depending upon when the control was initiated. In our example above, if a strategy were initiated in the fall (immediately following the setting of the summer peak demand), there would be no billing demand savings until a new summer peak was established the following year. Therefore, unless other savings were sufficient to warrant action, the implementation of the strategy could be delayed until prior to the following summer, especially if it involved a significant capital expenditure. Ratchets usually do not apply to time-of-use or other time-based rate designs.
- Time-of-use rates-Also called time-of-day rates,
this is a rate philosophy that separates the pricing of electricity
(demand and energy) into different periods of the day and year, based
upon the cost of production. The two most common forms are on- and
off-peak periods.
On-peak period refers to those times when it is more costly for a utility to produce electricity, usually during times of high capacity requirements. Therefore, the rates associated with on-peak periods are higher. Usual on-peak periods might be from 10:00 a.m. to 8:00 p.m. weekdays during the summer months. During other months, on-peak hours might be from 6:00 to 10:00 a.m. and 4:00 to 9:00 p.m.
Off-peak period refers to times when it costs less for the utility to produce electricity, usually during times of low capacity requirements. Therefore, the rates are lower. Usually, off-peak periods are any hours not specified as on-peak. There is usually no (or minimal) cost associated with off-peak demand; therefore, if load can be shifted off-peak (load leveling) the savings can be quite significant.
- Real time pricing-This is a rate philosophy that separates the pricing of electricity into hourly increments. Customers under this type of rate schedule are usually notified of prices the day before its use. The cost of electricity (usually on a $/kWh basis, inclusive of demand) is provided for each hour of the following day. The price can vary by a factor of nine or more, depending upon the time of day and year. A usual rate differential might be from $0.050/kWh to $0.450/kWh. The customer can then decide how much electricity to buy. Several states are studying real-time pricing, and limited pilot programs are available for commercial and industrial customers.
- Riders-A rider is an add-on, or extension to an existing rate that states specific conditions, terms of applicability, or charges. For example, a rider may permit seasonal operation under certain conditions. Therefore, billing provisions may only be applicable for selected times of the year. Another type of rider might actually reduce charges if the power factor or load factor of a facility is maintained above a specified value. Riders may also be used for fuel adjustments. In some cases the fuel adjustment provisions under a rider have been as much, or more, than the actual energy charge noted in the rate.
While the factors discussed can affect demand billing, in most rate structures only a few of them apply. Therefore, it is critical that the energy manager understand the rate structure in effect and exactly how these factors apply. There may also be alternative rates available that might be more beneficial. The supplier should be consulted to ensure that the current rate is the most beneficial now, and after any demand control strategy has been fully implemented.
Fundamental No. 2-Know Your Facility's Energy Requirements
Understanding a facility's energy requirements is crucial to the development of an effective demand control strategy. Knowing what the true requirements are and what loads can reasonably be controlled, without having an adverse impact on system operations, is essential.
How, though, does one determine if an opportunity for demand control exists and the magnitude (kW and dollars) of that opportunity? The most direct approach begins by reviewing the facility load profiles. This review can provide visual information with respect to peak demand values, frequency of occurrences, and patterns of use. Graphical representations of these data allow quick recognition of elevated peak demands and unusual variations or anomalies in use patterns, all of which might represent opportunities for control.
At a minimum, monthly load profile information should be available from the supplying utility or billing records. For purposes of identifying demand control opportunities, this level of information is of minimal value. For larger customers (500 kW and greater), utilities usually have electronic metering installed that can provide the data necessary to construct half-hourly or quarter-hourly load profiles (depending upon the demand interval; i.e., 30 minutes or 15 minutes). In some cases, these profiles can be supplied directly by the utility each billing period at little or no cost. Generally, the shorter the time frame, the greater the detail and more meaningful the data, thereby providing the best information on which to base decisions.
If your supplier does not have the metering to provide this level of information, additional meters can be installed (immediately downstream of the billing meter). Either leased through the supplier or individually purchased and installed, metering can be provided for a modest fee. To ensure accuracy with the billing meter, meter pulses will be required from the supplier. There may be an additional charge for these pulses.
Once this information has been obtained, the load profiles can be evaluated to determine the potential for demand control. For example, short-duration peaks (or spikes), elevated demands during low production periods, and unusual patterns of demand use can all be indicative of potential opportunities and dollar savings (see Figures 1 and 2 on page 30). Evaluating the magnitude of savings may be possible by comparing demand anomalies to consistent patterns of use and then applying the appropriate demand charges.
Figure 1 shows two distinct elevated peaks, one at approximately 9:30 a.m. and the other at 1:00 p.m. These values are obviously uncharacteristic, as compared to the others. While this information could be picked up from reviewing the numerical data, the use of the load profile makes it obvious and allows for a quick approximation (in kW) of the potential for demand control. With a maximum peak demand of approximately 3,250 kW (9:30 a.m. value) and a consistent requirement of about 2,850 kW, this use pattern represents the potential to reduce peak demand by 400 kW. This value could then be applied to the appropriate billing period(s) and rate for an estimate of cost savings.
Figure 2 reveals a less obvious savings opportunity. If the facility were a single-shift operation, the demand after a shift change at 4:00 p.m. would be expected to drop more than it does, which would indicate a problem. Depending upon specific requirements after production hours, this use pattern may represent a significant opportunity to reduce actual demand-a less obvious savings opportunity. However, since this demand reduction would not reduce the peak (billing) demand, the only savings that would be incurred would be energy savings, which could be quite large.
The use of profiles only identifies the opportunities and provides a starting point for evaluating options. They usually do not provide meaningful data to indicate what loads are creating the elevated demands. The next step in the process would be to identify the loads creating the demand and determine what loads could be controlled to provide the desired kW reduction or shift.
Summary
In order to develop an effective demand control strategy for any facility, it is essential that an energy manager have a comprehensive understanding of the two basic program building blocks:
1. How electricity is metered and billed
2. Knowledge of the process requirements and load profiles for the facility.
These are only two of a number of steps that are necessary for a successful program. However, they are the two most fundamental. Without fully understanding and developing the load control strategy around these, the best-intentioned program cannot succeed.
Power vs. Demand
An electric unit heater rated at 20,000 watts (20 kW), operated for 1 hour (hr) has a demand of 20 kW and consumes 20 kilowatt-hour (kWh) of electrical energy (20 kW x 1 hr = 20 kWh).
The same heater operated for 200 hours would still have a demand of 20 kW, but the energy consumed would increase to 4,000 kWh (20 kW x 200 hrs = 4,000 kWh).