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CHAPTER 24

CHARACTERISTICS OF DISTRIBUTION LOADS

Author: H. L. Willis

A T&D system exists to deliver power to electric consumers in response to their demand for electric energy. This demand for electricity, in the form of appliances, lighting devices, and equipment that use electric power, creates electric load, the electrical burden that the T&D system must satisfy. In a de-regulated power industry, quality of service - basically quality in meeting the customers’ needs - is paramount. Quality begins with a detailed understanding of the customer’s demand requirements, and includes the design of a system to meet those needs. This chapter discusses electric load and presents several important elements of its behavior that bear on T&D system engineering aimed at satisfying those requirements as economically as possible.

I. ELECTRICAL LOADS

1. Consumers Purchase Electricity for End Use Application

Electricity is always purchased by the consumer as an intermediate step towards some final, non-electrical product. No one wants electric energy itself, they want the products it can provide: a cool home in summer, a warm one in winter, hot water on demand, cold beverages in the refrigerator, and 48 inches of dazzling color with stereo commentary during Monday-night football. Different types of consumers purchase electricity for different reasons, and have different requirements for the amount and quality of the power they buy, but all purchase electricity as a way to provide the end- products they want. These various products are called end- uses, and they span a wide range, as shown in Table 1.

TABLE I—CUSTOMER CLASSES AND END-USE CATEGORIES

Some end-uses are satisfied only by electric power (televisions, computers). In others, electricity dominates in usage over other alternatives (there are gasoline-powered refrigerators, and natural gas can be used for lighting). But for many end-uses, such as water heating, home heating, cooking, and clothes drying in the residential sector, and pulp heating and tank pressurization in the industrial sector, electricity is but one of several possible, competing energy sources.

2. Power Systems Exist to Satisfy Customers, Not Loads

The traditional manner of representing customer requirements for power system engineering has been as aggregate electric loads assigned to nodes for electrical design. For example, customer needs in an area of a city may be estimated as having a maximum of 45 MW. That value is then assigned to a particular bus in engineering studies aimed at assuring that the required level of power delivery can be provided by the system.

Traditionally, the engineering methods used in those design studies have been system-based: performance and criteria are evaluated against the power system itself, not against the customers’ needs. Equipment loading limits, single- contingency backup criteria, and voltage drop/power factor guidelines defined on the distribution system and even at the customer meter point, all view electrical performance from the system perspective, and do not directly address customer needs.

Such engineering methods, while necessary to tailor many aspects of T&D design, are not sufficient to completely address the maximization of customer value. Power systems exist to satisfy customers, not loads. Understanding the specific needs of the customers — how much quality they require in power delivery as well as the quantity of power they need — can improve the value provided by the power system. The “two Qs” — quantity and quality — both need to be considered in designing and operating a power system to provide maximum customer value.

A: System Peak - 3,492 MW B: Residential - 4.2 kW/customer

Fig. l—Left: peak electric demand for a power system in the southern United States, broken out by customer class. Right: within the residential class, which accounts for 58% of the system peak, per capita usage at peak conditions falls into the end-use categories as shown.

End-use analysis of electric load — the study of the basic causes and behavior of electric demand by customer type and end-use category — is generally regarded as the most effective way to study consumer requirements from the standpoints of quantity, quality, and schedule. In any one household,

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business, or factory, the various individual end-use loads operate simultaneously, forming the composite load, as depicted in Fig. IB. The T&D system sees this composite load through the meter as a single load. In aggregate, the loads of all customers produce the system load (Fig. 1 A), with each type or class of customer contributing a portion to the overall system demand.

understanding of how customer loads interact with the power system. Most critical, however, is simply the act of keeping in mind that the “electric loads” used in T&D engineering studies represent the energy needs of people using electricity. The

best power system is one that satisfies their needs as economically as possible.

The amount of electric load created on a power system within any end-use category, for example residential lighting, depends on a number of factors, beginning with the basic need for lighting. People or businesses who need more lighting will tend to buy more electricity for that purpose. Also important are the types of appliances used to convert electricity to the end-use. Consumers using incandescent lighting rather than fluorescent lighting will use appreciably more electric power for otherwise similar end-uses.

II. CUSTOMER ELECTRIC LOAD BEHAVIOR

3. Connected Load

The schedule of demand for most end-uses varies as a function of time. In most households, demand for lighting is lowest during mid-day and highest in mid-evening, after dusk but before most of the residents have gone to bed. The daily schedule of lighting demand usually varies slightly throughout the year, too, due to seasonal changes in the daily cycle of sunrise and sunset. Some end-uses are only seasonal. Demand for space heating occurs only during cold weather. Peak demand for heating occurs during particularly cold periods, usually in early morning, or early evening, when household activity is at its peak.

The connected load is the sum of the full load (nameplate) continuous ratings of all electrical devices in the composite load system. A typical household in a developed country might have a 4,000-watt water heater, a l,OOO-watt water-well motor, a 5,000-watt central air conditioner, a 6,500-watt space heater, thirty lighting fixtures or lamps with an average load of 100 watts each, a 4,000 watt cooking range, a 3,500 watt clothes washer/dryer, a 500 watt refrigerator, and 2,500 watts of miscellaneous home entertainment, personal grooming, and other small appliances, for a total of 30,000 connected watts of load. Whether all or any of these are operating at any one time depends on a number of factors, including the demand for their various end-use products. It is rare that all the connected load in a system or at any one customer’s location would be operational at one time (for example, air conditioning and heating would not be running simultaneously).

The quality of the electric power supplied is more critical to some end-uses than to others. A power system that can provide the quantity of power required may still not satisfy the consumers, either because it does not provide sufficient availability of power (reliability), or because it does not provide sufficient voltage regulation or transient voltage performance (surges, sags). Reliability and voltage regulation needs vary from one end-use to another, as will be discussed later in this chapter, and depends mostly on the value of the end-use to the customer.

4. Electric Load Curves

The value that consumers place on any particular end-use is a function of its importance to their quality of life, or to the productivity of their factory or commercial business. An important (but for many power engineers, counter-intuitive) concept is that end-use value is not of a function of the cost of the electric power. For example, most personal computers and workstations use only 2-3# worth of power per hour, yet users typically report that an hour’s interruption due to lack of power has a cost of a dollar or more.

Use of the products created by electric power - light, heat, hot water, images on the TV, and so forth, varies as a function of time of day, day of week, and season of year. As a result, the electric load varies. A load curve plots electric consumption as a function of time. Fig. 2 shows seasonal peak day load curves for residential loads from two electric systems in the United States. In one system, demand is highest in summer, during early evening, when a combination of air conditioning demand and residential activity is at a peak. In the other, peak demand occurs on winter mornings, when a electric heating demand is highest.

Cost is a major factor in T&D design. In fact, cost is often a consumer’s primary concern, for which they are willing to accept major compromises in quality, and quantity, or service. The challenge facing T&D engineers is to meet consumer needs for both “Qs” - quantity and quality - at the lowest possible cost. Building a system that delivers higher reliability levels than customers need is exactly the same as building one that can deliver much more power than they need.

Fig. 2—Typical summer (solid line) and winter (shaded line) peak day load curves for a metropolitan power system in the southern US (left) and a rural system in New England (right).

Knowledge of the customer needs for quantity and schedule of power delivery, and of the value they place on reliability, voltage regulation, surge and sag protection, and other factors, are important factors in modern power factor design, as is an

Load curve shape - when peak load occurs and how load varies as a function of time - depends both on the connected load (appliances) and the activitv and lifestvles of the

786 Characteristics of Distribution Loads Chapter 24

consumers in an area. Differences between the electric demand patterns of otherwise similar types of customer (as in Fig. 2) occur because of differences in climate, demographics, appliance preferences, and local economy.

5. Demand

Demand is the average value of load over a period of time known as the demand interval. Often, demand is measured on an hourly or quarter-hour basis, but it can be measured on any interval - seven seconds, one minute, 30 minutes, daily, monthly, annually. The average value of power, p(t) during the demand interval is found by dividing the kilowatt-hours accumulated during the interval by the number of hours in the interval.

Demand is the average of the load during the interval. The peak and minimum usage rates during the interval may have been quite different from this average (Fig. 3). Demand intervals vary among applications, but commonly used interval lengths are 5, 15, 30, and 60 minutes.

Peak demand, the value often called “peak load,” in design studies, is the maximum demand measured over a billing or measurement period. For example, a period of 365 days contains 35,040 fifteen-minute demand intervals. The maximum among these 35,040 readings is the peak fifteen- minute demand. This value is often used as the basis for an annual demand charge if the readings measure a single customer’s usage, and as a capacity target in engineering studies: the maximum amount the system must deliver.

6. Demand Factor

The demandfactor of a system is expressed as the ratio of maximum demand to the connected load. Normally the demand factor is considerably less than 1 .O.

7. Load Factor

Load factor is the ratio of the average demand to the peak demand during a particular period. Load factor is usually determined by dividing the total energy (kilowatt hours) accumulated during the period by the peak demand and the number of demand intervals in the period, as

LF = Total usage during period (1) (Peak Demand) x m

where m = number of demand intervals in period

LF = Average Demand

Peak Demand

(2)

Load factor gives an indication of the degree to which peak demand levels were maintained during the period under study. Load factor is typically calculated on a daily, monthly, seasonal, or an annual basis.

8. Power Factor

All loads require real power - kilowatts - to perform useful work such as mechanical rotation or illumination. Reactive loads also require reactive volt-amperes (VAR) to do a type of

“non-productive work” required for their function, such as produce the magnetic field inside a transformer or motor, without which they can not function.

VAR flow on a power system consumes capacity in conductors, transformers, and other equipment, but provides no useful “real” work. It is mitigated by the use of capacitors and other devices, or by changes in the end-use device so that it consumes fewer VARS (see Chapter 8).

Fig. 3—Demand on an hourly basis (blocks) over a 24 hour period. Continuous line indicates demand measured on a one-minute interval basis. Maximum one-minute demand (at 552 PM) is about 4% higher than maximum one-hour demand (S-6 PM).

9. Voltage Sensitivity of Loads

The various electrical appliances connected to the power system exhibit a range of different load vs. voltage sensitivities. Important characteristics include their response to transient voltage changes and their steady state load vs. voltage behavior.

Transient voltage response is difficult to characterize and if important, should be modeled with detailed, and specific, study of the transient response of the particular loads involved. Classification of transient load response into categories is useful in some cases, but no simple generalization works in all cases.

For “steady state” representation, individual electric loads are generally designated as falling into one of three categories depending on how they vary as a function of voltage

Constant impedance loads, for example an incandescent light or the heating element in an electric water heater, are a constant impedance, whose resulting load varies as the square of the voltage.

Constant current loads, including some types of power supplies, many electroplating systems, and other industrial processes, are basically constant current loads. Energy drawn from the system is proportional to voltage.

Constant power loads, such as some types of electronic power supplies, and to an approximate degree, induction motors, vary their load only slightly in response to changes in voltage.

In each category, reference to a load as “ 1 kW” refers to its value at 1 .O PU voltage. Table 2 shows the value of a 1 kW load in each category, as a function of voltage.

Chapter 24 Characteristics of

TABLE 2 — ACTUAL LOAD OF A “1 KW LOAD” OF VARIOUS CATECKRIES

AS A FUNCTION OF THE PER UNIT SUPPLY VOLTAGE - WATTS

Correct representation of voltage sensitivity can be an important factor in analysis of power system performance, particularly on systems that are near permissible limits. Usually, engineering studies of transmission system are carried out using representations of the load as constant power. This works well, because the customer loads are usually downstream of load-tap changing transformers and voltage regulators and so are insensitive (in the steady state case) to changes in the voltages being modeled.

On the distribution system, however, correct representation of voltage sensitivity is critical for accurate analysis of voltage drop and equipment loads. As can be determined from study of Table 2, the difference between constant power and constant impedance “1 kW” loads, at 8% voltage drop (typical of the maximum primary feeder voltage drop permitted on many systems), is 15%. Thus, the incorrect categorization of load voltage sensitivity could lead to a significant over or under estimation of voltage drop and loading on a feeder.

Tests to determine voltage sensitivity on a feeder circuit or low-side bus basis, by varying LTC or voltage regulator tap position at the substation, are recommended to determine exact behavior. In the absence of specific information, representation as a constant current (load is proportional to voltage) is recommended. Within the United States, the following rule-of-thumb works somewhat better

Summer peaking residential and commercial feeders as a split of 67% constant power and 33% constant impedance.

Winter peaking residential and commercial feeders as a split of 40% constant power and 60% constant impedance.

Industrial feeders as constant power feeders

In developing countries, rural loads are best represented as 25% constant power and 75% constant impedance and those in urban areas as an even split of constant power and impedance.

Load flow and similar iterative engineering computations are faster and more stable in convergence if loads are represented as constant power than as constant impedance or current (fewer factors change value from iteration to iteration). In some cases, when a load flow commutation will not

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converge, changing input data to represent all loads as constant power will promote convergence to an approximate solution.

Analytical studies and digital programs can be simplified by deleting the constant current category and using only constant power and constant impedance type loads. Constant current load behavior (the rarest of the three types) can be represented over the range .88 to 1.12 PU voltage, with less than .75% error, if modeled as a mixture of 49.64% constant power, and 50.35% constant impedance load. The column labeled “Ratio” in Table 2 shows this mix of load types, with the right-most column giving the percentage error in representation of an actual constant current load.

10. Characterizing Customers by Class

Usually, electric consumers are grouped into classes of broadly similar demand behavior. A class is any subset of customers whose distinction as a separate group helps identify or track load behavior in a way that improves the effectiveness of the analysis being performed. Electric utilities most often distinguish customers by rate class (pricing category). Customer studies (load research) often make additional distinctions based on demographics, income, or SIC (standard industrial classification) code.

Regardless, usually all customers in a class have similar daily load curve shapes and per-customer peak demands, because they employ similar types of appliances, have similar needs and schedules, and respond in a similar fashion to weather and changes in season. Table 3 and Fig. 4 illustrate how customer class values vary in one power system.

TABLE 3—PEAK HOURLY DEMAND VALUES FOR CUSTOMERS IN A

UTILITY SYSTEM IN NEW ENGLAND. 1992

11. Customer Class Peaks Occur at Different Times

Often, the various classes do not demand their peak energy at the same time, as shown in Fig. 4. As a result, the system peak load may be substantially less than the sum of the individual customer class loads (Fig.5). This is called inter- class diversity, or inter-class coincidence, of load. A class’s or customer’s load at time of system peak is its contribution to system peak, and the ratio of its peak contribution to its own peak load is its peak responsibility factor. Table 4 shows the peak load and responsibility factors of various classes in a utility system in the central United States.


III. CONVERSION OF ELECTRICITY TO END USE

12. Appliances Convert Electricity to End Uses

Each end-use, such as lighting, is satisfied through the application of appliances or devices that convert electricity into the desired end product. For lighting, a wide range of

illumination devices can be used, from incandescent bulbs to fluorescent tubes, to sodium vapor and high-pressure mono- chromatic gas-discharge tubes and lasers. Each uses electric

power to produce visible light. Each has advantages with respect to the other illuminating devices that gives it an appeal in some situations. But regardless of type or advantages, all of these devices require electric power to function, and create an electric load when activated.

Fig. 4—Customer classes typically display different daily load curves. Shown here are the class summer peak-day loads from a metropolitan utility system in the southern United States.

Fig. 5—Peak system load in this metropolitan system in Europe occurs when a combination of both residential and commercial- industrial load is at a maximum.

TABLE 4—SYSTEM PEAK RESPONSIFHLITV BY CUSTOMER CLASS FOR A UTILITY SYSTEM IN THE CENTRAL UNITED STATES, 1992

The term load, in this context, refers to the electric power requirement of a device that is connected to and draws energy from the T&D system to accomplish some purpose (opening a garage door) or to convert that power to some other form of energy (light, heat). Loads are usually rated by the level of power they require, measured in units of volt-amperes, or watts. Large loads are measured in kilowatts (thousands of watts) or megawatts (millions of watts). Power ratings of loads and T&D equipment refer to the device at a specific nominal voltage. For example, an incandescent light bulb might be rated 100 watts at 115 volts. If provided more or less voltage, its load would be different from 100 watts. Loads can be single-phase or multi-phase, and they can have real (resistive only) or complex impedance (reactance), too.

The electric load in any one end-use category depends not only on the number of customers and their aggregate demand for the end-use, but also on the types of devices they are using to convert electricity to that end-use. For example, lighting load will be higher if most customers are using incandescent lighting to meet their needs, than if they are using only fluorescent lighting. Similarly, if a large percentage of customers use only resistive space heating instead of more efficient heat pumps, electric demand will be greater, even if the end-use demand is the same. Power quality needs also are function of appliance type. For example, variable-speed

chillers are more sensitive to voltage sags than traditional constant-speed building cooling systems.

Therefore, detailed analysis of electric load in a utility system generally proceeds into subcategories within each customer class’s end-use categories, with the subcategories characterized by appliance type, as shown in Fig. 6. The boxes indicate load curve models, the ellipses are multipliers corresponding to the number of customers or the percentage of customers in a class that have a certain appliance (e.g., thermal storage heating). Only part of the model is shown. Dotted lines indicate links to portions not illustrated.

In detailed load studies, behavior of load in each category is analyzed by use of temporal curves, plotting demand for the end-use (e.g., gallons of hot water, BTU of heating required) or the electrical load, or cost of service interruption, as a function of time. Information on the percentage of customers employing each type of appliance, their end-use demand schedules, and the electrical and efficiency characteristics of the appliances, comprises the end use model.

Chapter 24 Characteristics of Distribution Loads

Fig. 6—Structure of an “end-use analysis” based on customer, end- use, and appliance subcategory load curves.

13. Appliance Output Is Controlled by Varying Duty Cycle

Only a minority of electrical devices vary their load as a function of the end-use demand placed upon them. For example, the motor drive in a variable speed heat pump will control its RPM (and hence electric load) to correspond to the pumping requirements of the system, on a moment to moment basis. However, such appliances are a rarity. The majority of loads connected to a power system vary their output as a function of time by changing their duty cycle. Duty cycle is the portion of time the device spends operating during any period.

Fig 7—Electric load (bottom) and internal water temperature (top) of a 4,000 watt, 50-gallon storage electric water heater as a function of time.

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For example, most storage water heaters function in a simple manner to keep the water they provide at a constant temperature, regardless of demand, as illustrated in Fig. 7. A thermostat is set at the desired temperature, for example

172.5”F. The thermostat has a “deadband,” a narrow range of temperatures on each side of the setting, within which the

thermostat does nothing. A typical deadband might be 5°F -

for example from 170°F to 175°F when the thermostat is set to

172.5”F. Whenever the temperature drops below the deadband’s lower limit, the thermostat activates a relay (or electric circuit) that turns on the heating element. The element is left in operation until it raises the water temperature above

the upper limit of the thermostat’s deadband (175”F), at which point the thermostat activates the relay to shut off the heater. The water temperature rises and falls slightly as the unit cycles on and off, as shown, but the electric load cycles completely from “all on” to “all off,” as the device tries to maintain a constant temperature.

The 4,000-watt water heater, as illustrated in Fig. 7, creates a load of 4,000 watts whenever it is energized by its thermostat. Otherwise it creates no load at all. Over a period of 24 hours, it will vary its duty cycle in response to demand for hot water. When water heating demand is lightest, the water heater may operate only a few minutes in each hour. But when demand is highest, for example in the evening when dishwashing, clothes washing, bathing, and other activities are at a peak, it may operate continuously for an hour or more, as shown in Fig. 8.

Fig. 8—The water heater’s load profile over a typical day.

A large portion of the electric appliances in most electric systems, often a majority of the electric demand, operates in this manner. The consumer does not directly control the appliance’s on-off operation. Instead, the consumers sets a desired end-use measure (temperature, air pressure) on a controlling device (a thermostat, a pressure switch), and this device varies the appliance’s duty cycle in response to end-use demand. In the residential class, air conditioners, space heaters, refrigerators, freezers, water heaters, irons, and ovens fall into this category. In the industrial class, process heaters, air and water pressurization systems, and many fluid handling systems use this method of control. Fig. 8 shows the resulting daily load curve for a water heater. It cycles on and off, operating for longer times during periods of high demand, and only briefly when there is no demand and it must only make up for thermal losses. In all cases, however, when the water heater is operating its load is the same - 4 kW.


Fig. 9—Daily cycle of THI (temperature-humidity-illumination index) and air conditioner operation. The air conditioner’s connected load varies slightly as a function of THI.

Fig. 9 shows a slightly more complicated appliance behavior, in which duty cycle and device characteristics both vary. Here, an air conditioner cycles between on and off under thermostatic control. As temperature rises throughout the day, demand for cooling increases, and the air conditioner spends a greater portion of its time in the “on” state, until in late afternoon it is operating all but a few minutes in every hour. The diagram illustrates a common secondary effect due to AC unit compressor design. When ambient temperature (temperature of the air around the AC radiator) rises, back pressure in the compressor increases, forcing the unit’s inductive motor to work harder and creating a slightly higher electrical load. Thus, its connected load varies with temperature, as shown.

14. Appliance Duty Cycles and Coincidence of Load

Fig. 10 shows the type of load curve widely used throughout the power industry as representative of a residential water heater’s daily load curve. This particular load curve was taken from a comprehensive water heater load survey done in the 1980s by a utility in the northern United States, prior to design and implementation of a water-heater load control program. This curve shown has a maximum value of 1,100 watts during a brief early morning household activity peak, and a lower, but broader early evening peak.

Fig. 10—A average residential water heater’s coincident demand curve - l/100,000 of the load resulting from 100,000 water heaters. Any single water heater has a load curve similar to that shown in Fig. 8, but its contribution to system load is depicted as shown here. This curve is also the expectation of any one water heater’s load by time of day.

The daily water heater load curve in Fig. 10 looks nothing like the daily water heater load curve in Fig. 8. In Fig. 10, load varies smoothly from moment to moment, between a minimum of .53 kW and a maximum of 1.1 kW, displaying none of the blocky, on-off cycling shown in Fig. 8. Neither Fig. 10 nor Fig. 8 is incorrect. Each is accurate, but only within its own context. Their difference is attributable to intra-class coincidence of load.

Fig. 11 illustrates the relationship between the two water heater load curves. On the top row, load curves A, and B show the load curves for two electric water heaters in neighboring homes on the same day. Curve C shows the curve for the water heater in B, on another day. All three represent the same appliance under nearly identical conditions. Timing of the load blocks varies, but in all cases the load is “all or nothing.”

Load curve D shows the combined loads of both neighboring water heaters (the sum of curves A and B) on February 6, 1994. Even during the peak hour, the average water heater operates only a fraction of the time (in the system whose average water heater is shown in Fig. 10, exactly 1,100/4,000 of the time, assuming all water heaters are 4,000 watts connected load). For this reason, instances when the two water heaters operate simultaneously are rare, but this does happen several times each day, for brief periods.

Curve E shows the curve for five water heaters (the units in five neighboring homes, including A and B). With five units, the likelihood of two or more units operating at any one time is increased considerably. However, the likelihood of all five are operating at the same time is quite remote (roughly 1100/4000 raised to the fifth power, or less than .l percent). Curve F shows the combined load curve of 50 water heaters (all those served by one primary-voltage lateral).

Fig. 11—Daily load curves for different sized groups of residential water heaters.

-.

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Characteristics of P Distribution Loads 791

As an increasingly large number of water heaters is considered as a group, the erratic, back-and-forth behavior of the individual water heater load curve gradually disappears. The load curve representing a group’s load becomes smoother as the size of the group is increased, the peak load per water heater drops, and the duration at lengthens. By the time 1,000 water heaters are reached (Fig. 1 IG) the curve shape is quite smooth, and peak load is at its coincident value of 1,100 watts/unit.

While no single customer within the group depicted in Fig. 12 would have an individual load curve that looked anything like Fig. 12B (every customer’s load curve looks something like Fig. 12A), the smooth coincident load curve for the group has two legitimate interpretations.

Thus, Fig. 10 (same as Fig. 1 lG), while unlike any individual water heater’s actual load curve, is an accurate representation of water heater behavior from either of two perspectives. First, it is a diagram of average contribution to system load, or coincident load, on a per water heater basis — l/l 00,000 of the load of the 100,000 water heaters in the system. Second, it is the expectation of a water heater’s load as a function of time. To a certain extent, the exact timing of the “on” load blocks in Fig. 7- 9, and Fig. 11 is random from day to day. Fig. 10 is a representation of the expected load of one water heater, as a function of time; the best estimate, a day ahead, of load as a function of time.

I. The curve is an individual customer’s contribution to system load. On the average, each customer of this class adds this load to the system. Add ten thousand new customers of this type, and the system load curve will increase by ten thousand times this curve.

Note that energy per water heater (area under the load curve) is not a function of group size. The energy used per water heater is constant in any of the load curves in Fig. 11.

2. The curve is the expectation of an individual customer's load. Every customer has a load that looks something like the on-off behavior shown in Fig. 12A, but each has slightly different on-off times that vary in an unpredictable manner from day to day. Fig. 12B

gives the expectation, the probability-weighed value of daily load that one could expect from a customer of this class, selected at random. The fact that the

expectation is smooth, while actual behavior is erratic, is a result of the unpredictability of timing in when appliances switch on and off.

15. Coincident Load Behavior in General

Most of the major loads in any home or business behave in a manner similar to the on-off, coincident behavior shown in Fig. 7 - 9 and Fig. 11. Refrigerators and freezers, air conditioners, space heaters, water heaters, and electric ovens in homes; and pressurizers, water heaters, process and other finish heaters, and other equipment in industry; all turn on and off in a performance-regulated duty cycle manner. As a result, individual household load curves, and many commercial and industrial site load curves, display the blocky, on-off load behavior shown in Fig. 12A. As with the water heaters, when a group of similar loads (homes in this case) is considered as a single load, the load curve becomes smoother, the peak load drops, and the minimum load rises. Note that the vertical scale of all six load profiles shown in Fig. 12 is in “load per customer” for each group.

Commercial and industrial customers exhibit intra-class coincident behavior qualitatively similar to that discussed here, but the shape of their coincidence curves may be (usually is) different than for residential. By contrast, inter-class

coincidence is the difference in timing of peak periods among classes (Fig. 4).

The 22 kW non-coincident needle peak demand shown in Fig. 12A for a single household is high, but not extraordinary for homes in the southern United States. Load curve A represents a 2100 square foot residence with 36 kW connected load (sum of all possible heat pump, water heater, garage door opener, washer-dryer, other appliance and lighting loads). While customer characteristics vary from one system to another, the qualitative curve shape behavior shown in Fig. 12, as well as the tendancy of load curves to become smoother, and peak loads lower, as group size is increased, apply to all power systems.

16. Coincident Curve: Expectation of Non-Coincident Load

The interpretation of coincident load behavior as the expectation of non-coincident load behavior, as explained in sub-section 14 (water heater example) is generally applicable.

Fig. 12—Non-coincident (A) and coincident (B) winter peak day load curves for home in a suburban area of Florida. Curves B through F show the gradual transformation from non-coincident to coincident behavior as group size increases. Feeders see load curves similar to B. Every service drop sees a load curve like A.


17. Importance of Coincidence Assessment in T&D Design

Coincidence behavior of load, as depicted in Fig. 12, is important to T&D planning and engineering. Equipment such as service drops, service lines (LV), and service transformers, which serve small numbers of customers, must be designed to handle load behavior, including customer needle peaks, of the type depicted in Fig. 12A. Normal service does not require this equipment to handle these load levels for more than a few minutes at a time, a factor that can be considered in determining the load rating of this equipment. By contrast, equipment serving large groups of customers sees fully coincident load curve behavior (Fig. 12B). Peak load per customer is lower, but peak duration is much longer.

Usually, in spite of the high needle peak values, the thermal capacity of service drops, service (LV) circuits, and service transformers can be determined based on coincident peak load values. The thermal time constants for most conductor, cable, and transformers are much longer than the duration of any needle peak. As a result, thermal loading calculated on the basis of coincident curve shape is usually representative of the thermal loads that will result from the actual non-coincident load curves.

Voltage drop and losses are another matter, however. Fig. 13 compares the losses that result in a set of triplex service drops, for the two load curves Fig. 12A and Fig. 12B. The result shown is typical. Use of coincident rather than non- coincident load curve typically results in errors of up to 50% in estimating low voltage system losses, and up to 16% in estimating the total voltage drop to the customer’s meter.

18. Coincidence Factors and Curves

Fig. 13—Electric losses through a typical set of residential service drops, for the load curves in Fig. 12A (left) and 12B (right). Voltage drop would similarly show a significant difference.

Usually, coincident load behavior is summarized for application to power distribution system engineering by the coincidence factor, and the coincidence curve. Coincidence factor is a measure of how peak load varies as a function of group size for customers

C = observed peak for the group

I( individual peaks) (3)

Fig. 12 illustrates well that as the number of customers in the group increases, the peak load/customer usually drops by a considerable amount. Coincidence factor, C, can be represented of as a function of the number of customers, n, in a

group

C(n) = peak load of a group of n customers

n x (average individual peak load) (4)

where n is the number of customers in the group, and 1 < n < N = number of customers in the utility system

Diversity factor, D(n), is the inverse of coincidence factor. It measures how much higher the customer’s individual peak is than its contribution to group peak.

D = Diversity factor = l/ Coincidence factor (5)

The coincidence factor, C(n), has a value between 0 and 1, and varies with the number of customers in a fashion identical to the way the peak load varies. Fig. 14 shows a coincidence curve, a plot of how C(n) varies with n. Typically, for residential and small commercial load classes, C(n) tends toward an asymptotic value of between .33 and SO for large values of n. The value for larger commercial and industrial customers is usually higher, - .75 to .85 is typical, Table 5 gives representative asymptotic coincidence values for typical customer classes. Coincidence behavior varies greatly from one utility to another, and among customer classes. The curves and tables shown here are representative of the type of behavior seen in all power systems, but can not be quantitatively generalized to all power systems.

Usually, coincident load curve data is readily available, but accurate non-coincident load curve data is not. In addition, many types of recording systems and analysis methods distort non-coincident load curve data when it is recorded, producing a smoother curve and lower peak loads than actually existed in the load. Gathering and verifying accurate load curve shape, load factor, and losses factor data for non-coincident and “partially coincident” (groups of 5-20 customers) equipment analysis requires care and attention to detail. However, it is F’ recommended, due to the potential error that inexact data

lg. 14—Peak load per customer as a function of the number of customers in a group (left scale) and coincidence factor (right

creates in losses and voltage drop and flicker computations. scale) for residential class, from a power system in the central US.


TABLE ~-ASYMPTOTIC WINTER PEAK SEASON COINCIDENCE FACTOR

BY CUSTOMER CLASS, FROM A SYSTEM IN THE CENTRAL UNITED

STATES, BASED ON 15 MINUTE DEMAND PERIOD DATA

19. Coincidence of Load Varies as Demand Varies

The coincidence curves and coincident data normally gathered and applied to power system engineering represent peak period behavior - the load conditions for which the system design is targeted. On occasion, however, off-peak coincidence data are gathered, usually to support detailed study of load control, energy efficiency, and other integrated resource programs (discussed later in this section), or for detailed assessment of losses behavior and equipment performance on an annual basis.

The “connected” load on a power system does not vary substantially as a function of time. Electric demand varies because the portion of devices activated by their control system (whether manual or automatic) varies as a function of time. During peak periods, a greater fraction of all customer appliances are activated: There is a higher coincidence of loads. For example, in some areas in the southern United States, over 90% of all residential space heaters are operating at the time (15-minute demand period) of winter system peak. However, during the maximum demand period of an off-peak day (e.g., a day in late fall) only 20% will be operating.

Regardless, on either a winter peak day, or an off peak fall day, individual households create needle peak loads as major appliances operate through their on-off cycles. However, during off-peak times, there will fewer needle peaks, of less average duration. As a result, the likelihood of overlap of needle peaks (e.g., coincidence) among neighboring customers is less than at peak. As a result, coincidence curves representing load behavior during peak and an off-peak times will differ, as shown in Fig. 15.

Fig. 15—Coincidence curve for winter peak conditions, and for off- peak conditions (late fall).

I I

Fig. 17—Annual load duration curve for a power system serving a metropolitan area in the southeastern United States.

20. Load Duration Curves

A convenient way to study load behavior for some engineering purposes is to order the demand samples from greatest to smallest, rather than as a function of time, as shown in Fig. 16. The two diagrams shown in Fig. 16 consist of the same 24 numbers, in a different order. Peak load, minimum load, and energy (area under the curve) are the same for both.

Fig. 16—The hourly demand samples in a 24-hour load curve are “re-ordered” from greatest magnitude to least to form a daily load duration curve.

Load duration curve behavior will vary as a function of the level of the system. Load duration curves for small groups of customers will have a greater ratio of peak to minimum than similar curves for larger groups. Those for very small groups (e.g, one or two customers) will have a pronounced “blockiness,” consisting of plateaus - many hours of similar demand level (at least if the load data were sampled at a fast enough rate). The plateaus correspond to combinations of major appliance loads. The ultimate “plateau,” would be a load duration curve of a single appliance, for example a water heater that operated a total of 1,180 hours during the year. This appliance’s load duration curve would show 1,180 hours at its full load, and 7,580 hours at no load, with no values in between.

Annual load duration curves. Most often, load duration curves are produced on an annual basis, reordering all 8,760 hourly loads (or all 35,040 quarter hour samples if using 15- minute demand intervals) in the year from highest to lowest to form a diagram like that shown in Fig. 17. The load shown was above 997 MW (system minimum) 8,760 hours in the year, but above 2,000 MW for only 1700 hours.


Fig. 18—Examples of coincidence curve modification due to various types of demand-side management (DSM) programs. Thin solid line indicates base coincidence behavior. Heavier lines indicate the coincidence behavior of the load after DSM modification.

21. Coincidence Curve and DSM Interaction

Many integrated resource methods, such as appliance interlocking and load control, and other demand-side management (DSM) measures, change the coincidence behavior of customer loads, not the loads themselves. For example, adding insulation and weather-sealing to a building does nothing to change the load of its air conditioning and heating system. These energy conservation measures slow heat transfer into and out of the building, lengthening the the “off’ portions of every on-off cycle. The same needle peaks occur, but spaced farther apart in time. Basically, this DSM measure cuts the percent of time the AC/heater is on, and hence the coincidence of these appliances.

Fig. 18A illustrates the change in coincident load behavior made by universal use of appliance interlocking among all residential customers in a large group. Interlocking involves jointly wiring the thermostats for the electric water heater, and the air-conditioner/heater, so that the water heater cannot operate if the air-conditioner/heater is operating. It is a simple form of the appliance schedule optimization that can be affected with home automation systems.

The broad line in Fig. 18A shows the resulting coincidence curve. The 22 kW peak values, which occasionally resulted from the random overlapping of appliances activating simultaneously, are now completely avoided. As a result, the 22 kW peak values, and the value of the coincidence curve at the Y-axis, are both reduced by the magnitude of the water heater’s connected load (4 kW in this example).

However, the water heater is not denied energy. Its use is merely deferred until periods when the air conditioner or heater is switched off. As soon as the master (AC-heater) appliance

switches off, the water heater will activate. Over any lengthy period of time (an hour or more) both appliances usually receive all the energy they need. Thus, over any large group of customers, coincidence of energy usage within any demand period will not be affected. The asymptote is unchanged.

An opposite type of effect is shown by the broad line in Fig. 18B. Appliance load control is basically a method to limit duty cycle, and thus coincidence of load. Typically, load controllers are set to limit the operation of any appliance to no more than a certain number of minutes per demand period. For example, a controller might be set to limit its air conditioner to no more than 12 minutes operation out of any 15 minute period, a duty cycle of 80%. During peak conditions, the average thermostat may want to operate its air conditioner 90% of the time. Thus, this load control effects an 11% reduction in air conditioner energy usage. As a result, the asymptotic value of the coincidence curve, for large groups of customers with load control, is reduced.

Such a load control measure makes no impact on the maximum height of the needle peaks produced by any household. The AC unit is still the same connected load, and still likely to overlap with other appliances to create high needle peaks. As a result, load control has no impact on the value of the coincidence curve for individual customers. In cases where control is poorly coordinated, or the load control is aggressively used to maximize the reduction of coincident peak load, it can produce a “rebound effect,” increasing peak loads on some levels of the system, as shown by the dotted line in Fig. 18B. Fig. 18C through Fig. 18F represent the actions of other often-used DSM approaches.

Fig. 18 illustrates two very important points about DSM programs. First, DSM programs do not necessarily produce

Chapter 24

similar amounts of load reduction on all levels of the power system. Second, by use of coincidence curve analysis of the type shown in Fig. 18, it is possible to target a DSM program’s load reductions at particular levels of the power system. DSM measures that affect the peak loads of large groups of customers, or small groups, can be selected as needed to target feeder or service (LV) levels.

to zero. Demand recorders as used in revenue metering and most (but not all) electronic meters use this type of load recording.

IV. MEASURING LOAD CURVE DATA

Regardless of the actual behavior of the electric load, it is measured and sampled through the “eyes” of equipment and procedures which may introduce errors by not capturing completely all of the load’s characteristics. Many types of load recording perform a type of filtering that makes load behavior look more coincident (smoother, lower peak) than it actually was. Other types mis-recording of load cycles in a way that renders the load curve data virtually useless. In both cases, the data looks like load curves, but is inaccurate. Regardless, power engineers must be aware of the source of all load data, the method used in its recording, and any limitations it creates on the accuracy or use of the resulting data.

Essentially, instantaneous sampling records the actual load value at specific instants spaced an interval apart. Period

integration averages its load measurement over the entire sample interval between two of those instances. There can be,

and usually is, a considerable difference in the recorded data, depending on which of these two different sampling techniques is used.

22. Load Sampling Rate and Type

Most load measurement, recording, and analysis equipment and procedures work with load curve data as sampled data. Load values are measured and recorded at uniform intervals of time. For example, often load curves are represented in engineering studies as 24 hourly loads. Many load recorders measure and store load behavior on a 15-minute basis. There are two very important aspects of sampling. The first is the type of sampling used, the second is the rate of its application.

Discrete sampling measures and records the load’s value at specific periodic instances. For example, load recorder may measure electrical load every 15 minutes. Every quarter hour, this device “opens its eyes” to sample the load, and records the value, and begins a waiting period until the next sampling instant. What the load does in between those 15-minute sample periods is immaterial to the recorder.

This kind of sampling, which is often called instantaneous sampling, is the type normally dealt with in textbooks on signal processing as “discrete sampling.” Much of the load data used in power systems studies comes from this type of sampling. Many types of distribution load recorders (“load loggers”) do only instantaneous sampling. SCADA systems that “trap” load readings on a periodic basis do instantaneous sampling. Manual reading of load strip charts is basically discrete sampling: typically, load data is prepared for computer processing from strip charts by an engineer or analyst who reads the value every so often from the strip chart and codes it into the computer data base.

Fig. 19—Two different load sampling methods (middle, bottom) applied on an hourly basis to the residential load curve from Fig. 12A (top), produce quite different data.

Fig. 19 shows the single all-electric household daily load curve from Fig. 12A, along with versions of it obtained by sampling on an hourly basis with period integration (middle) and discrete sampling (bottom).’ nor instantaneous discrete sampling on an hourly basis captures all the details of the load behavior. However, in this case, discrete sampling produces a very spurious-looking load curve. for reasons that will be discussed later.

23. Observed Load Behavior and Sampling Rate

Demand sampling, also called period integration, measures and records the total energy used during each period. If applied on a 15-minute basis, period integration records the energy (demand) during each 15-minute period. At the beginning of each measurement interval, a watt-hour meter is re-set to zero and begins counting the energy used. At the end of the period, the reading is recorded, and the counter is re-set

The second important aspect of load curve sampling is the sampling rate. Fig. 20 shows Fig. 12A load curve sampled with period integration on a 5, 15, 60 and 120-minute basis. Note that the resulting data displays significantly different

The load curve in Fig. 12A was obtained using period (demand sampling) on a five-minute interval basis.

795

Neither demand sampling

integration

796 Characteristics of Distribution Loads

behavior, depending on sampling rate. As the sampling is done faster, the curve shape displays more of its blocky, on-off nature: the recorded data comes closer to representing the true load curve shape peak value.

But as shown, if a load is sampled by period integration applied at a slow rate, the resulting load data may look smooth, when, in fact, actual behavior is erratic, with high needle peaks. Fig. 21 shows peak demand for the data in Fig. 12, plotted as a function of period integration sampling rate. The measured peak load decreases as the sampling period increases from five-minutes to one hour. The reason is that the sampling rate, or demand interval, defines the meaning of “peak”. Sampled at one-minute intervals, the peak is the maximum 60- second demand. Sampling on an hourly basis smoothes out a lot of the needle peaks, and yields a curve whose peak is the maximum one hour demand. A non-coincident curve (top of Fig. 20) can look like it was smoother and very “coincident” simply because it was demand-sampled at too low a sampling rate.

Fig. 20—Single household load (Fig. 12A) sampled by period integration (demand recorder) on a 5,30,60,120-minute basis.

Fig. 21—Measured peak demand of a single residential customer varies greatly depending on the intervals used to sample its load.

As shown in Fig. 20 and Fig. 21, changing the sampling rate changes the perceived or measured peak value and the “choppiness” (variance) seen in the load curve. However, not all types of load curves are equally sensitive to this phenomenon, This effect is most pronounced when sampling non-coincident load curves - those representing small sets of appliances or just a few customer. It is minor or undetectable when sampling load of large groups of customers, such as an entire system.

Thus, the apparent coincidence of load changes as a function of sampling rate. Fig. 22 shows coincidence curves

for the residential customers used earlier in Fig. 12- 16, re- computed based on period integration sampling intervals of 5, 15, and 60 minutes. Because the peak load of a single customer, upon which coincidence factor computation is based, changes a great deal as a function of sampling rate (Fig. 21), the coincidence curve, itself, will change. Characteristics and sensitivity discussed here involve only period integration sampling (i.e., demand recorders), which is the most common approach to gathering load research and load curve data.

Fig. 22—Coincidence curves based on data measured at 60, 15, and 5 minute demand intervals for residential all-electric homes.

Aliasing. Instantaneous sampling has a far different interaction with sampling rate and recording accuracy than the period integration method discussed above. Fig. 23 shows the load for a single household (Fig. 12A) measured by instantaneous sampling on an hourly basis. One profile is the result of sampling instantaneously every hour, on the hour. The other is sampled hourly a quarter past the hour. The apparent load curve shape, and peak load of these two curves are different. Neither is an accurate representation of the actual load curve behavior.


The problem with instantaneous sampling applied in this 24. Signal Engineering Perspective on Load Sampling case is that its rate is much to slow to “see” the load behavior. But unlike period integration, which smooths the load curve when applied at a slow rate, instantaneous discrete sampling distorts it, badly, as shown. The load being recorded in this case (Fig. 12A), has very erratic on-off load behavior common to non-coincident loads. It is simply random chance whether a particularly hourly recording instant, falls upon a needle peak, or a “needle valley.” For a load that has needle peaks, as does any individual household load, instantaneous sampling at a low sampling rate gives very poor, even completely unusable results.

Load as a function of time is a signal, a value measured as a function of a continuously varying indexing parameter. A fundamental concept of signal engineering is that any signal can be represented as the sum of a set of sine waves of different frequencies and magnitudes. Low frequencies are slowly undulating sine waves, high frequencies represent rapid shifts in value. Any behavior that is characterized by rapid shifts in value is high frequency behavior. A load curve with a great deal of on-off “choppiness,” as for example Fig. 12A, has a large amount of relatively high frequency behavior. On the other hand, a smooth coincident load curve (Fig. 12B) has no high frequencies.

Fig. 23—Single household load curve (top of Fig. 20) sampled with hourly discrete sampling. Left: load curve sampled discretely every hour at the beginning of the hour. Right; sampled every hour 15 minutes after the hour.

A fundamental theorem of sampled signal theory is that for

cycling on an individual household basis. Better yet, one-

minute samples can be used when trying to identify appliance or individual household load behavior in detail.

instantaneously discrete sampled data to be valid, the sampling must be done at twice the rate of the highest frequency in the signal. Thus, to capture completely behavior of a load curve that has rapid shifts in load (and thus avoid errors as depicted in Fig. 23), it is necessary to sample it twice as often as its appliance loads cycle on and off. Since many appliances turn on and off within a fifteen or even ten-minute period, a minimum rate of five-minute sampling is necessary to see peak load, coincidence, and load curve behavior of such rapid

As mentioned in sub-section 23, instantaneous discrete sampling and period integration sampling differ dramatically in what they do if sampling rate falls short of these requirements. Essentially, period integration samples a load curve but filters it simultaneously. The averaging over each demand interval, as discussed above, smoothes out choppiness (removes high frequencies). To a very good approximation, this type of sampling can be thought of as responding only to frequencies in the signal that are in the band of frequencies below one-half its sampling rate. The period integration responds to frequencies in the band it can “see” (those below its sampling rate limit) and ignores those above that limit.

While the two load curves in Fig. 23 look quite different, and bear no resemblance to the actual load curve shape, they share one characteristic: Both seem to oscillate back and forth every three to five hours. This is called aliasing, or “frequency folding” in signal theory, and is essentially a “beat frequency” generated by interference between the sampling rate, and the duty cycle rate of the appliances in Fig. 12A. Something similar to this occurs any time the measured quantity being sampled cycles back and forth at a faster rate than the sampling. In this example, appliances are cycling on and off at a rate much too fast for the hourly sampling rate to track. The beat frequency, or “aliasing profile” shown here, is a characteristic of under-sampled curves, something to watch for in load data. This type of distortion is common. It is fairly easy to detect by manual inspection (at least if given some training and understanding of what causes it), and its presence means that the load curve data is probably completely invalid.

In the presence of a great deal of erratic on-off load shifts, as occurs in most non-coincident loads, neither period integration (demand sampling) or instantaneous discrete sampling gives a completely accurate measurement of the load curve behavior. The integration method averages behavior over each period. The instantaneous method may chance upon any value. If the load being measured is fairly smooth, for example the load of an entire power system, then the level of

Thus, sampling a load at half-hour intervals with period integration will obtain valid information on all frequencies in the load up to one cycle/hour, but will smooth out, or filter, fluctuations that are due to more rapid load behavior. (This perspective is slightly simplistic - i.e., only approximate on several minor technical points - but sufficient for this discussion). Instantaneous sampling, on the other hand, does not filtering, and tries to respond to everything it sees. However, it can only validly see frequencies below twice its sampling rate. It responds to frequencies above that limit by

aliasing them, interpreting high frequency changes as low frequency. The result is a recorded load curve that may be invalid for most engineering and analysis purposes, as are those in Fig. 23.

error in either case is minute and the issue unimportance. On the other hand, if there is a good deal of non-coincident load

25. Determination of the Sampling Method and Type

behavior, as usually with loads measured on the distribution Both period integration and instantaneous sampling record

system, then the sampling rate phenomena discussed here are only “approximate data” when applied at too low a sampling

of concern in the load analysis and subsequent engineering. rate to track non-coincident behavior in the load. Instantaneous


sampling aliases high-frequency load behavior, producing load curve data that is useless for engineering and load analysis purposes. On the other hand, period integration filters out the high-frequency behavior in the load, producing curves that appear “more coincident” than the actual load. While this introduces an inaccuracy in subsequent load analysis and engineering, the curves are at least correct within the context of coincident load analysis.

dividing by 1,000 may seem to be a proper way to produce a representative single-household non-coincident load curve, it gives a smooth coincident curve instead.

In all cases, the preferred approach is to use period integration applied at a high enough rate to sample all the behavior pertinent to the engineering. However, choice of sampling rate and method is often a compromise between cost and accuracy. There will always be some load behavior occurring at a rate faster than can be sampled. Most loads contain motor starting transients and switching fluctuations that can only be captured by very high (10 Mhz) sampling

Addition is a signal filtering process. The “average” curve obtained by addition/division of a number of customer sample load curves is filtered, in a way that removed high frequency load fluctuations. This is the major reason why many T&D engineering studies and load analysis procedures consistently underestimate non-coincident load behavior and often underestimate the amount of coincidence (value of C(n) for n very large). Most of the load curve data available to engineers has been obtained and processed by averaging a group of sampled customer load curves. This averaging produces only coincident load curve data. Most load curve data in use at electric utilities has been produced by averaging, over large enough customer samples, that it is effectively representation -

rates. of completely coincident behavior. The engineers and load analysts performing load research It makes no difference, in the example cited above, whether

must either select a load recording method that suits their the load curves added together were samples for 1,000 needs, or make only valid use of the data that has been given to households on the same day, as described above, or perhaps them. Recommended practice is to research fully where the 1000 days worth of one minute readings for one house. In load curve data came from and how it was recorded, and if it either case, the result of adding together the sampled curves has gone through any type of aggregation, filtering, or other and averaging them to create an average with create a smooth, process that might have altered coincident demand behavior. coincident load curve. Although a majority of recorded load research data comes from The usual reason that a set of load curves is averaged is to demand interval recorders (period integration), a surprising produce a single curve that is most representative of the set’s number of sources produce discrete sampling. This includes behavior. Simply put, algebraic methods (averaging) cannot data taken from SCADA systems, certain types of signal be used to produce average non-coincident curves: there is no recorders, as well as most portable devices made for logging work-around within normal algebraic approaches. Instead,

some form of pattern recognition or clustering analysis must be applied to find the “load curve most like all the others.” For

loads on feeder and service level circuits. In addition, many people forget that data “read by hand” from strip and circular charts is essentially discretely sampled data.

The fact that instantaneous sampling can, and often does, example, the k- .means method of cluster analysis can be used to identify one or more curves which have, individually, the most

severely alias non-coincident load behavior does not mean it is “average” peak load, variation rates, energy usage, and daily necessarily a bad recording method, but it must be used with curve shape. caution. Similarly, while period integration (demand recorders, etc.) always records accurately within its sampling rate limitations, it can be applied at too slow a rate to see needle peaks and non-coincident load behavior that are present.

High sample rate does not guarantee high frequencies. Sampling a signal at a fast rate does not guarantee that there will be high frequencies in the data. It could very well be that the load being sampled is smooth and has no high frequencies. Often, the sensors in recording machinery have a poor

27. Sampling Rate Influences Load Duration Curve Shape

Load duration curves will appear different depending on the sampling rate of the load data, too, as shown in Fig. 24. Since data sampled at faster rates “sees” non-coincident needle peaks, it yields load duration curves that reflect that load behavior. Fig. 24 shows annual load duration curves for Fig. 12A, based on 5- and 60-minute demand period sampled data.

response to high-rate fluctuations. For example, strip chart recorders with a very tight dampers cannot respond to fast load shifts. Essentially, such mechanical stabilizers remove high frequencies from the load curve signal.

26. Addition and Averaging Filter Load Curve Data

Suppose every one of 1,000 households served by a particular feeder is sampled on a one-minute demand basis, for a full day (creating 1,440 samples per customer). An average load curve can then be formed by adding all 1000 load curves and dividing by 1000. The result will be a smooth, coincident curve, in fact the same curve shape (except for losses) that would have been recorded by measuring the feeder load at the Fig. 24—Load duration curves of single residential customer (e.g., substation. While adding together 1,000 load curves and Fig. 12A) based on two sampling rates.


IV. DISTRIBUTION LOSSES ARE NOT PROPORTIONAL TO DEMAND SQUARED

One result of the coincidence behavior and sampling issues illustrated in this chapter is that the load-related losses on a power distribution system generally do not correspond to the square of the metered demand. The difference is due to interaction of demand sampling with the coincidence effects of the loads being served. Fig. 25 illustrates an extreme case, in which losses are a purely linear function of measured demand. The water heater operates for 15 minutes during the hour from 6 to 7 AM, and 30 minutes in the hour from 7 to 8 AM. Demand measured on an hourly basis doubles. Electrical losses in the wiring serving this water heater also double. They do not quadruple (as they would if losses varied as the square of demand) because the peak load in every demand interval is the same: as the demand changes from hour to hour, only the load factor changes.

In the extreme case shown in Fig. 25, losses in the line serving only the water heater, are a purely linear function of demand. This will be true regardless of the demand period intervals. Whether measured and compared on a minute, hour, day, or annual basis, losses are a linear function of demand.

Fig. 25—Load of a water heater over a four-hour period (left) and the losses that result in the line serving it (right).

Load behavior at the service (LV) level is seldom the perfect “all or nothing” on-off load situation depicted in Fig. 25, but neither is the relationship between losses and load an “I’R” relationship. Observed losses vs. demand behavior generally falls somewhere between two extremes characterized by fundamentally different behavior of the load:

Losses are a linear function of demand. In such cases, the peak load is identical in every demand period and load factor changes from one demand period to another.

Losses are a squared (quadratic) function of demand. The losses’ factor remains constant in each demand period but peak load varies in proportion to demand.

Fig. 2&A: Hourly losses vs. hourly demand over a one-week The exact nature of the losses vs. demand relationship period for the secondary circuit/drops serving one of the 282

observed in any situation will depend on the load curve itself, homes in a neighborhood served exclusively by a single

the demand period with which load and losses are measured, distribution primary feeder* Lower (curved) line indicates a

and possible errors in the monitoring and recording of the data. squared losses vs. demand relationship, upper (straight) line

Fig. 26 shows three examples of losses vs. demand indicates a linear relationship. B: Hourly load-related losses vs.

measurements on the distribution system. In all three, the hourly demand for the 12.47 kV distribution feeder serving these

observed 1OSSeS VS. demand relationship lies within an envelope 282 homes. C: Monthly load-related losses vs. monthly energy (this can be converted to “monthly demand be dividing energy by

defined by the two extremes - linear and squared behavior. 731 hours/month) for the same feeder over the same period.


28. Relationship Between Losses and Demand

Usually, electrical losses are modeled as a function of demand with an equation fitted to measurements taken during selected periods (e.g., the data in Fig. 26). Most often, the function used estimates hourly losses as a function of hourly demand, using the maximum recorded hourly demand, and maximum recorded hourly losses as factors in the computation. Either of two functional representations are often used. As applied to hourly data, they would be:

Losses(h) = L,,, x (a x D (h)/D,,, + b x (D(h)/Dma.J2) (6)

Losses(h) = L,,, x (D(h)/ D,,,) ’

Where h indicates the hour, D(h) is the demand observed in hour h, D max = maximum recorded hourly demand L max = losses during maximum demand hour a+b=l e is a value between 1 .O and 2.0

The values a and b in equation 6 are essentially the same as the “a and b factors” used in traditional computations of losses factor from load factor.2 They represent the extent to which losses behave in a linear, or squared, manner, respectively. Where losses are a linear function of load, a = 1 and b = 0, and the value e in equation 7 would be 1 .O. Where losses have a squared relationship to demand, a = 0, b = 1, and e = 2.0.

Significant “non-squared” losses behavior on distribution systems usually occurs in the equipment that serves individual customers with small loads. The most extreme “non-squared” losses vs. demand behavior that is routinely encountered is a single household load, as shown in Fig. 26A (data is taken from the same load as in Fig. 12A. This is the losses vs. load situation for the service drops leading to this single house.

As the measured hourly demand in Fig. 12A varies, both its peak load and load factor vary roughly in proportion to one another. As a result, hourly losses vs. demand behavior is a mixture of the two extremes discussed above. Modeling of hourly losses as a squared function of hourly demand (a = 0 and b = 1 in equation 6, or e= 2.0 in equation 7) gives 35% average absolute error. Error is 13.5% when using 15 minute intervals. Modeling of the losses as a linear function of demand gives roughly twice these levels of error (almost all distribution losses behavior is closer to squared than to linear).

Usually, proper selection of a, b, and e coefficients can cut error by about 3/4. Use of a = .33 and b = .66 in equation 6 minimizes average absolute error, reducing it from 35% to 8.9%. Use of e = 1.51 in equation 7 similarly minimizes error, at 9.1%. The two equations provide different estimates on an hourly basis (with an average absolute difference of 4%) but are roughly equal in overall modeling accuracy. When using quarter-hour demand periods in this example, a = .24, b = .76, and e = 1.6 minimizes average absolute error, at less than 5%.

The load curve shown in Fig. 12A is one of 282 residential loads in a neighborhood served by a 12.47 kV feeder. Fig. 26B

For example, see Electric Utility Distribution Systems Engineering Reference

Book, Westinghouse Electric Company, 1959, page 28.

shows the losses vs. demand data for this feeder, on an hourly demand period basis. The relationship appears much closer to squared than when the individual customer data was examined on the same hourly basis (Fig. 26A). Error in estimating losses as a function of demand occurs with a = .07, b = .93, and e = 1.91. (A larger value of b, and a value of e closer to 2, indicates a more “squared’ relationship). Generally, losses vs. demand behavior for equipment serving large groups of

customers appears less linear and more quadratic (squared) than for smaller groups.

In Fig. 26C, the feeder’s losses and energy (essentially the same as demand, demand = energy/173.33 hr./mth.) are compared on a monthly basis, instead of the hourly basis used in Fig. 26B. The observed relationship between losses and demand is much more linear than when hourly intervals were used to analyze the same load: error is minimized with a = .4 1, b = .59, and e = 1.52. The monthly demand period is much longer than the major cycle periods of the feeder’s load (daily and weekly variations). Generally, losses vs. demand behavior appears more linear if longer demand intervals are used in the analysis.

29. Mean Error in Estimating Loads

Representation of losses as a squared function of demand in equations like 6 and 7 usually results in underestimation of the average level of losses. Note the plotted lines, representing linear and squared losses behavior in Fig. 26. The curve representing losses as a function of demand squared is lower in all cases than the measured losses. The line representing losses as a linear function of demand is uniformly higher than any of the losses’ measurements. This is always the case when using losses estimation equations such as 6 or 7, calibrated against peak period demand and the values D,,, and L,,,.

Generally, if the long-term performance of a load analysis and prediction equation is to overestimate losses, then it is too linear in the calibration of its a and b, or e terms, regardless of the level of its average absolute hourly error. Similarly, if it consistently shows a bias toward underestimating the amount of losses over many demand periods, then it has been calibrated as too quadratic, even if it is giving satisfactory average error on a demand-period basis.

TABLE 6—COEFFICIENTS FOR LOSSES vs. DEMAND ON AN HOURLY

DEMAND PERIOD BASIS AS A FUNCTION OF SYSTEM LEVEL

Chapter 24

30. Modeling Losses on the Distribution System

The relation observed between losses and demand on a T&D system will depend on the customer load behavior, the measuring and recording equipment being used, and the demand period length of the recording and analysis. Generally, coincidence and demand period affect results:

I. Coincidence. Equipment that serves small groups of customers, exhibits more linear losses vs. demand behavior (higher ratio of a/b; lower e) than equipment with many customers downstream. For example, the single customer hourly data shown in Fig. 26A is much more linear than that for the group of 282 customers in Fig. 26B. The two plots show essentially the same load type, observed on the same (hourly) demand period basis. Losses vs. demand for coincident load situations is closer to quadratic. For non-coincident situations it is usually closer to linear.

Thus, the best values of a and b, or e, to estimate losses as a function of demand on an hourly basis, will depend on the level of the system being modeled. Table 6 gives typical values for b and e on power systems in North America.

2. Demand period length. The losses vs. demand relationship shown in Fig. 26A, for the service drops leading to a household like that shown in Fig. 12A, is a mixture of linear and squared behavior when sampled on an hourly demand basis. The hourly sampling rate is much longer than the natural on-off cycles of many of the major appliances (see sub-section 13 of this chapter). The losses vs. demand relation would appear to be nearly a perfect squared relationship if evaluated on a minute by minute basis (not shown).

Similarly, losses vs. demand data for the feeder has a considerable non-quadratic behavior when viewed on a monthly basis (Fig. 26C), because the demand periods are much longer than the daily and weekly load swings normally seen in the load, as well as the three- to six-

day weather-front cycles which often affect the weather-sensitive portion of these loads. Hourly demand periods (Fig. 26B) are much shorter than these cycles, and observed losses vs. demand behavior at this demand period length is very nearly a perfectly squared relation. Short demandperiods produce more quadratic losses vs. demand behavior; while long demand periods result in a relationship that appears more linear. “Short” and “long” as used here are relative to the dynamic cycles or periodicities of the load behavior.

Therefore, the overall losses vs. demand relationship depends on both the equipment level of the system being studied (amount of load or customers downstream) and the demand period being used for data and analysis. Fig. 27 shows values of b (for equation 6) that work well as a function of level of the system and demand period in a typical residential

801

Fig. 27—Values of b for equation 4 that give minimum error in estimating losses from demand for residential load in a utility system in the southwestern United States. Losses vs. demand behavior on other systems will differ quantitatively from the values shown here, but is generally qualitatively similar. “Number of Customers” less than 1 refers to individual appliances loads and household circuits.

31. Losses vs. Demand on the Entire Distribution System

From 25% to 66% of distribution losses occur on portions of the distribution system near the customer, portions that deviate significantly from a “squared’ losses vs. demand relationship. As a result, the overall losses vs. demand relationship for an entire distribution system will usually deviate noticeably from a squared relationship. The quantitative relationship varies from one system to another depending on customer loads, system equipment types, and layout and design used in the primary and service levels. Generally, b is in the range of .75 to .88, behavior is more quadratic than linear, but sufficiently non-quadratic that significant error(on the order of 25%) results in predicting hourly losses from demand if a purely squared relationship is assumed.

Fig. 28—Monthly energy vs. load-related losses for the system that area in the southwestern United States. The qualitative includes the feeder aid loads shown in Fig. 26. This includes behavior shown occurs on all power systems. losses on feeders, laterals, and secondary/service drops. b 578


VI. T&D SYSTEMS ARE BUILT TO SATISFY CUSTOMERS, NOT LOADS

32. Quantity, Quality, and Value

The diverse types of consumers purchasing electric power from the distribution system have different uses for the power they buy, different needs for quantity (amount of power purchased), and needs for quality (continuous availability, tight voltage regulation), and different dispositions to pay a premium price to get exactly what they need. The value a particularly consumer places on electric power is a function of his or her needs for electricity, primarily as defined by the economic or personal value of the end-use (i.e., watching television and keeping food cool, stamping sheet metal into equipment cases, operating a cash register/inventory system), and as fashioned by the demands of the appliances used to convert electricity into the end-use.

A personal computer exhibits demand characteristics exactly the opposite of the water heater’s. A typical PC has a connected load of about 180 watts, and a contribution to coincident peak of the same magnitude. But while its

connected load is one twentieth, and its peak demand only one sixth of the water heater’s, its demand for quality is much higher. Measured as the time it can go without power while continuing to perform its end-use function, a PC is about 15,000 times more sensitive to power continuity problems than a water heater. It is also vastly more sensitive to voltage sags and surges, and long-term changes in voltage.

The major element of customer quality is availability of sufficient quantities of power. Quality can be as or even more important than quantity in determining the customer value, but the important point is that both quantity and quality are major factors to be considered in determining how to maximize customer value. Two common residential appliances that illustrate the opposite extremes in these two “Q dimensions” that can exist among customers. These are an electric water heater and a personal computer.

Largely because of the different needs of their appliances and equipment, and the difference values of the net end-use products, electric customers vary greatly in their demand for electric power quality. Fig. 29 gives five examples of “cost of interruption” value of electric customers. The cost vs. time functions shown are not typical, because there is no typical need for power quality, just as there is no typical quantity of power requirement that suits all customers. In general, commercial and industrial consumers have a higher demand for both quantity and quality of power than residential consumers.

A typical 50-gallon storage water heater has a connected load of 4,000 watts, and a coincident contribution to system peak of about 1,100 watts. This is a relatively high demand for quantity of power as compared to most household appliances (typically only central air conditioners or heaters use more power). Power to a water heater can be interrupted routinely for several hours at a time (and often is under peak-shaving load control programs). Such interruptions make little impact on its value to the customer, because it can supply reasonable quantities of hot water from its storage tank during power interruptions. In addition, its end-use performance is virtually immune to voltage sags, surges, and even significant long term variations in supply voltage. Thus, while a water heater has a high demand for quantity, it has a low demand for power quality.

In a competitive electric power industry, and a world where attention to quality is taken for granted in many other industries, power system engineers should anticipate increasing levels of attention on quality of power delivered. This does not necessarily mean that quality must be or will be improved. Cost is an important element of value, and a large portion of consumers in most power systems would prefer to pay a lower price for power, even if that means they must sacrifice some amount of power quality in return. The important point is that like quantity of power, quality is an important attribute. As it is with quantity, it is possible to overbuild or underbuild a power system with respect to the amount of quality that needs to be delivered. The challenge facing power engineers is to design the lowest cost system that can deliver the required levels of both, and no more.

VI. GROWTH OF ELECTRIC LOAD AND T&D

CAPACITY REQUIREMENTS

Fig. 29-Cast vs. interruption duration when an interruption unexpected (top), and when one day’s notice is given (bottom).

is

Chapter 24

33. Spatial Distribution of Load Defines T&D Needs

Electric load is not evenly spread throughout a power system’s service area, but instead, non-homogeneously distributed, with high load density in some areas and no load in others, as shown in Fig. 30. This is due to the heterogeneous distribution of land use and activity within any city, town, or rural region - some areas are more densely settled and active than others. Not shown in Fig. 30, but an important fact in determining electric load, is that customer class varies by location, too. Some areas of a system are nearly entirely residential, others commercial, or industrial, and others mixed.

The load map in Fig. 30 shows some very common characteristics of spatial load distribution, shared by most large metropolitan areas: high load density in the urban core, gradually decreasing toward the periphery, with tendrils of higher load density following major transportation corridors.


Fig. 30—Spatial distribution of electric load for a city of about 1 million population in the eastern United States. Shading indicates load density. Lines indicate major roads. At the left, 1998 winter peak load. At the right, a forecast of peak load for year 2010, based on projected trends in load density, customer count, area development, peripheral expansion, and end-use loads. The city is projected to grow both up and out during the 12-year period. Some interior areas are projected to increase in load density, but others are not, and load density decreases in a few areas. Load develops in previously vacant areas, particularly along the south periphery.

The load maps in Fig. 30 outline the mission of the T&D system for the region shown. In the year 1998 it must deliver 2,3 10 MVA of electric power in the geographic pattern shown. Its ability to do so reliably and economically is the major measure of its performance as a power delivery system.

34. Load Density Varies With Location

Fig. 30 illustrates how load density varies as a function of location within a power system. Analysis of load in terms of kW/acre or MW/square mile is a convenient way of relating it to local T&D capacity needs and is often used in power delivery planning. Load density is an important aspect of T&D planning, since the capacity and location requirements of T&D equipment depend on local load characteristics, not system averages. Typical ranges of values for urban, suburban, and developed rural areas are given in Table 7. The values shown are typical, but values specific to each particular system should be obtained by measurement.

TABLE 7—TYPICAL LOAD DENSITIES FOR VARIOUS TYPES OF AREAS

35. Growth Drives System Expansion

Fig. 30B shows the projected load 12 years later than Fig. 30A, based on a detailed evaluation of economic growth of the region, land availability, demographic and zoning factors, and expected changes in per capita and end-use loads. After this 12-year period of growth, the T&D system will be expected to deliver 3,144 MW in the pattern shown. During the intervening 12 years, additions and changes to the system must be made so that it can grow along with the load. This load growth is the motivation for the equipment additions, and the expansion budget will be well spent only if the equipment is located, and locally sized properly, to match the evolving load pattern in Fig. 30B.

Comparison of Fig. 30A and Fig. 30B reveals several characteristics of load growth as it affects T&D systems:

Previously vacant areas develop load, e.g., the swath of load growth across the entire southern frontier of this city between 1998 and 2010. Entirely new parts of the system must be built into these areas.

Some vacant areas do not grow. For whatever reason, some areas remain vacant, often because of local covenants or because they are for public use (parks, etc).

Load in some developed areas increases in load density, perhaps substantially. Examples in Fig. 30 include the urban core and some areas in outlying areas.

Load in some developed areas remains constant, or falls slightly due to increasing appliance efficiency in areas that otherwise remain unchanged (no new building construction or population increase).

804 -_ Chapter 24

The difference between Fig. 30A and Fig. 30B represents the challenge facing this system’s T&D planners. They must make additions whose equipment types, capacities, locations, and interconnections to the existing system result in a “12- years hence” system that can reliably and economically serve the pattern shown.

36. Two Causes of Load Growth

Two simultaneous processes create electric load growth or change, both at the system and at the distribution level. Increases in the number of customers in the utility service area, and increases in the usage per customer cause electric load to grow. No other process causes load growth: If the electric demand on a power system increases from one year to the next, it can be due only to one or a combination of both of these processes:

I) New customers are added to a system due to migration into an area (population growth) or electrification of previously non-electric households. Customer growth causes the spread of electric load into areas that were “vacant” from the power system’s standpoint.

2) Changes in per capita usage occur simultaneously and largely independently of any change in the number of customers. In developing economies this is driven by the acquisition of new appliances and equipment in homes and businesses. In developing nations, per capita load growth often decreases, due to improving appliance efficiency.

In cases where per capita consumption is increasing, it is usually due to major shifts in appliance market penetration. For example, the percentage of homes and businesses using electric power to heat the interior of buildings may increase from 20% to 26% over a decade. In such a case, even if appliance efficiency is increased slightly, electric load will grow.

37. Spatial Load Growth and the “S” Curve Characteristic

When viewed from a total system basis, a growing power system generally exhibits a smooth, continuous trend of annual peak load growth. Given a healthy economy, and corrected for variations due to weather, the load in the region will simply continue to grow at a continuous rate.

Planners of the power supply to an entire region have no need of specific geographic information on the locations of loads, or the areas which are or are not growing rapidly. They have no need of spatial resolution in their planning, for their goal is to plan and operate sufficient power for the entire region.

Fig. 31—The “S curve” has an interval of high growth rate T&D planners, on the other hand, do have a need for sandwiched between two periods of lower rate growth. locational information in the planning, routing, design, and

By contrast, growth in any relatively small geographic area is not a smooth continuous trend from year to year. Instead, it follows the Gompertz curve, commonly referred to as an 5” curve, shown in Fig. 31. The “S” curve is the basic behavior of load growth as it affects T&D equipment, such as in feeder and substation areas. Nearly every small area within a large power system has a load growth history similar to that shown in Fig. 3 1, for a very simple reason: landfills up.

The S curve has three distinct phases, periods during the local area’s history when fundamentally different growth dynamics are at work:

Dormant. The time ‘before growth”, when no load growth is occurring. The small area has no load and experiences no growth: growth “hasn’t arrived yet.”

Growth ramp. During this period growth occurs at a relatively rapid rate, usually due to new construction.

Saturation. The small area is “filled up” - fully developed. Growth may continue, but at a very low level compared to that during the growth ramp.

What varies most among the thousands of small areas in a large utility service territory is the timing of their growth ramps. Seen in aggregate over several thousand small areas, and the overall system load curve looks smooth and continuous because there are always roughly the same number of small areas in their rapid period of growth. The continuous year-to- year trend for the whole system is due to diversity in the timing of when areas grow: any one area grows for only a short time, but new areas of growth are constantly being added to a growing city, so as a whole, it grows continuously.

Evidence of historical “S” curve load growth exists in every city. Most people can identify areas of their home town or city that developed in the 196Os, the 1970s the 1980s or the 1990s. The buildings in these areas are of a common age, because all were built during a “burst” of development in that area, at that time.

38. Relation of Load Growth Causes to “S” Curve Shape

These two causes of load growth are tied to different parts of the “S” curve characteristics, as shown in Fig. 31. The growth ramp occurring over a short period of time is due to new customers in the area. The slow, steady growth thereafter is due to increasing per-capita usage by the customers in the area. In some cases, the slow, steady trend is a reduction over time, due to improving appliance efficiency.

39. Growth Behavior as a Function of Spatial Resolution

Chapter 24 Characteristics of Distribution Loads

operation of their system. Facilities are utilized more efficiently if they are sited correctly. The need for locational detail in planning and engineering is called spatial resolution.

Spatial resolution requirements vary depending on application: feeder planning requires more detail on and is more sensitive to changes in the location of loads, than transmission planning. Table 8 gives typical range of spatial resolutions (knowledge of load as a function of location) that work well in T&D planning. The table indicates that knowledge of how load density, and load growth are usually needed to match equipment locations so that economy and reliability are maximized to the load. Resolution as used in the table refers to the width of a square area used for load studies, and within which reliable information on load locations is not available.

TABLE 8—TYPICAL SPATIAL RESOLUTION (LOCATIONAL DETAIL) FOR

PLANNING AS A FUNCTION OF SYSTEM LEVEL

Due to the “S” curve growth dynamics described earlier, observed load growth behavior varies as a function of the spatial resolution used in load analysis and planning. Load growth behavior will appear to be different simply depending on the small area size used to collect and analyze growth.

805

steady annual load growth over a long period of time, as shown. Except for weather and economy, many cities have in fact grown steadily in this manner: Denver, Phoenix, Indianapolis, Bangkok Caracas, and Rabat, to name just a few.

Imagine dividing the metropolitan area illustrated in Fig. 32 into quadrants. Each quadrant would still be very large (in a city like Atlanta or Houston, nearly a thousand square miles). If the exact load history of each quadrant could be plotted, all would be slightly different in amount of load and rate of growth, but all would still have a fairly smooth, continuous trend. This is shown in Fig. 33.

Fig. 33—Quadrants also display smooth, long-term growth trends.

But if this process of hierarchical sub-division continues, splitting each sub-quadrant into sub-sub-quadrants, then into sub-sub-sub-quadrants, and so forth, “S” curve load growth trends will begin to be discernible as the common characteristic of growth, when the sub-division reaches a size of about 16 square miles (square areas 4 miles, or 6 km, on a side). Most long-term trends at this spatial resolution would begin to display slight “kinks,” something like those shown in Fig. 34 - an “S” curve, rather than a smooth, long-term steady growth pattern.

Fig 34—Areas of about 16 square miles (areas 4 miles on a side) display discernible “S curves” load growth behavior . The city grows at a steady rate (Fig. 32) because the growth ramps of

Fig. 32—Annual peak load of a large city over a twenty-five year period, after correction for weather and other anomalies.

different areas occur at different times.

To understand this phenomenon, and to see how and why it occurs, it is useful to consider a diagram of the annual peak load of a growing city of perhaps 2,000,OOO population, as illustrated by Fig. 32. For simplicity’s sake, assume that there have been no irregularities in the historical load trend due to weather, changing economy, or shifts in service territory boundaries. This leaves a smooth growth trend, one that shows

Carrying the sub-division to the extreme, one could imagine dividing a city into areas so small that each contained only one building. At this level of spatial resolution, annual peak load growth would be characterized by the ultimate “S” curve, a step function. Although the timing would vary from one small area to the next, the basic load growth history of a small area of such size could be described very easily. For many years the area had no load. Then, usually within less than a year, construction started and finished (for example’s


sake, imagine that a house is built in this very small area), and a significant load established. For many years thereafter, this annual load peak of the small area varies only slightly - the house is there and no further construction occurs.

The quantitative behavior of the “S curve” growth characteristics will depend somewhat on the spatial resolution (small area size used). There are three important interactions with between growth characteristics and spatial resolution.

spatial resolution, growth is usually a short, intense period of development. It usually happens in areas where there was no previous load, and it does not always occur - many areas stay vacant.

I. The YY curve behavior becomes sharper as the service territory is subdivided into smaller and smaller areas. The smaller the small areas being studied (the higher the spatial resolution) the more definite and sharp the “S” curve behavior exhibited, as shown in Fig. 35. Quantitative behavior of this phenomena depends on growth rate, demographics, and other factors unique to a region, and varies from one utility to another. Qualitatively, all utility systems exhibit this behavior: “S” curve load trend becomes sharper as area size is reduced.

The three changes in growth character discussed above occur on(v because spatial resolution of data collection and analysis changes. The character of the load growth itself does not change, only the way it appears to the planner. By asking for more spatial information (the “where” of the T&D planning need) the very appearance of load growth itself, changes.

2. As the utility service territory is subdivided into smaller and smaller areas, the number of small areas that have no load and will never have any load increases. When viewed on a square mile basis (640 acre resolution) there will likely be very few “completely” vacant areas in a city such as Phoenix or Atlanta or Caracas: square miles that are completely devoid of electric load.

But if examined on an acre-parcel basis, a significant portion of land, perhaps as much as 15%, will be “vacant” as far as electric load is concerned, and will stay that way. Some of these vacant areas will be inside city, state, or federal parks, others will be wilderness areas, cemeteries or golf courses, and many other merely ‘useless land’ - areas on very steep or otherwise unusable terrain.

Fig. 35—As small area size for the load growth analysis is decreased, the average small area load growth behavior becomes more and more a sharp “S” curve behavior. (vertical scales of the four plots shown are different, with the full range in each case indicating 100% of the fully-developed load level).

40. Regions “Fill Up” In A Discontinuous Manner

3. The amount of load growth that occurs within previously vacant areas increases as small area size decreases. If the load growth of a city such as Denver or Houston were analyzed over the period 1980 to 1990, using a small area size of nine square miles (areas three miles to a side), almost all of the load growth during the period would have occurred in areas that had noticeable amounts of load in 1980.

Fig. 36 shows another way to examine the “S” curve growth behavior at the distribution level, and reveals another implication of this growth behavior. Shown is the growth of electric load in a region of about 24 square miles on the outskirts of a large, growing metropolitan area, over a 12-year period. Individual land parcels within this area generally follow the “S” curve growth behavior pattern, with a growth ramp (period from 10% to 90% of eventual saturated load) of about three years at the l/4 square mile resolution. The complete area, however, has a growth ramp of about 15 years.

By contrast, if those same regions were examined at a 2.5 acre spatial resolution (small areas l/l6 mile to a side) nearly half of the decade’s load growth would be found to have occurred in small areas that had no significant load in 1980 - areas that were vacant.

Thus, the observable dynamics of load growth appear somewhat different depending on the amount of where detail used in the load analysis. As spatial resolution is changed, the

character of the observed load growth changes, purely due to the change in resolution.

At low resolution (i.e., when using “large” small areas) load growth appears to behave as steady, long-term trends in areas with some load already established. Few, if any areas, are completely devoid of load. By contrast, if examined at high

The development of load within this area is geographically discontinuous, with the timing of various parcels displaying a somewhat random pattern. While growth usually develops from the southwest outward (this area is on the northeast edge of the metropolitan area), the timing of when a parcel of land begins to develop is somewhat random. Growth does not develop as a smooth trend outward, but instead appears to be a semi-random process. Once load has filled up one parcel, it does not automatically proceed to the next in line, but may jump to another nearby area. Thus, early in the process of growth for this whole area, some parcels develop to saturation on its far edge early in the process. The most unpredictable aspect of small area load growth is the exact timing of parcel development.

In contrast, experience and research has shown that the eventual load level in most small areas can be predicted fairly well, as can the expected duration of growth ramps (see Willis,

Chapter 24


, 1996). However, the exact timing of growth appears to be somewhat random, at least as viewed from apriori information likely to be available to the planner. Implications for T&D expansion are clear. The system cannot be extended incrementally outward from the southeast as load grows. Instead, substation siting and feeder expansion must deal with delivering “full load density” to an increasing number of neighborhoods scattered over the entire region, that develop geographically into a higher overall density. This means that full feeder capability (maximum designed load and maximum designed distance) may be needed far sooner than predicted by the “gradually increasing density” concept.

early, in order to reach these disparate locations. An economic dilemma develops because the utility will eventually need a good deal of capacity in these routes when the load fills in the area, but planners do not want to incur the cost of building now for load levels not expected for 1 O-12 years. The challenge is to find a way to expand the system without building a majority of the routes early, or having to build many long routes with higher capacity than will be needed for years.

41. “Putting Out Fires” Is the Norm in T&D Expansion

T&D planners often speak about “putting out fires” - having to develop plans and install equipment and facilities on a tight time schedule, starting at the last moment, without proper time to develop comprehensive plans or coordinate area development overall. A point illustrated here is that the load growth aspect of this situation is the norm: rapid growth that starts with little warning, fills in an area relatively quickly, and then moves elsewhere, not only happens on a regular basis, but is the normal mechanism of growth. The “S Curve” growth characteristic, its tendency to be sharper in smaller areas, and the semi-random, discontinuous pattern of load development described above, are very general characteristics that affect all power systems. Load development in a small area almost always begins with little long-term warning, grows at a rapid rate to saturation, and then moves to other areas, usually near by, but often not immediately adjacent.

This growth characteristic is the basic process that drives T&D expansion, equipment additions, and the planning and engineering process. T&D engineers will never change the nature of load growth and development. The recommended approach is to develop planning, engineering, and equipment procurement procedures that are compatible with this process. These include:

Fig. 36—Load grows as developing parcels of land. As a region fills in with load, individual parcels develop very quickly, but often leave vacant areas between them. The utility may have to build a majority of the primary feeder lines that kill de needed eventually, long before a majority of the growth has developed.

Such expansion is difficult to accomplish economically: feeders must be extended over much of this area early in the 12-year period, so the utility can serve the widely scattered pockets of high load density. Great capacity is not needed at that time, because the overall load is not high. However, a good portion of all the routes eventually needed is required

a) Master plan development based on projected area development. As noted above, the eventual load density for any small area, and the overall pattern of development for a region, can be predicted with reasonable accuracy fairly far in advance. Thus, long range plans optimized to the expected pattern of development can be developed.

b) Use of modular system layouts for transmission, substations, feeders and service (LV) parts of the system, that permit modular expansion on an incremental parcel basis. Some types of layout are more expandable on a “fill in the parts” basis that others. In particular, the growing use of multi-branched rather than large-trunk feeder layouts is one reaction to this situation. Such feeders can be expanded on a short range basis, to cover a growing area as needed, yet still fit into an optimized long-range plan.

c), Organization of the planning, engineering, and construction process with short lead times for implementation. Given that a long-range master plan exists for an area, the key to success is a short start-up and lead time for engineering of the details and project implementation, once development begins.


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REFERENCES

Power Distribution Engineering- Fundamentals and Applications, by J. J. Burke, Marcel Dekker, New York, 1994.

Trends in Distribution Reliability, by J. J Burke, ABB Electric systems Technology Institute, Raleigh, NC 1997.

Urban Distribution Load Forecasting, final report on project 079D 186, Canadian Electric Association, 1982.

Research into Load Forecasting and Distribution Planning, report EL- 1198, Electric Power Research Institute, Palo Alto, CA, 1979.

DSM: Transmission and Distribution Impacts, Volumes 1 and 2, Report CU-6924, Electric Power Research Institute, Palo Alto, Aug. 1990.

Tutorial on Distribution Planning, by M. V. Engel et al., editors, Institute of Electrical and Electronics Engineers, New York, 1992.

Edge City, by J. L. Garreau, Doubleday, New York, 199 1.

Computer Speeds Accurate Load Forecast at APS, by A. Lazzari, Electric Light and Power, Feb. 1965, pp. 3 l-40.

Model of Metropolis, by I. S. Lowry, Rand Corp., Santa Monica, 1964.

Sensitivity Analysis of Small Area Load Forecasting Models, by J. R. Meinke, in Proceedings of the 10th Annual Pittsburgh Modeling and Simulation Conference, University of Pittsburgh, April 1979.

Electrical Loads Can Be Forecasted for Distribution Planning,” by E. E. Menge et al., in Proceedings of the American Power Conference, Chicago, University of Illinois, 1977

Computer Model Offers More Improved Load Forecasting, by W. G. Scott, Energy International, September 1974, p. 18.

Load Forecasting Data and Database Development for Distribution Planning, by H. N. Tram et al., IEEE Trans. on Power Apparatus and Systems, November 1983, p. 3660.

Load Forecasting for Distribution Planning - Error and Impact on Design, by H. L. Willis, IEEE Transactions on Power Apparatus and Systems, March 1983, p. 675.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

Spatial Electric Load Forecasting, by H. L. Willis, Marcel Dekker, New York, 1996.

Power Distribution Planning Reference Book, by H. L. Willis, Marcel Dekker, New York, 1997.

Some Unique Signal Processing Applications in Power Systems Analysis, by H. L. Willis and J. Aanstoos, IEEE Transactions on Acoustics, Speech, and Signal Processing December 1979, p. 685.

Spatial Load Forecasting - A Tutorial Review, by H. L. Willis and J. E. D. Northcote-Green Proceedings of the IEEE, February 1983, p. 232.

Comparison of Fourteen Distribution Load Forecasting Methods, by H. L. Willis and J. E. D. Northcote-Green, IEEE Transactions on Power Apparatus and Systems, June 1984, p. 1190.

Introduction to Integrated Resource T&D Planning, by H. L. Willis and G. B. Rackliffe, ABB Guidebooks, ABB Power T&D Company, Raleigh, 1994.

Some Aspects of Sampling Load Curves on Distribution Systems, by H. L. Willis, T. D. Vismor, and R. W. Powell, IEEE Transactions on Power Apparatus and Systems, November 1985, p. 3221.

A Cluster-based V.A.I. Method for Distribution Load Forecasting, by H. L. Willis and H. N. Tram, IEEE Transactions on Power Apparatus and Systems, September 1983, p. 8 18.

Spatial Electric Load Forecasting by H. L. Willis, M. V. Engel, and M. J. Buri, IEEE Computer Applications in Power, April 1995.

Forecasting Electric Demands of Distribution System Planning in Rural and Sparsely Populated Regions, by H. L. Willis, G. B. Rackliffe, and H. N. Tram, IEEE Transactions on Power Systems, November 1995.

Short Range Load Forecasting for Distribution System Planning - An Improved Method for Extrapolating Feeder Load Growth, by H. L. Willis, G. B. Rackliffe, and H. N. Tram, IEEE Transactions on Power Delivery, August 1992.

characteristics of distribution loads - eep...demand factor is considerably less than 1 .o. 7. load...

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