Le Viet Tien, Ph.
D
EPSD, SEE, HUST
CONTENTS
1. Generality
2. Load characteristics
3. Load estimation
4. Load growth and forecasting
1
1. Generality
1.1. Basic definitions
• Electrical appliances or devices : Convert electricity
into the desired end products (lighting, heater,
motor…)
• Electric load : The characteristic of power consumption
of an individual electric device or a group of electric
devices. Load given in W, VAr, VA or A.
• Electric load presented to the power delivery system is
relative depending on the position in the power system
it is measured.
• Calculated Load : Forecasted load for system designs.
1. Generality
1.2. Heating by load current
• Conductor heating process under load current
Q I Q h Qc (1) where
R : Conductor resistant ()
Joule heating : I: Current (A), t: Time (s)
QI I 2 . R.t c: Specific heat capacity (J/kg.Co)
Internal heating : G : Mass (kg)
: Temperature change (Co)
Q h c .G .
q : Heat transfer coefficient (W/m2.Co)
Convection : S c : Outer conductor area (m2)
Qc q.Sc .( 1 )t 1, : Initial and after-t conductor
temperatures (Co)
2
1. Generality
1.2. Heating by load current
Solve (1), we get
(1 e t T ) 1 .e t T
0 0
(2)
c.G R .I 2 1
T0 t
q.Sc q.Sc
0 T0 : Heating time constant (10min. for Cu, Al)
1 1 0 : Equilibrium temperature difference
: Conductor temperature
1 : Initial conductor temperature
0 : Ambient temperature
1. Generality
1.3. Electric Load Classification
• On voltage level (Load location)
− High voltage load (Distribution substation)
− Medium voltage load (Primary distribution feeders
or lateral taps)
− Low voltage load (Service voltage electric
appliances)
• On load phase
− Three phase load
− Single phase load (Phase-to-phase, phase-to-
neutral, 2-wire, 3-wire)
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1. Generality
1.3. Electric Load Classification
• On customer classes
− Industrial (Cottage, small-scale, medium-scale,
large-scale, heavy industries)
− Domestic (Residential electric appliances)
− Commercial (Electric appliances in commercial
establishments)
− Municipal (Street lighting)
− Agriculture (Electric motor driven pumps for
irrigation)
1. Generality
1.3. Electric Load Classification
• On load criticality
− Vital load : Safety of personnel or cause serious
damage within the plant if loss of power.
A safety matter
Complete redundant of the energy source is required.
Standby generator, UPS needed.
Examples: Life support systems, emergency lighting,
control system supplies, fire and gas detection system,
navigation aids.
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1. Generality
1.3. Electric Load Classification
− Essential load : Loss of the manufactured product
(Production and Economy) if loss of power.
An economic matter.
The economics of partial or complete duplication of the
energy source shall be evaluated in relation to the
consequences of service interruptions.
Examples: Production line driven system, auxiliary facility in
industries.
− Non-essential (normal) load : No effect on safety or
production if loss of power.
Single supply source.
Examples: Power and lighting supplies to offices,
warehouses, residential areas, etc.
1. Generality
1.3. Electric Load Classification
Distribution
Transformer
G Standby
Generator
MCCB
ATS Notes:
PCD: Power Conditioning
Device
Normal Essential PCD ATS: Automatic Transfer
loads loads Switch
Critical MCCB: Molded Case
loads Circuit Breaker
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5
1. Generality
1.4. Electric Load Classification
• On load duty (for electric drives)
− Continuous duty : Operation at constant load for
enough time to reach temperature equilibrium.
(Process loads, control systems, lighting and small power
distribution boards, UPS, etc.)
− Short-time duty : Operation at constant load but not
long enough to reach temperature equilibrium.
(Standby loads, emergency systems, etc.)
− Intermittent periodic duty : Sequential, identical run
and rest cycles with constant load. Temperature
equilibrium is never reached. (Intermittent pumps and
process loads, automatic doors and gates, etc.)
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1. Generality
1.4. Electric Load Classification
Continuous duty Intermittent periodic duty
(oC) (oC)
1
1
C t(s) C O C O t(s)
tc
Short-time duty T
(oC)
Cyclic duration factor
: Period energized
1
CDF T : Duration of one
t(s)
T complete duty cycle
C O
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6
2. Load Characteristics
2.1. Load Curve
• Definition: A load curve is a chart showing the electric
consumption as a function of time.
− Load interval (): defined by load measuring device for load
accuracy. Typically 15min, 30min, 1 hour or even longer.
− Load curve period (T): The course of time (measurement
period or billing period) that can be a working shift, a day, a
month or a year. Based on the periodic variation of demand.
− Electric energy (A): used by the load is the area under the
load curve.
T T /
A P(t ).dt Pi .ti
0 i 1
13
24 hour (daily)
15 minute kW
demand curve
• Load curve types:
− Chronological load curve (CLC):
Show the load values in time
sequence.
− Load duration curve (LDC):
Rearrangement of LCL into the
descending order of magnitude
over a period of time.
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7
2. Load Characteristics
2.1. Load Curve
• Methods of establishing load curves
− Metering :
Demand interval defined. The shorter the demand
interval, the more accurate will be the value of the load.
Metering system needed.
Used for operation and future planning.
− Modeling :
Predict the load curve of required customer using the
Representative (Typical) Load Curve (RLC).
RLC is determined by historically surveyed load curves of
similar customers.
Probability methods applicable. Approximate analysis.
Used in system design stages.
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2. Load Characteristics
2.2. Power Demands
• Power ratings : Maximum power to be continuously
used by the device. The limit lower than the level where
the device will be damaged, to allow a margin of safety.
− For end-use electric devices, Pr is the maximum power that can
be safely dissipated by the device.
− For the power carrying devices, Pr is the maximum power flow
through the device.
• Installed power or load
connected : The sum of power
ratings of all electrical devices
in a composite load system.
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8
2. Load Characteristics
2.2. Power Demands
• Individual load
− Demand (P):
The load averaged over a
specified interval of time
(load interval).
− Maximum demand (Pmax):
The greatest demand of all
demand occurred over a
specified period of time
(load curve period).
− Average demand (Pave): A A: Energy
The demand averaged over Pave used by load
a specified period of time
T
(load curve period - T).
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2. Load Characteristics
2.2. Power Demands
• A group of loads Example (Ex.) 1
− Diversified demand or Time
1 2 3
coincident demand (Pg) : Interval
Sum of demands of the P1 2 4 (max) 3
loads in the group for P2 5 (max) 1 3
each time interval. Pgp 7 5 6
− Maximum diversified
demand (Pg.max) : The Pg.max = Max(Pgp1, Pgp2)
greatest demand of all =7
diversified demands over
the load curve period. Sum Pmax = P1max + P2max
=4+5=9
− Maximum non-coincident demand :
Sum of maximum demands of all loads in the group.
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9
2. Load Characteristics
2.3. Factors
• Load factor (FL) Applicable for individual loads.
Indicating how well the utility’s facilities
Pave are being utilized.
FL
Pmax
Pave1 3
Ex. 1, Pave1 = 3, Pmax1 = 4 FL1 0.75
Pmax 1 4
• Demand factor (DF) Applicable for a composite load system.
Indication of the percentage of electrical
Pmax devices that are on when the maximum
DF demand occurs.
PC
Pmax : Maximum demand (W) Ex. 1, Suppose Pc1 = 7, we have
Pc : Total Load connected (W) Pmax 1 4
DF1 0.57
PC1 7
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2. Load Characteristics
2.3. Factors
• Utilization factor (FU)
Load
S
FU max
SR Ex. 2 : Still Ex1, two loads
Smax : Maximum demand (VA) are supplied by a
SR : Rated system capacity (VA) distribution transformer,
Rating SR = 15.
Applicable for system devices
like transformer, distribution lines. Suppose cos = 0.7,
Indicating how well the capacity Smax = Pmax/cos
of an electrical device is being = 10.
utilized.
FU = Smax/SR
= 10/15 = 0.67
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10
2. Load Characteristics
2.3. Factors
Load factor, demand factor and utilization factor given for
types of industry and buildings Individual Facilities
Demand Load
Factor Factor
Utilization
Demand Load Communications – buildings 60-65 70-75
Type of Industry Factor
Factor Factor
(DF x LF) Telephone exchange building 55-70 20-25
Arc Furnace 0.55 0.80 0.44 Air passenger terminal building 65-80 28-32
Induction Furnace 0.90 0.80 0.72 Aircraft fire and rescue station 25-35 13-17
Steel Rolling mills 0.80 0.25 0.20 Aircraft line operations building 65-80 24-28
Mechanical/ Electrical Academic instruction building 40-60 22-26
a) Single Shift 0.45 0.25 0.11
Applied instruction building 35-65 24-28
b) Double Shift 0.45 0.50 0.22 Chemistry and Toxicology
70-80 22-28
Cycle Industry 0.40 0.40 0.16 Laboratory
Wire products 0.35 0.40 0.14 Materials Laboratory 30-35 27-32
Auto Parts 0.40 0.50 0.20 Physics Laboratory 70-80 22-28
Electrical and electronics systems
Forgings 0.50 0.35 0.17 20-30 3-7
laboratory
Cold Storage Cold storage warehouse 70-75 20-25
a) Working Season 0.60 0.65 0.39 General warehouse 75-80 23-28
b) Non-Working Season 0.25 0.15 0.04 Controlled humidity warehouse 60-65 33-38
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2. Load Characteristics
2.3. Factors
• Diversity factor (FD)
n
P max .i
Pmax.i : Maximum demand of load i (W)
Pg.max : Maximum diversified demand of
FD i 1
1
Pg . max group of n loads (W)
Applicable for a group of loads. FD depends on n.
When n increases highly, FD will be leveled out.
• Coincident factor (FC)
Pg . max 1
FC n
1
FD
P
i 1
max .i
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11
2. Load Characteristics
2.3. Factors
• Diversity factor (FD) given for different applications
as examples in Table 2.1 or coincident factor (FC) in
Table 2.2. – Residential loads.
Table 2.1. Table 2.2.
Diversity Factors Diversity
Apartment
Elements of System General Large Factor (ks)
Residential Commercial
Power Industrial 2 To 4 1
Between individual users 2.00 1.46 1.45 5To 19 0.78
Between transformers 1.30 1.30 1.35 1.05 10To 14 0.63
Between feeders 1.15 1.15 1.15 1.05 15To 19 0.53
Between substations 1.10 1.10 1.10 1.10 20To 24 0.49
From users to 25To 29 0.46
2.00 1.46 1.44
transformers
30 To 34 0.44
From users to feeder 2.60 1.90 1.95 1.15
35 To 39 0.42
From users to substation 3.00 2.18 2.24 1.32
40To 40 0.41
From users to generating
3.29 2.40 2.46 1.45 50 To Above 0.40
station
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2. Load Characteristics
2.3. Factors
• Load Diversity (LD)
n Pmax.i : Maximum demand of load i (W)
LD Pmax .i Pg . max Pg.max : Maximum diversified demand of
i 1
group of n loads (W)
Applicable for a group of loads. FD depends on n.
When n increases highly, FD will be leveled out.
• Contribution factor (FC)
Pg . max c1.Pmax1 c2 . Pmax 2 ... cn .Pmax n
ci: Contribution factor of load i th to the group max. demand.
Pmaxi: Max. demand of load i th
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3. Load Estimation
• Purposes: Load is estimated for system design,
equipment sizing (Calculated load).
• Calculated load is the assumed, continuous-duty
demand that heats the conductors or causes thermal
damage to conductor’s insulation the same as the
actual load causes in operation.
• Calculated load is the 30-minute maximum demand.
30 minute load interval is long enough for the
electric conductive parts (Copper, Aluminium) to
reach the equilibrium temperature.
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3. Load Estimation
• General positions for load estimation
3 Distribution
feeder
Medium voltage
Lateral
2
Distribution Low voltage
panel
1 Distribution
transformer
M M Appliances
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3. Load Estimation
• An individual customer (1)
− Using demand factor
Pmax : 30-min maximum demand (W)
CP Pmax DF . PC PC : Load connected (W)
DF : Demand factor (given)
Ex. 3. For a cold storage warehouse with total load connected of
1000kW, what is the CP?
Solve: Check the handbook, we have the load type of cold
storage warehouse has DF = 75%. So
CP = DF . PC = 1000x75%=750kW.
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− Using load survey
Perform a load survey of
similar customers in order to
determine the relationship
between the energy
consumption and the
maximum demand.
Example of linear regression
based on survey data
Load survey for residential customers
Pmax a b. E
Example of Velander’s
where formulae (for Nordic countries)
Pmax : Maximum demand (kW)
E: Energy consumption (kWh) Pmax a. E b. E
a, b : Coefficients
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• Group of customers (2)
1 n 1 n
CDg Pg . max . Pmax .i DF .P i C .i
FD i 1 FD i 1
Pmax.i , DFi and PC.i : Maximum demand (W), demand factor and
load connected of load i th
Pg.max : Maximum diversified demand (W)
FD : Diversity factor (given)
Ex. 4. Four general warehouses with connected loads of 250 kVA,
200 kVA, 150 kVA and 400 kVA, same power factor 0.9 and
demand factors of 90%, 80%, 75% and 85% respectively.
A diversity factor of 1.5 found in the handbook is applicable.
Solve: Pg.max = 0.9x(250x90%+200x80%+150x75%+400x85%)
= 0.9x837.5 = 753.75kW.
If these customers are fed from a distribution transformer, rating of
1000kVA, the utilization factor FU = 837.5/1000=0.8375
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• Feeder load (3)
1 n
CD feeder Pf . max . Pl max .i
F f . D i 1
Pl max.i : Maximum demand of the lateral k th (W)
Ff.D : Diversity factor of the feeder (given)
Ex. 5. A feeder supplying power to three lateral tabs for a
residential area with maximum demands 800kW, 560kW,
and 750kW. Feeder PF = 0.9. Calculate the feeder load?
Solve: Max. non-coincident demand = 800+560+750=2110kW.
Check the handbook, we have FD between laterals equals
1.3. So
2110
Pf . max 1623kW
1.3
Finally, the feeder load equals Pf.max/PF=1623/0.9=1803kVA
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15
3. Load Estimation
• Load estimation using demand density (W or VA/m2)
: Demand density of the load type (W/m2),
CP .S
given in handbook.
S : Demand area (m2)
Applicable for the uniform load distribution,
e.g. public lighting loads.
Ex. 6. Determine lighting load for a classroom, 100m2.
Solve: Check the handbook, lighting demand density is 15W/m2.
So lighting load for the classroom is
CP = . S = 100x15=1.5kW
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3. Load Estimation
• Load center
Loads are treated as masses. Load center location is established
by minimizing the algebraic sum of all moments (loads times
respective distances from the load center).
n
S .x ( y )
i i i (X,Y) : Co-ordinates of load center.
X (Y ) i 1
n (xi,yi) : Co-odinates of load ith
S
i 1
i
Si : Maximum demand of load ith
Applicable for locating system sources (substations or
distribution transformers)
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4. Load Growth and Forecasting
4.1. Generality
• Reasons for load growth
− New customer additions
− New uses of electricity
• Load forecasting classification
Time range Peak demand (MW) Energy (MWh)
Short-range 15 min. to few hours, 1 week to 1 month,
for power system for outage planning
operation control and maintenance
Medium- range 1 month to 1 year, for fuel planning,
coal, oil, water
Long-range 1 year to 10 years, planning for
new power system installations
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4. Load Growth and Forecasting
4.2. Load growth behaviors
• For small area, follows the “S” Small
area
curve, three distinct phases
− Dormant period. The time "before
growth" when no load growth Large
occurs. The small area has no load area
and experiences no growth.
− Growth ramp. During this period growth occurs at a relatively
rapid rate, because of new construction in the small area.
− Saturated period. The small area is "filled up" - fully
developed. Load growth may continue, but at a low level
compared to that during the growth ramp.
• For large area, simple growth ramp.
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4. Load Growth and Forecasting
4.2. Forecasting methods
• Trench methods : Extrapolate past load growth patterns
into the future.
Typical regression curves
− Multiple regression curve-fitting
Ct = a+bt (linear),
Ct f (t ) Ct =C0(1+m)t (Exponential),
n
[C
i 1
i f (ti )]2 Minimum Ct = a.tb (power).
Ct = a+b.t+c.t2 (polynomial).
− Simplicity and ease of use, do not consider factors related with
load growth.
• Simulation methods : Consider factors related with load
growth (Customer class, season, location, causes of
load growth…)
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References
http://electrical-engineering-portal.com/
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