On Composite Load Modeling
for
Voltage Stability
and
Under Voltage Load Shedding
Rasheek Rifaat, Sr. Member IEEE
Jacobs Canada - Calgary, Alberta, Canada
Introduction:
•
•
•
•
From UFLS to UVLS
Power Industry Changes in Last Decade
Advancement in Component Modeling
Importance of Load Modeling for UVLS
Static & Dynamic Load
Elements
•
•
•
•
•
Static: Lighting, heaters
Dynamic: Motors
PF Correction Capacitors & VAR Gen
In-Plant Generation
Distribution System Components;
Transformers, Cables etc.
• Load Tap Changers & Voltage Control
Devices
Definition of Load
Elements for UVLS
• Consumes, Generates, or control real
or reactive power
• Would be impacted by transient,
dynamic or steady state voltage
variations
• Connected with other load elements at
a given load bus to a power source
Static Model for Load
Elements (ZIP)
• Constant Impedance (Z)
• Constant current (I)
• Constant power (P)
Fig 1: Load Representation as ZIP
VS
Z Transmission
VL
Z “Constant Impedance”
I “Constant Current”
Power Source
ZIP Loads
P “Constant Power”
Static Modeling of Load
Elements
• Polynomial form:
⎛ Vk ⎞
Pk = x pk P0 k ⎜⎜ ⎟⎟
⎝ V0 ⎠
α
⎛ Vk ⎞
Qk = xqk Q0 k ⎜⎜ ⎟⎟
⎝ V0 ⎠
β
Composite Nature of Loads:
• Aggregated Load Model as sum of
load elements
m
Pn = ∑ Pk
k =1
m
Qn = ∑ Qk
k =1
Fig 2: Aggregation of Loads by Type &
Location
Large
Generators
Line impedance
Main Bus t, Pt , Qt
Line impedance
Line 1
Line impedance
Line 2
Lines to other loads
Subsystem Bus n, Pn , Qn
Type 1 Loads
Type 2 Loads
I.e. Motors
I.e. Heaters
Type 3 Loads
Type 4 Loads Small Generators
IEEE for SE Task Force Forms
2
⎛V ⎞
⎛V ⎞
⎛V ⎞
= p z ⎜⎜ ⎟⎟ + pi ⎜⎜ ⎟⎟ + p pc + p p1 ⎜⎜ ⎟⎟
Pfrac P0
⎝ V0 ⎠
⎝ V0 ⎠
⎝ V0 ⎠
P
⎛V ⎞
p p 2 ⎜⎜ ⎟⎟
⎝ V0 ⎠
npv 2
(1 + k
pf 2
∆f )
And
p z = 1 − ( pi + p p + p p1 + p p 2 )
npv1
(1 + k
pf 1
∆f ) +
IEEE for SE Task Force Forms (Cont.)
2
⎛V ⎞
⎛V ⎞
⎛V ⎞
Q
= q z ⎜⎜ ⎟⎟ + qi ⎜⎜ ⎟⎟ + q pc + q p1 ⎜⎜ ⎟⎟
Q frac Q0
⎝ V0 ⎠
⎝ V0 ⎠
⎝ V0 ⎠
⎛V ⎞
q p 2 ⎜⎜ ⎟⎟
⎝ V0 ⎠
nqv 2
(1 + k
qf 2
∆f )
And
q z = 1 − (qi + q p + q p1 + q p 2 )
nqv1
(1 + k
qf 1
∆f ) +
Fig 3: Block Reactive Power Model
Voltage
Qt
Reactive
x Qt
X
Power
x
1/T
e
+
Qs (V)
Dynamic and Generic Load
Modeling:
• Assume exponential functions:
dx
Tp
= Ps (V ) − xPt (V )
dt
dy
Tq
= Qs (V ) − yQt (V )
dt
V lo ad P U
Fig 4: Large Disturbance Dynamics
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Pre-disturbance
Post-disturbance
1
2
4
3
3a
4a
Qs
0
0.05
0.1
0.15
Reactive Power PU
0.2
0.25
Fig 5: General approach to Mathematical
Modeling
Load +
Problem
Power System
Identification
UVLS
Model
As seen at
Load Bus
Self
Consistency
Validation
if required
Precautions for use of
Dynamic Model
• Large disturbances verses small
disturbances
• Identification of transient portion of
model
• Model validation before and after
UVLS
• Model validation for both worst case
scenario and most probable scenario
Considerations in Load Modeling
and Model Verification for UVLS
• Demand real time variations
• Load Composition
• Real time nature of UVLS:
– Load portion to be shed
– Speed of shedding
– Undervoltage severity
Approaches in Load Modeling
• Deterministic: every element is modeled in
static or dynamic representation with its
state (On, off or partly loaded)
• Macro-analytical model for the overall
lumped load
• Stochastic with the use of probability
function that would allow some
representation of real time status
Factors Affecting the Selection of
Load Model:
• Load elements (motors, static,
VAR/SVC, in-plant generation)
• System configuration and
contingencies
• Availability of tools such as real time
measurements of P and Q
• Mechanisms of UVLS verses system
contingencies
Factors Affecting the Selection of
Load Model (continued)
• Ability to divide loads into
homogeneous blocks
• Load elements with special nature
(Capacitors, in-plant generation)
• Connection of shedable loads
• Non shedable loads
Future Work in Load Modeling for
UVLS:
• Use of real time measurements
• Applications of mathematical tools
such as Fuzzy logics, neural network)
• Benefit from load modeling for other
applications
Conclusions:
• Static and dynamic load models have progressed
however more work is required
• Approaches: deterministic, generic and stochastic
• Load elements, system configurations and
contingencies and UVLS strategy must be
considered when selecting load model
• When large voltage disturbances are considered,
generic load models that are based on small
system disturbances should be treated with care
• Real time data should be used in model tuning and
verification