TRANSMISSION &
DISTRIBUTION
A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
D2
DiSiltiPiilPt1
D
ay
2
-
D
ynam
i
c
Si
mu
l
a
ti
on
P
r
i
nc
i
p
l
es
P
ar
t

physical system
physical

system
2. Determination of a set of values of
constant and variable parameters
constant

and

variable

parameters

describing, in detail, the condition of the
p
h
y
sical s
y
stem at some instant
py y
3. Integration of the differential equations
with the values determined in Ste
p
2 as
p
initial conditions
eBook for You
Rocket Example





22
22
y
yx
y
yx
G
dt
dv
m




22
22
(1.1)
x
dy
v
dt
dx

y
v
dt

yy
ld
oldnew



(1.2)
dv
t
dt
dv
vv
y
old
new
x
o
ld
x
new
x



t
dt
vv
y
old
y

Rocket

Example
eBook for You
Rocket Example
13
BASIC DYNAMIC SIMULATION
Rocket

Example
 Python script
 Write a python script using the described
sequence
 Inputs:
7
7
10
222
6
10x134.2 mx 
7
/
6850
/3710
10
x
222
.
6
s

SIMULATION MODEL LIBRARY
Basic

Program

Structure
eBook for You
PSS®E Main Skeleton
16
SIMULATION MODEL LIBRARY
PSS®E

Main

Skeleton
 Contains logic for:
 Data input
 Data output
 Numerical integration
 Electric network solution
 Does not contain logic for:

Diff ti l ti f ifi i t

Diff
eren
ti
a
l
equa

t

t
o
b
e
simulated
 Called whenever the main skeleton logic
needs numerical values of time derivatives
eBook for You
Model Connection Subroutine
18
SIMULATION MODEL LIBRARY
Model

Connection

Subroutine
 Most models are called directly by PSS®E
 Other models may require user input or
are called throu
g
h linkin
g
routines CONEC
gg
and CONET (such as switched shunt
models)
eBook for You
19

q


Exact solution is
T
q
dt
q


Exact

solution

is


Tt
eqtq
/
0


eBook for You
Discharge of a Capacitor
22
NUMERICAL INTEGRATION STABILITY
Discharge

of

T
q
qq
old
oldnew








T
t
qq
oldnew
1
eBook for You
Discharge of a Capacitor
23
NUMERICAL INTEGRATION STABILITY
Discharge

of

a

Capacitor
 Python script

RC
T
06.0
10
0

eBook for You
Discharge of a Capacitor
24
NUMERICAL INTEGRATION STABILITY
Discharge

of

a

Capacitor
eBook for You
PSS®E Numerical Integration
25
NUMERICAL INTEGRATION STABILITY
PSS®E

Numerical

Integration

 Second-order Euler numerical integration
algorithm
 Time step should be kept smaller than 1/5