Phần 4 KHÓA ĐÀO TẠO TÍNH TOÁN ỔN ĐỊNH VÀ ỨNG DỤNG TRÊN PHẦN MỀM PSSE CHO KỸ SƯ HỆ THỐNG ĐIỆN (Nguyên tắc mô phỏng Ổn định động và thư viện mô hình mô phỏng trên Phần mềm PSSE)

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A Division of Global Power
POWER SYSTEM STABILITY CALCULATION TRAINING
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July 5, 2013Prepared by: Mohamed El Chehaly
eBook for You
OUTLINE
2
OUTLINE
• Basic Dynamic Simulation
• Simulation Model Library
• Numerical Integration Stability
eBook for You
3
BASIC DYNAMIC SIMULATION
BASIC

DYNAMIC

SIMULATION
eBook for You
D
y
namic Simulation of a Ph
y
sical
4
BASIC DYNAMIC SIMULATION
yy
Process
1. Construction of a set of differential
equations describing the behavior of the

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

5
BASIC DYNAMIC SIMULATION
Rocket

Example
eBook for You
Rocket Example
6
BASIC DYNAMIC SIMULATION
Rocket

Example
eBook for You
Rocket Example
7
BASIC DYNAMIC SIMULATION
Rocket

Example
 Newton’s law of universal gravitation in
vector form
 4 differential equations:
x
yx
x
yx
G
dt
dv
m

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

dy

eBook for You
Rocket Example
8
BASIC DYNAMIC SIMULATION
Rocket

Example
 Four variables: x, y, v
x
, v
y
x
y
 If known at instant t, it can be calculated
using at time t + ∆t:
d
dy
t
dt
d
x
xx
oldnew

dv
t
dt
dy

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

new
y



eBook for You
Rocket Example
9
BASIC DYNAMIC SIMULATION
Rocket

Example
eBook for You
Rocket Example
10
BASIC DYNAMIC SIMULATION
Rocket

Example
eBook for You
Rocket Example
11
BASIC DYNAMIC SIMULATION
Rocket

Example
eBook for You
Rocket Example
12
BASIC DYNAMIC SIMULATION

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

m
v
smv
my
x



2211
/.10x67.6
/
6850
kgmNG
s
m
v
y


eBook for You
14
SIMULATION MODEL LIBRARY
SIMULATION

MODEL

LIBRARY
eBook for You
Basic Program Structure
15

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

ti
ons o
f
spec
ifi
c equ
i
pmen
t
eBook for You
Model Subroutine Library
17
SIMULATION MODEL LIBRARY
Model

Subroutine

Library
 Contains the differential equation
i t lli th i t t b
i
n
t
e
lli
gence on
th
e equ
i
pmen

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

NUMERICAL INTEGRATION
STABILITY
STABILITY
eBook for You
Numerical stability
20
NUMERICAL INTEGRATION STABILITY
Numerical

stability
 Achieved only if the time increment ∆t is
sufficiently small in relation to the time
constants and natural frequencies of the
process being simulated
 If ∆t is large inaccurate results and
numerical instability
eBook for You
Discharge of a Capacitor
21
NUMERICAL INTEGRATION STABILITY
Discharge

of

a

Capacitor
 Simple differential equation
q
d

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

a

Capacitor
 First-order integration formula
dq





t
dt
dq
qq
old
oldnew












 t

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

 Write a python script to show the impact of the
time step
 Inputs:
k
R
VV
5
2
15
0


s
RC
T
mFC
k
R
10
4
5
.
2





CCVq
s

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

to 1/4 of the shortest time constant
 To avoid instability problems
 To obtain adequate accuracy
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