Power System Security Analysis With Renewable Energy ... - IIT Mandi

Power System Security Analysis With
Renewable Energy Systems
Trapti Jain
School of Computing and Electrical Engineering
Indian Institute of Technology Mandi

Outline
• Power System Security
• Security in Restructured Power System
• Review of Load Flow Analysis
• Load Flow Analysis with Wind Farm
• Load Flow Analysis with Photovoltaic System

Power System Security
•It is the ability of the system to withstand credible
contingencies without violating the normal operating
limits.
• Classified as
Static security
static security evaluation detects any potential
overload of a system branch or an out of limit voltage following a
given list of contingencies
Transient security
transient security evaluation pertains to system
dynamic behaviour in terms of rotor angle stability when
subjected to perturbations

Security Analysis
Outages of component(s)
Overstress on the other
components
No limit violation
limit violation(s)
operation of protective
devices and switching of the
unit(s)
partial or total loss of
load

Functions of System Security
System
Monitoring
System
Security
Contingency
Analysis
Security
Constrained
OPF

Contingency Analysis Procedure
START
SET SYSTEM MODEL TO
INITIAL CONDITIONS
SIMULATE AN OUTAGE OF A
GENERATOR OR A BRANCH
SELECT A
NEW OUTAGE
LIMIT VIOLATION
Y
ALARM MESSAGE
N
N
LAST OUTAGE
END
Y

Real-time applications require fast and reliable computation methods due to the high
number of possible outages in a moderate power system.
However, there is a well-known conflict between the accuracy of the method applied
and the calculation speed.
Exact solution
Full AC power flow
for each outage
Check the limit
violations
not feasible
for realtime
applications
.
approximate methods to quickly
identify conceivable
contingencies
real-time applications
AC power flows only for
critical contingencies.
Check the limit violations

APPROXIMATE CONTINGENCY ANALYSIS
Contingency ranking
• contingencies are ranked in an approximate order
of a scalar performance index, PI.
• contingencies are tested beginning with the most
severe one and proceeding down to the less
severe ones up to a threshold value.
• Masking effect causes false orderings and
misclassifications.
Contingency screening
• Explicit contingency screening is performed for all
contingencies, following an approximate solution
(DC load flow, one iteration load flow, linear
distribution or sensitivity factors etc.)
• Contingency screening is performed in the near
vicinity of the outages (local solutions)
Hybrid methods utilizing both the ranking and the screening

Security in Restructured Power Systems
•In deregulated environment, System Operator (SO) is
responsible for secure operation of the power system.
•Available Transfer Capability is a term defined to
reflect additional secure power transfer in the electricity
market environment.
•Congestion management is one of the major task
performed by SO to ensure system security.

Available Transfer Capability (ATC) Definition *
“ATC is a measure of the transfer capability remaining in the
physical transmission network for further commercial activity over
and above already committed use”.
Mathematically,
ATC = TTC – TRM – {ETC + CBM}
ETC: Existing Transfer Commitment
TTC: maximum amount of power which can be transferred over the
network while satisfying all security constraints.
TRM: margin required for uncertainties in the transmission system
conditions
CBM: margin reserved by load serving entities for generation
reliability requirements.
*
North American Electric Reliability Council (NERC), Available Transfer Capability Definitions and
Determination, NERC Report, June 1996.

ATC and Related Terms (NERC Report)
TRM – Transfer Reliability Margin
CBM – Capacity Benefit Margin
ATC – Available Transfer Capability
TTC – Total Transfer Capability
ETC - Existing Transfer Commitments
Usually, the TRM and CBM are decided by the utilities according to their
specific system condition and reliability requirements. Thus, the ATC can
be defined as,
ATC = TTC – ETC

ATC Determination
1. Static ATC Methods
• Line flow limits
• Bus voltage limits
•Generator real and reactive power
limits
• Static voltage stability limit
• Repetitive power flow based methods
•Continuation power flow based
methods
• Sensitivity based methods
•Optimal power flow based methods
2. Dynamic ATC Methods
• Line flow limits
• Bus voltage limits
•Generator real and reactive power
limits
• Small signal stability limit
• Large signal stability limit
• Trajectory sensitivity based
methods
• Energy function based methods
• Optimal power flow based
methods
• Single Machine Equivalent
(SIME)

Methods of Congestion Management
• Price Area based Congestion Management
- areas with excess generation will have lower prices,
and those with excess load will have higher prices
• ATC based Congestion Management
- use ATC information available there to determine if
system could accommodate transaction.
• OPF based Congestion Management
- optimal power flow (OPF) is performed to minimize
generators’ operating cost subject to set of constraints that
represent a model of the transmission system within which the
generator operate

Objective of Load Flow Analysis
•To determine the static operating state of the
power system for given loads
•To determine voltage magnitude and angle at
all the buses
•To determine line flows and system losses

Classification of load flow methods
• Deterministic Load Flow (DLF)
- a set of deterministic values are chosen by
the analyst for each input variable
- accuracy depends on the knowledge of the
input data
- ignores grid uncertainty
• Probabilistic Load Flow (PLF)
- utilizes different mathematical approaches
such as probabilistic approach, fuzzy sets, interval
analysis etc. for taking into account uncertainty
- requires inputs with PDF or CDF

DLF with Conventional Generators
Main steps to perform load flow analysis
• Develop the mathematical model of various elements
•Write the network equations relating current and
voltages
•Identify the nature of equations and apply suitable
solution technique

Mathematical Model of Various Elements
• Transmission line - nominal equivalent π model is used
• Transformers - equivalent π model is used
⎧A
=
⎪
⎨B
=
⎪
⎩C
=
y
12
/ a
(1/ a −1)
⋅ y
(1 −1/
a).
y
12
12
/ a
• Loads - constant power model
• Generators - real and reactive power output l

Bus Admittance Matrix or Y bus
• First step in solving the power flow is to create the bus
admittance matrix, often called the Y bus
.
• The Y bus
gives the relationships between all the bus
current injections, I, and all the bus voltages, V,
I = Y bus
V
• The Y bus
is developed by applying KCL at each bus in the
system to relate the bus current injections, the bus
voltages, and the branch impedances and admittances.
• The diagonal elements are the self admittance terms,
equal to the algebraic sum of all the primitive value of
admittances incident at the node or bus.
• The off-diagonal terms are equal to the negative of the
admittance connected between the two buses.

Load Flow Equations
Applying KCL at each bus-i, in an n-bus system, the
current injection I i
, is given by
I
i
=
I
ij
+
I
ik
+ ....... I
in
=
n
∑
v=
1
I
iv
Since I=Y bus
V, we also know
I
i
=
n
∑
j=
1
The net complex power injected into a bus-i is given by
*
S = P + jQ = V I
i
i
i
Taking complex conjugate of above equation,
*
P − jQ = V I
i
i
Y
ij
V
i
i
j
i
i

Load Flow Equations, Contd.
*
( Pi
− jQi
) = ( PGi
− PDi
) − j( QGi
−QDi
) = Vi
YijV
j
In polar form,
( P − jQ ) = ( P − P ) − j( Q − Q )
=
i
n
∑
j=
1
VV Y
i
i
j
ij
Gi
V Y V
Separating into real and imaginary parts
n
∑
j=
1
[ cos( δ −δ
−θ
) − j sin( δ −δ
−θ
)] i = 1,2,.... n
i
Di
j
ij
Gi
Di
=
i
n
∑
j=
1
j
i
ij
ij
j
∠δ
−δ
i
j
−θ
ij
P
i
=
P
Gi
−
P
Di
=
n
∑
j=
1
VV Y
i
j
ij
cos( δ − δ
i
j
−θ
ij
)
i
= 1,2,..... n
Q
i
=
Q
Gi
− Q
Di
=
n
∑
j=
1
VV Y
i
j
ij
sin( δ
i
− δ
j
−θ
ij
)
i
= 1,2,..... n

Classification of Buses
PQ bus PV bus Slack
bus
- Load bus
- Buses to which only
loads are connected
- Real and reactive
powers are specified
- Load flow solution
determines voltage
magnitude and angle
- Generator bus or voltage
controlled bus
- Buses to which generators
or reactive power sources
are connected
- Real power and voltage
magnitude are specified
- Load flow solution
determines reactive power
and angle
- Reference bus or
swing bus
- A generator bus
having largest output
- Real and reactive
powers are specified
- Load flow solution
determines voltage
magnitude and angle

Numerical Solution Techniques
• Gauss Iterative and Gauss-Siedel methods
• Newton-Raphson method
- Rectangular coordinates
- Polar coordinates
• Fast Decoupled Load Flow method

NRLF method in Polar coordinates
The power flow equations in polar coordinates can be
written as,
P
i
Q
i
=
=
n
∑
j=
1
n
∑
j=
1
VV
i
VV
i
j
( G cosδ
+ B sinδ
)
j
ij
i = 2,..... n
( G sinδ
−B
cosδ
) i = m + 1,..... n
ij
ij
ij
ij
ij
ij
ij
where,
δ
ij
=
δ
i
− δ
j
The correction vector can be written as
∆V
∆δ
n
∆δ
n
∆V
/ V
2
m+
1
/ V
n
∂P
∂P
H = L = V
= ∂δ
∂V
∂Q
∂Q
M = N = V
∂δ
∂V
∆P
∆P
∆Q
n
∆Q
m+
1
2
n

Computational steps to solve load flow problem
Step 1: Read network admittances, generator, load and
transformer data
Step 2: Form Y bus
matrix
Step 3: Assume initial values of bus voltages except at
slack bus. Initialize iteration count K to zero.
Step 4: Compute P at all buses except slack bus and Q
at all the load buses. Calculate ∆P at all buses
except slack bus, ∆Q at all the load buses.
Step 5: If all the elements of mismatch vectors (∆P, ∆Q)
are within the prespecified tolerance, load flow
solution is achieved. Calculate slack bus power,

Contd.
Step 6: Assemble Jacobian matrix, find its inverse and
calculate correction vector
Step 7: Update angles at all the buses except slack bus
and voltages at all the load buses and go to
step 4
The reactive power limits of generators can be
checked at step 4. If the calculated reactive
power of any PV bus is within the limit, it is
retained as PV bus. If it violates the limit, the
generator output is fixed to the limiting value
and the bus is solved as PQ type for that
particular iteration, with specified value of Q
taken as difference between the limiting value
and the calculated value.

Steady State Model of Wind Farm
• As a negative load (PQ bus)
- assumes a generated real power and a given power factor,
with which the consumed reactive power is calculated.
• As a voltage controlled (PV bus)
- when the voltage at the connection point need to be
controlled at normal voltage by providing reactive power support
• PX bus model
- the real power is known and the reactive power is calculated
as a function of the magnetizing reactance of the generator
• RX bus model
- assumes resistance and reactance of both stator and rotor
as well as the mechanical output power P m
to be known variables

Steady State Model of Wind Farm, Contd.
An improved PQ bus model has been proposed considering the
steady state properties of the induction generator, such that the
reactive power Q is calculated by
Q
≈V
2
⎛
⎜
⎝
X − X
X X
c m
+
c
where, X c
is capacitive reactance
X m
is magnetizing reactance
X is sum of stator and rotor reactances
V is terminal voltage
P is real power of the generator
The improved PQ bus model requires that the specified
reactive power Q be updated after each iteration of the load
flow
m
⎞
⎟ ⎠
X
V
*
A.E. Feijoo and J. Cidras, “Modeling of Wind Farms in the Load Flow Analysis”,
IEEE Transactions on Power System, Vol. 15, No. 1, Feb. 2000, pp. 110-115
2
P
2

PX bus model
• Constant reactance model
- assumes a constant active power generation and a
constant magnetizing reactance, neglecting the stator and
rotor reactances
- constant relation between the voltage level and the
reactive power consumption
• Variable reactance model
- considers saturation of magnetic circuit
- models magnetizing reactance as voltage
dependent

R
( s)
=
Let R(
s)
P
eq
IG
( V , s)
2
r
R
s
+ ( X
= R + R
=
R
s
2
R
r
X
s
m
V
eq
( s)
+
2
m
2
+
( s)
X
X
2
r
)
( s)
2
and
;
X
R(
s)
eq
( s)
=
X ( s)
=
;
Q
X
IG
R
s
r
+
X
s
2
m
2
r
R
s
X
eq
+
( V , s)
=
X
( s)
R
m
+ ( X
2
X
m
r
V
( s)
+
( X
+
2
X
X
m
r
2
)
+
2
( s)
X
r
)
X ( s)
*
N. paensuwan and A. Yokoyama, “Risk-based TTC calculation of a power system
with renewable energy resources”, IEEE Power Tech Conference, 2009

Contd.
This PX model introduces a new state variable i.e. the rotor
slip. Therefore, another equation is required to enforce P IG
to its specified value. The power balance equations are
modified as follows.
f
f
Pi
Qi
=
=
( δ , V ) − ( P
( δ , V ) − ( −Q
) = 0
To enforce P IGi
to its specified value, the following equation
is added.
spec
f P IGi
− P
− Q
The augmented power flow problem is
⎡ ∂f
P
⎢
∂δ
⎢
∂f
⎢ Q
⎢ ∂δ
⎢ ∂f
PIG
⎢
⎣ ∂δ
F
F
Pi
Qi
spec
IGi
Di
Di
IGi
( V
( V , s ) = −P
( V , s ) − P = 0
i
∂f
i
∂V
∂f
Q
∂V
∂f
P
P
IG
∂V
∂f
IGi
∂s
∂f
Q
∂s
∂f
P
P
IG
∂s
i
i
IGi
⎤
⎥
⎥⎡∆δ
⎤ ⎡ ∆f
⎥⎢
⎥ ⎢
⎢
∆V
⎥
= ⎢ ∆f
⎥
⎥⎢
⎥ ⎢
⎣ ∆s
⎦ ⎣
∆f
⎥
⎦
Q
P
P
IG
⎤
⎥ ⎥⎥ ⎦
i
, s
i
)) = 0

RX bus model
Equivalent circuit of induction generator
Voltage obtained from each iteration of load flow is used to calculate the slip
2 (1 −s)
P m
= R2
⋅ I
2
⋅
s
where,
I
2
=
−
Vt
[( R1
+ R2
/ s)
+ j(
X1
+ X
2)]
Once, the slip is known, power injections can be calculated
P
g
Q
g
= −V
t
= −V
t
2
2
⋅
( R
1
( R
⋅
1
( R1
+ R2
/ s)
+ R
2
/ s)
+ ( X + X
2
+ R
X
2
m
/ s)
⋅
2
1 2 m 1
2
2
((
R + R / s)
+ ( X + X ) )
1
1
+ ( X
2
+ X
2
)
2
) ⋅(
X
1
+ X
2
+ X
2
)

Solution Techniques of PLF
Numerical Method
•DLF is performed a large
number of times with inputs of
different combinations of nodal
power values
•exact non-linear form of load
flow equations can be used
•Monte Carlo simulation is
used
•time consuming
Analytical Method
•analyzes a system and its
inputs using mathematical
expressions
•uses linearized load flow
equations
•complicated mathematical
computation
•inaccurate due to different
approximations

Probabilistic Model of Wind Farms
• Probabilistic model of the wind speed
Weibull distribution is the best pdf for the description
of a wind speed
1
k ⎛ v − v ⎡
0 ⎞ ⎛ v − v0
f ( v)
= ⎜ ⎟ exp ⎢−
⎜
c ⎝ c ⎠ ⎢⎣
⎝ c
k − k
where, v is wind speed
v 0
is cut-out speed
k is shape parameter
c is scale parameter
⎞
⎟
⎠
⎤
⎥
⎥⎦
*
L. Dong, W. Cheng, H. Bao and Y. Yang, “Probabilistic Load Flow analysis for
power system containing wind farms”, IEEE 2010

Probabilistic Model of Wind Farms, Contd.
• Probabilistic model of wind turbine
P
w
⎧0
⎪
k1v
+
= ⎨
⎪ Pr
⎪
⎩0
P
k
2
v ≤
v
r
vci
≤ v ≤
vr
≤ v ≤
v > v
co
r
k1 = ; k2
= −k1
vr
−vci
v
v
v
ci
r
co
P
P r
0 v ci
v r
v co
Wind Turbine power output
curve curve
v
where, P r
is rated output power
v r
is rated wind speed
v ci
is cut-in speed
v co
is cut-out speed

Probabilistic Model of Wind Farms, Contd.
•Probabilistic distribution of the active power generated by
WT
F(
P
w
w
)
f ( P )
=
=
v
v
ci
∫
co
F
'
f ( v)
dv +
( P
w
)
=
Pw
−k
k
∫
v
1
ci
2
k ⎛ P
⎜
k1c
⎝
f ( v)
dv
w
−
k1v
k c
1
co
⋅ exp
•Probabilistic distribution of the reactive power absorbed
by WT
−
k
2
⎞
⎟
⎠
k −1
⎡ ⎛ P
⎢−
⎜
⎢⎣
⎝
w
−
k1v
k c
1
co
−
k
2
⎞
⎟
⎠
k
⎤
⎥
⎥⎦
f ( Q ) = tan θ
w
w
⋅
k
k c
1
⎛
⎜
⎝
P
w
−
k1v
k c
1
co
−
k
2
⎞
⎟
⎠
k −1
⋅exp
⎡ ⎛
⎢−
⎜
⎢⎣
⎝
P
w
−
k1v
k c
1
co
−
k
2
⎞
⎟
⎠
k
⎤
⎥
⎥⎦

AC Probabilistic Load Flow Model
Linearized Load Flow Model
⎧ w = f ( x)
⎨
⎩ z = g(
x)
;
⎪
⎧ ∆x
= J
⎨
⎪⎩ ∆z
= G
−1
0
⋅ ∆w
= S
Step 1: Input the system data and wind farm data
Step 2: Run the DLF using NR method, so that the
expected values of nodal voltages,line flows,
S 0
, and T 0
are obtained.
Step 3: Compute the cumulants of generation and load
according to their probabilistic distribution
Step 4: Compute the cumulants of the generated active
⋅ ∆ w
power, absorbed reactive power, power
injections and state variables (∆x and ∆z)
Step 5: Obtain the PDF and CDF of ∆x and ∆z
0
⋅ J
−1
0
0
⋅ ∆ w
⋅ ∆ w = T
0

Load Flow with AC-DC Systems
• Unified method
- solution vector is extended with the dc
variables
- complex to program and hard to combine
with developments in ac power flow solution
techniques such as fast decoupled method
• Sequential method
- ac and dc equations are solved separately
in each iteration
- easy to implement, but convergence
problems are there

Model of Photovoltaic Systems
PV
P
Array PV
V PV
I PV
Inverter
M, α
P i
, Q i
V i
Three
phase
system
P g
, Q g
Block diagram of grid connected PV system
• Model based on characteristics of PV array
•Model based on characteristics of specific
inverter structure
• Overall PV system model
Y.B. Wang, C.S. Wu, L. Hua and H.H. Xu, “Staedy-state model and power flow
analysis of Grid-Connected Photovoltaic Power System”,

Model of Photovoltaic Systems, Contd.
• DC part model
I
cell
=
d(
VI)
dV
I
L
mpp
− I
=
=
0
I
I
= 0
⎡ ⎛ Vcell
+ I
⎢exp⎜
⎣ ⎝ a
mpp
mpp
+ V
+ V
mpp
mpp
dI
dV
aR
cell
sh
mpp
R
s
− I
+ I
⎞ ⎤
⎟ −1⎥ ⎠ ⎦
− V
0
0
cell
+ I
R
sh
cell
R
⎛ Vmpp
+ ImppR
Rsh
exp⎜
⎝ a
⎛ Vmpp
+ I
RsRsh
exp⎜
⎝ a
s
s
mpp
⎞
⎟ − a
⎠
Rs
⎞
⎟ + aR
⎠
s
(1)
(2)
where, I cell
and V cell
are the current and voltage of PV cell
I L
and I 0
are the light current and diode reverse saturation
current
R s
and R sh
are the series and shunt resistance
a is the ideality factor

Model of Photovoltaic Systems, Contd.
V
I
P
PV
PV
PV
= N
= N
= V
s
pp
PV
N
I
I
ss
cell
PV
V
cell
(3)
(1)
where, I PV
, V PV
, and P PV
are the current, voltage and power of the
PV array
N s
is the series number of PV cell in a PV module
N ss
is the series number of PV modules
N pp
is the parallel number of PV modules
• Inverter part model
2
V
i
= Vi∠α
= MVPV
∠α
; Pi
=
4
P
PV
(4) ; (5)
where, M is amplitude modulation ratio
α is phase shift angle

Model of Photovoltaic Systems, Contd.
• AC part model
⎥
⎦
⎤
⎢
⎣
⎡
+
+
−
−
=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
−
−
=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
+
+
=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
−
+
=
23
23
12
12
12
12
23
23
12
12
12
12
12
12
13
13
12
12
12
12
13
13
12
12
sin
sin
)
sin(
3
cos
cos
)
cos(
3
)
sin(
sin
sin
3
)
cos(
cos
cos
3
φ
φ
φ
θ
α
φ
φ
φ
θ
α
φ
α
θ
φ
φ
φ
α
θ
φ
φ
z
V
z
V
z
V
V
Q
z
V
z
V
z
V
V
P
z
V
z
V
z
V
V
Q
z
V
z
V
z
V
V
P
g
g
g
i
g
g
g
g
g
i
g
g
g
g
i
i
i
i
g
g
i
i
i
i
(6)
(9)
(8)
(7)

Operation Modes of Grid-connected PV system
There are nine unknown variables of model and seven
independent equations (1), (4-9)
• Mode 1: PV system applies MPPT strategy and unit
power factor. In this mode, (2) is added and Q g
is set to zero. Then V PV
and P PV
can be carried
out by (1) to (3), and other variables can be
solved by (4) to (9)
• Mode 2: PV system applies MPPT strategy and exports a
certain amount of reactive power. In this mode,
the PV system can provide reactive power and
voltage support for power grid.

Input parameters of
power grid, PV system
and meteorology
Set V g
=rated value,Q g
=0, and solve
PV system model to achieve
M,α,V PV
,P PV,
V i
,P i
,Q i
and P g
PQ type
Traditional power
flow analysis
Node type of
PVPCC
PV type
Traditional power
flow analysis
Set the
parameter at the
limit
Yes
Solve PV system model
to achieve M,α,V PV
,P PV,
V i
,
P i
,Q i
,P g
and Q g
If any
parameter
exceeds a
limit No
If the iteration
converges
No
Yes
Output operating
parameters of PV
system and power grid

Thank You