100 Chapter 5 AVAILABLE TRANSFER CAPABILITY CALCULATIONS AND CONTINGENCY ANALYSIS IN DEREGULATED POWER SYSTEMS The available transfer capability work is well established [3, 71-89] and introduction about ATC and contingency is given in chapter 1. In this chapter, only methods for computation of ATC, problem formation and algorithm are given. Also computation of ATC for 7-bus system, 26-bus system, IEEE 118-bus system and case studies of 124-bus real-time Indian utility power system of Andhra Pradesh State grid are presented and discussed. A brief description of contingency analysis along with complete results of Andhra Pradesh State grid is presented. 5.1. METHODS FOR COMPUTATION OF TRANSFER CAPABILITY In recent years, there has been a rapidly growing interest for power engineers to formulate and solve this complex transfer capability problem. As a result, many methods and techniques have been developed; very few methods are practical for large realistic applications [81]. Only three of them are practical for large realistic applications. These are follows: 1) Continuation Power Flow (CPF) method [86]
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100
Chapter 5
AVAILABLE TRANSFER CAPABILITY
CALCULATIONS AND CONTINGENCY ANALYSIS
IN DEREGULATED POWER SYSTEMS
The available transfer capability work is well established [3, 71-89]
and introduction about ATC and contingency is given in chapter 1. In
this chapter, only methods for computation of ATC, problem
formation and algorithm are given. Also computation of ATC for 7-bus
system, 26-bus system, IEEE 118-bus system and case studies of
124-bus real-time Indian utility power system of Andhra Pradesh
State grid are presented and discussed. A brief description of
contingency analysis along with complete results of Andhra Pradesh
State grid is presented.
5.1. METHODS FOR COMPUTATION OF TRANSFER
CAPABILITY
In recent years, there has been a rapidly growing interest for power
engineers to formulate and solve this complex transfer capability
problem. As a result, many methods and techniques have been
developed; very few methods are practical for large realistic
applications [81]. Only three of them are practical for large realistic
applications. These are follows:
1) Continuation Power Flow (CPF) method [86]
101
2) Optimal Power Flow (OPF) method.
3) Repeated Power Flow (RPF) method.
CPF is first introduced for determining the maximum loadability,
and is also useful for ATC computation. The advantage of CPF is a
successful method even for ill-conditioned power flow equations and
at voltage collapse points. However a major disadvantage is that it
involves complicated implementation of its parameterization, predictor
and corrector and step-size control elements.
OPF and Security-Constrained OPF (SCOPF) are powerful tools [26]
that have been under very active development for the past 30+ years.
OPF can be used to maximize the power transfer between two areas
assuming that all OPF optimized parameters can be centrally
dispatched needs large number of optimal power flows under different
conditions and needs more time.
The RPF method, power flow equations are repeatedly solved at a
succession of points along the specified load/generation increment,
for TTC calculation. Compared with SCOPF and CPF, the
implementation of RPF is much easier [71].
There are a number of methods and algorithms [76, 78] for
computing TTC, which are discussed in the chapter 1.
5.2. PROBLEM FORMULATION
Referring to Figure 5.1, a simple interconnected power system can
be divided into three kinds of areas, which are: receiving area, sending
102
area and external area. “Area” can be defined in an arbitrary fashion.
It may be an individual electric system, power pool, control area, sub-
regions, etc. which consist of a set of buses. The transfer between two
areas is the sum of the real powers flowing on all the lines which
directly connect one area to the other area. A base case transfer
(existing transmission commitments) is determined, the transfer is
then gradually increased starting at the base case transfer until the
first security violation is encountered. The real power transfer at the
first security violation is the total transfer capability.
R – Receiving area; S – Sending area;
E – External area; .……transfer path
Figure 5.1. A simple interconnected power system
The objective is to determine the maximum real power transfers
from sending areas to receiving area through the transfer path.
During a transfer capability calculation, many assumptions [82] may
arise that would affect the outcome. The main assumptions used in
this study are as follows:
S S
S R
E E
103
• The base case power flow of the system is feasible and
corresponds to a stable operating point.
• The load and generation are changing very slowly so that the
system transient stability is not jeopardized.
• The system steady state stability is maintained with sufficient
damping.
• Bus voltage limits are maintained before the system loses voltage
stability.
Therefore, at this stage only the thermal limits and voltage limits
will be taken into consideration together with generator active and
reactive power limits.
The power flow solution is the most common and important tool in
power system analysis, which is also known as the “load flow”
solution. It is used for planning and controlling to determine the
voltage magnitudes and phase angle of voltages at each bus and
active and reactive power flow in each line. The four quantities
associated with each bus are voltage magnitude, voltage phase angle,
real power injection and reactive power injection.
The Newton-Raphson equations are used in natural power system
form solving for voltage magnitude and angle, given real and reactive
power injections and these can be used in the calculation of transfer
capability [26, 91]. The same thing can express in the mathematical
form as follows [81]:
104
Power Flow Equations:
The complex power injected by the source into the ‘i’ th bus of a
power system is
*
iiiii IVjQPS =+= ; i = 1, 2… n (5.1)
The load flow problem is handled more conveniently by use of Ii
rather than Ii*. By taking the complex conjugate of equation (5.1),
iiiii IVjQPS**
=−= ; i = 1, 2… n (5.2)
Then real and reactive powers can be expressed as
)δδ(θ||Y|V|VP jiijijj
n
j
ii +−= ∑=
cos1
(5.3)
)δδ(θ||Y|V|VQ jiijijj
n
j
ii +−−= ∑=
sin1
(5.4)
and Operational constraints
maxmin GiGiGi PPP ≤≤ (5.5)
maxmin GiGGi QQQ ≤≤ (5.6)
maxijij SS ≤ (5.7)
maxmin iii VVV ≤≤ (5.8)
105
The objective function to be optimized is
∑∉∈
=RkRm
kmrPP
,
(5.9)
The control variables in the above formulation are generator real
and reactive power outputs, generator voltage settings, phase shift
angles, transformer taps and switching capacitors or reactors. The
dependent variables in the formulation are slack bus (swing bus)
active and reactive power injections, regulated bus (generator bus)
reactive power injection and voltage angle. All the equality and
inequality constraints considered in this work are given in the above
problem formulation.
5.3. ALGORITHM FOR REPEATED POWER FLOW
METHOD
Repeated power flow (RPF) method [81] involves the solution of a
base case, which is the initial system conditions, and then increasing
the transfer. After each increase, another load flow is done and the
security constraints tested. The computational procedure of this
approach is as follows:
Step 1. Establish and solve for a base case
Step 2. Select a transfer case
Step 3. Solve for the transfer case
Step 4. Increase step size if transfer is successful
Step 5. Decrease step size if transfer is unsuccessful
106
Step 6. Repeat the procedure until minimum step size
reached
The flow chart of this method is given in Appendix-C.2.
5.4. METHODS FOR COMPUTATION OF AVAILABLE
TRANSFER CAPABILITY
A report by NERC in 1996 establishes a framework for determining
ATC of the interconnected transmission networks for a commercially
viable wholesale market. The report defines ATC principles under
which ATC values are to be computed and it permits individual
systems, power pools, regions and sub regions to develop their
procedure for determining ATC in accordance with these principles.
Reference [79] discussed some theoretical aspects of ATC and the
problem of its evaluation under open access environment.
In [86], a method based on continuation power flow incorporating
limits of reactive power flows, voltage limits as well as voltage collapse
and line flow limits is described. However, with this method, the
computational effort and time requirement are large. In [81], the
topological information of a system is stored in matrix form and
constants for different simultaneous cases and critical contingencies
have been calculated before hand and used for determination of ATC
values. For very large systems, the method may be quite cumbersome.
In [83], the localized linearity of the system is assumed and additional
load required to hit the different limits are separately calculated and
107
the minimum of all these is taken as ATC. Ashwani Kumar et al. [90]
proposed a simple and efficient non-iterative method to calculate ATC
under bilateral and multilateral contracts based on ACPTDF. The
ACPTDFs have been calculated at base case NRLF results utilizing a
sensitivity-based approach.
METHODS BASED ON DISTRIBUTION FACTORS:
In order to consider line flow (MW) limits for static AC
determination under the system intact, AC power transfer distribution
factors is used. To consider voltage limits in ATC determination under
the normal cases Voltage Distribution Factors [VDF] are used.
1. AC POWER TRANSFER DISTRIBUTION FACTORS
Consider a bilateral transaction ‘tp’ between a seller bus, ‘m’ and
buyer bus, ‘n’. Further consider a line, ‘l’ carrying a part of the
transaction power. Let the line be connected between a bus-i and a
bus-j. For a change in real power transaction between the above seller
and buyer, say, by ‘∆ tp’ MW, if the change in transmission line
quantity ‘ql’ is ‘∆ql’, the AC power transfer distribution factors can be
defined as:
(ACPTDF)ql-tp p
l
t
q
∆
∆ (5.10)
The transmission quantity ‘ql’ is taken as real power flow from bus-
i to bus-j.
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2. VOLTAGE DISTRIBUTION FACTORS
Voltage Distribution Factors (VDFs) are defined as the change in
the bus voltage magnitude ‘∆Vi’ at any bus-i to the change in the pth
transaction, say, by ‘∆ tp’ between seller bus and the buyer bus. Let
the base case voltage magnitude at any bus-i be ‘Vi0’ and, after the
change due to a transaction, the new bus voltage be Vi-tp. The voltage
distribution factors are defined as:
VDFi-tp=p
i
t
V
∆
∆ (5.11)
Where, ∆Vi = Vi-tp – Vi0
5.4.1. PROBLEM FORMULATION FOR DISTRIBUTATION FACTORS
ATC determination using ACPTDF and Voltage distribution factors:
The distribution factors have been computed with the base case
load flow results using the sensitivity properties of the NRLF Jacobin.
The procedure for calculation of these distribution factors is described
below:
Consider the sensitivity relationship provided by the Newton-
Raphson load flow equations in the polar coordinates for a base case
load flow as:
∆V
∆δ = [ ]TS
∆Q
∆P (5.12)
Where, ST = [ ] 1−
TJ is a sensitivity matrix and JT is the full Jacobian
defined for all the buses except for the slack bus.
109
At a base case load flow, if only one of the bilateral transactions,
say the pth transaction, between a seller bus, ‘m’ and a buyer bus, ‘n’
is changed by ‘∆ tp’, only the following two entries in the mismatch
vector [ ∆P, ∆Q ] T of equation (5.12) will be non-zero.
∆Pm = ∆ tp, ∆Pn = -∆ tp (3.13)
With the above mismatch vector, changes in the voltage angle and
voltage magnitude at all the buses can be computed from equation
(5.12), and hence, a new voltage profile can be calculated. These can
be utilized to compute new values of transmission quantity ‘ql’ and
thus the change in the quantity ‘∆ql’ from the base case. Once ‘∆ql’ is
known for all the lines and change in the voltage magnitude is
computed at all the buses corresponding to a transaction ‘∆ tp’, the
ACPTDFs and VDFs for each line and buses, respectively, can be
obtained from (5.10) and (5.11).
ATC from a bus/zone ‘m’ to another bus/zone ‘n’ can be found
using the full AC load flow by varying the amount of transaction until
one or more line flows in the transmission system considered or a bus
voltage at some bus reaches the limiting value. However this method
is computationally involved. Instead, the distribution factors
described above can be used to quickly calculate ATC considering
both the line flow limits and voltage limits, as follows.
110
i) ATC for base case, between bus/zone ‘m’ and bus/zone ‘n’
using the line flow limit criterion has been calculated using
ACPTDFs as
ATCmn = min
∈−
l
ij,mn
ijijNij
PTDF
)P(P 0max
(5.14)
Where,
Pijmax is the MW power flow limit of a line between bus-i and bus-j.
Pij0 is the base case power flow in the line between bus-i and bus-j.
PTDFij-mn are the Power Transfer Distribution Factors for the line
between bus-i and bus-j, when ‘Nl’ is the total no. of lines.
ii) Similarly ATC at base case considering voltage limit violation
can be calculated as:
ATCmn = min
∈−
−
B
i,mn
iti NiVDF
)V(Vmin
(5.15)
Where,
Vi-t is the voltage at bus-i under change in the transaction tp.
Vimin is the minimum voltage limit at each bus-i.
VDFi-mn is the voltage distribution factor at bus-i, when the
transaction is taking place between bus/zone ‘m’ and bus/zone ‘n’
and ‘NB’ is the total number of buses.
111
CONTINGENCY ANALYSIS
5.5. INTRODUCTION
With the global development towards the deregulation in the power
system industry, the volume and complexity of the CA results in the
operation and the system studies have been increasing. Not only has
deregulation resulted in much larger system model sizes, but also CA
is computed more frequently in the restructured power markets to
monitor the states of the system under “what if” situations in order to
accommodate the maximum number of power transfers. The net
impact of these changes is a need for more effective CA results are
required to help with the comprehension of the essential security
information, information which could be buried in the enormous and
complex CA data sets [29], [30].
The CA application is based on detailed electrical model of power
system, called the “network model”. This is a simulated model of the
real power system that is prepared by each utility’s system planners
and network engineer specialists. They translate the real world
equipment and connections of a power system (one –line diagram) into
a mathematical model of the power network that is suitable for
solution by computer algorithms. This network model contains the
connection information and electrical characteristics of the
equipment. The algorithm in contingency analysis uses this network
information and the network model to simulate, and calculate the
112
effects of, removing equipment from the power system. With an
initialized power network model, CA now can be executed with a
series of contingency events that is prepared by the CA user. A
“contingency list” contains the each of the elements that will be
removed from the network model, one by one, to test the effects for
possible overloads of the remaining elements. The criteria for selection
of elements for the contingency events are further described below.
In its basic form, CA executes a power flow analysis for each
potential problem that is identified on a contingency list. The voltages,
currents, real and reactive power flows (MW and Mvar) in each part of
the power system can be obtained from power flow solution in
contingency analysis. Results of each contingency test and the
network solution are compared with the limits for every element in the
power system. The lists of violations are saved in the CA data base.
CA actually provides and prioritizes the impacts on an electric
power system when problems occur. Contingency is also called an
unplanned "outage". CA is a computer application that uses a
simulated model of the power system, to evaluate the effects, and
calculate any overloads resulting from each outage event. In other
word, CA is essentially a "preview" analysis tool that simulates and
quantifies the results of problems that could occur in the power
system in the immediate future. This analysis is used as a study tool
for the off-line analysis of contingency events, and as an on-line tool
to show operators what would be the effects of future outages. It
113
allows operators to be better prepared to react to outages by using
pre-planned recovery scenarios.
After a contingency event, power system problems can range from:
• None: When the power system can be re-balanced after a
contingency, without overloads to any element.
• Severe: When several elements such as lines and transformers
become overloaded and have risk of damage.
• Critical: When the power system becomes unstable and will quickly
collapse.
By analyzing the effects of contingency events in advance,
problems and unstable situations can be identified, critical
configurations can be recognized, operating constraints and limits can
be applied, and corrective actions can be planned.
5.6. METHODS OF CONTINGENCY ANALYSIS
The following are the various methods used for contingency
analysis purpose.
• DC load flow method of contingency analysis
• Z-matrix method of contingency analysis
• Voltage stability index (L-index) computation
• Decoupled load flow
• Fast decoupled load flow
114
The tool for detecting overloads is analyzing contingency of the
power system planner which should have execution speed and ease of
detection are the vital considerations. Among the methods mentioned
above, AC power flow calculations methods are accurate when
compared to DC power flow methods but they are a bit complex and
need more execution time.
5.7. RESULTS AND DISCUSSION OF ATC
Results of the ATC for 7-bus, 26-bus, IEEE 118-bus systems and
124-bus Indian utility power system of Andhra Pradesh State grid are
presented and analyzed are given below:
5.7.1. 7-bus System
The computations were done on 7-bus test system with 3-areas as
shown in Figure 5.2. Data for this system is given in Appendix A.1.
Figure 5.2. 7-bus test system
115
The system has been divided into three areas, namely; area A, area
B and area C. Area A includes buses 1, 2, 3, 4 and 5. Area B consists
of bus 6 whereas area C consists of bus 7.
5.7.1.1. Model calculation for PTDF:
The PTDF values are calculated by use of the power world
simulator software with lossless DC approximation and are given in
Table 5.1.
Table 5.1: PTDF values of 7-bus system
S.no. From bus To bus % PTDF
1 1 2 80.41
2 1 3 19.59
3 2 4 2.47
4 2 5 46.47
5 2 6 32.16
6 3 4 18.91
7 4 5 21.38
8 5 7 67.84
9 6 7 32.16
5.7.1.2. Model calculation for ATC:
ATC is calculated by use of the equation (5.14).
ATC =
∈−
l
ij,mn
ijijNij
PTDF
)P(P 0max
Consider a transmission line connected between bus 2 and 6, then
the maximum power limit is max
ijP = 160MW,
116
The power flow in the line in base case is 0
ijP =74.7MW
and PTDF from Table 5.1 is 0.3216
Then ATC = (160- 74.7)/ (0.3216) = 265 MW
Similarly, ATC is calculated for the remaining part of 7-bus system,
26-bus system, IEEE 118- bus system and 124-bus real-time Indian
utility power system of Andhra Pradesh State grid.
ATC values of 7-bus system are shown in Table 5.2.
Table 5.2: 7-bus case, ATC data
Transfer
areas
Transfer
buses
ATC
(MW)
Limiting
line
A-B
1-6 54 1-2
2-6 265 2-6
4-6 281 2-6
A-C
1-7 56 1-2
2-7 106 2-5
4-7 152 4-5
B-C 6-7 111 6-7
5.7.2. 26-bus system
ATC is calculated from all generator buses to normally heavily
loaded load buses by use of PTDF’s, and variation of ATC is given in
Tables 5.3 to 5.8 for different load conditions vary from 50% to 100%.
Thermal limits used for calculating ATC are given in Appendix A.2.
117
Table 5.3: Variation of ATC from bus 1 to other buses of 26-bus