Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
INTERNATIONAL
JOURNAL OF ELECTRICAL
ENGINEERING &
30-31, December, 2014, Ernakulam, India
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 12, December (2014), pp. 111-122
© IAEME: www.iaeme.com/IJEET.asp
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IJEET
©IAEME
GA BASED OPTIMAL FACTS CONTROLLER FOR
MAXIMIZING LOADABILITY WITH STABILITY
CONSTRAINTS
VISHNU J*,
RISHI MENON**, TIBIN JOSEPH***,
CHITTESH V C*, VIPIN DAS P*,
SASIDHARAN SREEDHARAN****,
SEBIN JOSEPH*
*PG Scholar, Electrical & Electronics Engineering Department, Saintgits College of Engineering, Kottayam, India,
**Asst. Professor, Electrical & Electronics Engineering Department, Saintgits College of Engineering, Kottayam, India,
***Marie Curie Early Stage Researcher, Institute of Energy, Cardiff University, Cardiff, UK
****Postdoctoral Researcher, Renewable Energy Design Laboratory, University of Hawaii, USA,
ABSTRACT
Nowadays, the electric load demand has been continuously increasing all over the world. But, due to economical
and environmental restraints, the expansion of existing power system is limited. The sudden increase in load demand
enforces power systems to operate closer to the limits of instability. Loading margin of existing power system can be
enhanced by optimal placement and setting of FACTS devices to accomplish more power transfers with less network
expansion cost. This paper presents a Genetic Algorithm (GA) based methodology to find the optimal location and
setting of FACTS devices in order to improve the loading margin as well as voltage stability and small signal stability.
The objective function is formulated as maximizing the loadability of the power system with load generation balance as
equality constraint as well as voltage stability, generation limit and line limit constraints as inequality constraint. IEEE 14 bus standard system is taken into consideration to test the efficiency of the proposed approach using MATLAB/PSAT
environment.
Keywords: Genetic Algorithm, IEEE-14 bus standard system, Loading Margin, Optimal placement, Power system,
Stability, STATCOM.
1. INTRODUCTION
Recently, the electric power demand has been extensively increasing worldwide. But, there is not much
expansion in existing power generation and transmission networks due to limited resources and environmental
constrains. As a consequence some transmission lines are heavily loaded and system stability will be affected. The
continual increase in electric power demand compels utility companies to operate their systems much closer to the limits
of instability. This has rised in stressed operating conditions, with related problems associated to system security. One of
the primary issues that may relate with such a stressed system is voltage collapse or voltage instability. Many events of
system blackout have been announced worldwide due to voltage collapse. Reactive power imbalance in the system is the
main reason for voltage instability. In order to recover the system from voltage collapse under stressed condition, FACTS
controllers can be placed at convenient locations to provide reactive power support. The response of FACTS devices is
faster than capacitor banks. Installing FACTS devices is the most cost effective way for utilities to enhance the loading
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margin and voltage profile of the system. However, proper installation of FACTS devices is vital to get better
performance from these controllers.
Various methods have been proposed to decide the optimal location and control of FACTS devices to improve
loadability margin in transmission system. The two main techniques used for optimal placement of FACTS devices are
index based methods and optimization based methods. Fuzzy logic and Real Coded Genetic Algorithm based strategies
were proposed for location and sizing of shunt FACTS controller [1]. Particle Swarm Optimization (PSO), Nondominated Sorting Particle Swarm Optimization (NSPSO) and Genetic Algorithm based optimization techniques are
introduced to identify the optimal location together with setting of FACTS devices to improve voltage stability of the
modern power system [2, 3, 4]. The optimal location of shunt-series FACTS controllers can also be decided by multiobjective optimization techniques [5, 6].
Enhancing the system’s reactive power handling ability by Flexible AC transmission System (FACTS) devices
is a solution for avoiding voltage instability issue. Continuation power flow is used for examining the improvement of
static voltage stability margin with STATCOM, TCSC and SSSC [7, 8]. Mostly, adequate reactive power support at the
‘weakest bus’ or ‘sensitive node’ advances system loading margin and static stability margins. The bus which is ranked
highest is tagged as the weakest bus as it is capable of withstanding a small amount of load before causing voltage
collapse. A sensitivity based analysis termed as L-index method is used for identifying weakest bus in IEEE - 14 bus
system [9, 10]. Newton Raphson power flow algorithm has been recommended for attaining desired power transfer with
Flexible AC Transmission Systems (FACTS) devices. FACTS devices can be incorporated in the Newton Raphson
power flow algorithm and thus, whole system can be easily converted to power injection models without change of
original admittance and the Jacobian matrices. Power flow algorithm has been modelled in such a way that it can easily
be extended to multiple and multi-type FACTS devices by adding a new Jacobian corresponding to that new device only
[11].
Most of the researches on optimal FACTS placement are adapted to technical, economic or both concerns. In
technical concerns, FACTS devices are practically installed at different locations for analysing the enhancement of
system loadability margin. In order to select suitable locations for FACTS positioning to enhance system security as well
as loadability, genetic algorithm (GA) based approach can also be used [12]. Differential Evolution (DE) is another
important algorithm proposed for the optimal location and control of FACTS devices for maximizing the loadability
margin. Maximization of power system loadability can be attained by formulating a problem called mixed discretecontinuous nonlinear optimization problem (MDCP) for optimally fitting two types of FACTS devices, especially
thyristor controlled series compensator (TCSC) and static var compensator (SVC) and for network reinforcement [13].
The complexity of MDCP generates extensive simulations necessary with high computational requirements. Hence an
ordinal optimization (OO) technique is proposed to solve the MDCP connecting above flexible ac transmission systems
(FACTS) devices, to boost system loadability limit [14].
There are several techniques used for incorporation of differential algebraic equations (DAE) model of FACTS
controllers as well as different type of loads such as a static, dynamic and composite load model in large-scale emerging
power systems can be utilized to improve the loadability of power system network. Serious improvements in operating
parameters of the power system networks such as small signal stability, transient stability, voltage profile, power transfer
capability through the lines, power system oscillation damping, power system security, less active power loss, congestion
management, efficiency of power system operations, quality of the power system, dynamic performances of power
systems, and the increased loadability of the power system network can be attained via optimal allocation and
coordination of multiple FACTS controllers in large-scale emerging power system networks [15,16].
In this paper, Genetic Algorithm (GA) based technique is proposed for the optimal placement and setting of FACTS
device, particularly STATCOM for loadability enhancement incorporating stability constraints. i.e., voltage stability, line
stability and small signal stability. The paper is organized as follows, the first section gives an introduction and optimal
placement methods of FACTS devices, section 2 describes the modelling of STATCOM. The problem formulation
including stability constraints is explained in section 3. Section 4 gives some promising numerical results with some
discussions based on the test systems used. Section 5 summarizes the conclusions and major contributions.
2. STATCOM MODELLING
Static Synchronous Compensator (STATCOM) is a shunt connected Voltage-Source Inverter (VSI) that
generate a synchronous voltage of fundamental frequency, controllable magnitude and phase angle from a DC input
voltage. STATCOM can inject or absorb reactive power to or from the bus to which it is connected and thus regulates the
voltage at the connected bus to the reference value by adjusting voltage and angle of internal voltage source. Figs. 1 and
2 show the schematic diagram and equivalent circuit of STATCOM, respectively. The STATCOM can be represented by
a controllable voltage source
in the equivalent circuit. The
can be regulated to control local bus voltage.
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Fig. 1: Basic structure of a STATCOM.
Fig. 2: Equivalent circuit of a STATCOM connected to a local bus.
Power flow control equation of the STATCOM is given by equation (1) and the active power exchange through
the DC link (operating constraint) is described by equation (2). Also, the mathematical description of the bus control
equation is shown in equation (3) [18].
(1)
(2)
(3)
where,
- ith bus complex voltage
- STATCOM complex voltage
- shunt transformer impedance
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- apparent power through STATCOM
- the bus voltage control reference.
3. PROBLEM FORMULATION
3.1. Objective Function
The goal of the optimization problem is to decide the optimal location of STATCOM for maximizing secured
loadability of all buses in the system satisfying the power system stability constraints. The real and reactive power loads
are increased simultaneously by loadability factor λ in same ratio. The value of λ alters from base case (1 p.u.) to the
maximum value without violating the stability constraints. So, the objective function can be formulated as:
(4)
Where is the load ability factor in p.u.
Subjected to the following:
3.1.1. Equality constraints
The real and reactive power balance equations with load ability factor are:
(5)
(6)
where,
- total number of buses
- real power generation
- real power demand
- reactive power generation
- reactive power demand
- injected active power
- injected reactive power.
3.1.2. Inequality constraints
Slack bus real power generation constraint
(7)
Slack bus reactive power generation constraint
(8)
Bus voltage constraint
(9)
Transmission line power flow constraint
(10)
where,
- total number of generators
- total number of transmission lines
- maximum limit of slack real power generation
- maximum limit of slack reactive power generation
and
– minimum and maximum limits of bus voltage
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- magnitude of bus voltage
S - apparent power flow
- maximum limit of apparent power flow.
Then, the real and reactive load demands (
and
) for the load buses (PQ buses) with λ can be modified
as:
(11)
(12)
where,
and
are the initial real and reactive load power at bus i and
and
are the modified values.
3.1.3. Power System Stability Indices
3.1.3.1. Small Signal Stability: For the small signal stability analysis, the power system with distributed generators is
modelled as a set of differential equations and a set of algebraic equations as given below [21].
(13)
(14)
where, x is the vector of the state variables and y the vector of the algebraic variables. The differential algebraic
equations (DAEs) can be linearized at an operating point to obtain the system state matrix
(15).
=
=
Eliminating the algebraic variables, the state matrix
(15)
is given by,
(16)
where,
,
,
,
are Jacobian Matrices as given in (15).
The eigenvalues of
provide the information of small signal stability. Power system is considered stable in the
small-signal sense if all the eigenvalues of
lie on the left side of the imaginary axis. Then the power system is said to
be asymptotically stable and would be able to withstand small disturbances. The small signal stability analysis is
incorporated in the constraint by the equation in PSAT.
(
=0
(17)
The eigenvalue based stability assures grid stability under various levels of system loadability.
3.1.3.2. Fast Voltage Stability Index: The safe bus loading of the system is assured by incorporating the Fast Voltage
Stability Index (FVSI) proposed by Musirin [19].
(18)
If
≈ 1.00: bus connected to the line is approaching its instability point. If
≥ 1.00: one of the buses
connected to the line will experience a sudden voltage drop and the bus will collapse due to overloading.
3.1.3.3. Line Stability Index (LSI): The line stability index symbolized by
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index
Moghawemi et al. [20] is formulated based on a power transmission concept in a single line. The line stability
is given by,
(19)
where
is the line reactance,
is the reactive power at the receiving end,
is the sending end voltage,
is the line
impedance angle and is the angle difference between the supply voltage and the receiving voltage. The value of
must be less than 1.00 to maintain a stable system.
3.1.3.4. Line Stability Factor: System Stability is also assured by Line Stability Factor (LQP) proposed by A Mohamed
et al. [19]. The LQP should be less than 1.00 to maintain a stable system.
LQP assure that at no level of bus loading the line is overloaded.
The flow chart for the proposed methodology for maximizing the loadability by optimally placed STATCOM is
shown in fig. 3 below.
Fig. 3. Flow chart for the proposed methodology.
Table I: Optimal Values of GA Parameters
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Parameters
Population Size
Stall Generation Limit
Selection Function
Crossover Function
Mutation Probability
Crossover Probability
Value
50
100
Roulette wheel
Single point crossover
0.01
0.8
4. CASE STUDY AND SIMULATION RESULTS
4.1. Specification of Test System
The single line diagram of the IEEE 14 - bus standard test system is shown in fig. 4, which consists of five
synchronous machines, including two generators, located at buses 1 and 2 as well as three synchronous compensators
used only for reactive power support, located at buses 3, 6 and 8. It has four transformers with off-nominal tap ratio in
lines 4-7, 4-9, 5-6 and 8-9. The lower voltage magnitude limits at all buses are 0.9 p.u. and the upper limits are 1.1 p.u.
Total real and reactive power of load is 259 MW and 81.4 MVAr respectively. Total generation includes real power
generation of 272.6 MW and 108.83 MVAr of reactive power. Load bus voltages are maintained between 0.9 and 1.1 p.u.
.
Fig. 4. Single line diagram of the IEEE 14-bus standard system
The modified test system is realized by locating STATCOM at bus 14 in the original IEEE 14 - bus test system
and making it as PV bus. The proposed technique was tested on IEEE 14-bus modified system. The modified test system
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consists of 2 generators, 3 synchronous compensators, 16 lines, 4 transformers, 11 loads and 14 buses, of which one is
slack and five are PV buses. It is observed that, bus No. 14 is the weakest bus in IEEE 14-bus test system. Generally,
shunt FACTS controller is located at the weakest bus in the system and correspondingly, STATCOM is located at bus
No. 14. Constant power loads (PQ loads) were used for load model and the problem was solved using Newton - Raphson
power flow program. The program was coded in MATLAB.
4.2 Results and Discussions
The bus load levels at base case without STATCOM is compared against that at the maximum loadability case
with STATCOM together with GA controller and is shown in fig. 5. The white bars indicate the base case load levels at
various buses without STATCOM and the thick dark blue bars represent that at maximum loadability case with
STATCOM. The figure clearly indicates that loads at various buses in IEEE 14 - bus system are maximized except load
at bus 11, satisfies the objective function.
Base case (without STATCOM)
1.80
Maximum Loadability (with STATCOM & controller)
Real power load (pu)
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1
2
3
4
5
6
7
8
Bus no.
9
10
11
12
13
14
Fig. 5. Typical load levels with and without STATCOM.
Table II: Generation and load at maximum system loading
System Loadability
Base Case
At Maximum Loading
Difference = (maximum load – base load)
PG
(p.u)
2.72
4.62
1.9
QG
(p.u)
1.08
2.74
1.66
PL
(p.u)
2.59
4.18
1.59
QL
(p.u)
0.81
1.29
0.48
From the table it is clear that with optimal placement and setting of STATCOM, more load demand can be met.
In the present work 1.59 p.u additional active load can be accommodated without driving the system into instability i.e.
an increase of 61.39% loading capability.
Fig.6 shows the various bus voltage levels with STATCOM at maximum loadability case and without
STATCOM at base case. The figure explains that optimal placement of STATCOM slightly adjusted the voltages of PV
buses for maximizing the loadability. It can be seen that at maximum system loading, the voltages in all the buses are
maintained within the set limits of 0.9 and 1.1 p.u.
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Base Case (without STATCOM)
Maximum Loadability (with STATCOM & controller)
Bus voltage (pu)
1.10
1.05
1.00
0.95
0.90
1
2
3
4
5
6
7
8
Bus no.
9
10
11
12
13
14
Fig. 6. Typical voltage levels with and without STATCOM.
Base case (without STATCOM)
5.00
Real power generation
(pu)
Maximum Loadability (with STATCOM & controller)
4.00
3.00
2.00
1.00
0.00
1
2
3
4
5
6
7 8 9
Bus no.
10 11 12 13 14
Fig.7. Typical generation levels with and without STATCOM.
Fig.7 shows the bus generations with and without STATCOM. The thick dark brown bars show the active
power generation at different buses at maximum loadability case with STATCOM and the white bars, the base case
without STATCOM. The figure definitely shows that the slack generator increases its generation from the base case to
meet the additional load demand.
The line flows in various lines are shown in fig. 8. The thick red stacked area represents the power flows with
STATCOM at maximum loadability case and the blue stacked area gives the power flows without STATCOM, the base
case. The line flows are increased after the implementation of STATCOM.
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Fig. 8. Typical line flows with and without STATCOM.
The stability constraints at the best compromise solution represented by their eigenvalue, FVSI, LSI and LQP
are shown in fig. 9 and fig. 10. It is clear that the incorporation of small signal stability constraint into the GA controller
assures grid stability with all the eigenvalues in the left hand side of the S-plane for the best compromise solution. Also it
can be seen that voltage and line stability indices (FVSI & LQP) are well within acceptable limits. This maintains grid
stability at various loading ensuring no bus collapses due to overloading and no line is overloaded under any grid
condition.
Fig. 9. Eigen values of the stable system.
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Fig. 10. Stability Indices FVSI, LSI, LQP.
5. CONCLUSION
In this paper, implementation of GA is executed, efficiently and successfully to identify optimal location of
STATCOM to maximize the transmission system loadability as well as to enhance the voltage profile and small signal
stability margins. With this algorithm, it is able to find out the optimal solutions easily with less computational effort.
Tests are performed on the IEEE - 14 bus standard system. Results show that the implementation of GA has enhanced the
transmission system loadability with increased voltage profile. Incorporation of Small signal stability, Fast voltage
stability index (FVSI) and Line stability factor (LQP) constraints in the optimization problem ensures grid stability at
various levels of system loadability.
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