Enhancement of Dynamic Performance of Automatic Generation … · 2018. 3. 15. · Enhancement of...
Transcript of Enhancement of Dynamic Performance of Automatic Generation … · 2018. 3. 15. · Enhancement of...
Enhancement of Dynamic Performance of
Automatic Generation Control of a
Deregulated Hybrid Power System
1Dillip Kumar Mishra,
2Subhranshu Sekhar Pati,
3Tapas Kumar Panigrahi,
4Asit Mohanty and
5Prakash Kumar Ray
1,2,3,5Department of Electrical Engineering , IIIT, Bhubaneswar, India
4Department of Electrical Engineering, CET, Bhubaneswar, India
Abstract In recent days Fractional order control has been widely established as an
effective and alternative control approach. In order to increase the
performance of dynamic systems factional order controllers has been used.
The widely used traditional Proportional Integral and Proportional Integral
Derivative (PID) controllers are commonly implemented in the automatic
generation control (AGC) to enhance the dynamic performance and to
decrease or eliminate steady state error. This study develops Fractional
order (FO) PID controller based AGC system to enhance the system
stability and performance. The study uses the PI/PID/optimized FOPID
having ITAE is the objective function. The paper explores AGC for
interconnected power system with diverse source and demonstrates that
TLBO optimized based FOPID performs better than traditional PI and PID
controllers. Furthermore, robustness analysis is carried out with their
performance index.
Key Words:Automatic generation control (AGC), fractional order, PID
controller, teaching learning based optimisation (TLBO).
International Journal of Pure and Applied MathematicsVolume 118 No. 5 2018, 303-319ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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1. Introduction
In recent years, power are consists of several large interconnected multi source
area to meet the load demand. For smoothing operation of power system the
cycles per second should have constant. Hence generation speed should have a
fixed value and also relative power angle in an individual area.in general load
demand and losses must match with power generated. Due to the sudden
variation of load by the user may mismatch the power balance. And it enter into
the system affecting the speed variation of rotor and hence frequency of the
overall system. This mismatch problem is commonly solved by solved by
abstraction of kinetic energy from the system. Hence rotor speed decreases and
also frequency. As the frequency slowly declines, the old load consumption also
decreases. To avoid these deviations automatic generation control (AGC) is
included in the system which regulates the set point speed of multiple
generation sources in each area. Hence it becomes our primary objective of
AGC to control the power from different plant so that the overall frequency kept
within given limits in the power system [1].
Several areas are interrelated via tie lines. These tie lines have mainly two
functions. Firstly for mutually power exchange between different area and
secondly inter area support in case of anomalous operating condition. To
overcome this problem high voltage direct current (HVDC) is adopted for
transmitting power from one area to another. HVDC owns eye-catching
features such as fast controllability of power in HVDC links by the help of
convertor control, facility to reduce transient stability difficulties linked with
AC tie lines and other economic benefits [2].
Electrical power is generated by different types of units such as gas, thermal,
hydro, nuclear power plant. As the efficiency of nuclear power plant is
maximum. Hence it is operated at base load so it does not take part in AGC
control as the output is always be at maximum. Nuclear power plant are suitable
for fluctuating loads so for peak load condition Nuclear power plants are one of
the suitable choices for meeting the varying load demand. For our study of AGC
process, grouping of multiple units in a control area with taking their
participation factor and nonlinear characteristics using time delay (TD) are
genuine investigation [3].
To realize these objectives, an enormous number of studies have been conceded
out for an robust design of AGC controller [4], with the revolutionary works by
Elgerd and Fosha [5].The control methods such as conventional [6] and optimal
control [7] have been proposed for AGC. R K. Cavin et al [8] has
demonstrated fault of AGC in the interrelated power system from the optimal
stochastictics concept.Thus steadying of frequency oscillations becomes
challenging and greatly expected in the view competitive market analysis .As a
result control design should be sophisticated in AGC in order to balancing the
frequency oscillation.
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Now days, engineering and science uses fractional order controller in design
and simulation purpose. With advancement of fractional calculus Podlubny[9]
given a more adaptable structure PIλD
μ by extended in traditional notion of PID
controllers [9] by including two degree of freedom in the controller design.
Hence the traditional controller performance improved. As a result more
accurate system performance can be identified and analyzed.
By discussing the above feature of FOPID controller, a maiden approach has
been taken out to apply the ABC optimisation algorithm to tune the FOPID, PID
and output feedback controller for hybrid source multi area with AC-DC link.
To make the system more actual, nonlinear parameter such as time delay (TD)
is added in the system modelling. It is observe by comparing the result that,
FOPID controller gives better performance with respect to conventional PID
and optimal controller. The effectiveness and healthiness of suggested controller
is also checked by changing the system and load constraints. Finally overall
response is investigated by the use of AGC for same interconnected control area
with AC-DC link.
2. Nomenclature
B1, B2 are the frequency bias parameters in area-I, II resp..
1u & 2u stand for control outputs of the area-I,II resp.
1GP & 2GP stand for change in governor power of area- I,II resp.
1TP & 2TP stand for change in turbine output power in area- I,II resp.
TieP is the tie line power deviation (p.u) in area- I,II resp.
1PST & 2PST stand for power system time constant in area-I,II resp.
1ACE & 2ACE are the area control errors in area- I,II resp.
1R & 2R stand for governor regulation parameter of area- I,II resp.
1VP & 2VP are the change in governor valve positions (pu) area- I,II resp.
1GT , &GH GNT T
stand for governor time constants thermal, gas & nuclear resp.
1TT & ,&W RST T
stand for of turbine time constant thermal, gas & nuclear resp.
1 &r RHT T Stands for of turbine time constant thermal & nuclear resp
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1PSK & 2PSK are the power system gains in area- I,II resp.
12T is the synchronizing coefficient and
1f & 2f are the frequency deviations in Hz in area- I,II resp;
&DC DCK TStands for HVDC parameters
3. System Modeling
Proposed Power System Model
The system under examination comprises of two interconnected area with AC-
DC link as shown in fig. 1. The area consists of reheat thermal, gas and nuclear
power generation unit. The impact to the nominal loading is decided by own
regulation parameter and participation factor of each control area. Sum of the
entire participation factor in each control area should equal to one. The
proposed investigation model can be represented by its transfer function which
is shown in fig.2 [2]. Each area have size of 2000 MW and nominal loading as
1000 MW. Contribution of loading in each area is 600 MW in thermal, 250 MW
gas and 150 MW in nuclear as power generation. Time delay of 50 ms has been
taken in each controller for each area. Power rating of area -1 and area-2 is
represented by Pr1 and Pr2 in MW respectively. Let it be assuming for area-1 the
constants are represented as Kt1, Kh1 and Kn1 for the portions of power generated
from thermal, gas, and nuclear source.PGt1, PGh1 and PGg1 are power generations
in MW with thermal, gas and nuclear units in area-1.
1 1 1 1 1 1 1 1 1; ;Gt t Gt Gg h G Gn n GnP K P P K P P K P (1)
The power generated under nominal operating conditions, PG1 for area 1 is
given by:
1 1 1 1G Gt Gg GnP P P P (2)
1 1 1 1t g nK K K (3)
The power flowing between area-1 and area-2 is given by:
12max 1 2sin( )TieACP P (4)
For small load variation Eq. (4) can be written as:
12max 1 2( )TieACP T (5)
T12is called as synchronizing coefficient and expressed as:
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12 12max 1 2cos( )T P (6)
When incremental power flow at rectifier end in DC link is modelled, it can
adjust the incremental change in frequency .
For small load perturbation AC tie-line flow, TieACP is given by
121 2
2( )TieAC
TP F F
s
(7)
The nonconformity of power flow,∆Ptie12 Ptie12=∆PtieAC
For small perturbation the DC tie-line flow, TieDCP can be given as:
1 2( )1
DCTieDC
DC
KP F F
sT
(8)
power ,Ptie12 can be written as:
12Tie TieAC TieDCP P P (9)
Conv-1 Tie - LineAREA-I AREA-II
Conv-II
Figure 1: Multi-Area Power system
For small load variation, eq (9) can be written as:
12Tie TieAC TieDCP P P (10)
The area control errors ACE1 and ACE2 by considering AC-DC tie line are
given by:
1 1 1 TieAC TieDCACE F P P (11)
2 2 2 12 ( )TieAC TieDCACE F P P (12)
Where β1 and β2 are frequency influenced parameter.
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α12 is called as area size ratio:
12 1 2/ 1r rP P (13)
The transfer function model of thermal, gas and nuclear plant is shown in fig 2.1
(a,b & c)
Ts G11
1
T rs
T rK rs
11
111
Ts t11
1
Figure 2.1.a: Thermal with Reheat Plant Transfer Function
1
1 GNsT
2
1 1 2
1
(1 )(1 )(1 )RH T RH
sA S B
sT sT sT
Figure 2.1.b: Nuclear Power Plant Transfer Function
2
2
X
Y
2
2
2
1
1
X
Y
sT
2
1
b cs
2
2
CR
F
T
T
2
2
2
1
1
CR
F
T
T
sF
2
1
1 CDsT
Figure 2.1.c: Gas Power Plant transfer function
Fractional Order PID Controller(FOPID)
In recent year, FOPID controller is used in system design and PIλD
μ controller is
the generalised form. It have extra features such as design controller gains
(KP,KI,KD) and design commands of integral and derivative. The order of
integral and derivative controller should have any real number. It simplifies the
conventional integral order PID controller and provide more elasticity in PID
control design. The transfer function of the controller is given by
sK
s
KKsG D
IP )(
(17)
If λ and μ value are taken as 1 then it will become classical PID controller.
Above all these classical controllers are special type of PIλDμ controller is
depicted in fig.3
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PK 1
Proportional
IK -λs
μsDK
Fractional Integral
Fractional Derivative
Figure 3: Block Diagram of FOPID Controller and FOPID
Controller Characteristics
In the design section of controller, the objective function should be predefined
first based upon the selective specification and constraints using teaching
learning optimization technique. Although, it is observed that Integral of Time
multiplied Absolute Error (ITAE) has been chosen as an objective function in
AGC problems. Thus in this study, TLBO technique is employed to optimize
the PID and FOPID parameter with ITAE criterion.
The ITAE objective function can be written as. (18).
simt
1 2 Tie
0
J=ITAE= ΔF + ΔF + ΔP ×t×dt (18)
∆F1and ∆F2 are called as system frequency deviation and Ptie is power
deviation in the tie line and tsim is the duration of simulation.
Teaching Learning Based Optimization (TLBO)
Teaching Learning Based Optimization (TLBO) optimization technique was
first developed by [11] Rao et al (2011, 2012a, b) and Rao & Savsani (2012).
This method is now very popular and most effective technique and employed in
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many fields of application. This technique has numerous advantage like lesser
time is required for the best solution and give more stable performance with
multiple frequency constraint. TLBO is mainly divided into two phases
First phase (Teacher phase)
Second phase (learner phase)
During the first phase students learn from the teacher and in the second phase
students learn by communicating with other students. The above two phases of
TLBO algorithm can be described as follows:
Initialization
Initially generate the random number of population and number of dimension
variable parameters. i:e Np and D. The mark secured by each number of
students in different subject can be written in matrix form i:e ith column with ith
subject. Here initial population taken as X.
P
11 12 1D
2,1 2,2 D
NP 1 NP 2 NP-D (N ×D)
x x .... x
x x .... x
X= . . .
. . .
x x .... x
First phase (Teacher phase)
In the first phase, the influence of teacher of the students in a class. The
Teacher has to play a major role in this phase and he must have very strong
knowledge in their assigned subject and to teach the students to get the best
score and performance. The best score shows the shine of a best teacher as
compared to another teacher, i:e Xbest
The mean value of result of each student in each subject can be estimated as:
d 1 2 DM = m ,m ,.....,m (3)
The results can be compared with mean value of same subject & results of
assigned teachers is given by
diff best F dM = rand(0,1) X - T M (4)
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-a12
+
+
-
+
+
-
-
+
a12
DP
K H
KT
+
+
+
+-
+-
-
NK
DP
K H
K T
+
+
+
+
+
+
+
1ACE
2ACE
B1
2B
1
1
R2
1
R3
1
R
1
1
R2
1
R3
1
R
Thermal with Reheat
Plant
Gas Plant
Nuclear Power Plant
Power
System
Power
System
Thermal with Reheat
Plant
Gas Plant
Nuclear Power Plant
Tie-
Line
NK
TL
BO
Op
tim
ized
FO
PID
Co
ntr
oll
er
TL
BO
Op
tim
ized
FO
PID
Co
ntr
oll
er 1u
1u
1u
2u
2u
2u
HVDC
HVDC
Figure 2.2: Proposed model of Two-Area diverse source power system
Where FT can be represented as teaching factor with )1,0(rand has been
considered as random number among 0 &1. Value of TF can be either 1 or 2 &
is chosen randomly from the equation (5)
FT =round[1+rand(0,1)] (5)
The old population is now calculated by equation (6)
new diffX =X+M (6)
New value of population is accepted (New) o if newf X <f X
else X old are
accepted.
Second phase (Learner phase)
In the second phase, the learner can improve their knowledge into two ways.
One can go through more discussion with the teacher and other can
communicate with other learner themselves. A learner takes advantages from
other learner with random selection of learner and interacts with him or her. So
the learner can get a more knowledge. The process of this phase can be
expressed as:
Choose two learners randomly, iX and jXwhere ji .
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new i i jX =X +rand(0,1)(X -X ), if i jf(X )<f(X )
(7)
Else
new i j iX =X +rand(0,1)(X -X ). Accept newX
if it is best solution
Choice of objective function
The main objective of the AGC is to reduce the Area Control Error (ACE) with
a very short period of time. In order to get low value of ACE, the cost function
can be defined as
t
1 2
0
f= Δw -Δw .tdt (8)
Where, dt is change in time , 1Δwand 2Δw
are the frequency deviation in area-I
and area-II respectively. Present study, a step load disturbance of 1% is changed
in area-I and start simulation with TLBO optimization technique for 50 times to
get the optimal values of gain of the PID controller.
4. Simulation Results and Discussion
The Matlab/Simulink based model is designed here to analyze the system
performance with Teaching Learning based optimization having ITAE is the
objective function. Primarily, a Proportional Integral (PI) controller is employed
for each area and the performances are shown on fig.4.Then the PID controller
is utilized in the same model and responses are shown in fig.4. Meanwhile, in
order to reduce the steady state error, settling time, overshoot, undershoot and
ITAE TLBO optimisation being used to tune the FOPID parameter. This shows
the better performance as compared to other two controllers. The TLBO
algorithm was repeated 100 times and best value is selected from 100 runs to
minimize the objective function.
To study the transient response of the system a step load perturbation (SLP)
10% is applied at time t=0 sec in area-I and the response are shown in fig.4 (a-
c). Then, 10% SLP in area-I and 5% in area-II are applied and shown in fig.4 (d-
f). To show the dynamic response of proposed system, frequency deviation in
area-I, frequency deviation in area-II and tie line power deviation characteristics
are shown in fig.4 (a-f) and also measured the performance indices (settling
time, overshoot % ITAE) are shown in table-II. Robustness analysis is done to
show the vigor of the system with ±25% loading and parameter variation. The
parameters are TSG, TGN, TT, TGH varied from their nominal values. The
measured value (settling time, overshoot, & ITAE) of proposed system is
represents as performance indices. It is clear that, there is negligible effect in the
system with parameter variation and loading. Accordingly, proposed system
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gives robust control during the change in system parameter and loading.
Table 1: Tuned Controller Parameters
Controller
gains PID FOPID
KP1 -1.448 -1.644
KP2 -1.5369 -0.311
KI1 -0.8430 -0.5035
KI2 -1.170 1.015
KD1 -1.872 -0.3163
KD2 0.692 -0.9662
λ1 --- 0.8031
λ2 --- 0.4051
μ1 --- 0.8451
μ2 --- 0.6294
Table 2: Settling Time, Overshoot and Error
Controller
Settling time (sec) Peak Overshoot
ITAE ∆F1 ∆F2 ∆Ptie ∆F1 ∆F2 ∆Ptie
PI 24.08 21.52 17.17 0.1369 0.1693 0.0128 8.901
PID 20.32 19.04 13.13 0.069 0.0398 0.0006 7.8106
TLBO- FOPID 5.14 4.09 7.05 0.035 0.0286 0.0023 4.562
Figure 4.A
Figure 4.B
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Figure 4.C
Figure 4.D
Figure 4.E
Figure 4.F
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Figure 4.G: Settling Time
Figure 4.H: Overshoot
Figure 5.A
Figure 5.B
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Figure 5.C
Figure 5.D
Fig.4 (a-c) Dynamic responses for 1% step load change in area I
(a) Frequency deviations of area 1 (b) Frequency deviations of area II (c) Tie
line power deviations
Fig.4 (d-f) Dynamic responses for 1% step load change in area I and 0.5% step
load change in area II (a) Frequency deviations of area 1 (b) Frequency
deviations of area 2 (c) Tie line power deviations
Fig.5 (a-d) Robustness analysis figure
Table 3: Robustness Analysis (Settling Time)
Parameters variations
Per
cen
tage
chan
ge
Settling Time in (Sec)
Overshoot ITAE
∆ F1 ∆ F2 ∆ PTie ∆ F1 ∆ F2 ∆ PTie
Nominal 0 4.19 3.82 6.45 0.0454 0.0502 0.0043 4.5771
Loading conditions
+25 4.20 3.87 6.54 0.0589 0.0671 0.0024 4.5957
-25 4.18 3.80 6.47 0.0512 0.0408 0.0053 4.5694
TT -25 4.17 3.75 6.59 0.0662 0.0623 0.0070 4.5899
+25 4.21 3.87 6.41 0.0466 0.0471 0.0072 4.5784
TSG -25 4.24 3.6 6.55 0.0497 0.0612 0.0012 4.5948
+25 4.128 3.79 6.47 0.0432 0.0575 0.0045 4.5784
TRH -25 4.08 4.60 6.63 0.0564 0.0661 0.0036 4.5848
+25 4.54 4.01 5.93 4.19 3.82 6.45 4.5801
TCN -25 4.18 4.59 6.43 4.20 3.87 6.54 4.5921
+25 4.58 4.15 5.89. 4.18 3.80 6.47 4.5730
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5. Conclusion
The study was conducted on a two area interconnected power system, where
dynamic performance of FOPID, PID and optimal controller have been shown
for parallel AC-DC links. To establish the power system more realistic, the non-
linearity parameter such as time delay is included in the system model. Gains of
the optimal/PID/FOPID controllers have been optimized with TLBO
techniques. To establish the superiority of the FOPID controller, results have
been compared with conventional PID controller. The proposed controllers are
found to be robust and ensures satisfactory system performance in system
operating load conditions.
Appendix: Power System Parameters
Area-1 Area-2
Thermal: Tg=0.08s, Kr1=0.3 ,
Tr1=5s, Tt1=0.3s
Thermal: Tg=0.08s, Kr1=0.3 ,
Tr1=5s, Tt1=0.3s
Gas:X1=0.6s,T1=1s,b1=0.05s,
c1=1s,TCR=0.3s,TF=0.25s,TCD=0.2s
Gas:X1=0.6s,T1=1s,b1=0.05s,
c1=1s,TCR=0.3s,TF=0.25s,TCD=0.2s
Nuclear:TRH1=7s,TRH2=9s,TT1=0.5s,
TGN=0.08s
Nuclear:TRH1=7s,TRH2=9s,TT1=0.5s,
TGN=0.08s
Power system: Kp=120, TP=20s,
HVDC: KDC=1, TDC=0.2s,
Tie Line: T12=0.045.
β=0.425 puMW/Hz, R=2.4Hz/pu
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