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International Journal on Electrical Engineering and Informatics - Volume 6, Number 4, December 2014 Variable Structure Fuzzy Gain Schedule Based Load Frequency Control
of Non-Linear Multi Source Multi Area Hydro Thermal System
K. R. M. Vijaya Chandrakala1, S. Balamurugan1, N. Janarthanan1, and B. Anand2
1Department of EEE, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. 2Department of EEE, Hindustan College of Engineering and Technology, Coimbatore, India.
Abstract: The article focuses on the issues of Load Frequency Control (LFC) under non-linear strategies in multi source multi area hydro thermal system. On practical perspective dead band, boiler dynamics, reheat steam turbine along with hydro turbine operating under two different area capacities are considered in the system. When subjected to random load variations in both the areas, the system exhibits higher oscillations. The speed governor matches the generation with the demand. The offset in the area frequencies and tie-line power is removed by using secondary Proportional Integral (PI) controller. The PI controller is tuned using Ziegler Nichols’ (ZN) and Fuzzy Gain Scheduling (FGS) method. The influence of high Proportional (P) controller gain during steady state and high Integral (I) controller gain during transient affects the system performance. Variable Structure System (VSS) helps to switch from P to PI controller during transient to steady state based on control error. The concept of VSS is applied to Fuzzy Gain Scheduling (FGS) PI controller. The performance of the optimal Variable Structure Fuzzy Gain Scheduled (VSFGS) controller under non-linear environment is judged and validated using performance indices. Keyword: Load Frequency Control, Multi Source Multi Area System, Hydro Thermal System, Proportional Integral Controller, Fuzzy Gain Scheduling, Variable Structure System Controller
1. Introduction Power system control is the most significant task for its secure operation because of dynamic variations in loads. The main objective of the LFC is to maintain the system frequency and the power flow in the tie-line as per the contract made between the areas and to do the generation scheduling optimally [1-3]. The frequency and tie-line power variations are retrieved to nominal value with the help of speed governor in the control area. Speed governor acts as primary controller matches the generation with the demand and fine tuning is carried out by secondary controller. Practically, each area will have both hydro and thermal power plant. Such system is named to be multi source multi area hydro thermal system [4]. The researchers [5-9] failed to focus the LFC problem of Multi Source Multi Area (MSMA) system considering the non-linearities such as, dead band, boiler dynamics and reheat steam turbine. Moreover, LFC problem is dealt by various researchers, are based on equal area capacities and with unit step load disturbance [10-13]. In practice, area capacities are not same and the system is subjected to random load variations. Taking into account the impact of non-linearities in multi source multi area system under unequal area capacities with random load variations is identified as the LFC problem in this work. Conventionally, PI controller is used for controlling the tie-line power and frequency oscillations along with the speed governor. In this paper, ZN method [14-16] and FGS [17-22] are used for the PI tuning. In PI controller, P improves the transient response but weakens the steady state. Similarly, I controller improves the steady state but spoils the transient behavior. This problem is overcome by Variable Structure System (VSS) controller [23-25] which switches between P to PI during transient to steady state period.
Received: August 12nd, 2014. Accepted: December 27th, 2014
785
Integrating VSS with FGS forms VSFGS [26] controller. VSFGS is used for tuning the PI controller of MSMA hydro thermal system considering non-linearities and unequal area capacities when subjected to random load variations. The paper is structured as follows: Section 2 deals with the modeling of multi source multi area hydro thermal system with non-linearities, section 3 focuses on tuning methods adopted for the PI controller, section 4 identifies the optimal controller based on performance indices. 2. Modeling of Multi Source Multi Area Hydro Thermal System including non-linearities A. Modeling of Thermal System Practically, non-linearities in thermal power plant are; dead band, boiler dynamics and reheat steam turbine [9]. The mathematical model of thermal power plant furnished by IEEE committee report and researchers [1],[2],[27] with the non-linearities is shown in Figure 1.
1
1R
1+P
P
KsT
11 HsT+
11
r r
r
sK TsT
++
gPΔ1DPΔ
1refPΔ ExΔ FLSΔfΔ1
1+ TsT
RPΔ TPΔ
Figure 1. Transfer function model of thermal power plant with governor dead band, boiler
dynamics and reheat turbine
In thermal power plant, dead band results due to the function of overlapping of the valves in the hydraulic relays, backlash effects and coulomb friction caused in different governor linkages. It is the magnitude of the frequency deviation of the system which impinges the effect of the dead band on the speed governor response [2], [9]. The speed governor dead band non-linearity is deduced out of describing function approach [9]. In conventional thermal power plant, drum type boiler is basically used. As per the requirement of the generation to meet with the demand, the turbine control valves are controlled by means of immediate control action imparted by the boiler by sensing the change in steam flow and the drum pressure. This type of control response imparted by the boiler leads to long term dynamics. Generally, researchers concentrate mostly on non-reheat steam turbine but in practice reheat turbine is used. Reheat steam turbine is of second order type since it has different stages due to high and low pressure steam [2], [9]. The transfer function of reheat steam turbine is represented in Equation (1). 1
1G r r
R r
P sK TP sT
Δ +=
Δ + (1)
The turbine power output drives the generator which provides the electrical power to the power system. The transfer function of the power system comprising of generator with load disturbance is given in Equation (2) as; 1
1 111
pT D
p
KP P f
sTΔ − Δ = Δ
+
(2) B. Modeling of Hydro System In this work, low head hydro power plant is taken into consideration for the study. The transfer function model of hydro power plant as furnished by the IEEE committee report [27-28] is shown in Figure 2.
K. R. M. Vijaya Chandrakala, et al.
786
2
1R
2
21P
P
KsT+
1
11K
sT+1
1 0.5W
W
sTsT
−+2
11
RsTsT
++
Δ HgP 2DPΔ
2fΔHVPΔ HTPΔ
Figure 2. Transfer function model of hydro power plant.
The functioning of speed governor of hydro power plant is similar to that of steam power plant. The transfer function of hydro governor [2] is given by Equation (3) as;
2
11
RHV Hg
sTP PsT
+Δ = Δ
+ (3) where; 1
2 21 2
1( )1Hg ref
KP P fsT R
Δ = Δ − Δ+
.
The reset time RT is given in Equation (4) [5.0 ( 1.0)0.5]WR WT T T= − − (4) in which; TW is the water time constant whose value varies between 1sec to 4secs for low head hydro turbines. T1 is transient droop time constant in sec which is given in Equation (5)
1
TDR
PD
RT TR
=
(5)
where; TDR is the temporary droop which is given in Equation (6)
[2.3 ( 1.0)0.15] WTD W
M
TR TT
= − −
(6)
in which TM is equal to 2H ; where H is Inertia constant. Water is used as an inlet to drive the turbine which is controlled by hydro governor. The transfer function of hydro turbine is given in Equation (7) (1 )
(1 0.5 )W
HT HVW
sTP PsT
−Δ = Δ
+ (7)
The transfer function of generator connected to power system with a provision to give load disturbance is similar to that in thermal power system as furnished in Equation (2). C. Modeling of Tie-line The control areas are interconnected by means of a tie-line to improve the reliability and stability of the system [3]. The power flow through the transmission line is expressed in Equation (8) as;
12 1 2
2 ( )tie
TP f fsΠ
Δ = Δ −Δ (8)
Variable Structure Fuzzy Gain Schedule Based Load Frequency Control
787
D. Modeling of Multi Source Multi Area Hydro Thermal System The transfer function model of multi source multi area hydrothermal system shown is developed using the thermal model discussed in section 2.1, hydro model in section 2.2 and tie-line model in section 2.3 and furnished in Figure 3.
111
HsT+
1refPΔ gPΔ
111
TsT+
RPΔ
2refPΔ 1
11 sT
K+ 21
1sTsTR
++HgPΔ
GPΔ
HVPΔ
W
WsT
sT5.01
1+− HTPΔ
1DPΔ
1
11 P
PsT
K+
1fΔ
3refPΔ
4refPΔ
1
11 sT
K+ 21
1sTsTR
++
HgPΔ HVPΔ
W
WsT
sT5.01
1+−
HTPΔ
2DPΔ
2
21 P
PsT
K+
2fΔ
sTΠ2
12A
12tiePΔ2
1R
1
1R
2
1R
1B
12A
2B
ACE
ACE
1
1R
111
HsT+
gPΔ RPΔGPΔ
111
TsT+
Figure 3. Transfer function model of multi source multi area hydro thermal system with
secondary controller including non-linearties with different area capacities Multi source multi area system is designed to operate at a capacity of 2000 MW with nominal operating load in
area1 and area2 of 1250 MW and 750 MW respectively. 3. Secondary PI Controller Tuning Methods When the system is subjected to disturbance, based on the error signal, the optimal secondary PI controller tuned using the following methods will control the frequency and tie-line power flow by adjusting the power reference setting of the governor. A. Zeigler Nichols’ Method In this method, the process is kept under closed loop P control, the gain of the P controller at which the loop is at the threshold of instability is the ultimate gain (Kcu). Ultimate period (Tu) is the time for one cycle during the period of sustained oscillations. PI controller is tuned using these parameters Kcu and Tu [16]. The tuned values of Kp and Ki for the MSMA system shown in Figure 3 are 0.27 and 0.135 respectively.
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B. Fuzzy Gain Scheduled PI Controller The PI controller as discussed in the section 3.1 has fixed gain values irrespective of the system changes. Depending on the system conditions, the PI controller gains Kp and Ki have to vary. This is accomplished by scheduling the gain values of PI controller using Fuzzy Gain Scheduling (FGS) [20-22]. The inputs to the FGS are ACE and derivative of ACE (ACE1). The output of the FGS is Kp of P controller and Ki of I controller. Seven linguistic variables are used for both the inputs and outputs namely Large Negative (LN), Medium Negative (MN), Small Negative (SN), Zero (Z), Small Positive (SP), Medium Positive (MP) and Large Positive (LP). LN and LP are of trapezoidal, where as the remaining are of triangular membership functions. The rules of FGSPI [24] controller is furnished in Table 1.
Table 1. Fuzzy rules for scheduling Kp and Ki
ACE
AC
E1 LN MN SN Z SP MP LP
LN LP LP LP MP MP SP Z MN LP MP MP MP SP Z SN SN LP MP SP SP Z SN MN Z MP MP SP Z SN MN MN SP MP SP Z SN SN MN LN MP SP Z SN MN MN MN LN LP Z SN MN MN LN LN LN
C. Variable Structure Fuzzy Gain Scheduled (PI) Controller Based on error, VSS helps to switch between P to PI to uphold the predominance action of P during transient period and PI during stead state only. This nullifies the effect of I controller during transient period. VSS does the switching, based on the error signal and Fuzzy incorporates conventional design (PI) and fine tune it to certain plant non-linearities due to universal approximation capabilities. To adapt w.r.t varying system conditions, VSS is integrated with the FGS to form VSFGS for faster switching control action. The functional diagram of VSFGS [26] is represented in Figure 4. Kp and Ki values of PI controller are decided by Fuzzy based on ACE and ACE1. Meanwhile, the VSS switches the PI controller from P to PI based on ACE i.e. if ACE is greater thanε , then P controller alone will be in action whose gain is decided by FGS. If ACE is less than equal toε , then PI controller will take the control action whose gains are scheduled by Fuzzy.
ddt
∑
ε
ε
Δ refP
Figure 4. Schematic diagram of Variable Structure Fuzzy Gain scheduling
VSFGS holds the system variations under varying conditions in control and improves the controller flexibility when compared to the fixed gain imparted by conventional PI controller. 4. Simulation Results Multi source multi area hydro thermal system shown in Figure 3 under non-identical area capacities is simulated using MATLAB/Simulink [29]. The system is subjected to random load variations. Preferably, three load disturbances are given at 0 sec, 40 sec and 80 sec at area 1,
Variable Structure Fuzzy Gain Schedule Based Load Frequency Control
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out of which, two is increase in demand and one is decrease in demand of 0.01 p.u. magnitude. Similarly in area2, two load disturbances are given, out of which, one is decrease in demand at 20 sec and the other is increase in demand at 60 sec of 0.01 p.u. magnitude. ZN tuned PI gain values as furnished in section 3.1, FGS rule as furnished in section 3.2 and VSFGS as explained in section 3.3 is incorporated as secondary controllers and comparison response are shown in Figure 5.
Figure 5. Comparison response of secondary controllers in multi source multi area hydro
thermal system with non-linearities under random load variations From the response, it clearly states that ZN tuned PI controller removes the offset but provides overshoots with longer settling time. To improve its adaptivity w.r.t system conditions, FGS provided reduced peak value and faster settling time when compared to ZN tuned PI. By switching between P to PI, VSFGS has much more evidently improved the system response when compared to all the controllers retaining the system faster to its nominal value. The controller performance is evaluated based on ISE, ITAE and ITSE performance indices [30-31] whose values are furnished in Table 2 and shown in figure 6.
Table 2. Comparison of various controller performances of the system Performance Indices ZN tuned PI controller FGS PI controller VSFGS
ISE 0.04858 0.006333 0.005687 ITAE 286.9 54.25 50.13 ITSE 4.209 0.5187 0.4633
Figure 6. Bar chart showing the performance indices
In practical prospective, from the performance indices, it clearly suffices that VSFGS proves to be the best optimal secondary controller. It helps in controlling the area frequencies and tie-line power variations of multi source multi area system effectively under non-linearities, unequal area capacities subjected to random load variations.
K. R. M. Vijaya Chandrakala, et al.
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5. Conclusion In this analysis, multi source multi area hydro thermal system with the non-linearities, unequal area capacities subjected to random load variations was considered. The response of VSFGS as secondary controller was compared with ZN tuned PI and FGS PI controller. The transient frequency and tie-line power oscillations were effectively reduced using VSFGS and thus retained the system stability at a faster rate. The performance of the controller was also validated using performance indices ISE, ITAE and ITSE. 6. Appendix Thermal Power Plant
1R =Speed regulation of governor = 2 Hz/p.u. MW;
HT = Turbo governor time constant = 0.08 sec;
TT = Non-reheat turbine time constant = 0.3 sec;
rK = Reheat steam turbine gain constant = 0.333;
rT = Reheat steam turbine time constant = 10 sec;
1B = 2B = Frequency bias constant of area 1 and area 2 respectively = 0.425 p.u.MW/Hz;
1DPΔ = Change in load demand power in area 1 = 0.01 p.u.;
1refPΔ = Change in reference power of area 1 in p.u.;
4refPΔ = Change in reference power of area 2 in p.u.;
gPΔ = Change in governor power of the thermal power plant in p.u.;
FLSΔ = Change in steam power flow imparted to the steam turbine in p.u.;
RPΔ = Change in steam turbine power in p.u.;
GPΔ = Change in reheat steam turbine power in p.u.;
1fΔ = Change in frequency of area 1 in Hz;
1pK = Power system gain constant of area 1 = 80;
1pT = Power system time constant of area 1 = 16; Hydro power plant
2R = Speed regulation = 2.4 Hz/p.u. MW;
1K = Hydro governor gain = 1;
1T = Hydro governor time constant = 48.7 sec;
RT , 2T = Hydro power plant time constants = 5.0 sec, 0.513 sec;
WT = Water time constant = 1.0 sec;
2DPΔ = Change in load demand power in area 2 = 0.01 p.u.;
2refPΔ = Change in reference power of area 1 in p.u.;
3refPΔ = Change in reference power of area 2 in p.u.;
2fΔ = Change in frequency of area 2 in Hz;
2pK = Power system gain constant of area 2 = 133.33;
Variable Structure Fuzzy Gain Schedule Based Load Frequency Control
791
2pT = Power system time constant of area 2 = 26.67;
HgPΔ = Change in hydro governor power in p.u.;
HVPΔ = Change in hydraulic valve power in p.u.;
HTPΔ = Change in hydraulic turbine power in p.u.; Tie-line
12A = Synchronizing power coefficient = -1;
T = Synchronizing coefficient =10% of area capacity = 0.1Cos δ12 = 0.0707;
12tiePΔ = Change in tie-line power between area 1 and area 2 respectively in p.u.; s = Laplace transform operator; ACE = Area Control Error;
1ACE = Rate of change of Area Control Error; ε = Threshold value of the switch; ddt
= rate of change w.r.t time;
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