Variable Structure Fuzzy Gain Schedule Based Load Frequency Control of Non-Linear Multi Source Multi Area Hydro Thermal System

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1 International Journal on Electrical Engineering and Informatics - Volume 6, Number 4, December 04 Variable Structure Fuzzy Gain Schedule Based Load Frequency Control of Non-Linear Multi Source Multi Area Hydro hermal System K.. M. Vijaya Chandrakala, S. Balamurugan, N. Janarthanan, and B. Anand Department of EEE, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. Department of EEE, Hindustan College of Engineering and echnology, Coimbatore, India. krm_vijaya@cb.amrita.edu, Abstract: he 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. he speed governor matches the generation with the demand. he offset in the area frequencies and tie-line power is removed by using secondary Proportional Integral (PI) controller. he PI controller is tuned using Ziegler Nichols (ZN) and Fuzzy Gain Scheduling (FGS) method. he 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. he concept of VSS is applied to Fuzzy Gain Scheduling (FGS) PI controller. he 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 hermal System, Proportional Integral Controller, Fuzzy Gain Scheduling, Variable Structure System Controller. Introduction Power system control is the most significant task for its secure operation because of dynamic variations in loads. he 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 [-3]. he 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]. he 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 [0-3]. In practice, area capacities are not same and the system is subjected to random load variations. aking 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 [4-6] and FGS [7-] 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. his problem is overcome by Variable Structure System (VSS) controller [3-5] which switches between P to PI during transient to steady state period. eceived: August nd, 04. Accepted: December 7 th,

2 K.. M. Vijaya Chandrakala, et al. Integrating VSS with FGS forms VSFGS [6] 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. he paper is structured as follows: Section 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.. Modeling of Multi Source Multi Area Hydro hermal System including non-linearities A. Modeling of hermal System Practically, non-linearities in thermal power plant are; dead band, boiler dynamics and reheat steam turbine [9]. he mathematical model of thermal power plant furnished by IEEE committee report and researchers [],[],[7] with the non-linearities is shown in Figure. P ref P g + sh x E S FL + s P + skrr + s r P P D KP + s P f Figure. ransfer 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 [], [9]. he speed governor dead band nonlinearity 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. his 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. eheat steam turbine is of second order type since it has different stages due to high and low pressure steam [], [9]. he transfer function of reheat steam turbine is represented in Equation (). PG + skrr = P + s r () he turbine power output drives the generator which provides the electrical power to the power system. he transfer function of the power system comprising of generator with load disturbance is given in Equation () as; K P P = f p D + sp () B. Modeling of Hydro System In this work, low head hydro power plant is taken into consideration for the study. he transfer function model of hydro power plant as furnished by the IEEE committee report [7-8] is shown in Figure. 786

3 Variable Structure Fuzzy Gain Schedule Based Load Frequency Control K + s P Hg + s + s P HV sw + 0.5s W P H P D KP + s P f Figure. ransfer function model of hydro power plant. he functioning of speed governor of hydro power plant is similar to that of steam power plant. he transfer function of hydro governor [] is given by Equation (3) as; + s PHV = P + s where; = K ( ). Hg PHg Pref f + s he reset time is given in Equation (4) = [5.0 ( W.0)0.5] (4) W (3) in which; W is the water time constant whose value varies between sec to 4secs for low head hydro turbines. is transient droop time constant in sec which is given in Equation (5) D = (5) PD where; D is the temporary droop which is given in Equation (6) [.3 (.0)0.5] W D = W (6) M in which M is equal to H ; where H is Inertia constant. Water is used as an inlet to drive the turbine which is controlled by hydro governor. he transfer function of hydro turbine is given in Equation (7) ( sw ) PH = P ( s ) W HV (7) he 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 (). C. Modeling of ie-line he control areas are interconnected by means of a tie-line to improve the reliability and stability of the system [3]. he power flow through the transmission line is expressed in Equation (8) as; Π P = ( f f ) (8) tie s 787

4 K.. M. Vijaya Chandrakala, et al. D. Modeling of Multi Source Multi Area Hydro hermal System he transfer function model of multi source multi area hydrothermal system shown is developed using the thermal model discussed in section., hydro model in section. and tieline model in section.3 and furnished in Figure 3. B P ref Pg + s H P + s P G A ACE K P Hg + s + s P + s ref P ref 3 P HV sw + 0.5sW P D P tie P Hg PHV P H K + s sw + s + s + 0.5sW PH A Π s KP + sp f B ACE P ref 4 P g +s H P + s P G P D KP + sp f Figure 3. ransfer 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 000 MW with nominal operating load in area and area of 50 MW and 750 MW respectively. 3. Secondary PI Controller uning 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 tieline 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 (K cu ). Ultimate period ( u ) is the time for one cycle during the period of sustained oscillations. PI controller is tuned using these parameters K cu and u [6]. he tuned values of K p and K i for the MSMA system shown in Figure 3 are 0.7 and 0.35 respectively. 788

5 Variable Structure Fuzzy Gain Schedule Based Load Frequency Control B. Fuzzy Gain Scheduled PI Controller he PI controller as discussed in the section 3. has fixed gain values irrespective of the system changes. Depending on the system conditions, the PI controller gains K p and K i have to vary. his is accomplished by scheduling the gain values of PI controller using Fuzzy Gain Scheduling (FGS) [0-]. he inputs to the FGS are ACE and derivative of ACE (ACE ). he output of the FGS is K p of P controller and K i 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. he rules of FGSPI [4] controller is furnished in able. able. Fuzzy rules for scheduling K p and K i ACE ACE 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. his 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. o adapt w.r.t varying system conditions, VSS is integrated with the FGS to form VSFGS for faster switching control action. he functional diagram of VSFGS [6] is represented in Figure 4. Kp and K i values of PI controller are decided by Fuzzy based on ACE and ACE. 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. ε ε P ref d dt 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 esults Multi source multi area hydro thermal system shown in Figure 3 under non-identical area capacities is simulated using MALAB/Simulink [9]. he system is subjected to random load variations. Preferably, three load disturbances are given at 0 sec, 40 sec and 80 sec at area, 789

6 K.. M. Vijaya Chandrakala, et al. out of which, two is increase in demand and one is decrease in demand of 0.0 p.u. magnitude. Similarly in area, two load disturbances are given, out of which, one is decrease in demand at 0 sec and the other is increase in demand at 60 sec of 0.0 p.u. magnitude. ZN tuned PI gain values as furnished in section 3., FGS rule as furnished in section 3. 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. o 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. he controller performance is evaluated based on ISE, IAE and ISE performance indices [30-3] whose values are furnished in able and shown in figure 6. able. Comparison of various controller performances of the system Performance Indices ZN tuned PI controller FGS PI controller VSFGS ISE IAE ISE 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 nonlinearities, unequal area capacities subjected to random load variations. 790

7 Variable Structure Fuzzy Gain Schedule Based Load Frequency Control 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. he response of VSFGS as secondary controller was compared with ZN tuned PI and FGS PI controller. he transient frequency and tie-line power oscillations were effectively reduced using VSFGS and thus retained the system stability at a faster rate. he performance of the controller was also validated using performance indices ISE, IAE and ISE. 6. Appendix hermal Power Plant =Speed regulation of governor = Hz/p.u. MW; H = urbo governor time constant = 0.08 sec; = Non-reheat turbine time constant = 0.3 sec; K r = eheat steam turbine gain constant = 0.333; r = eheat steam turbine time constant = 0 sec; B = B = Frequency bias constant of area and area respectively = 0.45 p.u.mw/hz; = Change in load demand power in area = 0.0 p.u.; P D P ref P ref 4 P g = Change in reference power of area in p.u.; = Change in reference power of area in p.u.; = Change in governor power of the thermal power plant in p.u.; S FL P P G f = Change in steam power flow imparted to the steam turbine in p.u.; = Change in steam turbine power in p.u.; = Change in reheat steam turbine power in p.u.; = Change in frequency of area in Hz; K p= Power system gain constant of area = 80; p= Power system time constant of area = 6; Hydro power plant = Speed regulation =.4 Hz/p.u. MW; K = Hydro governor gain = ; = Hydro governor time constant = 48.7 sec;, = Hydro power plant time constants = 5.0 sec, 0.53 sec; = Water time constant =.0 sec; W P D P ref P ref 3 f = Change in load demand power in area = 0.0 p.u.; = Change in reference power of area in p.u.; = Change in reference power of area in p.u.; = Change in frequency of area in Hz; K = Power system gain constant of area = 33.33; p 79

8 K.. M. Vijaya Chandrakala, et al. p = Power system time constant of area = 6.67; = Change in hydro governor power in p.u.; P Hg P HV P H = Change in hydraulic valve power in p.u.; = Change in hydraulic turbine power in p.u.; ie-line A = Synchronizing power coefficient = -; = Synchronizing coefficient =0% of area capacity = 0.Cos δ = ; P tie = Change in tie-line power between area and area respectively in p.u.; s = Laplace transform operator; ACE = Area Control Error; ACE = ate of change of Area Control Error; ε = hreshold value of the switch; d = rate of change w.r.t time; dt 7. eferences [] O. I. Elgerd, Electric Energy Systems heory an Introduction, ata McGraw Hill Edition, 983. [] P. Kundur, Power System Stability and Control, McGraw Hill Inc., Newyork, 994. [3] N. Cohn, echniques for improving the control of bulk power transfers on interconnected systems, IEEE ransactions on Power Apparatus and Systems, Vol. 90, pp , 97. [4] K. P. Parmar Singh, S. Majhi and D. P. Kothari, Load Frequency Control of A ealistic Power System With Multi-Source Power Generation, International Journal of Electrical Power and Energy Systems, Vol. 4, pp , 0. [5] Shashi Kant Pandey,. Soumya Mohanty and Nand Kishor, A Literature Survey on Load-Frequency Control for Conventional and Distribution Generation Power Systems, enewable and Sustainable Energy eviews, Vol.5, , 03. [6] Dola Gobinda Padhan and Somanath Majhi, A New Control Scheme for PID Load Frequency Controller of Single-Area and Multi-Area Power Systems, ISA ransactions, Vol. 5, pp.4-5, 03. [7] H. Bevrani, Yasunori Mitani, Kiichiro suji, Hossein Bevrani, Bilateral Based obust Load Frequency Control, Energy Conversion and Management, Vol. 46, pp.9-46, 005. [8] K. P. Parmar Singh, S. Majhi and D. P. Kothari, LFC of an Interconnected Power System with Multi-Source Power Generation in Deregulated Power Environment, International Journal of Electrical Power and Energy Systems, Vol. 57, pp.77-86, 04. [9] S. C. ripathy,. Balasubramanian and P. S. Chandramohanan Nair, Effect of Superconducting Magnetic Energy Storage on Automatic Generation Control Considering Governor Dead Band and Boiler Dynamics, IEEE ransactions on Power Systems, Vol. 7,pp.66-73, 99. [0] M. Mohamed Ismail and M.A. Mustafa Hassan, Load Frequency Control Adaptation Using Artificial Intelligent echniques for One and wo Different Areas Power System, International Journal of Control, Automation and Systems Vol., pp.-3, 0. [] Lalit Chandra Saikia, Sukumar Mishra, Nidul Sinha and J. Nanda, Automatic Generation Control of A Multi Area Hydrothermal System Using einforced Learning Neural 79

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10 K.. M. Vijaya Chandrakala, et al. K.. M. Vijaya Chandrakala born at Bangalore, India. She obtained her B. ech., in Electrical and Electronics Engineering from NSS college of Engineering, Palakkad, India. M.ech., in Power Systems from hrissurr College of Engineering, India. She obtained her Ph.D., Degree from Anna University, Chennai, India. Presently she is working as Assistant Professorr (SG) at Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. Her area of interest is Load Frequency control, Energy Management, Soft computing techniques and Smart grid. S. Balamurugan born at Nagapattinam, India. He completed his B.E., in Electrical and Electronics Engineering from Annamalai University, India by 00. M.E., in Power Systems from same University by 00. He obtained his Ph.D., Degree from Anna University, Chennai, India by 00. Presently he is working as Associate Professor at Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. His research interest areas are Power System Control, Soft computing techniques, Energy management, Deregulation. N. Janarthanan was born in Chennai, India. He received his B.ech Degreee from Bharathidasan University, India in 000, M.E., (power systems) from Annamalai University, India in 008. He is at present working as Assistantt Professor (Sr.Gr.) at Amrita school of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India. Presently he is also carrying out his Doctoral Degree esearch at Amrita Vishwa Vidyapeetham, Coimbatore. Anand B. was born in irunelveli District, amil Nadu State, India. He obtained his B.ech.., Degree in Electrical and Electronics Engineering in the year 00 from Government College of Engineering, irunelveli and Master s Degree with specialization in Power Systems Engineering from Annamalai University, Chidambaram, India in the year 00. He got his Ph.D Degree from Anna University Chennai, India. At present he is serving Hindustan College of Engineering and echnology, Coimbatore, India as Head of the Department of Electronics and Instrumentation 794