Tie-Line Frequency Deviation Control of an Interconnected System using Wind Turbine Generator

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ISSN (Print) : 2278-8948, Volume-2, Issue-6, 2013

131

Tie-Line Frequency Deviation Control of an Interconnected System using Wind Turbine Generator

Mukta & Balwinder Singh Surjan

Electrical Engineering Department, PEC University of Technology, Chandigarh, Chandigarh-160 012 E-mail : [email protected], [email protected]

Abstract - This paper shows the effect the decrease in deviations of tie-line power in an interconnected system using a Wind Turbine Generator. Two different power systems are interconnected via a tie-line and their tie-line power deviation is seen via graph. Then the Wind Turbine Generator is designed and installed in the system and thus the deviations are studied and thus found to be diminished.

The system is drawn using transfer function approach in MATLAB simulink environment.

Keywords - Tie-Line, Interconnected System, Wind Turbine Generator, Tie-Line Power deviation, simulink

I. INTRODUCTION

In an interconnected system automatic generation control is implemented in such a way that each area, or subsystem, has its own central regulator. As shown in Fig. 1, the power system is in equilibrium if, for each area, total power generation PT, the power demand PL

and the net tie-line interchange power P_tie satisfy the equilibrium condition [1]. The objective of each area regulator is to maintain frequency at the scheduled level (frequency control) and to maintain net tie-line interchanges from the given area at the scheduled values (tie-line control).The regulation is executed by changing the power output of the turbines in the area through varying Pref in their governing systems. Fig 1.2 shows a functional diagram of the central regulator. Frequency is measured in the local low voltage network and compared with the reference frequency to produce a signal that is proportional to the frequency deviation ∆ƒ.

The information on power flows in the tie-lines is sent via telecommunication lines to the central controller which compares it with the reference value in order to produce a signal proportional to the tie-line interchange error ∆Ptie. Electricity grid interconnections have played a key role in the history of electric power systems. Most national and regional power systems that exist today

began many decades ago as isolated systems, often as a single generator in a large city. As power systems expanded out from their urban cores, interconnections among neighbouring systems became increasingly common. Groups of utilities began to form power pools, allowing them to trade electricity and share capacity reserves. One of the great engineering achievements of the last century has been the evolution of large synchronous alternating current (AC) power grids, in which all the interconnected systems maintain the same precise electrical frequency.

Fig. 1 : Power balance of control area

II. SYSTEMMODELLING

A single area power system is used as the basic system comprising of power system block representing the generation transmission, prime-mover and its control. The load variation has been simulated as step change. The transfer function model has been built using MATLAB simulink [13]. The system component blocks used in transfer function model are simplified from the differential equations of the system [2]. The whole functions are used in s domain only. The basic model developed is single area and then it is interconnected [4,6]. Then the model is interconnected via tie-line using equations [2]. In an isolated control area case the

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132 incremental power (∆PG - ∆P_D) was accounted for by the rate of increase of stored kinetic energy and increase in area load caused by increase in frequency. Since a tie line transports power in or out of an area, this fact must be accounted for in the incremental power balance equation of each area. Power transported out of area 1 is given by

(i) where = power angles of equivalent machines of the two areas.

For incremental changes in δ1 and δ₂, the incremental tie line power can be expressed as

(ii) where

(iii)

=synchronising coefficient

Since incremental power angles are integrals of incremental frequencies, we can write Eq. (ii) as

(iv) where ∆ƒ1 and ∆ƒ₂ are incremental frequency changes of areas 1 and 2, respectively.

Similarly the incremental tie line power of area 2 is given by

(v) where

The incremental power balance for area 1 can be written as[n]

(vi) It may be noted that all quantities other than frequency are in per unit in Eq. (vi).

Taking the Laplace transform of Eq. (vi) and reorganizing, we get

(vii) where K_ps and T_ps are power system gain and time constants. The isolated control area case, the only change is the appearance of the signal ∆Ptie,1(s) is obtained as

(viii)

Fig. 2 : Tie Line Block Diagram

The corresponding block diagram is shown in Fig. 3.

For control area 2, ∆Ptie,2 is given by Eq. (ix)

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Fig. 3 : Block showing tie line of both power systems

III. INTERCONNECTEDSYSTEMUSINGTIELINE The two single area system of Load frequency control are combined using tie-line function as shown in Fig.4.

Fig. 4 : Interconnected Two Area System

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133 IV. WINDTURBINEGENERATOR

The full transfer function of the wind turbine is of very high order and contains a number of nonlinearities as described in the next section. In case of a real wind turbine (instead of a simulation model as used here) the full transfer function is most likely unknown. It can be shown however that the wind turbine can actually be described with a second order equivalent transfer function. Such a second order transfer function can be found via the step response of the wind turbine. Due to the nonlinear nature of the wind turbine, step responses have to be conducted in different operating regions, leading to different transfer functions in the respective operating regions. We are considering the transfer function for linear region as we have linearized the linearities[7].

The main sources of electrical power have been fuel burning engines, which use the energy from non- renewable fuels to mate a shaft connected to an electric generator. These systems have seen vast improvements in the areas of efficiency, emissions and controllability because they have always been the primary power sources. The deregulation of electricity has seen rise in research geared towards alternative energy sources.

Some of the major sources being investigated include fuel cells, micro-turbines and wind turbines. Wind turbines are the main focus of this research. The wind turbine plant model was divided into two main parts.

The first part was the wind turbine, which included a turbine rotor on a low-speed shaft a gearbox and high- speed shaft. The second part was the electric generator whose input was constant angular rotation from the turbine plant and whose output was electrical power.

Fig. 6 illustrates the general block diagram of the wind turbine system [8].

Fig. 5 : Block Diagram of a Wind turbine System Although the goal of this control sequence is to maintain a constant angular speed and constant power, P_m. Only the angular speed is fed back to accommodate the wind speed fluctuations. This is because controlling the angular speed automatically means that the aerodynamic torque T_A that causes the rotation, is controlled and hence the extracted mechanical power, P_m. This is derived from the fact that these three quantities, P_m, T_A and ω are related by equation [8] (x).

P_m=T_A ω (x) Therefore controlling T_A and ω to remain constant will cause the power P_m to remain constant as well. The dynamic modelling of wind power generators (WTG), in order to estimate their impact on the power system dynamic behaviour, is a matter of high interest. The development of these models has been the subject of many discussions: it requires a compromise between making substantial simplifications to reduce computational efforts on the one hand, and maintaining the necessary adequacy to be able to predict the wind power’s influence on the electrical power system’s dynamic behaviour on the other hand. By investigating the dynamic behaviour of wind power generators, more insight is obtained concerning the ability of a wind farm to provide frequency control [3,10]. The ‘Wind Power Model’ contains the following basic formula to calculate the turbine mechanical power P_mech[3]_.

(xi) The dynamic modelling of wind power generators(WTG), in order to estimate their impact on the power system dynamic behaviour, is a matter of high interest. The development of these models has been the subject of many discussions: it requires a compromise between making substantial simplifications to reduce computational efforts on the one hand, and maintaining the necessary adequacy to be able to predict the wind power’s influence on the electrical power system’s dynamic behaviour on the other hand. By investigating the dynamic behaviour of wind power generators, more insight is obtained concerning the ability of a wind farm to provide frequency control. It is independent on any other power system and it is working as a deregulated system here. A WTG is designed using the system parameters given[10-13]. The two transfer functions are used here for low pass filter and for high wind speed. In the upper part the the wind speed is low-pass filtered.

This time constant depends on the average wind speed, but is assumed constant for this simplified model. The lower part is used for maintaining high speed of wind and then both are added to a summer.

Fig. 6 : Transfer Function of WTG

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134 The output of wind turbine generator depends on the wind speed at that instant. The wind turbine system contains several nonlinearities. When a wind turbine uses its pitch controller to counteract utility grid frequency oscillations, its output power varies between maximum, or rated power, and zero power. The pitch angle set point is nonlinearly limited by these boundaries. The pitch system, which turns the pitch angle according to wind speed, introduces nonlinearity.

The wind turbine can be simplified to a first order system. The transfer function of the WTG and generator is represented by a first-order lag [10] as

T T

T

sT

s K

G  

) 1

(

(xii)

G G

G

sT

s K

G  

) 1

(

(xiii) Thus using MATLAB simulink we have drawn

interconnected two area system with wind turbine generator as shown in Fig. 7.

Fig. 7 : Two Area Power Interconnected System with Wind Turbine Generator

V. FUZZYCONTROLLER

The inherent characteristics of the changing loads, complexity and multi-variable conditions of the power system limits the conventional control methods giving satisfactory solutions. Artificial intelligence based gain scheduling is an alternative technique commonly used in designing controllers for non-linear systems. Fuzzy system transforms a human knowledge into mathematical formula. Therefore, fuzzy set theory based approach has emerged as a complement tool to mathematical approaches for solving power system problems. Fuzzy set theory and fuzzy logic establish the

rules of a nonlinear mapping. Fuzzy control is based on a logical system called fuzzy logic which is much closer in spirit to human thinking and natural language than classical logical systems. Nowadays fuzzy logic is used in almost all sectors of industry and science. One of them is AGC. The control signal is given by[4]

u (t)= -( K_p y+ K_i ∫y dt) (xiv) K_p and K_i are the proportional and the integral gains respectively and taken equal to one. For the proposed study, Mamdani fuzzy inference engine is selected and the centroid method is used in defuzzification process.

Table I. Rules for the fuzzy logic controller [6]

A Ċ E

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

LN: large negative, MN: medium negative, SN: small negative, Z: zero, SP: small positive, MP: medium positive and LP: large positive

Fig. 8 Membership functions used in the study

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135 Fuzzy logic shows experience and preference through membership functions which have different shapes.

These rules are obtained based on experiments of the process step response, error signal, and its time derivative. The membership functions of the fuzzy logic pi controller presented in Fig.8 consist of three memberships functions (two-inputs and one-output)[6].

Each membership function has seven memberships comprising two trapezoidal and five triangular memberships.

Seven numbers of rules have been taken in inference mechanism. Therefore, 49 control rules are used for this study. The range of X is selected from simulation results. All memberships are selected to describe the linguistic variables.

Fig. 9 : Block of Subsystem 1with Fuzzy Controller

Fig. 10 : Block of subsystem 2 with Fuzzy Controller

These functions have different shapes depending on system. For the determination of the control rules, it can be more complicated than membership functions, which depend on the designer experiences and actual physical system. The control rules are built from the if-then statement (i.e. if input 1 and input 2 then output 1).

Table I taken from [4,6], indicates the appropriate rule base used in the study. Let us consider the fourth row and fifth column in Table 1 e.g. if ACE is Z and is SP then y is SN.

The System is now modelled with Fuzzy Controller as shown in Fig. 9, 10. Then implemented to two area interconnected system.

VI. SYSTEMDATA

The Single area and wind turbine generator data used for the system study in this paper has been given in Table II and III,IV[4,6,10] :

Table II Parameters of Area 1 Parameters of Area 1

K_P Power System Gain 100 T_P Power System Time

Constant 20

Ksg Governor Gain 1

T_sg Governor Time Constant 0.4

K_t Turbine Gain 1

T_t Turbine Time Constant 0.5 R Speed regulation Droop 3 B Frequency Sensor Gain 0.425 K_i Integral Controller Gain 0.09

Table III Parameters of Area 2 Parameters of Area 2

K_P Power System Gain 120 T_P Power System Time

Constant 20

K_sg Governor Gain 1

T_sg Governor Time Constant 0.08

K_t Turbine Gain 1

T_t Turbine Time Constant 0.3 R Speed regulation Droop 2.4 B Frequency Sensor Gain 0.42 K_i Integral Controller Gain 0.09

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136 Table III Parameters of Wind Turbine Generator [3]

Parameter

K_T 1

T_T 1.5

K_G 1

TG 0.5

VII. SIMULATIONRESULTS

In this paper, a deregulated WTG has been used along with integral and fuzzy logic controller to control the tie-line power deviation of the power system. The implementation worked with Matlab-Simulink software.

The values of system parameters as explained above are used for all simulations to facilitate a comparative study.

Firstly the tie-line deviation is seen without fuzzy controller and Wind Turbine Generator for area 1 and 2.

Then Fuzzy Controller is added to each area. Then the Wind Turbine generator transfer function is added to tie line. The following Figs. illustrate the decrease in deviation.

Fig. 11 : Tie Line Power Deviation of area 1 without Fuzzy Controller and WTG

Fig. 12 Tie Line Power Deviation of area 2 without Fuzzy Controller and WTG

Fig. 13 Tie Line Power Deviation of area 1 with Fuzzy only

Fig. 14 Tie Line Power Deviation of area 2 with Fuzzy only

Fig. 15 Tie Line Power Deviation of area 1 with Fuzzy and WTG

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137

Fig. 16 Tie Line Power Deviation of area 2 with Fuzzy and WTG

Fig. 17 Tie Line Power deviation of area 1 with Fuzzy,WTG and increased gain of integral controller

Fig. 18 Tie Line Power deviation of area 2 with Fuzzy,WTG and increased gain of integral controller

VIII. CONCLUSION

Thus we can see that using Fuzzy Controller and WTG the tie line power Deviation has been decreased.

Thus we have proposed a new idea for improving the power deviations in tie-line in an interconnected two area system.

IX. REFERENCES

[1] Jan Machowski, Janusz Bialek, J. James Richard Bumby, “Power System Dynamics and Stability”

First Edition, Wiley and Sons Publications, March 1998.

[2] I.J. Nagrath and D.P. Kothari, “Modern Power System Analysis” 3^rd Edition, Sixteenth reprint 2009, Tata Mc-Graw Hill publication.

[3] Jorris Soens, Johan Driesen, Ronnie Belman,

“Equilvalent Transfer Function for a Variable Speed Wind Turbine in a Power System Dynamic Simulations” International Journal of Distributed Energy Resources ,Vol. 1 ,Number 2, ISSN 1614-7138, Pp 111-131.

[4] Mukta, Balwinder Singh, “Grid Stability of Interconnected System with Fuzzy-logic controller & HVDC in Deregulated Environment” IJSCE( International Journal of Soft Computing and Engineering) Vol.2,Issue 6,January 2013,pp. 283~288,ISSN :2231-2207.

[5] Kamalesh Chandra Rout, “Dynamic Stability Enhancement of Power System Using Fuzzy Logic Based Power System Stabilizer”, M.Tech Thesis Report,NIT RourKela,May,2011

[6] Yogendra Arya, Narender Kumar, Hitesh Dutt Mathur, “Automatic Generation Control in Multi Area Interconnected Power System by using HVDC Links” IJPEDS( International Journal of Power Electronics and Drive System) Vol.2,No.1,March 2012, pp.67~75, ISSN :2088- 8694.

[7] Clemens Jauch, Syed M. Islam, “Identification of a Reduced Order Wind Turbine Transfer Function from the Turbine’s Step Response”

AUPEC’05,Vol.1,S115 ,

http://itee.uq.edu.au/~aupec/aupec05/AUPEC200 5/Volume1/S115.pdf

[8] Bongani Malinga ,Dr. John E. Sneckenberger, Dr.

Ali Feliachi, “Modeling and Control of a Wind Turbine as a Distributed Resource” IEEE Conference on System Theory ,Proceedings of the 35th Southeastern Symposium, ISBN 0-7803- 7697-8. pp 108~112,2005

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138 [9] Mukta,Balwinder Singh,” Load frequency

Control through Fuzzy Logic Controller in a Deregulated Environment” National Conference on Recent Innovations in Electrical Electronics

and Communication

Engineering(RIEECE),November 2012,paper code, RIEECE-173

[10] Dulal Ch Das, A K Roy, N Sinha, “PSO Optimized Frequency Controller for Wind-Solar thermal-Diesel Hybrid Energy Generation System: A Study” International Journal of Wisdom Based Computing, Vol. 1 Issue. 3, December 2011, pp. 128-133.

[11] Charles Vartanian, “Grid Stability Battery Systems for Renewable Energy Success” IEEE Conference on Energy Conversion Congress and Exposition (ECCE), ISBN 978-1-4244-5287,pp 132 - 135 , October 2010.

[12] Bijaya Pokharel, “Modelling, Control And Analysis of a Doubly Fed Induction Generator based Wind Turbine System with Voltage Regulation” Master Thesis in Electrical Engineering, Graduate School Tennessee Technological University, December 2011.

www.tntech.edu/files/cesr/StudThesis/Bijaya.pdf [13] Lucas Friedrich,Matthias Gautschi, “Grid Stabilization Control and Frequency Regulation for Inverter‐connected Distributed Renewable Energy Sources” Master Thesis report, University of Wisconsin-Madison, September 2009.

[14] www.mathworks.com/products/matlab- For MATLAB help with simulink

[15] Timothy J. Ross, “Fuzzy Logic with Engineering Applications” Second Edition, Wiley Publication, John Wiley & Sons, Aug-2004

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