Improved Speed Characteristics of a Synchronous Machine using Discrete PID Controller
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This paper explores the enhancement of speed characteristics in synchronous machines through a discrete PID controller, demonstrating improved active power output and reduced overshoots. The simulations conducted using MATLAB/Simulink validate the effectiveness of the method compared to systems without the controller. Overall, the findings indicate significant improvements in stability and performance of the synchronous machine using the proposed control technique.
![57 International Journal for Modern Trends in Science and Technology
Volume: 2 | Issue: 05 | May 2016 | ISSN: 2455-3778IJMTST
Improved Speed Characteristics of a
Synchronous Machine using Discrete PID
Controller
Sk. Saidavali1
| Murali Krishna2
1Department EEE, Srivani school of engineering, Chevuturu, A.P., INDIA
2Department EEE, Srivani school of engineering, Chevuturu, A.P., INDIA
In this paper speed characteristics of a synchronous machine are improved using a discrete PID controller so
that active power output characteristics are also improved. The numbers of overshoots are also reduced for
the speed output and the speed characteristics attain a steady state. The active power output characteristics
are also improved. The advantage of using PID here is auto tuner is provided for PID values. The required
simulation is conducted on mat lab2013/simulink environment.
KEYWORDS: Synchronous Machine, Discrete PID Controller, Speed, MATLAB Simulink.
Copyright © 2015 International Journal for Modern Trends in Science and Technology
All rights reserved.
I. INTRODUCTION
The stability studies are more concerned in
synchronous machines [1].the power obtained is
not stable all the time. Excitation system is
provided to regulate the voltage. Use of power
system stabilizer provides stable power to some
extent. But, the conventional power system
stabilizer does not give the stable power to our
satisfaction. Using discrete PID controller
improves the characteristics of output and
improvements compared to without controller.
In this paper the characteristics of power,
speed are compared with using PID controller
with pss and without using PID and pss.
The model diagram of the synchronous
machine is shown in Fig.1.
II.SYNCHRONOUS MACHINE
The diagram shown in fig.1.Consists of
hydraulic turbine and governor, excitation
system, power system stabilizer, discrete PID
controller. The synchronous machine employed
here is of salient pole type [2].the excitation
system consists of AVR,PSS etc.the main aim of
excitation system is to decrease the transients in
the rotor angle which leads to instability and to
maintain constant voltage. The system used here
is modeled as single machine infinite bus system
(SMIB) in mat lab/simulink.
The AVR is to regulate the terminal voltage when
it drops due to sudden load changes.
By using the discrete PID controller the speed
characteristics are improved. The swings are
reduced much. The general mechanical torque
equation of synchronous machine is given as
below [2].
𝑇𝑒 + 𝑇𝑚 = 𝐽 × 𝑝𝑤𝑟 + 𝐷 × 𝑤𝑟 (1)
When 𝐷 × 𝑤𝑟 is neglected
𝑇𝑒 + 𝑇𝑚 = 𝐽 × 𝑝𝑤𝑟 (2)
The assumptions made during transient analysis
of synchronous machine are [2]:
(a) The machine is running initially on no load
under steady state.
(b) Speed before and after short circuit remains
unchanged at synchronous speed.
The voltage equations of synchronous machine
are:
𝑣𝑓 = 𝑟𝑓 + 𝐿𝑓𝑝 𝑖𝑓 − 𝑀𝑑 × 𝑝𝑖𝑑 (3)
𝑣𝑑 = 𝑀𝑑 × 𝑝𝑖𝑓 − 𝑟𝑎 + 𝐿𝑑𝑝 𝑖𝑑 + 𝐿𝑞 × 𝑤𝑟 × 𝑖𝑞 (4)
𝑣𝑞 = 𝑀𝑑 × 𝑤𝑟 × 𝑖𝑓 − 𝐿𝑑 × 𝑤𝑟 × 𝑖𝑑 − 𝑟𝑎 + 𝐿𝑞𝑝 𝑖
(5)
Where
𝑣𝑓: 𝑓𝑖𝑒𝑙𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
ABSTRACT](https://image.slidesharecdn.com/49-160525181831/85/Improved-Speed-Characteristics-of-a-Synchronous-Machine-using-Discrete-PID-Controller-1-320.jpg)
![60 International Journal for Modern Trends in Science and Technology
Improved speed characteristics of a synchronous machine using discrete PID controller
f: frequency
F: friction factor
peo: activepoweroutput
VIII.REFRENCES
[1] Srinivas singirikonda, G.sathish Gouda, M.harika
reddy.”Transient stability of a.c.generator
controlled by using fuzzy logic
controller.int.journal of engineering research and
application, Vol.4, issue.3, pp.389-395, March
2014.
[2] Dr.p.s.bimbra, generalized theory of electrical
machines, 5th edition, khanna publishers-2013](https://image.slidesharecdn.com/49-160525181831/85/Improved-Speed-Characteristics-of-a-Synchronous-Machine-using-Discrete-PID-Controller-4-320.jpg)
Improved Speed Characteristics of a Synchronous Machine using Discrete PID Controller
- 1. 57 International Journal for Modern Trends in Science and Technology Volume: 2 | Issue: 05 | May 2016 | ISSN: 2455-3778IJMTST Improved Speed Characteristics of a Synchronous Machine using Discrete PID Controller Sk. Saidavali1 | Murali Krishna2 1Department EEE, Srivani school of engineering, Chevuturu, A.P., INDIA 2Department EEE, Srivani school of engineering, Chevuturu, A.P., INDIA In this paper speed characteristics of a synchronous machine are improved using a discrete PID controller so that active power output characteristics are also improved. The numbers of overshoots are also reduced for the speed output and the speed characteristics attain a steady state. The active power output characteristics are also improved. The advantage of using PID here is auto tuner is provided for PID values. The required simulation is conducted on mat lab2013/simulink environment. KEYWORDS: Synchronous Machine, Discrete PID Controller, Speed, MATLAB Simulink. Copyright © 2015 International Journal for Modern Trends in Science and Technology All rights reserved. I. INTRODUCTION The stability studies are more concerned in synchronous machines [1].the power obtained is not stable all the time. Excitation system is provided to regulate the voltage. Use of power system stabilizer provides stable power to some extent. But, the conventional power system stabilizer does not give the stable power to our satisfaction. Using discrete PID controller improves the characteristics of output and improvements compared to without controller. In this paper the characteristics of power, speed are compared with using PID controller with pss and without using PID and pss. The model diagram of the synchronous machine is shown in Fig.1. II.SYNCHRONOUS MACHINE The diagram shown in fig.1.Consists of hydraulic turbine and governor, excitation system, power system stabilizer, discrete PID controller. The synchronous machine employed here is of salient pole type [2].the excitation system consists of AVR,PSS etc.the main aim of excitation system is to decrease the transients in the rotor angle which leads to instability and to maintain constant voltage. The system used here is modeled as single machine infinite bus system (SMIB) in mat lab/simulink. The AVR is to regulate the terminal voltage when it drops due to sudden load changes. By using the discrete PID controller the speed characteristics are improved. The swings are reduced much. The general mechanical torque equation of synchronous machine is given as below [2]. 𝑇𝑒 + 𝑇𝑚 = 𝐽 × 𝑝𝑤𝑟 + 𝐷 × 𝑤𝑟 (1) When 𝐷 × 𝑤𝑟 is neglected 𝑇𝑒 + 𝑇𝑚 = 𝐽 × 𝑝𝑤𝑟 (2) The assumptions made during transient analysis of synchronous machine are [2]: (a) The machine is running initially on no load under steady state. (b) Speed before and after short circuit remains unchanged at synchronous speed. The voltage equations of synchronous machine are: 𝑣𝑓 = 𝑟𝑓 + 𝐿𝑓𝑝 𝑖𝑓 − 𝑀𝑑 × 𝑝𝑖𝑑 (3) 𝑣𝑑 = 𝑀𝑑 × 𝑝𝑖𝑓 − 𝑟𝑎 + 𝐿𝑑𝑝 𝑖𝑑 + 𝐿𝑞 × 𝑤𝑟 × 𝑖𝑞 (4) 𝑣𝑞 = 𝑀𝑑 × 𝑤𝑟 × 𝑖𝑓 − 𝐿𝑑 × 𝑤𝑟 × 𝑖𝑑 − 𝑟𝑎 + 𝐿𝑞𝑝 𝑖 (5) Where 𝑣𝑓: 𝑓𝑖𝑒𝑙𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 ABSTRACT
- 2. 58 International Journal for Modern Trends in Science and Technology Improved speed characteristics of a synchronous machine using discrete PID controller 𝑣𝑑: 𝑑𝑖𝑟𝑒𝑐𝑡 𝑎𝑥𝑖𝑠 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑣𝑞: 𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑥𝑖𝑠 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑟𝑓, 𝐿𝑓, 𝑖𝑓: 𝑓𝑖𝑒𝑙𝑑 𝑟𝑒𝑠𝑖𝑡𝑎𝑛𝑐𝑒, 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒, 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝: 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 𝑀𝑑: 𝑚𝑢𝑡𝑢𝑎𝑙 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑖𝑑, 𝑖𝑞: 𝑑𝑖𝑟𝑒𝑐𝑡 𝑎𝑛𝑑 𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑥𝑖𝑠 𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝑠 𝐿𝑑, 𝐿𝑞: 𝑑𝑖𝑟𝑒𝑐𝑡 𝑎𝑛𝑑 𝑞𝑢𝑎𝑑𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑥𝑖𝑠 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 III.DISCRETE PID CONTROLLER The block diagram for discrete PID controller is shown in Fig.2.The block diagram shown in Fig.2.consists of a discrete PID controller, power system stabilizer (PSS), excitation system, hydraulic turbine governor etc. Speed is given as reference input to the PID controller. The output of PID is given to the power system stabilizer; from there it is given to excitation system which is connected to synchronous machine. The field voltage is fed to synchronous machine which is responsible for the required characteristics. The compensator equation for PID controller is given as: 𝑃 𝑏 × 𝑟 − 𝑦 + 𝐼 𝑠 𝑟 − 𝑦 + 𝐷 × 𝑁 1+ 𝑁 𝑠 (𝑐. 𝑟 − 𝑦) (6) IV.RESULTS AND DISCUSSIONS The output waveform for speed and active output power without discrete PID controller and PSS are shown in Fig. (3) - (4). The waveforms for speed and active power output with discrete PID controller and PSS are shown in Fig. (4)- (5). The speed without PID controller shown in Fig.3.is having more transients and the output active power is also having more transients.inorder to decrease these transients and overshoots we are using a PID controller and the related waveforms shows the improved characteristics of speed and output active power. The speed characteristics are improved a lot. The results are satisfactory compared to without controller. DISCRETE PID CONTROLLER REF IN VSTAB PS S EXCITATION SYSTEM SYNCHRONOUS MACHINE Vf Vf HTG Pm Pm Fig.2.block diagram of discrete PID control 3PHASE SUPPLY Synchronous machine HTG Exciter PID PSS Speed Fig.1.model diagram of synchronous machine
- 3. 59 International Journal for Modern Trends in Science and Technology Volume: 2 | Issue: 05 | May 2016 | ISSN: 2455-3778IJMTST V.CONCLUSION The speed characteristics are improved using discrete PID controller which is executed on mat lab/simulink software. The results of speed characteristics are compared with and without discrete PID controller. The results obtained were satisfactory. VI.APPENDIX 𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑃𝐼𝐷 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑒𝑟 𝑑𝑎𝑡𝑎: 𝑃 = 0; 𝐼 = 0.549541 ; 𝐷 = 0; 𝑁 = 100; 𝑏 = 1; 𝑐 = 1; 𝑠𝑦𝑛𝑐𝑟𝑜𝑛𝑜𝑢𝑠 𝑚𝑎𝑐𝑖𝑛𝑒 𝑑𝑎𝑡𝑎: 𝑝𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑖𝑛𝑔: 200𝑀𝑉𝐴 𝑣𝑜𝑙𝑡𝑎𝑔𝑒: 13.8𝐾𝑉 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 𝑟𝑎𝑡𝑖𝑛𝑔: 210𝑀𝑉𝐴, 13.8𝐾𝑉/230𝐾𝑉 Source=230KV VII.NOMINCLATURE Te: electromagnetic torque Wr: rotor speed J: moment of inertia Tm: mechanical torque D: damping factor r: reference input y: output N: filter coefficient b, c: set point weights Rs: stator resistance P: number of poles 0.97 0.98 0.99 1 1.01 1.02 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.5 1 0.5 0 2 4 6 8 10 12 14 16 18 20 time(sec) Fig.6.output active power with discrete PID controller and PSS 2 4 6 8 10 12 14 16 18 20 t Fig.3.speed without discrete PID controller 2 4 6 8 10 12 14 16 18 20 t Fig.4.active output power without discrete PID controller 2 4 6 8 10 12 14 16 18 2 t Fig.5.speed with discrete PID controller and PSS
- 4. 60 International Journal for Modern Trends in Science and Technology Improved speed characteristics of a synchronous machine using discrete PID controller f: frequency F: friction factor peo: activepoweroutput VIII.REFRENCES [1] Srinivas singirikonda, G.sathish Gouda, M.harika reddy.”Transient stability of a.c.generator controlled by using fuzzy logic controller.int.journal of engineering research and application, Vol.4, issue.3, pp.389-395, March 2014. [2] Dr.p.s.bimbra, generalized theory of electrical machines, 5th edition, khanna publishers-2013