Optimal tuning of pid power system stabilizer in simulink environment

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 1, January- February (2013), © IAEME
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 4, Issue 1, January- February (2013), pp. 115-123
IJEET
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OPTIMAL-TUNING OF PID POWER SYSTEM STABILIZER IN
SIMULINK ENVIRONMENT FOR A SYNCHRONOUS MACHINE

Mr. Gowrishankar kasilingam1, Ms.Tan Qian Yi2
1&2
Faculty of Engineering & Computer Technology, AIMST University, Kedah, Malaysia
Email:gowri200@yahoo.com

ABSTRACT

In this paper, an optimum algorithm approach is presented for determining the
optimal Proportional-Integral-Derivative (PID) Controller parameters of a typical power
system stabilizer (PSS) in a single machine infinite bus system. The paper is modeled in the
MATLAB Simulink Environment to analyze the performance of a synchronous machine
under normal load conditions. The functional blocks of PID controller with PSS are generated
and the simulation studies are conducted to observe the dynamic performance of the power
system. This paper suggests the use of Ziegler-Nichols method to form the intervals for the
controller parameters in which the tuning to be done. In order to assist the estimation of the
performance of the proposed PID-PSS controller, a time-domain performance criterion
function has been used. The proposed approach yields better solution in term of rise time,
settling time, and maximum overshoot of the system. Analysis in this paper reveals that the
Ziegler-Nichols method of optimal tuning PID controller gives better dynamic performance
as compared to that of conventional trial and error method. Simulation results indicate that
the performance of the PID controlled system can be significantly improved by the Ziegler-
Nichols-based method.

Keywords: Power System Stabilizer, Z&N method, PID Controller

1. INTRODUCTION

Tuning of supplementary excitation controls for stabilizing system modes of
oscillations has been the focus of many researches during the past two decades. PID control is
one of the earlier control strategies. Since many control systems using PID control has been
proven satisfactory, it still has a wide range of applications in industrial control [1]. The

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reason is that it has s simple structure which is easily understood and under practical
conditions, it performed with higher reliability compared to more advanced and complex
controllers. The main purpose of designing a PID controller is to determine the three gains
which are proportional gain (Kp), integral gain (Ki) and derivative gain (Kd) of the controller.
However, the three adjustable PID controller parameters should be tuned appropriately. A
purely mathematical approach to the study of automatic control is certainly the most
desirable course from a standpoint of accuracy and brevity [2].
Many approaches have been developed to determine the PID controller parameters for
single input single output (SISO) systems. Among the well-known approaches are the
Ziegler-Nichols (Z-N) method, the Cohen-Coon method, integral of squared time weighted
error rule (ISE), integral of absolute error rule (IAE), and the gain-phase margin method.
Ziegler and Nichols proposed rules for tuning PID controllers are based on the transient
response characteristics of a given plant [2]. The Ziegler-Nichols formulation is a classical
tuning method which is found in a wide range of applications in the controller design process.
However, computing the gains does not always give best results because the tuning criteria
presume a one-fourth reduction in the first two peaks [3]. Hence the industrial controllers
designed with this method should be tuned further before actual usage [4].
In a power system, the excitation system performs control and protective functions
essential to the satisfactory performance of the power system by controlling the field voltage
and field current. Properly tuned, a PSS can considerably enhance the dynamic performance
of a power system stabilizer [5]. The power system, however, is a highly complex system.
The system of study is the one machine connected to infinite bus system through a
transmission line having resistance (re) and inductance (xe) shown in Figure 1.

Figure 1: One machine to infinite bus system

This paper presents the optimal tuning Proportional-Integral-Derivative (PID) Controller
with power system stabilizer (PSS) for a synchronous machine in a MATLAB Simulink
model environment. The aim is to compare the optimal tuning of Ziegler-Nichols method
with the conventional trial and error tuning method. Several simulations have been carried
out in order to generate the output using a single machine infinite bus power system. The
main features of the proposed PID PSS is that it is simpler for practical implementation and
yields better dynamic performances than that obtained with conventional lead-lag stabilizer
[6]. Results presented in this paper clearly show the effectiveness of tuning the PID controller
with Ziegler-Nichols method in comparison to other methods.
This paper is organized as the following. Section II defines and explains the power
system stabilizer (PSS). Section III discusses the design of a PID controller. In Section IV,
optimum tuning with performance estimation of PID controller is provided. The simulation
results and discussion is established in Section V and Section VI provides important
conclusions.

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2. POWER SYSTEM STABILIZER

Damping of low frequency oscillations in interconnected power system is essential for
secure and stable operation of the system. The basic function of power system stabilizer is to
add damping to the generator rotor oscillations by controlling its excitation using auxiliary
stabilizing signal(s). In this paper, an optimal method based on the PID controller is
considered to the tuning parameters of the PID-PSS. Power system stability is similar to the
stability of any dynamic system, and has fundamental mathematical underpinnings. In order
to provide damping, the stabilizer will produce electrical torque in phase with rotor speed
deviations. The excitation system is controlled by an automatic voltage regulator (AVR) and
a power system stabilizer (PSS). Figure 2 shows the block diagram of the excitation system,
including the AVR and PSS. The stabilizer output limits and exciter output limits are not
shown as we are only concerned with small-signal performance.

Figure 2. Power System Stabilizer

The PSS representation in Figure 2 is made up of: a phase compensation block, a gain
block and a signal washout block. The phase compensation block provides the appropriate
phase-lead characteristic to compensate for the phase lag between the exciter input and the
electrical torque of generator. The stabilizer gain KSTAB determines the amount of damping
introduced by PSS whereas the signal washout block serves as a high-pass filter.

3. DESIGN OF PID CONTROLLER

Proportional–integral–derivative (PID) controller is a generic control loop feedback
mechanism widely used to enhance the dynamic response as well as to eliminate the steady
state error. A PID controller will correct the error between a measured process variable and
the desired input or set point by calculating and giving an output of correction that will adjust
the process accordingly. The PID Controller transfer function relating the error e(s) and
controller output u(s) is given as,

Where, Ti and Td are the reset and the derivative times, respectively. The first term in the
equation represents proportionality effect on the error signal, whereas the second and third
term represents the integral effect and the derivative effects.

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The control signal u(t) from the controller to the plant is equal to the proportional gain
(Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error
plus the derivative gain (Kd) times the derivative of the error. It is given as:

u(t) = Kp e(t) + Ki + Kd

Figure 3. Block Diagram of a PID controller.

The process of determining the PID controller parameters Kp, Ti, and Td to achieve high and
consistent performance specifications is known as controller tuning. In the design of a PID
controller, these controller parameters must be optimally selected in such a way that the
closed loop system will give desired response.
Typical steps for designing a PID controller are:

• Determine what characteristics of the system need to be improved.
• Use KP to decrease the rise time.
• Use KD to reduce the overshoot and settling time.
• Use KI to eliminate the steady-state error.

PID Controllers are widely used in industry due to its simplicity and excellent if not
optimal performance in many applications. PID controllers are used in more than 95% of
closed-loop industrial processes [7]. It can be tuned by operators without extensive
background in Controls, unlike many other modern controllers that are much more complex
but often provide only marginal improvement. In fact, most PID controllers are tuned on-site.
In addition to design the controller, the lengthy calculations for an initial guess of PID
parameters can often be circumvented if we know a few useful tuning rules. In the past four
decades, there are numerous papers dealing with the tuning of PID controllers.

4. OPTIMUM TUNING WITH PERFORMANCE ESTIMATION OF PID
CONTROLLER

There are several rules of thumb for determining how the quality of the tuning of a
control loop. Traditionally, quarter wave decay has been considered to be the optimum decay
ratio. This criterion is used by the Ziegler Nichols tuning method, among others. There is no
single combination of tuning parameters that will provide quarter wave decay. If the gain is
increased and the reset rate decreased by the correct amount the decay ratio will remain the
same. Quarter wave decay is not necessarily the best tuning for either disturbance rejection or
set point response. However, it is a good compromise between instability and lack of
response [8].

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Figure 4. Quarter Wave Decay

There are several criteria for evaluating tuning that are based on integrating the error
following a disturbance or set point change. These methods are not used to test control loops
in actual plant operation because the usual process noise and random disturbances will affect
the outcome. They are used in control theory education and research using simulated
processes. The indices provide a good method of comparing different methods of controller
tuning and different control algorithm. The followings are some commonly used criteria
based on the integral error for a step set point or disturbance response:

IAE - Integral of absolute value of error

ISE - Integral of error squared

ITAE - Integral of time times absolute value of error

ITSE - Integral of time times error squared

Ziegler-Nichols method is also known as Ultimate Gain method (or Closed-Loop method).
In 1942, J. G. Ziegler and N. B. Nichols, both of the Taylor Instrument Companies
(Rochester, NY) published a paper [2] that described two methods of controller tuning that
allowed the user to test the process to determine the dynamics of the process. Both methods
assume that the process can be represented by the model (described above) comprising the
process gain, a “pseudo dead time”, and a lag. The methods provide a test to determine
process gain and dynamics and equations to calculate the correct tuning.
The Ziegler Nichols methods provide quarter wave decay tuning for most types of
process loops. This tuning does not necessarily provide the best ISE or IAE tuning but does
provide stable tuning that is a reasonable compromise among the various objectives. If the
process consists of a true dead time plus a single first order lag, the Z-N methods will provide
quarter wave decay. If the process has no true dead time but has more than two lags (resulting
in a “pseudo dead time”) the Z-N methods will usually provide stable tuning but the tuning
will require on-line modification to achieve quarter wave decay.
Because of their simplicity and because they provides adequate tuning for most loops, the
Ziegler Nichols methods are still widely used.
Ziegler Nichols closed loop method is straightforward. At first, the controller is set to PID
mode by using trial and error value. Next, adjust Kp until a response is obtained that produces

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continuous amplitude oscillation. This is known as the ultimate gain (Gu). Note the period of
the oscillations (Pu) from the continuous oscillation as shown in Figure 5.

Figure 5. Constant Amplitude Oscillation

The final PID gain settings are then obtained using equation below:

Kp: 0.6 GU Nm/rad; Nm/(rad·sec); Nm/(rad·sec)

Based on previous trial and error results, the optimum PID gains according to Zigler-Nichols
method are then:

Kp = 30 Nm/rad Ki = 3.226 Nm/(rad·sec) Kd = 2.8 Nm/(rad·sec)

It is unwise to force the system into a situation where there are continuous oscillations as this
represents the limit at which the feedback system is stable. Generally, it is a good idea to stop
at the point where some oscillation has been obtained. It is then possible to approximate the
period (PU) and if the gain at this point is taken as the ultimate gain (GU), then this will
provide a more conservative tuning regime. Changes in system’s closed loop response
because of the changes in PID parameters with respect to a step input can be best described
using the chart shown in Table 1 below.

Table 1: Changes in PID parameters with respect to a step input
Response Rise Time Overshoot Settling Time Steady State Error
Kp Decrease Increase Small change Decrease
Ki Decrease Increase Increase Eliminate
Small
Kd Decrease Decrease Small change
change

Algorithm for tuning PID Controller
The closed loop (or ultimate gain method) determines the gain that will cause the loop to
oscillate at a constant amplitude. Most loops will oscillate if the gain is increased sufficiently.
The following steps are used:

• Place controller into automatic with low gain, no reset or derivative.
• Gradually increase gain, making small changes in the set point, until oscillations start.
• Adjust gain to make the oscillations continue with a constant amplitude.
• Note the gain (Ultimate Gain, Gu) and Period (Ultimate Period, Pu).

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5. SIMULATION RESULTS AND DISCUSSION
In this study, an optimal tuning method for determining the PID Controller parameters
was carried out. A Simulink model of PID Power System Stabilizer was developed and simulated
to tune the controller. The Ziegler-Nichols rules were used to form the intervals for the design
parameters in tuning the controller by minimizing an objective function. Through the simulation
of PID-PSS, the results show that the proposed controller can perform an efficient search to
obtain optimal PID controller parameter that can achieve better performance criterion. The
controller gains were computed by using both trial and error method and Ziegler-Nichols rules.
The gains found from both methods were listed in Table 2.
Table 2: Controller parameters defined from the two methods
Method Kp Ki Kd
Trial & Error 50 5 2
Ziegler-Nichols 30 3.226 2.8
Figure 6 showed the response of speed deviation with continuous oscillations. The result is
obtained by adjusting the Kp value of the PID Controller to maximum. This is known as the
ultimate gain (Gu). From the output, we can note the period of the oscillations (Pu).

Figure 6. Calculation of Gu & Pu

Figure 7. Response of Speed Deviation

Figure 7 shows both the results of the PID power system stabilizer with tuning done using Trial
and Error method and Ziegler-Nichols method. It is clearly shown in figures that the optimal
tuning of Ziegler-Nichols method is less oscillatory than the trial and error method. The
overshoot is slightly higher for Ziegler-Nichols method. Although a comparatively smaller rise
time (Tr) were obtained from trial and error method, Ziegler-Nichols give shorter settling time
(Ts). It takes about 2.5 sec to settle down while the system using trial and error method needs 3

121


sec to finally settle. These results were presented in Table 3. In conclusion, superior results were
obtained in terms of system performance and controller output by using Ziegler-Nichols method
for tuning PID controllers when these values compared on tables and figures.
Table 3: Response characteristics of the System
Settling
Rise time, Oversho
Method time,
Tr (sec) ot (p.u.)
Ts (sec)
Trial & Error 3 0.055 0.0082
Ziegler-Nichols 2.5 0.065 0.01267

Figure 8-10 shown below are the response for rotor angle deviation, load angle and field voltage of
the PID PSS. It is clear that PID controller with Ziegler-Nichols tuning method provides a
comparatively better damping characteristic to low frequency oscillations by stabilizing the system
much faster.

Figure 8. Response of Rotor Angle Deviation

Figure 9. Response of Load Angle

Figure 10. Response of Field Voltage

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6. CONCLUSION

In this study, the proportional-integral-derivative power system stabilizer (PID-PSS)
has been proposed for the enhancement of the dynamic stability of single machine infinite
bus. Gain settings of PID-PSS have been optimized using the proposed methods. The Ziegler-
Nichols method was used to form the intervals for the PID tuning. Analysis reveals that this
method gives much better dynamic performances as compared to that of trial and error
method. It has more robust stability and efficiency. Hence, it can help to solve the searching
and tuning problems of PID controller parameters more easily and quickly than the trial and
error method. Analysis also shows that the PID gain settings obtained for nominal loading
condition gives satisfactory dynamic performances. Modeling of proposed controller in
Simulink environment provides an accurate result when compared to mathematical design
approach.
REFERENCE
1. N.M. Tabatabaei, M. Shokouhian Rad (2010), “Designing Power System Stabilizer with
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