Tuning a PID controller for digital excitation control

21st February 2013

Today's digital excitation systems offer numerous benefits for performance improvements and tuning over its analogue voltage regulator predecessor. Dr Kiyong Kim and Richard C Schaefer report.

Many digital regulators utilise a PID controller in the forward path to adjust the response of the system. For main field excited systems, the derivative term is not utilised.

The proportional action produces a control action proportional to the error signal. The proportional gain affects the rate of rise after a change has been initiated into the control loop. The integral action produces an output that depends on the integral of the error.

Dirivative action

The integral response of a continuous control system is one that continuously changes in the direction to reduce the error until the error is restored to zero. The derivative action produces an output that depends on the rate of change of error.

For rotating exciters, the derivative gain measures the speed of the change in the measured parameter and causes an exponentially decaying output in the direction to reduce the error to zero.

The derivative term is associated with the voltage overshoot experienced after a voltage step change or a disturbance.

In addition to PID block, the system loop gain (KG) provides an adjustable term to compensate for variations in system input voltage to the power converting bridge. When performance is measured, the voltage rise time is noted at the 10 per cent and 90 per cent level of the voltage change. The faster the rise time, the faster the voltage response.

An optimally-tuned excitation system offers benefits in overall operating performance during transient conditions caused by system faults, disturbances, or motor starting. During motor starting, a fast excitation system will minimize the generator voltage dip and reduce the I2R heating losses of the motor.

Fast excitation system

After a fault, a fast excitation system will improve the transient stability by holding up the system and providing positive damping to system oscillations.

It also offers numerous advantages, improved relay coordination and first swing transient stability, however an excitation system tuned too fast can potentially cause MW instability if the machine is connected to a voltage weak transmission system. For these systems a power system stabilizer may be required to supplement machine damping.

The evaluation of system performance begins by performing voltage step responses to examine the behavior of the excitation system with the generator. It is performed with the generator breaker open, since the open circuited generator represents the least stable condition, ie the highest gain and the least saturation.

A voltage step test with the generator breaker closed also is performed. In this test, very small percentage voltage steps are introduced to avoid large changes in generator vars. In this case, a 1-2 per cent voltage step change is typical.

To tune the digital controller, two methods are predominantly used: pole placement and pole zero cancellation.

PID controller

Every PID controller contains one pole and two zero terms with low-pass filter in the derivative block ignored.

For generators containing rotating exciters, the machine contains two open loop poles, one derived from the main field and the other derived from the exciter field.

A pole represents a phase lag in the system while the zero tends to provide a phase lead component. The location of poles and zeros with relation to the exciter and generator field poles determines the performance of the excitation control system.

In the pole placement method, the desired closed-loop pole locations are decided based on meeting a transient response specification.

The design forces the overall closed-loop system to be a dominantly second-order system. Specifically, we force the two dominant closed-loop poles (generator and controller) to be complex conjugate pair resulting in an underdamped response.

The third pole (exciter) is chosen to be a real pole and is placed so that it does not affect the natural mode of the voltage response.

The effect of zeros to the transient response is reduced by a certain amount of trial and error and engineering judgment.

The pole placement method generally requires specific information of the exciter field and main generator field time constants to determine the gains needed for the digital controller for adequate response.

Voltage overshoot of at least 10-15 per cent is anticipated with the pole placement method with a two to three second total voltage recovery time, although its voltage rise time can be less then one second.

Dynamic behaviour

This method uses the fact that the dynamic behavior of the pole is cancelled if zero is located close to the pole. The PID controller designed using pole-zero cancellation method forces the two zeros resulting from the PID controller to cancel the two poles of the system.

The placement of zeros is achieved via appropriate choice of the PID controller gains. Since exciter and generator poles are on the real axis, controller has zeros lying on the real axis.

Unlike the pole placement method that uses high integral gain, a proportional gain is set to be at least four times greater than the integral term.

The ratio between the integral term and the proportional term must be a minimum of four for good performance.

Hence, with an Integral gain of 20, the Proportional gain will be 80. It has been found that it works best to have an Integral gain of not more than 20 in most cases to obtain satisfactory performance.

The derivative term will affect the voltage overshoot, and here, a value of 20 will generally be adequate. For faster voltage rise time, the proportional term is increased. On slow speed hydro machines where the generator and exciter time constant tend to be quite large due the slow speed of the turbine.

Inductive lag

Often the KP term is increased to 150 to help overcome the large inductive lag of the machine's field which will normally slow the voltage reaction time of the machine's response.

Sometimes, an additional damping factor also may be required to make the field voltage more stable, known as TD, an additional filter that reduces the effect of noise. Values of 0.01 to 0.08 can be used to reduce the noise content of the field voltage.

Using the pole zero cancellation method of tuning PID gains, commissioning can be accomplished very quickly with excellent performance results.

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Dr Kiyong Kim is Consulting R&D Engineer - Technology Development Engineering and Richard C Schaefer is Senior Application specialist Excitation Systems with Basler Electric, Highland, Illinois, USA and Wasselonne, France. . <a href=""target=_blank></a>

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