Influence of flow curves

Besides the nonlinearities of the compression system described by the Greitzer model, the nonlinear flowcurves of the control valve can play an important role. So far, the flow curves are assumed to be linear,see (4.2). In this section, the effect of these nonlinear curves on compression system behavior is studied.Moreover, the flow curves can often be adjusted to the needs of the user. Therefore, it is useful to get

PID tuning: Tuning a control loop refers to adjusting its control parameters, that is, the proportional, integral and derivative gains, so as to obtain the desired system response.

For systems having a degree of non-linearity, gains that work out well at full load conditions, give erroneous results at starting or light load conditions. To solve this problem, gain scheduling may be used. It uses different gains at different operating regions. Default tuning might give the desired results in some cases, but in others, careful tuning of the PID is required. To deal with the difficult problem of PID tuning (so that the gains satisfy complex criteria within the limitations of PID control), various methods of PID control are available. Of these methods, relay-oscillation method (Ziegler-Nichols method) and Pole Placement method have been used for the design of the PID controller for speed control of DC servo motor. These methods have been explained below: MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 45

1. Relay oscillations method:

The following Simulink model is used, for this method.

Fig 3.17: Relay oscillation Simulink model

This is similar to bang-bang control, where whatever the response, the relay block pushes it in the opposite direction. This gives automatic oscillations of the process output. (This bypasses the limitation imposed by the method where the proportional gain is to be increased till for its minimum value, the relay output starts to oscillate. So, it is difficult to obtain the range of the proportional gain, which is different for each process.) MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 46

The scope output showing the relay output and the process output is as shown below:

Fig 3.18: Scope output showing the relay output and the process output

Say, the relay output (shown in green) oscillates with an amplitude of‗d‘, and the process output (shown in blue) oscillates with an amplitude of ‗a‘. Then, the ultimate gain is given by:

And the ultimate time-period = Time period of oscillation of process output Then, the PID gains are given by: MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 47

From the graph shown above,

Then And (measured from the graph) So, the PID gains obtained by the relay – oscillations method are: MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 48

2. Pole-placement method:

The block-diagram for the closed loop system, using PID controller is as given below:

Fig 3.19: Closed loop PID controller

For this system, the open loop transfer function is given by: Where = And So, And the feedback transfer function H = 1 MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 49

So, the characteristic equation in terms of PID gains is given by:

…….. (1) Say, the desired poles are (-3+j) and (-3-j). But, since the characteristic equation needs to be a cubic equation, so another pole needs to be chosen such that it does not affect the speed of the response, and also does not bring about much change in the overall system-response. For this, it needs to be located at an optimally large distance from the dominant poles. Say, the third pole is at (-10). So, the desired characteristic equation is:

…….. (2)

Comparing the characteristic equation in terms of PID gains (1) and the desired characteristic equation (2), MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 50

…… (3)

…….. (4) ………………. (5) Solving equations (3), (4) and (5):

and Using the PID gains obtained above, and then, fine-tuning, the PID gains are obtained as: and MATLAB Based real time control implementation of DC servo using PCI card

PagecardPage 51

These PID gains are then entered, in the following Simulink model:

Fig 3.20: Closed loop PID controller

When this model is run, the output of the closed loop system is seen to closely follow the input from the signal generator. This indicates optimum performance of the system. The signal generator‘s input, as well as, the process output is shown in the simulation result, shown on the next page: MATLAB Based real time control implementation of DC servo using PCI card PagecardPage 52

Fig 3.21: TF Output

Here, the input from the signal generator is shown in green, and the output of the closed loop control system is shown in blue.

II. FREE GOVERNOR MODE OF OPERATIONThe Governor is an important controller in the powerplant as it regulates the turbine speed, power andparticipates in the grid frequency regulation. It is the mainoperator interfacea) To start the turbine from still condition,b) To vary the load on the turbo-generator when it is onbars (Synchronized) andc) To protect the turbine from damages in the cases of anyunsafe operating conditions.The steady state and dynamic response behavior of theturbine is influenced mainly by the characteristics of theGoverning system.2.1 Need for the Governing SystemThe load on the turbo-generator does not remain constantbut vary as per the consumer (Grid) demand requirements.The presence of a perpetual mismatch between thegeneration and the demand in a larger network results intovariations in frequency and necessitates a continuousadjustment of generation at the turbo-generators. If not,the speed / frequency will be oscillating which is anindication of poor power quality. A state of unchangingsystem frequency and zero acceleration indicates that thegeneration meets the system demand.The governing system provides for this regulation /adjustment, when the turbo-generator is on bars, bycontrolling the steam inflow to the turbine. The regulationis envisaged by various control logics and by operatingthe control valves in the turbine. Stop valves provided inthe governing system protect the turbine in case of unsafeconditions by blocking the steam flow into the turbine.

2.2 How Governing System WorksThe Speed / Power of the steam turbine are controlledby varying the steam flow to the turbine, which in turn is

FREQUENCY REGULATION BY FREE GOVERNOR MODE OF OPERATIONIN POWER STATIONSP. Nelson Vinotha Kumar Xavier1, S. Muthukumar2

1M.Tech Student, Centre for Information Technology and Engineering, M. S. University, Tirunelveli, India2Research Scholar, C I T E, Manonmaniam Sundaranar University, Tirunelveli, India(nelcynth@gmail.com, su.muthukumar@gmail.com)2010 IEEE International Conference on Computational Intelligence and Computing Research2varied by manipulating the control valve lift. The controlvalve is operated by a servomotor driven by a hydraulicsignal. The governing system is a closed loop controlsystem which processes speed error, power error andpressure error to operate the steam control valves.In a Mechanical Hydraulic governing system,mechanical speed sensors viz., fly balls and hydraulicspeed transmitters to sense the speed and hydraulicservomotors and hydraulic amplifiers to drive the finalcontrol elements (i.e.) control valves are employed.In an Electro Hydraulic governing system, Hallsprobe or pulse generators to sense the speed, variouslogics and control circuits to process the error and electrohydraulic converters / amplifiers and a hydraulic actuatorto drive the control valves are used.

Figure-2.2 Basic Elements of a Governing System

Figure-2.3 Electro – Hydraulic Governor Scheme

2.3 Droop or Regulation:Droop can be defined as the percentage changein speed for a change in load. Whenever there is amismatch in power, speed changes. As mentioned earlier,the governing system senses this speed change and adjustsvalve opening which in turn changes power output. Thisaction stops once the power mismatch is made zero. Butthe speed error remains. What should be the change inpower output for a change in speed is decided by the‘regulation’. If 4% change in speed causes 100% changein power output, then the regulation is said to be 4 % (inper unit 0.04).The regulation can be expressed in the form ofpower – frequency characteristic as shown in Figure-2.4.At 100 % load the generation is also 100 %, frequency (orspeed) is also 100%. When load reduces frequencyincreases, as generation remains the same. When loadreduces by 50 %, frequency increases by 2 %, in thecharacteristic shown. When load reduces by 100 %,frequency increases by 4 %. In other words 4 % rise infrequency should reduce power generation by 100 %. This4 % is called ‘droop’ of 4 %. The characteristic is of‘drooping’ type. Droop or regulation is an importantparameter in the frequency regulation. In thermal powerplants droop value is generally 4 % to 5 %.The sensitivity of the governor for a givenchange in load varies inversely with the percentage droop.The droop of the hydro turbines will be around 2 to 3%where as that of the steam turbines will be 4 to 5%

where as that of the steam turbines will be 4 to 5%

Figure-2.4 Droop Characteristics of a Governor

Figure-2.5 Droop Characteristics

2.4 Operation of the GovernorThe governor operation of a turbo-generator can beexplained using the following diagram.

Figure-2.6 Governing Operation - Primary andSecondary ResponseConsider that a unit is delivering a power ‘P’ at afrequency of ‘N’ Hz denoted by the operating point ‘A’.Let us assume that due to some reasons, the frequencydips to ‘NB’. Now because of the droop characteristics ofthe governor, the operating point of the generator willmove to ‘B’ and the generation will increase from ‘P’ to‘PB’. This response of the governor is called the primaryresponse as discussed earlier. The operator subsequentlywill try to restore the generation to the original value ‘P’,the new operating point of the set will be ‘C’ and thefrequency will drop further to ‘NC’. This response of theoperator is called the secondary response. A secondary

response of 1% of the capacity per minute of the set isprescribed by the Load Despatch Center. If no correctiveaction has been initiated by the Grid Managers by way oftripping out excess demand, then the frequency will settleat ‘NC’.

If the generator is at a higher load denoted by thepoint ‘F’ and its load limiter is set at ‘PL’, the rise ingeneration along the droop line will be limited to only‘PL’ and the operating point will only be ‘L’, whatever bethe dip in frequency. As the generation does notcompensate the additional load, the frequency will furtherdrop to NH. The load limiter action is a classic example ofrestricting the FGMO.On the other hand, if any of the feeders tripped,then the frequency will rise to ‘ND’ and the primaryresponse governing action will reduce the load to ‘PD’.The new operating point of the set now will be D. If thefrequency is within the operating range, the operator willbring the unit to the point E and the frequency will furtherrise to ‘NE’. The effect of further increasing thegeneration under high frequency conditions will only raisethe frequency and several procedures like AvailabilityBased Tariff, Guidelines for Unscheduled Interchangesetc., have been laid down by the regulatory commissionsin this regard.

The Ziegler-Nichols frequency response method suggest PID parameters based on a system's ultimate gain Ku

and ultimate period Tu according to the following table. The method provides a convenient method for tuning

PID controllers, since Ku and Tu can be estimated through simple experiments. Once Ku and Tu have beendetermined, the controller parameters are directly given by the formulas above.

(a) Show that the parameters Ku and Tu can be determined from the sustained oscillations that may occur inthe process under relay feedback. Use the describing function method to give a formula for computingKu and Tu based on oscillation data. (amplitude A and angular frequency ! of the oscillation). Let therelay amplitude be D.Recall that the ultimate gain and ultimate period are de_ned in the following way. Let G(s) be thesystems transfer function, and !u be the frequency where the system transfer function has a phase lag of¡180 degrees. Then we have