Development and application of a turbogenerator model.
Dvornik, Josko ; Tireli, Enco ; Orovic, Josip 等
1. INTRODUCTION
The model of marine steam turbine machinery which drives electric
synchronous generator (Hind, 1968) has two essential situations of
energy accumulation: in the steam volume (steam area, steam volume of
the turbine) and in the turbine rotor. The main condenser is observed as
a special governing object. Each of the stated parts can be described by
its mode equation, that is, by the differential equation which describes
the performance dynamics.
2. SIMULATION MODELLING OF MARINE STEAM TURBINE
The system dynamic mathematical model of the marine steam turbine
can be defined by means of differential equations. Equation of the
turbine steam volume (Nalepin, 1975):
-- (1)
Equation of the turbine rotor dynamics (Nalepin, 1975):
-- (2)
Where the following symbols stand for:
[[psi].sub.1]--relative increment of the steam pressure in the
steam volume, [phi]--relative increment of the turbine rotor angular
velocity, [T.sub.[psi]1]--time constant of the turbine rotor,
[T.sub.[psi]]-- time constant of the turbine rotor, [R.sub.u]--time
constant of the steam volume, Rv1--time constant of the steam volume,
[[psi].sub.0]--relative increment of the steam pressure before the
manoeuvring valve, [R.sub.[psi]0]--time constant of the turbine rotor,
u.--relative change of the position of the manoeuvring valve,
[[psi].sub.2]--relative increment of the steam pressure in the main
condenser, [T.sub.[psi]2]--time constant of the boiler.
On the basis of a mathematical model, or the explicit form of the
mode equation of the marine steam turbine (1) and (2), it is possible to
determine the mental-verbal model of the marine steam turbine.
If the relative increment of the steam pressure in the turbine
steam volume [[psi].sub.1] increases, the speed of the relative
increment of the steam pressure in the turbine steam volume
[[psi].sub.1] will decrease. This gives a negative cause-effect link.
If the relative increment of the steam pressure before the
manoeuvring valve [[psi].sub.0] increases, the speed of the relative
increment of the steam pressure in the turbine steam volume will
increase. This gives a positive cause-effect link.
If the relative change of the position of the manoeuvring valve
[mu] increases, the speed of the relative increment of the steam
pressure in the turbine steam volume will increase. This gives a
positive cause-effect link.
If the time constant of the steam volume [R.sub.[mu]] increases,
the speed of the relative increment of the steam pressure in the turbine
steam volume will decrease. This gives a negative cause-effect link.
If the time constant of the turbine rotor [R.sub.[mu]0] increases,
the speed of the relative increment of the steam pressure in the turbine
steam volume will decrease. This gives a negative cause-effect link.
If the time constant of the steam volume [R.sub.[mu]1] increases
the speed of the relative increment of the steam pressure in the turbine
steam volume will increase, which gives a positive cause-effect link.
If the relative increment of the steam pressure in the steam volume
[[psi].sub.1] increases, the speed of the relative increment of the
turbine rotor angular velocity will increase. This gives a positive
cause-effect link.
If the relative increment of the turbine rotor angular velocity
[phi] increases, the speed of the relative increment of the turbine
rotor angular velocity will decrease. This gives a negative cause-effect
link.
If the relative increment of the steam pressure in the main
condenser [[psi].sub.2] increases, the speed of the relative increment
of the turbine rotor angular velocity will decrease. This gives a
negative cause-effect link.
If the time constant of the turbine rotor [T.sub.[psi]1] increases,
the speed of the relative increment of the turbine rotor angular
velocity will decrease. This gives a negative cause-effect link.
If the time constant of the turbine rotor [T.sub.[phi]] increases,
the speed of the relative increment of the turbine rotor angular
velocity will increase. This gives a positive cause-effect link.
If the time constant of the turbine rotor [T.sub.[psi]1] increases,
the speed of the relative increment of the turbine rotor angular
velocity will decrease. This gives a negative cause-effect link.
If the time constant of the turbine rotor [T.sub.[psi]2] increases,
the speed of the relative increment of the turbine rotor angular
velocity will increase. This gives a positive cause-effect link.
On the basis of the stated mental-verbal models it is possible to
produce structural diagrams, flowcharts and quantitative simulation
model of the marine steam turbine in the POWERSIM simulation language (Munitic, 1989).
3. INVESTIGATING PERFORMANCE DYNAMICS OF THE MARINE STEAM TURBINE
IN LOAD CONDITIONS
After system dynamics qualitative and quantitative simulation
models were produced, all possible operating modes of the system will be
simulated in a laboratory, using one of the simulation packages, most
frequently DYNAMO (Richardson & Aleksander, 1981) or POWERSIM
(Byrknes).
After the engineer, designer or a student has conducted a
sufficient number or scenarios to verify the model, and an insight has
been obtained about the performance dynamics of the system using the
method of heuristic optimisation, the optimisation of any parameter in
the system may be performed. In the presented scenario the two phases of
the momentum (starting) of the marine steam turbine will be presented,
as well as connecting the marine synchronous generator in TIME = 100
seconds in the following way:
1. The manoeuvring valve of the marine steam opens for 5% of the
rated opening in TIME = 1o seconds. The lower RPM is maintained for 5o
seconds (about 5% of the rated RPM or 500-600/min.) for even heating of
turbine masses.
2. In TIME = 50 seconds the manoeuvring (governing) valve opens to
the rated opening (100%) MI=STEP (.05, 10) +STEP (.95, 50) and increases
the marine steam turbine to the rated RPM. In TIME = 10 seconds the
relative increment of the steam pressure in steam volume (PSI1) and the
relative increment of the angular speed of the marine steam turbine
rotor (FI) are increasing.
3. In TIME = 100 seconds a step load is made from 50% of the rated
load, the same as in the previous scenario, and by adding stochastic
load: TFI.K=STEP (2.5,100)*(1-NOISE()) 4.Electronic PID governor has
been installed with parameters: KPP = 100, KPI= .1 and KPD = 100.
5. In the period between Time=140-180 seconds a scenario is
simulated in which the relative pressure in the main condenser is equal
to 2,5 times of nominal pressure. The consequence is a sudden increase
in steam chest pressure. Graphic presentation of the simulation results:
[FIGURE 1 OMITTED]
The results of the simulation show the real performance dynamics of
the marine steam turbine, which at idle speed starts in at least two
stages, and which gives sufficient time for all the parts to heat
equally. This scenario may be used in heuristic optimisation of the PID
governor coefficient. In fact, if the allowed criteria are reached, then
in normal operating conditions the selected combination of PID governor
will certainly be satisfactory.
[FIGURE 2 OMITTED]
The scenario shows that when selecting the coefficient of the
universal PID governor (KPP = 100, KPI = .1, KPD = 100), it will soon
lead to stabilisation of the transition phase, within the limits of the
rated speed deviation of the marine steam turbine rotor (approx. 4% of
the rated RPM). The model can also be used to simulate deviation of
operating parameters such as main condenser pressure (as shown in the
example), inlet steam pressure, opening and closing of manoeuvring valve
and etc. Change of these parameters will have an important influence on
the performance (frequency and voltage) of turbo generator when working
in load operating condition. All these results of simulation are very
valuable in process of failure diagnosis, optimization of steam turbine
thermodynamic process and educational purposes for future marine
engineers.
4. CONCLUSION
System dynamics is a scientific method which allows simulation of
the most complex systems (Forester, 1973/71). The method used in the
presented example demonstrates a high quality of simulations of complex
dynamic systems, and provides an opportunity to all interested students
or engineers to apply the same method for modelling, optimising and
simulating any scenario of the existing elements.
Furthermore, the users of this method of simulating continuous
models in digital computers have an opportunity to acquire new
information in dynamic system performance. The method is also important
because it does not only refer to computer modelling, but also clearly
determines mental, structural and mathematical modelling of the elements
of the system.
This brief presentation gives to an expert all the necessary data
and the opportunity to collect information about the system in fast and
scientific method of investigation of a complex system. This means:
"Do not simulate the performance dynamics of complex systems using
the method of the "black box", because education and designing
practice of complex systems confirmed that it is much better to simulate
using the research approach of the "white box", i.e. System
dynamics methodology."
This simulation method can be applied to engine models, steam
boiler models, gas turbine models and etc.
5. REFERENCES
Byrknes, A. H. Run-Time User's Guide and Reference Manual,
Powersim 2.5, Powersim Corporation, Powersim AS, 12007 Sunrise Valley
Drive, Reston Virginia 22091 USA.
Forrester, Jay W. (1973/1971). Principles of Systems, MIT Press,
Cambridge Massachusetts, USA
Hind, A. (1968). Automation in merchant marines, London
Munitic, A. (1989). Computer Simulation with Help of System
Dynamics, Croatia, BIS Split, p. 297
Nalepin R. A.; Demeenko O.P. (1975). Avtomatizacija sudovljih
energetskih ustanovok, Leningrad, Sudostroennie
Richardson, George P. & Aleksander L. (1981). Introduction to
System Dynamics Modelling with Dynamo, MIT Press, Cambridge,
Massachusetts, USA