US3446224A - Rotor stress controlled startup system - Google Patents

Description

May 27, 1959 E. E. zwlcKY, JR

ROTOR STRESS CONTROLLED STARTUP SYSTEM Sheefl Filed Jan. 5, 1967 HIS ATTORNEY.

May 27, 1969 E. E. zwlcK-Y, JR 3,446,224

ROTOH STRESS CONTROLLED'STARTUP SYSTEM Filed Jan. 5, 1967 Sheet 2 0f 4 @W Y cLocK PULSE ROTOR SURFACE TEMPERATURE (ANALOG) SAMPLER S5 (DIGITAL) BT(DIGITAL) I NVENTORI EVERETT E. ZWICKY,JR.

HIS ATTORNEY.

May 27, 1969 E. E. zwlcKY, JR 3,446,224

Y ROTOR STRESS CONTROLLED STARTUP SYSTEM Filed Jan. 3, 1967 S1196??I 3 Of 4 LOW VALUE GATE BY il HIS ATTORNEY.

May 27, 1969 E. E. zwxcKY, JR 3,446,224

yROTOR STRESS CONTROLLED STARTUP SYSTEM Filed Jan. 3. 1967 Sheet 4 of 4 HEAT SOURCE VALVE ACTUATOR RoToR SURFACE sTREss SS (ANALOG) 2 PREmcToR B RoToR aoRE sTREssmNALos) LOW S v VALUE BSLIMIT GATE ROTOR BORE i soRE STRESS W L B "i:

T TEMP. mm LlMmANALoG E PRED'CTOR SPEED (ANALOG) INVENTOR: EVERETT E. ZWICKY,JR.

BY O- HIS ATTORNEY.

United States Patent O U.S. Cl. 137--26 12 Claims ABSTRACT F THE DISCLOSURE Startup and loading of steam turbine is controlled by simulated rotor bore and surface stresses derived by analog or digital means from temperature and speed measurement.

Background of the invention This invention relates to an improved method and apparatus for starting up and loading a steam turbine. More particularly, it relates to an improved method of control and a control system to carry out the method, wherein acceleration of the turbine from standstill to rated speed and rate of applying load to the turbine after it is at full speed both take place at the maximum safe rate without imposing undue stresses upon the turbine rotor.

Control systems are known wherein acceleration of the steam turbine rotor from stanstill to full speed is accomplished in a controlled fashion by limiting the time rate of change of the rotor speed to a safe Value. The allowable acceleration may be modied at different speeds so as to provide for a hold period to allow the rotor to adjust to changing temperatures or to speed up acceleration through certain critical speed ranges of the rotor. Systems are also known wherein the rate of applying load to the turbine after it reaches full speed is accomplished in a controlled fashion.

Although the foregoing acceleration and load rate cont-rol may be carried out manually, as is usually done with older systems, a system for controlling both acceleration and load rate in accordance with an adjustable acceleration reference signal or load rate reference signal respectively is disclosed in copending application Ser. No. 542,157 filed Apr. 12, 1966, now Patent No. 3,340,883 of Sept. 12, 1967 in the name of Jacob R. Peternel and assigned ot the assignee of the present invention.

Even with the improved automatic features of the Peternel application, there is still substantial judgment required on the part of the steam turbine operator in setting the allowable acceleration reference and load rate refernce. This is because the stresses in the turbine rotor are an important limitation on the starting and loading rate. Since the steam turbine rotor is a massive steel member and temperature changes take place rather slowly therethrough, the allowable acceleration and loading rates depend to some extent upon the temperature distribution in the rotor at the time a change is dictated. For example, a turbine which has been shut down and is being restarted shortly thereafter in what is known as a hot start can be brought up to speed and loaded much more quickly than a cold turbine.

It is usually desired to start up and load the turbine at the maxium rate. However, cracking may develop at the rotor surface if the thermal stresses are too high, or at the rotor bore if the combined thermal and centrifugal stresses are too high. Since it is not feasible to directly measure these stresses on the rotating member, prior control systems have relied upon other parameters to control the powerplant.

Accordingly, one object of the present invention is to provide an improved control system for starting up and 3,446,224 Patented May 27, 1969 loading a steam turbine in accordance with the rotor stresses so as to load the turbine at the maximum safe rate.

Another object of the invention is to provide an improved method of starting and loading a steam turbine at the maximum safe rate without undue stress on the rotating member.

Summary of the invention Brielly stated, the invention provides an improved apparatus and method for obtaining simulated rotor surface stress and rotor bore stress from measurements of steam temperature and rotor speed, converting these values to surface and bore stress margins, and applying the lowest margin as an acceleration reference signal or a load rate reference signal to a known turbine control system utilizing such signals to control the turbine startup and loading.

Brief description of the drawing FIG. 1 of the drawing is a simplified schematic view of the steam turbine powerplant and control system with the improvement enclosed within dotted lines.

FIG. 2 is a simplified cross section taken through a steam turbine rotor and casing,

FIG. 3 is an enlarged schematic view of the portion of the control system shown within dotted line sin FIG. 1,

FIG. 4 is a flow chart illustrating operation of the stress and temperature calculators as carried out in digital fashion,

FIG. 5 is a simplified schmeatic of a modified form of the invention wherein stresses and temperatures are calculated in analog fashion, and

PIG. 6 is a schematic view similar to FIG. 4 for the lmodified analog form of the invention.

Prior art portion of the disclosure Referring rst to FIG. 1 of the drawing, the previously known portions of the control system will be described A steam turbine 1 drives a load such as generator 2, the speed and load being controlled by a steam admission valve 3. The generator 2 supplies electric power to electrical network lines 4 when a main circuit breaker 5 iS closed. Valve 3 is operated by a servo 6 through a high pressure hydraulic ram 4which is positioned in accordance with a DC electrical valve positioning signal amplified in amplier 7.

A variable reluctance speed sensor 8 adjacent the turbine shaft generates electrical pulses which are amplified at 9 and converted by a frequency-to-voltage converter 10 to a DC electrical signal proportional to actual speed appearing in line 11. An opposite polarity DC speed reference signal is generated in an adjustable voltage source 12 and summed with the actual lspeed signal in summer 13 to provide a DC speed erro-r signal in line 14.

To provide an acceleration signal, the actual speed signal in line 11 is differentiated with respect to time in diiferentiator 15 and applied as an actual acceleration signal to an integrating summer 16. The other input to integrating summer 16 is a refeernce or desired acceleration which appear as a DC voltage of opposite polarity to actual acceleration at terminal 17 by means later to be described and is modilied by suitable gain adjustments such as a rheostat at 18. The actual acceleration and reference acceleration voltages are summed and the time integral of the difference appears in line 19 as an acceleration error signal.

A low value gate 20 admits only the lower error signal (speed or acceleration) which will result in the most closed valve position. Thus the turbine will accelerate in accordance with the acceleration reference signal appearing at terminal 17 until it nears rated speed, whereupon speed will be controlled in accordance with the speed reference signal set in voltage source 12.

When the generator is synchronized with the main line by closing the main circuit breaker 5, the control system switches to the load control mode of operation in the prior art control system being described. Summer 13 supplies a load error signal rather than a speed error signal to low value gate 20. In analogous fashion, integrating summer 16 supplies a time rate of change of load error signal 'to low value gate 20 and the lowest error vsignal of the two controls the position of turbine valve 3.

To provide the load error signal and load rate error signals, input signals corresponding to actual load, rate of change of load, and appropriate reference signals must be provided. Actual load is sensed by a wattmeter device 21 which is equipped to provide a DC signal in line 22 proportional to actual load. An adjustable voltage source 23 provides a load reference signal of opposite polarity. The load reference signal (superimposed upon the speed reference signal) and the actual load signal (superimposed upon the actual speed signal) are supplied to summer 13 when the contact bars are in the lower position.

In analogous fashion to acceleration, the rate of change of load is obtained with a diiferentiator 24 by dierentiating the actual load signal from sensor 21 and is supplied as one input to the integrating summer 16. Similarly, a load rate reference signal appears as a DC voltage of opposite polarity on terminal 25 by means later to be described and, after adjustment -by a suitable gain adjuster 26, is supplied as the other input to integrating summer 16.

The foregoing comprises a description of a prior art control system as described in the aforementioned Peternel patent and in that patent, manually adjustable acceleration reference voltage and load rate reference voltage Awere supplied `at terminals 17, 25 by the operator, using his discretion.

Description of the preferred embodiment Turning now to the improvements of the control system, the portion inside dotted line 29 in FIG. l is a system for calculating simulated rotor bore and surface stresses by means of temperature and speed measurements, calculating safe stress margins, applying the lowest safe stress margin as either an acceleration reference signal or load rate reference signal to the previously described control system.

Inner casing steam temperature of turbine 1 is sensed by one or more thermocouples 27, and converted to a DC voltage corresponding to steam temperature. This voltage is converted to periodic pulses of varying magnitude by a timed sampler 30, converted to digital form by a conventional analog to digital converter 31 and applied to a surface stress calculator 32, a temperature-induced bore stress calculator 33 and a bore temperature calculator 34. The surface stress from calculator 32 is compared with an adjustable surface stress limit value generated in device 330 by means of a suitable summing device 340. A predictor 35 modifies the surface stress margin by calculating the future surface stress margin in accordance with the rate of change of the surface stress margin. The predicted surface stress margin is applied as one input to a low value gate 36.

The temperature-induced bore stress from calculator 33 is applied to summer 37 which is similar to summer 340. The bore temperature from calculator 34 is used to calculate a bore stress limit in device 38, which is applied to summer 37.

A digital bore stress component due to centrifugal forces caused by rotation of the rotor is also calculated and applied to summer 37 This is obtained by multiplying actual rotor speed by itself in multiplier 39 to obtain a voltage proportional to the square of speed, sampling the signal at 40 and converting it to digital form at 41.

The output from summer 37 represents the bore stress margin and is applied to predictor 42. The predicted bore stress margin is applied to low value gate 36. Low value gate 36, which is digital in the embodiment shown, compares the two stress margin values and supplies the lowest of the two to a digital-to-analog converter 43. The result is a DC signal appearing at terminals 44 which is proportional to the lowest of the two stress margins applied to the low value gate 36. This voltage serves either as an acceleration reference signal or a load rate reference signal depending upon the position of the contact bar and the adjustments of the gain device 18, 2.6.

Referring now to FIG. 2 of the drawing, a simplified cross section through a double casing high pressure steam turbine is shown in simplied form. Portions are shown of an outer casing 50, inner casing S1, stator blades 52, and diaphragm seal 53. The rotating portions include a rotor body 54 having turbine blades 55 and having a bore hole 56 along its axis.

The critical parameters in determining whether or not the rotor will crack are the surface stress Ss and the bore stress BS. The bore stress is composed of two parts, one dependent on temperature and one dependent on centrifugal force BSC is proportional to the square of the rotor speed N.

The surface stress and the bore stress component due to temperature BST depend on the radial temperature distribution throughout the massive rotor member 54, and this in turn depends upon past surface temperature history, material of the rotor, and diameter of the rotor. The surface temperature TS may be taken as being very close to the steam temperature inside the inner casing. This is measured with a suitable thermocouple device 27.

The bore temperature BT is the temperature inside the rotor bore hole 56 along fthe axis which is approximately the same as the temperature along the inner surface of the bore hole.

It will be observed that due to the rotation and high temperature of rotor 54, actual measurements of SS, BS and BT are exceedingly difficult if not impossible. In the invention, simulated measurements of these valeus are calculated using temperature of the steam in the inner casing and speed of the rotor which can be conveniently taken from the electrical speed signal already present in the control system.

The theoretical equations for calculating temperature at any point in the rotor are for calculating surface and bore stress due to temperature will be familiar to those skilled in the art, but are set forth for reference as follows:

T=temperature Ts-:surface temperature t=time rrradius a=outer radius Ss=surface stress BST=bore stress due to temperature kzconductivity p=density O=specic heat E=Youngs modulus a=Poissons ratio ac-:thermal expansion coefficient Referring now to FIG. 3 of the drawing, there is shown an enlarged block diagram of a system for digital calculation of rotor bore and surface stress margins to be used as acceleration or load rate reference signals. The functions indicated may be carried out either in a general purpose programmed digital computer 0r in a special purpose digital computer which is wired to accomplish the calculations indicated. The surface stress SS, bore stress due to temperature BST and the bore temperature BT are calculated in digital fashion in calculators 32-34 which will be explained more fully in connection with FIG. 4. A digital surface stress limit is set by means of control knob 57 as determined by the characteristics of the particular rotor. The difference between the surface stress limit and the surface stress is the surface stress margin. A large margin will produce a large acceleration or load rate reference signal allowing faster startup and loading of the steam turbine. The surface stress margin is periodically applied to predictor 35. In accordance with the time period between applications to the predictor and the change in value of the margin during each time period, a predicted margin for some selected time in the future is supplied to low value gate 36.

A suitable function calculator 38 receives the bore temperature as an input value and generates a specied function thereof as an output. The output acts as a bore stress limit and is combined with values of bore stress due to temperature (BST) and bore stress due to speed (BSC) in summer 37. The output from summer 37 is the bore stress margin. The predicted value of the bore stress margin after a suitable time interval is determined in predictor 42 in the same manner as predictor 35. The two digital values from the predictors are periodically compared with one another and the lower of the two margins is supplied to a digital-to-analog converter as indicated in FIG. l.

FIG. 4 illustrates in diagrammatic form the means by which values SS, BST and BT are calculated digitally. The boxes 60 represent memory storage locations in a digital computer wherein a given value can be stored in digital form until replaced by another value. The values TS1, T S2, TSS represent the values of the inner casing steam temperature in digital form at three consecutive intervals of time. As each succeeding value of TS is obtained, the information moves from one storage location to the next as indicated by the arrows, i.e., TS1 becomes TS2 in each of the calculators and TS2 becomes TSS. Since all of the three calculators operate in the same fashion, the surface stress calculator 32 will be taken as exemplary. The three values of TS are multiplied by predetermined constants al, a2 and a3. Also the two preceding values of the calculated surface stress SS2 and SSS are multiplied by predetermined constants b2 and b3. The summation of these in digital fashion is the new value SSl which is supplied to summer 330 (FIG. 3). As the next value of TS is obtained, movement of the information takes place in the manner indicated and a new value of SSI is obtained. However, as will be observed, it depends upon the previous values of S52 anad S53.

Calculations of bore stress BS and bore temperature BT in calculators 33, 34 take place in a similar manner except that the constants used are dierent. These constants are arrived at by solving for the constants in numerical equations which approximate the theoretical equations given previously. Thus the numerical equations solved by calculators 32, 33, 34 are:

Where a through f are constants.

As is known to those familiar with the theoretical equations, the temperature distributions in rotors with different diameters or different materials are similar, provided the time scale is adjusted in the proper way. Similarly, in the digital equations, I have discovered that it Cit is unnecessary to change the constants (such as where they are wired into a special purpose digital computer) when rotors of different diameter or materials are used. It is only necessary to change the pulse rate of the clock timer 30. For example, a smaller diameter rotor would have shorter time lags in temperature change due to its smaller mass. Accordingly, the stress and temperature calculations can be performed accurately for the smaller rotor by merely shortening the length of time between pulses from the timer. It is thus possible to use a single calculator design for all conditions bypmerely changing the sampling rate.

The predictors 35, 42 operate in a similar fashion to the calculators shown in FIG. 4. The values of the stress margin from sequential calculations are stored and shifted from one location to the next, then used to predict a future value of stress margin using the formula:

Mp=predicted stress margin T=time into the future for which the margin is predicted Mzpresent stress margin The operation of the invention is as follows. Referring to FIG. 1, when turbine 1 is at standstill, the main breaker 5 and the other contacts are in the position shown. As the turbine accelerates, the steam temperature measurements from transducer 28 and speed measurements from transducer 8 are used to continually calculate simulated surface stress and bore stress values. These are compared with stress limits and the predicted values of the stress margins are applied to low value gate 36. The lowest stress margin is gated and is converted to a DC voltage which is applied to terminal 17. This DC voltage acts as an acceleration reference signal which is summed with actual acceleration in summer 16. The resulting acceleration error signal from summer 16 serves to position steam turbine valve 3. If the calculated rotor stresses increase, the allowable stress margins decrease and the acceleration reference applied to summer 16 becomes smaller, thus acting to reduce the opening of valve 3 causing the turbine to accelerate at a lower rate.

When the turbine reaches rated speed, the speed error signal from summer 13 will be smaller than the acceleration error signal and it will be substituted (by low value gate 20) and will serve to position valve 3. Under this condition, the speed and temperature transients associated with startup are not present and the rotor stresses will always be within allowable limits.

When load is applied by closing breaker 5, and it is desired to increase the load on turbine 1, temperature changes occur inside the turbine inner casing which affect the rotor stress once again. There will Abe no substantial speed changes because the speed of the turbine is constant when tied to the electrical network. The rotor surface and bore stress margins are continuously calculated as before and the lowest of these now appears at terminal 25 as a signal representing a reference or desired rate of load change to integrating summer 16. The load rate error appearing at low value gate 20 will be less than the load error, and this will serve to position valve 3 to load the turbine at the maximum rate without exceeding allowable stresses. As the turbine approaches its set load, control will revert to the summer 13 and the system will be in the load governing mode.

Description of modilied form of the invention A modified form of the invention appears in FIGS. 5 and 6 wherein the calculation of bore and surface stress is done with an analog model thermally similar to the rotor rather than using digital calculations based on the actual rotor characteristics.

Referring to FIG. 5, a disk of material 61 which is thermally and dimensionally analogous to the rotor of 7 turbine 1 is enclosed between insulating Walls 62 and surrounded by a hollow ring 63 through which heating fluid can be passed. The temperature of the fluid is caused to be varied by actuating a three-way valve 64 so las to bypass a variable portion of the uid through a heat exchanger 65. A suitable valve actuator 66 compares the temperature of the fluid measured by a thermocouple 67 in ring 63 and inner casing steam temperature measured by thermocouple 27 as before. Suitable scaling of the actual steam temperature signal is performed by a multiplier 67 so that the temperature 0f the fluid inside ring member 63 varies between limits selected to provide analogous action on disk 61 to variation of steam temperatures on the steam turbine rotor. For example, disk 61 may suitably be made of an Epoxy resin and the temperature of the uid in member 63 be made to vary between 70 to 100 degrees to approximate the change in steam temperature from room temperature to 1050 F.

A strain gage 68 at the outer surface of the disk measures surface stress directly. Similarly, a strain gage 69 in the bore of the disk measures the bore stress component due to temperature changes directly. A thermocouple 70 in the bore of the disk -measures bore temperature.

Referring to FIG. 6 of the drawing, the rotor analog model is shown in another view. The only difference between the lower portion of FIG. 6 and FIG. 4 is that the function generators, limit generators, summers, etc. are done using conventional analog devices rather than digital devices. The functions indicated are typically carried out using high g-ain DC operational amplifiers with suitable selected feedback impedances to accomplish the desired functions. Techniques for accomplishing the foregoing are well known to those skilled in the art.

Thus it will be seen that the invention serves to provide an improved apparatus and method for controlling startup and loading of a steam turbine wherein, rather than depending upon operator judgment to select a desired acceleration rate or a desired loading rate, these values are selected automatically to provide the maximum safe starting and loading rates. Thus the time lag 'associated with changes in temperature in the massive rotor are suitably compensated for and the past temperature hitsory of the turbine affects the time in which it takes to start up and load the turbine in automatic fashion.

While there has lbeen described herein what is considered to be the preferred embodiment and one modification of the invention, other modifications will become apparent to those skilled in the art. It is of course intended to cover in the appended claims all such modications as fall within the true spirit and scope of the invention.

What is claimed as new and desired to secure by Letters Patent of the United States is:

1. An improved control system for a prime mover with a rotor having stresses therein which change in accordance with change of a first operating condition of the prime mover, said control system including means to compare actual rate of change of said first operating condition with a reference rate of change of said first condition to thereby control the prime mover, wherein the improvement comprises:

means calculating a varying simulated stress in said rotor, means comparing said simulated stress with an allowable stress to provide a stress margin signal, and

means applying said `stress margin signal to said control system to control said reference rate of change of the first operating condition.

2. The combination according to claim 1, wherein said simulated stress is calculated from a second operating condition which changes along with said rst operating condition.

3. The combination according to claim 1, wherein said first operating condition is the speed of the prime mover and wherein said simulated stress is calculated from the prime mover temperature and speed.

4. The combination according to claim 1, wherein said i first operating condition is the load on the prime mover and wherein said simulatd stress is calculated from the prime mover temperature and speed.

5. The combination according to claim 1, wherein simulated stresses are calculated for the rotor surface and bore, and wherein said comparing means provides stress margin signals for the rotor surface and bore respectively, and including gating means admitting only the one of said stress margin signals to said applying means, which represents the condition of greatest rotor stress.

6. The combination according to claim 1, wherein said calculating means 'performs digital sequential storing of said simulated stresses and wherein each previously calculated value of stress affects the current value of stress.

7. The combination according to claim 1 where said calculating means includes an analog model of said rotor and having strain gages attached thereto to measure said stresses directly from said analog model, and means to change the condition of the analog model in accordance with changes in theirst operating condition of the prime mover.

8. An improvedv control system for a steam turbin with a rotor having stresses therein which change in accordance with rotor speed and temperature when the turbine is starting up and as load is applied to the turbine, said control system including means to compare an acceleration reference signal with actual acceleration when the turbine is starting up and to compare a loadlrate reference signalwith actual load rate as load is being applied to the turbine, wherein the improvement comprises:

means calculating the simulated stress in the rotor in response to speed of the rotor and temperature of the steam adjacent the rotor, means comparing said simulated stress with an allowable stress to provide a stress margin signal,

first means applying said stress margin signal as an acceleration reference signal when the turbine is acceleratin g, -a-nd second means applying said stress margin signal as a load rate reference signal when loadis being applied to the turbine.

9. The combination according to claim 8, wherein simulated stresses are calculated for the rotor surface and bore, and wherein said comparing means provides stress margin signals for the rotor surface and Ibore respectively, and including gating means admitting only the lowest of said stress margin signals to said applying means.

10. The combination according to claim 8, wherein said calculating means performs digital sequential storing of said simulated stresses and wherein each previously calculated value of stress affects the current value of stress.

11. The combination according to claim 8 where said calculating means includes a thermally similar analog model of said rotor and having strain gages attached thereto to measure said stresses directly from said analog model, and means to change the temperature of the analog model in accordance with temperature changes of the steam in said turbine.

12. An improved control system for a prime mover with a rotor having stresses therein which change in accordance with-changes of a plurality of operating couditions of the prime mover, said control system being operative to control the rate of change 'of at least one of said operating conditions, wherein the improvement comprises: t

first means responsive to selected operating conditions affecting rotor stress,

second means responsive to the rst means and vcalculating at least two simulated rotor stresses varying with the operating conditions,

third means comparing said simulated stresses With allowable stresses to provide respective stress margin 9 10 signals representing at least two predicted rotor stress conditions, References Cited fourth means gating the one of said stress margin sig- UNITED STATES PATENTS rlessgcr represents the Coudrtwn 0f greatest rotor 3,291,146 12/1966 Walker 137 17 5 3,340,883 9/1967 Peternel 137-17 X fifth means applying said gated stress margin sign-a1 to said control system to control the rate of chanve of the controlled operating condition. a NATHAN L MINTZ Primary Examiner'

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