STANDARD DROOP/SPEED CONTROL compared to other LOAD/SPEED CONTROL

PungentReindeerKing is correct. The WORST mistake most people make--especially with GE-design heavy duty gas turbines--is to operate in a mode that's always trying to maintain a load setpoint, and adjusting the turbine speed reference in doing so. In GE-speak it's called Pre-Selected Load Control, and in it's most basic form what happens when the grid frequency deviates from normal which causes the actual speed to deviate from normal is that Droop Speed Control changes the fuel flow-rate because the speed error changes, which changes the actual load--making it deviate from the setpoint--and then Pre-Selected Load Control changes the turbine speed reference to try to return the load to the setpoint, and from there it's a horse race! In other words, the load fluctuates, sometimes by a lot. And this in turn contributes to the grid instability--making it worse!

GE will let Customers pay for a fix for their (GE's) problem--it's called PFR, Primary Frequency Response. And, it will sense a deviation in actual speed--which is an indicator of a grid frequency problem--and will temporarily disable Pre-Selected Load Control so that Droop Speed Control can do what it's supposed to do. It works; sort of. It's just a band-aid, actually.

In reality, no one really needs to operate with Pre-Selected Load Control enabled. Why? Because once the desired load is achieved (by the operator raising or lowering the load to the desired value) and stops using the RAISE- and/or LOWER SPEED/LOAD buttons the turbine speed reference stops changing. So, the speed error stops changing. And when the grid is stable, the speed error doesn't change. So, the fuel flow-rate doesn't change. So, the load stays the same. In most cases, the load is actually more stable than if Pre-Selected Load Control is not active!

But, no one can convince operators, or their supervision, that the unit will remain stable if Pre-Selected Load Control isn't active. Not no how. Not no way. They won't try it for one minute (60 seconds). Or even for 30 seconds. Because the just KNOW that if Pre-selected Load Control isn't active the unit load is going to drift, or worse--it's going to jump. And even worse, it's going to be completely unstable. And someone will lose their job. So, good luck trying to convince anyone to try operating the unit without Pre-Selected Load Control inactive. It just won't happen.

So, what happens when the grid frequency does deviate from rated? Well, if the unit has been outfitted with PFR and Pre-Selected Load Control is active, the fun begins. Not only is the unit load changing because of the grid frequency instability, but it's even more unstable because of the Pre-Selected Load Control fighting with Droop Speed Control. Which only makes the grid frequency more unstable.

And, those same operators and their supervision who believe in the heart and soul that the unit will be unstable if not operated with Pre-Selected Load Control active also believe in the heart and soul that their unit should NOT change it's load under any circumstances--even if the grid frequency is unstable! So, the Mark* is deemed to be the cause of the problem--when it's only making the problem worse because of the way it's being operated.

But, good luck convincing anyone of that. "If GE had wanted Pre-Selected Load Control to self-cancel when the desired load setpoint was reached, they would have programmed it to work that way!" That's what Pre-Selected Load Control was designed to do--make it easy for the operator to change load without a lot of button-pushing, or handle twisting, or clicking. It was intended that once the setpoint was reached, the function would be cancelled--because, again, when the speed reference and the actual speed are both not changing, then the speed error is not changing, and the fuel flow-rate will not change, and the load will not change. BUT, they just forgot to do that one little thing--automatically cancel Pre-Selected Load Control when the desired setpoint was reached. They left that up to the operator, but, operators simply can't be bothered to take that extra step--especially when they firmly believe if they do the unit will go unstable, and someone will lose their job.

Anyway, as for the rest of what PungentReindeerKing wrote, it's all true. A lot of these functions are "layered" on top of each other (in the way Pre-Selected Load Control is layered on top of Droop Speed Control) and they need to be tuned or adjusted to all work together properly. In some cases, they can't be made to work together--but that doesn't stop people from continuing to try to force them to work together. And, in the end--it's always the Mark*'s fault that they can't work together.

Such is life.
 
Hi CSA ,

Thanks a ton for your out of the box explanation and deep learning. My OEM doesn't say it as speed control rather its defined as load control. looking at the algorithms and your explanation I could understand that GAIN is what they derived from the equation.
Droop setting : 4 %
Base Load : 200 MW
Thus the frequency range is from 50 to 52 % ( At full load speed reference @52 Hz ?)
GAIN = 200/2 = 100 (I inferred this as gain of P controller as per your explanation )
Error = Speed Ref - Actual Spd
FR MW = Error*100 (Loaded or Deloaded depending up on the error whether +/-)

Does this make sense as simple P controller? Does this work in real life for paralleling turbo-generators ?

Thank you
 
mariselvan,

Let's consider a machine with 4% droop regulation (as it's typically called by the ivory tower references and OEM documentation). Further, let's say the machine is a prime mover (steam turbine, or gas turbine, or reciprocating engine) driving a 50 Hz generator. AND, let's further say the machine is capable of producing 200 MW and is operating on Droop Speed Control and IS NOT synchronized to any other prime mover/generator or grid. This is important--this is the part that most texts and references and OEM documentation DON'T SAY!!! If the load on the unit, with the generator breaker closed and powering the transmission and distribution system is 0 MW, the output frequency of the unit will be 50.0 Hz. As soon as motors and lights and televisions and computers and computer monitors and tea kettles are turned on the load will increase (based on the number of devices turned on and the power being drawn by the devices which were turned on). Let's say the load increased to 50 Mw, which is one fourth of the rated output of the prime mover and generator. That would mean that the frequency of the grid had decreased to 49.5 Hz, which is a 1% decrease in the nominal frequency, which is equal to 25% of the machine's capacity with 4% droop regulation. Let's now say that some more loads were switched on, and the load increased to 150 MW, which is 75% of the machine's rating, which is 3% of the 4% droop regulation. Now the frequency of the machine (and the transmission and distribution system--and all the loads connected to the system!) is at 48.5 Hz. If the load increases to 200 MW, the frequency will decrease to 48.0 Hz.

That is proportional control.

Now, let's say the same machine--NOT synchronized to any grid or other prime mover/generator--is operating at 50.0 Hz with 200 MW of load. If 50 MW of load is turned of, the frequency of the output will increase to 50.5 Hz; if another 50 MW of load is de-energized, the frequency will increase to 51.0 Hz, and if another 50 MW of load is turned off the frequency will increase to 51.5 Hz. And, if all the loads are shut off, the machine frequency will increase to 52.0 Hz.

That is also proportional control.

Again--the part that most references and texts and OEM documents FAIL to include is the bit about a single unit, operating under Droop Speed Control, unsynchronized with any grid or any other prime mover/generator when they are talking about speed changes. It's unfortunate, but that's the problem with most written descriptions of Droop Speed Control--they almost ALWAYS say the speed of the system changes when load changes-- and that's simply NOT true for one or even multiple machines synchronized together on a well-regulated grid with other prime movers and generators. The concept of AC (Alternating Current) power generation is that is done at a fairly constant frequency. And, the concept of multiple generators synchronized together means they operate at the SAME frequency--all of them!!! No single generator synchronized to a grid with other prime movers and generators can operate at any other frequency (speed) than entire grid. That's what make synchronized and synchronism such an important and critical concept. And, yet people with little or no experience--and poor critical thinking skills--still keep espousing this idea of individual machines changing speed when synchronized to a grid with other machines. It's just doesn't happen in the real world. (Actually, it doesn't even happen in the theoretical world--it's a fallacy.)

Now, let's talk about what does happen to a grid with multiple machines synchronized together when the load exceeds the generation capacity (such as when a machine trips off the grid and all the other machines are running at or very near their rated capacity). In this case, the grid frequency starts to decrease, and that means the difference between the actual frequency (speed) and the frequency (speed) reference starts to increase. This causes the amount of energy flowing into ALL of the machines NOT operating at their rated output to increase. This in turns help to support grid stability--but it DOES NOT return the grid to rated frequency. Operators (usually grid operators) have to do this, either manually or automatically. The number of loads and the current drawn by the loads is not changing--but the amount of energy being produced by the machines synchronized to the grid is not what is required to supply the load(s) AND maintain rated frequency (speed).

I know people don't like my bicycle analogies, or the train analogies--but they are perfectly analogous to this situation. It's all about carrying a load (or loads) at a constant speed (frequency) and dealing with changes in load or changes in the torque being supplied to maintain the constant speed (frequency). An AC grid is "carrying" load(s) at a constant frequency (speed) and to do so it has to supply the loads AT the rated speed, otherwise the frequency will deviate from rated.

Proportional, Droop Speed Control says the amount of energy flowing into the prime mover of a synchronous generators is a function of (proportional to) the difference between the actual speed (frequency) of the machine and the machine's speed (frequency) reference. Increase the error between the actual speed and the speed reference--by changing EITHER the actual speed OR the speed reference--and the amount of energy being supplied to the synchronous generator's prime mover will also increase. Decrease the error between the actual speed and the speed reference--by changing EITHER the actual speed OR the speed reference and the amount of energy flowing into the prime mover will decrease. And, the amount of change is a function of (proportional to) the Droop regulation percentage.

But, when a prime mover/synchronous generator is synchronized to a well-regulated grid with other prime movers and synchronous generators two things should be very apparent: First, the speeds--and frequencies--of all the machines synchronized together on the grid constant, and the frequencies of all the machines are the same, and all the machines are running at their particular synchronous speeds (which are constant). Second, the machines can ONLY share in carrying (supplying) the loads (the motors and televisions and computers and computer monitors and tea kettles) if they are operating in Droop Speed Control--or, proportional control. Base it on load or speed--it has to be something. And beginning over a hundred years ago--it was speed, because speed and frequency are directly related. Mechanical governors for prime movers back then had no way of understanding amperes--only speed. And since all the machines synchronized to the grid had to run at their synchronous speeds to produce the same frequency Droop Speed Control--using speed--was "chosen" (really; there wasn't any other way to do it!).
 
It is about the "standard droop speed control" and how it can be affected by the FPRG or a bad calibration of the gas valves...etc.

Compared to the CONSTANT SETTABLE DROOP SPEED/LOAD CONTROL, The STANDARD DROOP/SPEED CONTROL has "no FSR value feedback" in its regulation loop. This mode of governor control changes FSR in proportion to speed error (droop) directly under the following equation:

FSRN = FSKRN1 + FSKRN2(TNR - TNH)

where FSKRN1 is the Initially set full speed no load fuel reference as calculated, and FSKRN2 is the ratio of percent change in fuel flow reference to percent change in speed/load reference.

OK! at full speed no load TNR-TNH would be equal to 0. and the FSRN value would be equal to FSKRN1, initially caclulated by the OEM for a particular fuel flow rate. And this value is the opening command of the GCV, so for this particular fuel flow rate it depends on the fuel heating value! also of the P2 pressure refrence FPRG!

Lets have an example: suppose FSKRN1 = 30%, when the machine finishes its start-up sequence normally the TNH (HP shaft speed) would be equal to TNR(turbine speed reference). The FSRN = FSKRN1 = 30%, as the machine was firstly commissioned for sure at this stage everything would be stable, because the 30% value was enough to make the machine stable at FSNL 100% speed, for example with an FPRG (gas ration valve control pressure reference) = 13bar.

Lets suppose we have a problem with the P2 pressure either the FPRG constant value or the SRV valve or even the P2 transmitter. This problem causes the P2 pressure to be 10bar when the machine at FSNL. So when the machine reaches FSNL and FSRN = 30% > we won't be having enough energy to make it stable, and TNH would to tend to drop. When it drops, TNR-TNH would be higher than 0 which will make FSRN higher than 30% to reach the FSNL speed again. We will be having a non stable state of the machine fluctuating at FSNL

Myself I'm having a problem with this mode and how it is vulnerable to any misbehave from the gas valves or P2 transmitter, the P2 set point (FPRG), and even a problem with the fuel injectors because we do not have an FSR feedback value in the loop.

NOTE 1: This enquiry is the same for the base load GCV opening value, at base load. And if the droop value is 4%, so TNR-TNH = 4% and 4% * FSKRN2 + FSKRN1 = FSRN, so there is no FSR Feedback value in the loop, at any load point we will be having an particular opening command of the GCV NO MORE!

NOTE 2: i am comparing this regulation loop to all other load regulation loops for single or double shafts where the FSR feedback value is always present. So we will be adding a certain value the actual FSR until we reach the load reference. So the for a certain load point we won't be having a particular pre-calculated value of FSRN which will make the system control adapt the FSRN value to the present conditions and parameters.

example: load output = 100MW, FPR2 = 12bar, FSRN = 40 %
if the the P2 drops for whatever the reason we will be having - load output = 100MW, FPR2 = 9bar, FSRN = 60 %

So the control system rises the FSRN value to maintain the load output.
 
Take a look to this:

CONSTANT SETTABLE DROOP ANTI WINDUP

Some protection is provided after the gas fuel system goes non-critical due the loss off gas supply pressure, or other cause which limit output. If gas supply pressure drops, at some point the P2 pressure begins to decrease. Later the load will start to drop off, and the speed error will respond by requesting more fuel flow. The FSR will integrate to 100% with the Stop/Speed Ratio Valve 100% open. The modification compares a limit (TNKERRLIM) "Minimum Speed Error Limit" (0,7%) to the speed error signal (TN-ERR) to create an error limit logic. If the error limit exceeds the request for more than some TD in seconds (K3TNRERRX) "T.D. On Load Below Speed Error Limit" (5 Sec), a lower signal is automatically given (L3TNRERRX) "DWATT TOO LOW TO SUPPORT TNR-TNR LOWER". This signal will break any "base load" or "preselect load" commands. The lower rate used is manual rate (6 minutes, from FSNL to base or base to FSNL) to provide reasonable response. A drop in Hz will cause the (TN-ERR) to go positive, and will for a short time be greater than 0,5%, however, if the drop in Hz is greater than 0,5% the logic (L30AFL) "System Frequency Low" will pickup and the anti-windup will be locked out as long as logic is true.
 
PFC is a dangerous term to use these days when referring to proportional, Droop Speed Control, I am presuming your usage to mean proportional Droop Speed Control. Not Pre-Selected Load Control. Not PFR (Primary Frequency Response). Basic proportional Droop Speed Control. (Proportional meaning the energy flow-rate into the prime mover of a generator set changes in proportion to the change in the prime mover's speed error.)

Why, because some OEMs (Original Equipment Manufacturers) are using this term to refer to slightly different aspects of Droop Speed Control.
Hi CSA ,

Hope you are doing great and continue to support power plant community with your wisdom and experience. Thank you. I should have I am referring PFC or Primary Frequency Response as Governor Proportional droop speed control. I have took some time to look into your thread again and well understood your real world true working principle of governor. To make my understanding simple and universal for any turbine manufacturers I put the The simple proportional control is is a straight line equation Y= m X + C . X= (Ref speed-Actual Speed) , m = Proportional Gain /Proportional Band (DROOP SETTING) . C = Control constant . Here the units I worked had two setpoint change options for the operator. Load Set Point in MW ( I checked the references this is the term C in the straight line). Second option is turbine RPM setpoint (Speed) , I always found that as 3000 RPM (50 Hz). lets say my unit's rated power is 200MW and I set the load C as 150 MW and grid frequency is 50 Hz precisely then the straight line equation would be Y= 0 + 150 MW , that is Y = 150 . Grid stable and the prime mover runs on stable 3000 RPM , now if there was a change in grid frequency , say 1 % and frequency goes down as 49.5 the equation would be Y = (3000-2970)*m+150 , depending upon the term "m" the frequency response output (output caused by error change ) will be added to the term "C", as per theory 1% change of frequency , it should be 50 MW addition to the 4% droop setting in my understanding. Thus the governor add more fuel to the turbine to bring the speed to 3000 RPM and same time the more fuel converted as additional 50 MW and load would be reaching the rated load of 200 MW. I am not so sure if my understanding is correct or can work in real life. Now , coming to the term "m" , all the equation define as Droop= ((Ref speed-Actual Speed)/Rated Speed ) or ((NL speed-FL Speed)/NL Speed ) here NL , No Load and FL full load. I do not see any name plate referring to NL/FL speed however we always see rated speed as 3000 RPM. How do we find the term "m" , how do we employ in the control settings ? whether we set as GAIN or PB ? I do not really understand that text book or OEM explanation of droop as speed drop as MW/Load increases with the XY Plot where x co-ordinate as Load (0-100%) and Y co-ordinate as Frequency droop(1-5%) as below.
1634011172071.png
 
marislevan,

Yes; Droop Speed Control is a straight line, of the equation form y=mx+b (at least that's the form I learnt in grade school, where "m" is the gain and "b" is the offset. "y" is the total amount of energy flow that's required to make a certain amount of power (electrical power). The DIFFERENCE is that in Droop Speed Control the "x" term, the variable, is actually two (2) variables: actual speed and speed reference.

It takes a certain amount of energy flow just to keep a generator and its prime move at rated speed--which is defined by the formula: N=(120*F)/P, where F=Frequency (in Hz), N=Speed (in RPM) and P=Number of generator field poles. That amount of energy flow is the "b" term in y=mx+b. That is not really ever going to change for any prime mover and generator combo.

Remember one VERY important thing about AC (Alternating Current) power generation: The speeds of EVERY generator and prime mover connected to--synchronized to--a grid with other generators and prime movers is fixed (controlled) by the grid frequency. So, if the grid is stable, so will be the speed of all the generators and prime movers synchronized to that grid. That is a fact. If the grid frequency is unstable, so will be the speed of EVERY generator and prime mover synchronized to that grid. No matter how much anyone wants that be different for their machines at their site--it just can't be (different). It's a physical "law." Full stop. Period.

Let's try an example. And let's use speed, in RPM, for the "x" terms. From N=(120*F)/P we know that a two-pole synchronous generator must run at 3000 RPM to produce 50.0 Hz. Let's say we want the unit to have a speed regulation of 4%. That means that the unit speed reference would be (1.04*Rated Speed), or 3120 RPM. Technically, that number (3120 RPM) is the "Full Load Speed." Further, let's say it requires (and this is just a sample value--I have NO IDEA if it's a valid number for ANY prime mover/generator combo--it's just a sample value for discussion purposes!!!) 10,000 BTU/sec just to maintain rated speed (rated frequency at the generator terminals). Again, using SAMPLE values, let's say it requires 60,000 BTU/sec for the prime mover/generator combo to produce rated power output. If we subtract 10,000 BTU/sec from 60,000 BTU/sec, that leaves 50,000 BTU/sec as the change in flow-rate required to go from zero power output to rated power output. Now, we can arrive at the amount of BTU/sec required for a change of 120 RPM (3120 RPM (Full Power Output Speed Reference)-3000 RPM (Zero Power Output Speed at Rated Frequency): (50,000 BTU/sec)/(120 RPM)=416.67 BTU/sec/RPM. This is our "m" (gain) value.

Let's plug some values into the equation and see what we get. Let's choose a 25% change in load, which would be a 1% change in Speed Reference with a 4% speed regulation (25% of 4% is 1%), and 1% of 3000 RPM is 30 RPM--so to achieve a 25% change in load the Speed Reference would have to change by 30 RPM (which is 25% of 120 RPM). The formula for Droop Speed Control is:

Total Energy Flow-rate=((Speed Reference-Actual Speed)*Gain)+Offset

y=((416.67 BTU/sec/RPM)*(3030 RPM-3000 RPM))+10,000 BTU/sec=(416.67 BTU/sec/RPM*30 RPM)+10,000 BTU/sec

y=12,500 BTU/sec+10,000 BTU/sec=22,500 BTU/sec

22,500 BTU/sec is required to produce 25% of rated power output for this particular prime mover/generator combo while running at rated frequency (50.0 Hz; or, 3000 RPM).

This says that to increase the load from zero to 25% of rated on a machine with 4% speed regulation (4% Droop) using a generator rated at 50 Hz, the Speed Reference would have to increase from 3000 to 3030.

Let's say we wanted to increase the power output from the generator to 50% of rated. That's half of a 4% speed regulation

y=((416.67 BTU/sec/RPM)*(3060 RPM-3000 RPM))+10,000 BTU/sec=(416.67 BTU/sec/RPM*60 RPM)+10,000 BTU/sec

y=25,000 BTU/sec+10,000 BTU/sec=35,000 BTU/sec

35,000 BTU/sec is required to produce 50% of rated power output for this particular prime move/generator combo while running at rated frequency (50.0 Hz; or, 3000 RPM).

So, now we know that it requires 12,500 BTU/sec for every 25% change in power output from this particular prime mover/generator combo running at rated frequency (speed).

Let's say we want to increase power from 50% of rated to 75% of rated, or from 2% speed regulation to 3% speed regulation on a prime mover/generator combo with 4% speed regulation and a gain of 416.67 BTU/sec/RPM and a BTU flow of 10,000 BTU/sec for rated frequency, 50.0 Hz (3000 RPM). We already know from the second calculation above that it requires 35,000 BTU/sec to produce 50% of rated power for this combo, so we just add 12,500 BTU/sec to the energy flow-rate to get 47,500 BTU/sec. (This desired power output would translate to 3% of 4% speed regulation, or 90 RPM of a120 RPM speed reference change.)

Finally, let's say we want to produce rated power output from this prime mover/generator combo.

y=((416.67 BTU/sec/RPM)*(3120 RPM-3000 RPM))+10,000 BTU/sec=(416.67 BTU/sec/RPM*120 RPM)+10,000 BTU/sec

y=50,000 BTU/sec+10,000 BTU/sec=60,000 BTU/sec

60,000 BTU/sec--that's the number we said was required to produce rated power output from this particular prime mover/generator combo running at rated frequency (speed).

Droop Speed Control is a straight line--but with two variables. If you plot the results above on a graph with the "x" in RPM (from 3000 RPM to 3120 RPM) and the "y" axis in energy flow-rate (from 10,000 BTU/sec to 60,000 BTU/sec) you will end up with a straight line. You could make the "x" axis speed regulation, from 0% to 4%. You could also make the "x" axis in percent of rated speed, from 100% to 104% (for a machine with 4% speed regulation, or, Droop). It's all the same.

I'm not going to do the maths, but you can if you want to see what happens when the unit is producing 50% of rated power output at rated speed (which would require a speed reference of 3060 RPM) and suddenly the frequency decreases--which would decrease the actual speed of the unit--let's say by 0.5% (of 50.0 Hz, which would be 0.995*50.0=49.8 Hz, which translates to a speed decrease of 15 RPM, from 3000 RPM to 2985 RPM (3000 RPM*0.995=2985 RPM)). The energy flow-rate would INCREASE by 6,250 BTU/sec which would cause the power output of the generator to increase by 12.5%, from 50% to 62.5%. That's the OTHER side of Droop Speed Control--what happens when the grid frequency changes but the speed reference remains the same. It's all about the ERROR between the Speed Reference and the Actual Speed (which is a function of the frequency of the machine output, which, when connected to a well-regulated grid, will remain pretty much at rated (100% frequency).

I loathe and despise those two graphs (and many like them) you attached to your response. When a prime mover and its generator are synchronized to a well-regulated grid it's speed does not change--even if the operator tells it to change. It's the DIFFERENCE between the actual speed and the speed reference that causes the power output to change. The speed doesn't change on a well-regulated grid. It just doesn't. And to describe Droop Speed Control by saying that it's the change in speed as load changes is just, well, it's not what really happens in the real world. Yes; in a mathematical model, or on a grid which is NOT well-regulated, or if a SINGLE prime mover and its generator is operating in Droop Speed Control and the load(s) it is powering change--then, yes, the speed will change--but that's NOT how machines are operated in real life. It's just not. But, those graphs, and many like them, don't EVER come with the proper scenario description. They just don't for the real world. And, it's very confusing.

And, so is this thread, I'm sure. Just read it several times. Do the maths yourself. I don't know about other control systems, but GE-design heavy duty gas turbine control systems used to use speed reference in percent of rated speed for their Droop Speed Control calculations. Now they use a load-biased speed reference, called, inappropriately, Constant Settable Droop Speed Control, which can be VERY confusing. And, the "output" of both calculations is called FSR--Fuel Stroke Reference. It's akin to energy flow-rate--which is what was just described above, and which most generator prime mover control systems did for decades. THAT'S how generators and prime movers of ANY MAKE OR TYPE can all be synchronized together on a grid--because they all use some form of Droop Speed Control. It's genius, really. Really it is.

Think about when AC power generation began--the ONLY variable which could be used as feedback to the governors for the prime movers at that time was: Speed. There was no way to convert watts (kW; MW) into a mechanical force to apply to the governor as a feedback. So, they had to relate a change in speed reference to a change in generator power output. They didn't have any choice--and when you think about it, it was genius then, and it's still genius today. If EVERY prime mover and generator uses the same method of control, they can all "communicate" with each other simply by means of changes in grid frequency, which we know is directly related to actual speed. Genius. If ALL generators see the change in speed (which they do when synchronized to a grid) they will all respond similarly. Genius. And over the decades since AC power generation began, the same principles have been used. Genius.

I sincerely hope this helps...!
 
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