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# How to calculate "H" from "Ta"?

## How to calculate "H" from "Ta"?

(OP)
How to calculate H from Ta?
H/pu - generator per unit inertia constant
Ta/sec - Starting time constant of complete aggregate

### RE: How to calculate "H" from "Ta"?

Please, would you rephrase Ta/sec-Starting Time Constant of Complete Aggregate or refer to some source where it is stated this way.

### RE: How to calculate "H" from "Ta"?

I believe gaber is referring to the term Ta which is often used to describe the net accelerating torque of a generation system when exposed to a sudden load rejection or sudden load increase. The inertia constant is supplied by the manfacturer of the combined prime mover-generator combination. Numerous references provide estimates for all types of machines. Jbartos is correct in noticing that this term, as used in the question, is one that is unfamiliar. Kimbark Vol. I is a reference which describes the relation between the H constant and the term Ta. Power System Stability by Edward Wilson Kimbark, John Wiley & Sons

### RE: How to calculate "H" from "Ta"?

Reference:
1. IEEE 399-1990 (and more recent one in 1997) "IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis"
includes, in Fig 46 "IEEE Type 1 Excitation System" on page 110, a constant Ta in the regulator.

### RE: How to calculate "H" from "Ta"?

This expands my post of 11/23 concerning the term Ta and the inertia constant H. The reference for this information is the General Electric publication GET-6449 Load Shedding, Load Restoration and Generation Protection Using Solid -tate and Electormechanicl Underfrequency Relays-published in 1997.
Ta is used to descbibe the net accelerating torque on a per unit basis of the generation system. This torque is the difference between the generator torque and the load torque (Tg-Tl).  The term Ta is used in the following equation.
ds/dt=Taf0/2H and the terms are described as follows:
ds/dt= rate of change of frequency in HZ/sec.
Ta=described above
fo=base frequency
2=constant
H=system inertia constant in (MW-Seonds)/MVA
When Ta is positive, the net accelerating torque will cause the system frequency to increase. A minue sign in front of  Ta will result in a system frequency decay

This equation can be illustrated by an example.
Suppose you have a generator operating in parallel with a utility system and the utility tie is opened. For the example, assume the load prior to the seperation is 20 MW and the in-plant generator is supplying 13MW of this load. Loss of the utility tie will expose the generator to an additional load of 7 MW. The plant has under frequency relays installed on the bus. What is the rate of frequency decay?

If this the generator is a steam turbine generator. The manufacturere will supply the combined inertia constant of the turbine and generator and the  H constant is 2.2 Mw-Sec/MVA for this 17 MVA t-g.. This is a typical value for non-condensing tubines.
The rotating load has inertia and a typical value for the rotating load, H= .5MW-Sec./MVA.
Ta can also be expressed as Pm-Pe where Pm = the per unit mechanical input to the steam turbine and Pe= the per unit electrical load on the steam turbine generator.  All quantities must be referred to the same MVA base. I personally use a base of 10 MVA. It is necessary to seperate the load on the system into rotating load and non-rotating load such as lighting, heaters etc. For the example, assume the rataing load is 80 % of the total load of 20 MW.  Rotating load = 16MW with an inertia constant of .5 MW-Sec./MVA.

The calculation is

Total system inertia is the sum of the generato inertia and the rotating load inertia and must be expressed on the same base. For the example the H is (17/10) X 2.2 = 3.74 + (16/10) x .5 =.8 for a sum of 4.54 MW-Sec./MVA. The per unit power input to the turbine is 13 MW/10 MVA= 1.3 MW/MVA and the per unit electrical load is 20MW/10 MVA is 2.0 MW/MVA.  Thus the calculated decay rate is

ds/dt = 30 x (1.3-2.0)
ds/dt = -21 Hz/sec.

This sytem is heading downhill very rapidly and will not survive.  System frequency relays may operate to shed load but it is doubtful if the action will be operate before a total collapse occurs.
Of course the turbine system willl try to respond, but the time constant of the boiler and the turbine governor is relatively long and will have no effect in first few cycles which is an eternity to the electrical system.

Another reference which is useful is the Westinghouse Silent Sentinels publication Applied Protective Relaying. This book has been republished by ABB and can be obtained through their sales organization for about \$100.

### RE: How to calculate "H" from "Ta"?

In my post of earlier today, I neglected to divide by the system inertia constant of 4.54 and the correct answer is -4.62 Hz/sec.  The system frequency relays should operate and if sufficient load is shed to create a positive net torque, the system should survive.  Sorry about the error-

### RE: How to calculate "H" from "Ta"?

Suggestion: Consider
Reference:
1. Hurley J.D., Baldwin M.S. "High-Response Excitation Systems on Turbine-Generators: A Stability Assessment," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 11, pp. 4211-4217, November 1982
This reference describes the H constant, which is internal to the generator model described by stability constants including H; Exciter Block (IEEE Type 1, in Fig. 2), which includes Ta constant (0.02 sec); voltage regulator block; and downstream network (system) to be able to evaluate the complete agregate in Fig. 1. Also, a Power System Stabilizer (PSS) is studied therein. Therefore, it appears the the Ta utilized at the exciter regulator has a rather complex context with the constant H.
2. Knable A. H. "Electrical Power Systems Engineering," McGraw-Hill Book Co., 1967, page 133
This reference appears to present similar equation to the Jack Nov 24 posting where
df/dt=Pa x 30 / H
f .... frequency in Hz
t .... time in seconds
Pa ... accelerating power in per units (p.u.) (not torque!)
H .... energy loss in a rotating mass in p.u.-sec
There is no sign of Ta/sec (starting time constant of the complete aggregate).

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