one embodiment of the present invention is now explained with reference to the drawings . fig1 shows an embodiment of the present invention in which the like numerals to those used in fig6 designate the like or corresponding elements . different portions in fig1 from fig6 are now explained . numeral 25a corresponds to the generation output correction command unit 25 of fig6 . when the rotating speed n is between the settings nklg and nkug , the output signal is kept at zero , and when the rotating speed n falls below the setting nklg , the output signal is decreased in proportion to the decrease of the rotating speed n . on the other hand , when the rotating speed n rises above the setting nkug , the output signal is increased in proportion to the rise of the rotating speed n and the backup speed control operation is started . the settings nklg and nkug are determined in the following manner . assuming that the lower limit of the optimum rotating speed command na in the generation mode is nalg and the upper limit thereof is naug , that is , the adjustable speed operation range by the normal pump turbine speed control in the generation mode is nalg ˜ naug ( normal operation range ), they are set to meet : namely , they are set outside of the normal adjustable speed operation range . further , ( nalg - nklg ) is set to be larger than a single amplitude of a continuous rotation fluctuation which possibly occurs in the steady state . this is due to the consideration that the backup speed control conducted through the secondary exciting control unit 3 does not interfere with the speed control by the turbine output control even if the optimum rotation speed command nag is at the lower limit and the stable continuous operation is attained . fig3 shows an embodiment of a transient characteristic control unit 25b which controls the response and the stability of the backup speed control unit through the secondary exciting control unit 3 . fig1 shows an example of a primary delay element ( as fig3 ( a ) and 3 ( b ) do ) although it may be replaced by a pi operator as shown in fig3 ( c ) in which s represents a laplace operator . numeral 26 denotes an adder which sums the output δpi of the transient characteristic control unit 25b and the externally applied generation output command po to produce the induction motor output command pg . in the control unit of the present embodiment , a response when the generation output command po is increased stepwise at time t0 as shown in fig9 ( a ) in order to increase the generation output p stepwise when the rotating speed n is around the lower setting nalg of the normal operation range is explained . when the generation output command po is increased at the time t0 , the rotating speed n temporarily decreases as shown in fig9 ( f ) as opposed to the change of the optimum rotating speed command na as it does in fig8 . when the rotating speed n becomes lower than the lower limit setting nklg of the backup speed control , the induction motor output command inputted to the secondary exciting control unit 3 by the generation output correction command signal δpi becomes smaller than the external generation output command po . accordingly , the time t1 at which the turbine output pt corresponds to the generation output is earlier than the time t2 at which the turbine output pt corresponds to the generation output command po . accordingly , in accordance with the present invention , the time at which the rotating speed n is minimum shifts from the time t2 to the time t1 as shown by a broken line in fig9 ( f ). further , the transient back overshoot can also be reduced materially . in accordance with the present invention , since the predetermined difference is given between the lower limit nalg of the normal operation range of the optimum rotating speed command na and the lower limit setting nklg of the backup speed control , the backup speed control is not effective when the change of the generation output command po is small . in addition , in the speed control by the turbine , it is unavoidable that certain continuous rotation vibration occurs even in the steady state due to a non - sensitive band and a non - movable band present in the rotating speed control unit 16 , a hysteresis and a response delay in the output characteristic of the turbine itself . in the present invention , as described above , the difference ( αg in fig2 ) between the lower limit nalg of the normal operation range of the optimum rotating speed command na and the lower limit nklg of the backup speed control is set to be larger than a half of a peak - to - peak amplitude of the continuous rotation vibration . and , in the steady state , the backup speed control is made ineffective . referring to fig2 the upper limit control of the operation state is explained . in the adjustable speed pumping up generator , it is a common practice to set the adjustable range of the rotating speed , that is , the normal operation range as large as is permitted by the frequency converter so that the adjustable range of the input is as large as possible . in fig2 the lower limit nalp to the upper limit naup of the normal operation range in the pumping up mode corresponds to it . on the other hand , in the generation mode , it is common that the normal operation range is narrow as shown in fig2 because the rotating speed which assures the maximum efficiency is lower than that in the pumping up mode . particularly , the adjustable speed upper limit naug of the normal operation range is , in many cases , lower than the upper limit naup in the pumping up mode . accordingly , the next problem to be solved is where the upper limit setting of the backup speed control through the secondary exciting control unit 3 is to be set , particularly where the upper limit setting nkug in the generation mode is to be set . in the present invention , it is set to be lower than naup and higher than naug as shown in fig2 . further , it is set such that a difference βg from the upper limit naug of the normal operation range in the generation mode is not too large . it is never shared with the upper limit setting nkup of the backup speed control in the pumping up mode . referring to fig4 and 5 , an operation of the apparatus of the present invention is now explained . in fig5 βg is too large . when the generation output command po abruptly decreases as shown , the rotating speed n temporarily rises as shown in fig5 ( f ) because the response of the generation output p is faster than that of the turbine output pt ( rather it is set faster so that the feature of the adjustable speed apparatus is brought ). then it swings back largely and drops violently . the larger the amplitude of the previous temporary rise is , the larger is the strength of the swing - back drop . thus , the rotating speed n drops below the lower limit nalg of the normal operation range and further tends to drop below the lower setting nklg of the backup speed control . when it reached the lower limit setting nklg , the backup speed control becomes effective through the secondary exciting control unit 3 to apply the brake , but the rotation is not stopped immediately but overruns to some extent . the amount of overrun relates to the width of the temporary rise of the rotating speed immediately after the start of the drop of the generation output command po . if a large value is permitted to the latter , the former is also large . in other words , when the rotating speed command po is abruptly decreased immediately after the overshoot , the rotating speed command po and the overshoot swing - back overlap and the overrun is too large . as the overrun becomes too large , the operation range of the secondary exciting control unit 3 is departed and the function is disordered . in this manner , the overshoot in the lower limit of the adjustable speed range deeply relates to the upper limit setting nkug of the backup speed control which , at a first glance , appears to be of no connection . thus , as shown in fig4 in the generation mode , the setting nkug of the backup speed control at the upper limit of the normal operation range is set around the upper limit naug of the normal operation range to suppress the temporarily rise of the rotating speed n . as seen from the above , when the difference between the upper limit naup of the normal operation range in the pumping up mode and the upper limit naug of the normal operation range in the generation mode is large , it is not appropriate to share the upper limit setting nkug of the backup speed control in the generation mode with the upper limit setting nkup of the backup speed control in the pumping up mode . at the lower limit end , as shown in fig2 the lower limit setting nklg of the backup speed control in the generation mode may be set to be equal to the lower limit setting nklp of the backup speed control in the pumping up mode . in accordance with the present invention , the backup speed control in the generation mode is effected such that the lower limit setting is set in accordance with the rotation vibration continuously generated during the operation in the generation mode and the upper limit setting is set optimally in consideration of the overrun which accompanies with the swing - back of the overshoot of the rotating speed . thus , the stable and continuous operation is attained without departing from the predetermined adjustable speed range . the backup speed control may be readily incorporated as a portion of software of the control unit .