Usually the voltage will fluctuate if you have the RVC system which is regulated voltage control and that extends battery life but they system came on later models. Therefore, your alternator may be going out or perhaps the "new" battery is bad.
Here is some info on your charging system:
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Service Information
2001 Chevrolet Tahoe - 4WD | Sierra, Silverado, Suburban, Tahoe, Yukon VIN C/K Service Manual | Engine | Engine Electrical | Description and Operation | Document ID: 656170
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Charging System Description and Operation
Generator
The AD-230 and AD-244 generators are non-repairable. They are electrically similar to earlier models. The generators feature the following major components:
• The delta stator
• The rectifier bridge
• The rotor with slip rings and brushes
• A conventional pulley
• Dual internal fans
• A voltage regulator
The pulley and the fan cool the slip ring and the frame.
The AD stands for Air–cooled Dual internal fan; the 2 is an electrical design designator; the 30/44 denotes the outside diameter of the stator laminations in millimeters, over 100 millimeters. The generators is rated at 102 and 130 amperes respectively.
The generator features permanently lubricated bearings. Service should only include the tightening of mounting components. Otherwise, the generator is replaced as a complete unit.
Regulator
The voltage regulator controls the field current of the rotor in order to limit system voltage. The regulator switches the current on and off at a rate of 400 cycles per second in order to perform the following functions:
• Radio noise control
• Obtain the correct average current needed for proper system voltage control
At high speeds, the on-time may be 10 percent with the off-time at 90 percent. At low speeds, the on-time may be 90 percent and the off-time 10 percent.
Auxiliary Battery Charging
The auxiliary battery is charged in the same manner as the primary battery with the ignition switch in the run position and the engine running. The system contains the following components:
• Auxiliary battery.
• Auxiliary battery relay.
• Mega fuse.
• Junction block battery cable.
• Associated wiring.
The auxiliary battery relay coil is energized with the engine running through the fuse block and wiring, thus closing the relay contacts which allow the battery to be charged from the vehicle's generator via the battery junction block. The auxiliary battery relay is permanently grounded so any time the ignition switch is in the run position the relay will be energized.
The auxiliary battery is only used for accessories and is not part of the vehicle starting system. However if the primary battery fails and in need of an jump start, follow the service information for Jump Starting In Case Of Emergency using appropriate battery jumper cables.
Charging System Indicator
The IPC illuminates the charge indicator in the message center when the following occurs:
• The PCM detects that the generator output is less than 11 volts or greater than 16 volts. The IPC receives a class 2 message from the PCM requesting illumination.
• The IPC determines that the system voltage is less than 11 volts or greater than 16 volts. The IPC receives a class 2 message from the body control module (BCM) indicating the system voltage.
• The IPC performs the displays test at the start of each ignition cycle. The indicator illuminates for approximately 3 seconds.
• The ignition is on, with the engine off.
© 2013 General Motors. All rights reserved.
If you have the NP8 code (check your service options label) 2 speed auto transfer case which is NVG236/246 you require AUTO TRAC II fluid.
If you have the NVG263 transfer case you must use MANUAL TRANS FLUID GM #88861800.
****CAUTION - any transfer case where your owners manual specs AUTOMATIC TRANSMISSION fluid has been UPDATED to the GM manual transmission fluid. This is because up to 2006 some transfer cases did use DEXRON 3..my Sierra Denali 2006 is one of these with the full time auto transfer case. 2006 GM went to Dexron 6 and that is NOT approved for any older transfer cases where older DEXRON 3 was used. Dexron 3 is not licesed to be made anymore however, I have used MOBIL 1 ATF fluid since even before this change occurred as it meets the specs needed.
SO - if you have the NVG263 case use the GM manual transmission fluid or Mobil 1 ATF is fine but no Dex 6. With the NVG 236/246 use AUTOTRAC 2 fluid ONLY.
From the bulletin:Dexron III is being phased out as a product name. It is being renamed Manual Transmission Fluid and carries p/n 88861800 U.S. (88861801 Canada).
DO NOT use Dexron VI in place of manual transmission fluid in any manual transmissions or transfer cases that specify Dexron III, as a failure may result.
Here is the entire bulletin:
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Service Information
2006 GMC Truck GMC Sierra Denali | Sierra, Silverado VIN C/K Service Manual | View All Bulletins | Document ID: 2622890
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#04-07-30-037E: Release of DEXRON-VI Automatic Transmission Fluid (ATF) - (Apr 7, 2011)
Subject: Release of DEXRON®-VI Automatic Transmission Fluid (ATF)
Models: 2008 and Prior GM Passenger Cars and Light Duty Trucks
2003-2008 HUMMER H2
2006-2008 HUMMER H3
2005-2007 Saturn Relay
2005 and Prior Saturn L-Series
2005-2007 Saturn ION
2005-2008 Saturn VUE with 4T45-E
2005-2008 Saab 9-7X
Except 2008 and Prior Chevrolet Aveo, Equinox
Except 2006 and Prior Chevrolet Epica
Except 2007 and Prior Chevrolet Optra
Except 2008 and Prior Pontiac Torrent, Vibe, Wave
Except 2003-2005 Saturn ION with CVT or AF23 Only
Except 1991-2002 Saturn S-Series
Except 2008 and Prior Saturn VUE with CVT, AF33 or 5AT (MJ7/MJ8) Transmission Only
Except 2008 Saturn Astra
Attention: DEXRON®-VI Automatic Transmission Fluid (ATF) is the only approved fluid for warranty repairs for General Motors transmissions/transaxles requiring DEXRON®-III and/or prior DEXRON® transmission fluids.
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This bulletin is being revised to update information. Please discard Corporate Bulletin Number 04-07-30-037D (Section 07 – Transmission/Transaxle).
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MANUAL TRANSMISSIONS / TRANSFER CASES and POWER STEERING
The content of this bulletin does not apply to manual transmissions or transfer cases. Any vehicle that previously required DEXRON®-III for a manual transmission or transfer case should now use P/N 88861800. This fluid is labeled Manual Transmission and Transfer Case Fluid. Some manual transmissions and transfer cases require a different fluid. Appropriate references should be checked when servicing any of these components.
Power Steering Systems should now use P/N 9985010 labeled Power Steering Fluid.
Consult the Parts Catalog, Owner's Manual, or Service Information (SI) for fluid recommendations.
Some of our customers and/or General Motors dealerships/Saturn Retailers may have some concerns with DEXRON®-VI and DEXRON®-III Automatic Transmission Fluid (ATF) and transmission warranty claims. DEXRON®-VI is the only approved fluid for warranty repairs for General Motors transmissions/transaxles requiring DEXRON®-III and/or prior DEXRON® transmission fluids (except as noted above). Please remember that the clean oil reservoirs of the J-45096 - Flushing and Flow Tester machine should be purged of DEXRON®-III and filled with DEXRON®-VI for testing, flushing or filling General Motors transmissions/transaxles (except as noted above).
DEXRON®-VI can be used in any proportion in past model vehicles equipped with an automatic transmission/transaxle in place of DEXRON®-III (i.e. topping off the fluid in the event of a repair or fluid change). DEXRON®-VI is also compatible with any former version of DEXRON® for use in automatic transmissions/transaxles.
DEXRON®-VI ATF
General Motors Powertrain has upgraded to DEXRON®-VI ATF with the start of 2006 vehicle production.
Current and prior automatic transmission models that had used DEXRON®-III must now only use DEXRON®-VI.
All 2006 and future model transmissions that use DEXRON®-VI are to be serviced ONLY with DEXRON®-VI fluid.
DEXRON®-VI is an improvement over DEXRON®-III in the following areas:
DEXRON®-VI
Fluid Service Change Interval
160,000 km (100,000 mi) For Cars and Light Duty Trucks*
80,000 km (50,000 mi) (Severe Use) For Cars and Light Duty Trucks*
Clutch Friction Stability
Improved 100%
Clutch Durability Due To Fluid
Improved 120%
Oil Film Thickness
Increased 20%
Fluid Oxidation
Improved 100%
Foam/Aeration
Improved 150%
Shear Stability
Improved 200%
* These ATF change intervals remain the same as DEXRON®-III for the time being.
2006–2008 Transmission Fill and Cooler Flushing
Some new applications of the 6L80 six speed transmission will require the use of the J 45096 – Flushing and Flow Tester to accomplish transmission fluid fill. The clean oil reservoir of the machine should be purged of DEXRON®-III and filled with DEXRON®-VI.
Parts Information
Part Number
Description
88861003 (US)
DEXRON®-VI Auto Transmission Fluid (1 qt bottle)
88861045 (US)
DEXRON®-VI Auto Transmission Fluid (1 gal bottle)
88861046 (US)
DEXRON®-VI Auto Transmission Fluid (55 gal drum)
19264717 (Canada)
DEXRON®-VI Auto Transmission Fluid (1L bottle)
19264718 (Canada)
DEXRON®-VI Auto Transmission Fluid (4L bottle)
19264719 (Canada)
DEXRON®-VI Auto Transmission Fluid (205L drum)
GM bulletins are intended for use by professional technicians, NOT a "do-it-yourselfer". They are written to inform these technicians of conditions that may occur on some vehicles, or to provide information that could assist in the proper service of a vehicle. Properly trained technicians have the equipment, tools, safety instructions, and know-how to do a job properly and safely. If a condition is described, DO NOT assume that the bulletin applies to your vehicle, or that your vehicle will have that condition. See your GM dealer for information on whether your vehicle may benefit from the information.
WE SUPPORT VOLUNTARY TECHNICIAN CERTIFICATION
© 2013 General Motors. All rights reserved.
. Anyway, I purchased the 01 from its original owner, who has done a wonderful job of keeping it up. It has a couple of minor issues though: 
