1998 Hyundai Elantra Loosing power

First thing to check is the belt tension, could be slipping, you didnt say how many miles are on it, but belt and tensioners get shaky around 70,000 miles on some models. Then perform these tests.
VOLTAGE DROP TEST Connect voltmeter positive lead to terminal "B" at generator and negative lead to positive battery post. Ensure that voltmeter leads are clear of all moving components. Start engine. Turn on blower motor and headlights. If voltage reading is.2 volt or less, output wire is okay at this time. If voltage reading is greater than.2 volt, repair output wire or fusible link between generator and battery. GENERATOR OUTPUT TEST NOTE: If battery is fully charged, disable ignition system. Crank engine for about 15 seconds to partially discharge battery. Ensure generator belt tension is correct. Turn ignition off. Disconnect battery ground cable. Disconnect output wire from terminal "B" of generator. Securely connect test equipment as shown. See Fig. 1. Attach engine tachometer, and connect battery ground cable. 1. If voltmeter indicates battery voltage, go to next step. If voltmeter indicates zero volts, check for open wire between positive battery terminal and generator terminal "B", blown fusible link or poor ground. 2. Start engine. Turn headlights on high beam, and operate blower motor at high speed. Quickly increase engine speed to 2500 RPM, and observe maximum current readout on ammeter. Ammeter reading should not be less than minimum output amps. Refer to the GENERATOR OUTPUT SPECIFICATIONS table. If generator output is not as specified, remove and bench test generator. 3. 75 amp puts out 52.5 amps and a 90 amp puts out 63 during this test. REGULATED VOLTAGE TEST Ensure battery is fully charged and generator belt tension is correct. Turn ignition off. Disconnect battery ground cable. Disconnect output wire from terminal "B" of generator. Securely connect test equipment as shown. See Fig. 2. Attach engine tachometer, and connect battery ground cable. 1. Turn ignition on. If voltmeter indicates battery voltage, go to next step. If voltmeter indicates zero volts, check for open wire between positive battery terminal and generator terminal "S", blown fusible link or poor ground. 2. Start engine. Operate engine at about 2500 RPM with all lights and accessories off. When generator output drops to 10 amps (ammeter reading) or less, note voltage output on voltmeter. Ensure voltage is as specified. See REGULATOR VOLTAGE SPECIFICATIONS table. If voltage is not as specified, test generator and related wiring. If generator and related wiring are okay, replace voltage regulator. 3.