Date: 201705
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: Cloudy; 1
Light: Night
Aircraft: PA-34-220T Turbo Seneca III
Operator: Air Taxi
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Final Approach
Airspace: Class E N90
ATC / advisory: TRACON N90
Reporter organization: Air Taxi
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Flight Instructor
Anomaly: Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Diverted; Flight Crew Executed Go Around / Missed Approach
Contributing factors: Weather
Primary problem: Weather

Narrative: The latest weather reports; to my best recollection; indicated the following conditions: ZZZ 8 miles visibility and ceiling at 300 feet. ZZZ1; my designated alternate; 3 Miles Visibility and 600 feet ceiling. The latest weather reports also indicted available alternates in ZZZ2 and ZZZ3. The minimum required fuel for the trip taking in account the flight to destination; to the alternate plus 45 minute in cruise was 1:30 hours. [Prior to departure] we added 10 gallons of fuel to get a total of 65 gal.; which gave us an endurance of 2:15 hours. This gave us an additional 45 minutes of reserve. The estimated duration of the flight was 30 minutes.During our flight we monitored the weather at ZZZ and ZZZ1. The indication was that weather was changing. Nevertheless; visibility and ceilings indicated greater than 1 mile visibility and 200 feet respectively.During our attempts to execute the ILS to runway 6 at ZZZ; we realized that as a result of a 90 degree cross wind that may exceeded 30 kts between 2000 feet and 1000 feet. In the 3 attempts; we decided slightly below 1000 feet to execute a missed approach and go to our alternate ZZZ1. The reported weather was 1 mile visibility and 200 feet ceiling. The wind was from 160 which made ILS 14 a very good choice.During our approach we discovered the prevailing wind gave us ground speed of about 50 kts. Reaching DA (277feet) we executed a missed approached. At this point we decided to divert to ZZZ2 where the weather report was ceiling greater than 1000 feet and visibility 2 miles. In to attempt to land at ZZZ2; we were unable to land as the runway light failed to activate. At this point we had exhausted all of our reserve fuel. We diverted yet again to ZZZ3 with controller latest weather report was way above minimums.  We had [advised ATC] because we had enough fuel for 2 attempts on ILS runway 2.We made a plan that if the 2nd attempts fails; we would ditch the plane in the water. During the first approach at DA we made no contact with the runaway environment. Fortunately on the second attempt at about 300 feet we made contact with the runway environment and made a successful landing.


Second narrative: Conditions at ZZZ were about 300 feet and 10 miles visibility. We filed as an alternate ZZZ1; where visibility was about 5 miles and the ceiling was 600 to 800 feet. We departed with about 70 gallons of fuel in a Seneca for which we planned for a 28 GPH fuel burn; so we more than enough fuel for the 30 minute flight and required IFR reserve. We shot at least three approaches into ZZZ; but the cross winds were so strong that we had to go missed each time. Next; we tried to shoot the ILS 14 approach into ZZZ1; where the winds were more favorable; but upon reaching minimums did not see the field; and had to go missed. We next tried at least two approaches into ZZZ2; but the airport lights would not turn on via our pilot operated attempts to light them; so we next flew to nearby ZZZ3. After we didn't see the airport on the first ILS 2 attempt we had to declare [minimum] fuel with the air traffic controller. On the second ILS 2 attempt we saw the airport at very near minimums; and landed.


Synopsis: PA-34 flight crew reported a training flight resulted in multiple diversions and minimum fuel condition due to weather conditions and inoperative runway lights.