It was created at the Alaska Base beneath the ice where it made use of Reflex Furnaces to power it and was developed from the technology discovered from the crash of the SDF-1. This weapon fell under the jurisdiction of the United Earth Government to be used as a weapon of defense against the alien Zentraedi invaders.
First Robotech War
The weapon began construction following the arrival of the SDF-1 on Earth. During reconstruction efforts on the battle fortress, they discovered the aliens were fifty-foot tall giants, and began developing weapons to counter them should they come to Earth. One of them was the Grand Cannon.
After the SDF-1 returned to Earth after a year in exile, they discovered that the UEG had declared them dead and showed very little interest in the Zentraedi threat, claiming the Grand Cannon could protect them. Henry Gloval, while appreciating the power of the weapon, adamantly declared that it would not be enough. (Macross Saga: Homecoming)
The weapon saw critical use during the final battle of the First Robotech War when Dolza's Imperial Grand Fleet folded around Earth orbit. Despite the Zentraedi unleashing planetary-level devastation, both Alaska Base and the Grand Cannon survived. As such, Donald Hayes fired the weapon, and did marginal damage to the Imperial Grand Fleet. However, it exposed their location, and as the weapon could not fire in quick succession the Zentraedi promptly launched a counterattack that left it inoperative as a result. Anyone who could have fired it or repaired it perished in the attack. (Macross Saga: Force of Arms)
The Pioneer Expedition
The Grand Cannon was later mentioned by T.R Edwards during the Pioneer Expedition. When Rick Hunter commented on the impressive nature of the SDF-3's war room, Edwards compared it to the Grand Cannon, and asked Rick if he ever saw it. He responded with "only in ruins, where it belonged." (Robotech II: The Sentinels)