Two-phase electrical power was an early 20th-century polyphase alternating current electric power distribution system. Two circuits were used, with voltage phases differing by one-quarter of a cycle, 90°. Usually circuits used four wires, two for each phase. Less frequently, three wires were used, with a common wire with a larger-diameter conductor. Some early two-phase generators had two complete rotor and field assemblies, with windings physically offset to provide two-phase power. The generators at Niagara Falls installed in 1895 were the largest generators in the world at that time, and were two-phase machines. Three-phase systems eventually replaced the original two-phase power systems for power transmission and utilization. Active two-phase distribution systems remain in Center City Philadelphia, where many commercial buildings are permanently wired for two-phase, and in Hartford, Connecticut. Comparison with single-phase power The advantage of two-phase electrical power over single-phase was that it allowed for simple, self-starting electric motors. In the early days of electrical engineering, it was easier to analyze and design two-phase systems where the phases were completely separated. It was not until the invention of the method of symmetrical components in 1918 that polyphase power systems had a convenient mathematical tool for describing unbalanced load cases. The revolving magnetic field produced with a two-phase system allowed electric motors to provide torque from zero motor speed, which was not possible with a single-phase induction motor (without an additional starting means). Induction motors designed for two-phase operation use a similar winding configuration as capacitor start single-phase motors. However, in a two-phase induction motor, the impedances of the two windings are identical. Two-phase circuits also have the advantage of constant combined power into an ideal load, whereas power in a single-phase circuit pulsates at twice the line frequency due to the zero crossings of voltage and current. Comparison with three-phase power Three-phase electric power requires less conductor mass for the same voltage and overall power, compared with a two-phase four-wire circuit of the same carrying capacity. It has replaced two-phase power for commercial distribution of electrical energy, but two-phase circuits are still found in certain control systems. Two-phase circuits typically use two separate pairs of current-carrying conductors. Alternatively, three wires may be used, but the common conductor carries the vector sum of the phase currents, which requires a larger conductor. The vector sum of balanced three-phase currents, however, is zero, allowing for the neutral wires to be eliminated. In electrical