This paper proposes analytical expressions for finding optimal size and power factor of four types of distributed generation (DG) units. DG units are sized to achieve the highest loss reduction in distribution networks. The proposed analytical expressions are based on an improvement to the method that was limited to DG type, which is capable of delivering real power only. Three other types, e.g., DG capable of delivering both real and reactive power, DG capable of delivering real power and absorbing reactive power, and DG capable of delivering reactive power only, can also be identified with their optimal size and location using the proposed method. The method has been tested in three test distribution systems with varying size and complexity and validated using exhaustive method. Results show that the proposed method requires less computation, but can lead optimal solution as verified by the exhaustive load flow method.