The design of a measurement system to perform Harmonic State Estimation (HSE) is a very complex problem. Among the reasons for its complexity are the system size, conflicting requirements of estimator accuracy, reliability in the presence of transducer noise and data communication failures, adaptability to change in the network topology and cost minimization. In particular, the number of harmonic instruments available is always limited. Therefore, a systematic procedure is needed to design the optimal placement of measurement points. This paper presents a new HSE algorithm which is based on an optimal placement of measurement points using Genetic Algorithms (GAs) which is widely used in areas such as: optimization of the objective function, learning of neural networks, tuning of fuzzy membership functions, machine learning, system identification and control. This HSE has been applied to the Simulation Test Power System for the validation of the new HSE algorithm. The study results have indicated an economical and effective method for optimal placement of measurement points using Genetic Algorithms (GAs) in the Harmonic State Estimation (HSE).