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Neural networks are receiving attention as controllers for many industrial applications. Although these networks eliminate the need for mathematical models, they require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. This paper discusses the application of neural networks to control DSTATCOM using direct power control (DPC). A neural network is used to emulate the state selector of the DPC The training algorithms used in this paper are the adaptive neuron model and the extended Kalman filter. Computer simulations of the DPC with neural network system using the above mentioned algorithms are presented and compared. Discussions about the adaptive neuron model and the extended Kalman filter algorithms as the most promising training techniques are presented, giving their advantages and disadvantages.