Harmonic oscillations as integer multiples of the fundamental frequency in a power system are caused by nonlinear physical effects such as switching or saturation. Modelling and detection of these harmonics are crucial for power system control and protection. The present paper proposes the use of wavelet networks with smooth local trigonometric functions as activation functions. A new algorithm is proposed, together with the use of the Cross Entropy function as a tool for evaluating the model quality. The algorithm consists of recursive dual iterations with biorthogonal smooth local sine and cosine wavelet packets in order to calculate the adjustable parameters related to the activation functions. The algorithm efficiently minimizes the Shannon Entropy function by adaptively choosing the best time-frequency cells on the wavelet packet tree. During every loop the Cross Entropy function between estimated outputs and target outputs is checked. A procedure by using trigonometric wavelet packets is proposed as an effective tool for disturbance detection, power quality analysis and non-linear harmonic circuit modelling. Simulations of a converter bridge for traction drives are included to illustrate the effectiveness of the algorithm and the choice of the activation function.