A Local Linear Black-Box Identification Technique For Power Converters Modeling Guido Ala, Antonino Spagnuolo, Fabio Viola Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni Università degli Studi di Palermo Palermo, Italy guido.ala@unipa.it Abstract— In this paper, a black-box modeling technique for power electronic converters, also used in automotive environment is presented. The aim of this work is to provide a simple yet versatile and powerful tool to schematize complex electric devices in vehicular appliances, in order to fulfill the electromagnetic compatibility already during the project stage. By using input and output measured data, a composite local linear state space model is built up. Radial basis functions are used as weights for the local systems. The proposed approach is validated and applied in modeling a DC/DC converter for DC motors, a pulse width modulation inverter and a controlled rectifier. Keywords-black box technique; power electronic converters; state space model; electromagnetic compatibility I. INTRODUCTION During the last years, the automotive systems have deeply changed. New technologies, new services and new expectations from the customers gave rise to new problems and new challenges. New propulsion systems are changing the content of vehicles. The future automotive systems will incorporate high power electric drive systems as well as today’s conventional ones. The advances in power electronics as well as in motor design and manufacturing have made electric drives very attractive. They have high efficiency with lower mass due to the implementation of adjustable speed or frequency drives. The ElectroMagnetic Compatibility (EMC) methods and approaches must keep up with these changes. In fact, the massive use of electrical and electronic equipment increase the pollution of the electromagnetic environment, and, as a consequence, the functional safety can be compromised if EMC compliance is not achieved. In order to achieve EMC requirements already during the project stage, so reducing cost and time-to-market, effective and robust models are needed. These models must be simple, suitable to be interconnected in different modes and they have to require no excessive computational resources. The models belonging to the black- box family are preferable in this sense, because they do not require any knowledge about the physical system, but only the sampling of input and output. In this paper, an identification method for nonlinear dynamical systems based on the Composite Local Linear State Space (CLLSS) model is presented and discussed. This method, already used to build behavioral models of electronic devices [1], is used here to model power electronic converters also used in automotive environment. The proposed approach is validated and applied in modeling a DC/DC 42 V converter, a Pulse Width Modulation (PWM) inverter and a controlled IGBT rectifier. II. THE BLACK-BOX MODEL In order to obtain a black-box model, let us consider the following discrete state space equation: () ( ) ( ) () () () () ⎩ ⎨ ⎧ + + = - + - = k v k Du k Cx k y k Bu k Ax k x 1 1 , (1) where A, B, C, D are the matrices defining the system, () n R k x ∈ represents the state vector, () m R k u ∈ is the system input, () l R k y ∈ is the system output and () k v is the measurement noise. Local linear models can be successfully used to approximate dynamical systems. In fact, the model represented by (1) can be combined with other similar models and weighted by normalized functions with local support [1-2]. By splitting the operating time range of the system into smaller local portions, and by using convenient weight functions with local support, it is possible to combine local models into a global one, in order to obtain the global dynamical system with a little computational effort [2]. The complete model can be represented by the following equations: () () ( ) ( ) ( ) ( ) () () ( ) () () () ( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + + = - + - = ∑ ∑ = = S j j j j S j j j j k v k u D k x C k k y k u B k x A k k x 1 1 ˆ 1 1 ϕ ρ ϕ ρ , (2) in which () ( ) k i ϕ ρ are the selected weight functions, φ(k) is the output of the local state space system (depending on the input u(k) and the state x(k)), () k y ˆ is the output obtained by the black-box model and S is the number of local models. In local linear modeling [2], it is common practice to use normalized radial basis functions. The i-th function can be chosen as: () ( ) () ( ) () ( ) ∑ = = S j j j j i i i i w c k r w c k r k 1 , , , , ϕ ϕ ϕ ρ , (3) 978-1-4244-2601-0/09/$25.00 ©2009 IEEE 257