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An electrical cathode model (ECM) of a high-pressure sodium (HPS) lamp based on physical laws has been developed. The proposed ECM calculates the instantaneous voltage drop in a cathode sheath and the temperature distribution inside the cathode using as input parameter the cathode geometry and the positive column current. The model is based on the electrode heat transport equation, which is solved using the finite-element method. So, since it stems from the physics describing the cathode behavior, it is found that the ECM predicts in a satisfactory way the cathode voltage drop over a wide range of work conditions. The obtained results were compared with those reported in the current literature. It can be concluded that the ECM is a useful tool in understanding the interaction between the positive column and the cathode in order to improve, for instance, HPS lamp ballast designs, as measuring the potential drop across the cathode sheath using a commercial lamp is particularly difficult. The model takes into account the temperature dependence of the thermal conductivity, the electrical cathode resistivity, and the total emissivity. [ABSTRACT FROM AUTHOR]

In this paper, an electrical model for a high-pressure sodium discharge based on the energy-balance equation is presented. A database containing the transport-coefficient values for different temperatures and pressures was used to solve the energy-balance equation. The resultant model is implemented in SIMULINK as a two-terminal device, providing a powerful tool for simulating the electrical-discharge behavior at low and high frequencies under different power requirements. This model reveals that the temperature depth modulation is very low when the current source has a square waveform, even at low frequencies. The model was validated with experimental results. Finally, in order to decrease the complexity and the computing time of the electrical-discharge characteristics, an approximation of the used database is proposed, obtaining very acceptable results. [ABSTRACT FROM AUTHOR]