A cluster model is proposed to describe the excitations in solid tungsten oxide. The density-functional theory approach is used to calculate the ground-state electronic structure of the model cluster and its optimum geometry; subsequently, time-dependent density-functional theory calculations are performed to obtain the oscillator strengths and energies of the excited states. The results are reported both for the electrically neutral cluster and for the cluster with an extra electron (mimicking the effect of electron injection from the cathode). They correctly locate the electrochemically active transition. The corresponding wave functions are delocalized, suggesting that electron localization at one tungsten center is rather unlikely, thereby shedding doubt as to the validity of the polaron model. Local lattice distortions presumably created at the stage of sample preparation are found to affect the excitation energies to a considerable extent, which explains the experimentally observable large width of optical absorption responsible for electrochromism.