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Within the problem of the finding of the mean potential energy of the chargedparticle in the plasma in this work a classification of physical systems(electrolytes, dusty plasmas, plasmas) is made based on consideration, or lackthereof, of a few special additional conditions. The system considered here, aswell as other systems which are described with those additional conditionsimposed are treated as the systems of the "closed" type, while the systemswhere those conditions are fully neglected - as being of the "open" type. Inthe our previous investigation one- and two component systems were examined.Here, as the object of investigation fully ionized electron-ion plasma withpositive charged ions of two different kinds, including the plasmas of highernon-ideality, is chosen for the first time. For such plasma a newself-consistent model method of describing electrostatic screening is developedwhich includes all the necessary additional conditions. By this method suchextremely significant phenomena as electron-ion and ion-ion correlations areincluded in the used model. The characteristics of the considered plasmas in awide region of electron densities and temperatures are calculated. All theobtained results, including a comparison with systems of the "open" type arespecifically discussed.

The new model method of the electrostatic screening describing: three-component system of the 'closed' type