  Within the problem of the finding of the mean potential energy of the charged
particle in the plasma in this work a classification of physical systems
(electrolytes, dusty plasmas, plasmas) is made based on consideration, or lack
thereof, of a few special additional conditions. The system considered here, as
well as other systems which are described with those additional conditions
imposed are treated as the systems of the "closed" type, while the systems
where those conditions are fully neglected - as being of the "open" type. In
the our previous investigation one- and two component systems were examined.
Here, as the object of investigation fully ionized electron-ion plasma with
positive charged ions of two different kinds, including the plasmas of higher
non-ideality, is chosen for the first time. For such plasma a new
self-consistent model method of describing electrostatic screening is developed
which includes all the necessary additional conditions. By this method such
extremely significant phenomena as electron-ion and ion-ion correlations are
included in the used model. The characteristics of the considered plasmas in a
wide region of electron densities and temperatures are calculated. All the
obtained results, including a comparison with systems of the "open" type are
specifically discussed.
