High-power solar arrays for satellite power systems are presently being planned with dimensions of kilometers, and with tens of kilovolts distributed over their surface. Such systems will face many plasma interaction problems, such as power leakage to the plasma, enhanced surface damage due to particle focusing, and anomalous arcing to name a few. In most cases, these effects cannot be adequately modeled without detailed knowledge of the plasma-sheath structure and space charge effects. A computer program (PANEL) has been developed to model the solar power satellite (SPS)-plasma interaction by an iterative solution of the coupled Poisson and Vlasov equations. PANEL uses the "inside-out" method and a finite difference scheme to calculate densities and potentials at selected points on either a two or three dimensional grid. PANEL was originally developed by Dr. Lee W. Parker to solve the Laplace equation for the potential distribution about a planar spacecraft and to calculate the plasma currents to the spacecraft surface. After some improvements, this version was tested and used to model the plasma interaction of the MSFC/Rockwell design for the SPS. Those results are presented in chapter three. More recently, with the aid of Dr. Parker, charge density calculation routines have been added to PANEL to include space charge effects. These routines along with some necessary improvements have been installed, resulting in the present version of PANEL. Among these improvements are: selectable boundary conditions, stop and start capability, a grid cell division technique to improve trajectory accuracy, and a method of phase space boundary tracking that greatly increases program efficiency by avoiding the repeated tracing of most trajectories. In this thesis, the history of the spacecraft charging problem is reviewed, the theory of the plasma screening process is discussed and extended, program theory is developed, and a series of models is presented. These models are primarily two-dimensional (2-D) for two reasons; one being that large 3-D models require more computing time than I have been able to afford, and the other being that most analytic models suitable for testing PANEL are 1-D and the 3-D capabilities were not required. These models include PANEL's predictions for two variations on the Child-Langmuir diode problem and two models of the interaction of an infinitely long one meter wide solar array with a dense 10 eV plasma. These models are part of an ongoing effort to adapt PANEL to augment the laboratory studies of a 1 x 10 meter solar array in a simulated low Earth orbit plasma being conducted in the Chamber A facilities at the NASA/Johnson Space Center. Also included are two 3-D test models. One is a "point potential" in a hot plasma and is compared to the Debye theory of plasma screening. The other is a flat disc in charge free space. For the Child-Langmuir diode problem, a good agreement is obtained between PANEL results and the classical theory. This is viewed as a confirming test of PANEL. Conversely, in the solar array models, the agreement between the PANEL and Child-Langmuir predictions for the plasma sheath thickness is presented as a numerical confirmation of the use of the Child-Langmuir diode theory to estimate plasma sheath thickness in the spacecraft charging problem.