About the so-called usual models, in which the total momentum is conserved, it is well known that the total energy is not conserved due to the nonuniformity of space caused by spatial grids. It fluctuates and increases in time from a stochastic origin. In order to see the accuracy of the plasma simulations, it is important to evaluate the fluctuation K_g, which is more dominant for small errors during the shorter time. We study its standard deviation in t, σ K_g, and the correlation time of dK_g/K · dt, T, τ_c about periodic one-dimensional systems, where K is the kinetic energy. We evaluate σ K_g by invoking the stochastic theory and obtain a scaling law: σ{K_g}/K (2/π)^1/2 · η · {(2M)^1/2n_sλ_D}⁻¹ · (tτ_cω_p²)^1/2, where 2M is the number of the grids per one period, n_s, is the electron density, λ_D is the Debye length, and ω_p is the plasma angular frequency. The coefficient η depends on the magnitude of the unphysical grid force of each model. Our simulations with the usual models (CIC-PIC, modified SUDS, and method 2/2) support this scaling law. We obtain the correlation time empirically. It is found that τ_c ΔAt if Δt is sufficiently large, and if Δ/(Δt · ν_th) > 3, where Δt is the time step, Δ is the grid distance, and ν_th is the thermal velocity of the electron.