Harris hawks optimization (HHO) algorithm, which is inspired from Harris hawks hunting strategy, uses uniform random numbers in the optimization process. This paper proposes modifying HHO with seven types of random distribution function definitions that are chi-square distribution, normal distribution, exponential distribution, Rayleigh distribution, Student's distribution,Fdistribution, and lognormal distribution to show effects on stochastic search-based optimization algorithm performance. The modified HHO algorithm is tested via some benchmark test functions. Results are compared with each other and with classical HHO solutions. Then, the HHO and its modified versions are applied to optimum power flow (OPF), which is an important problem for power system engineering for decades. The algorithms are applied to IEEE 30-bus test system to minimize total fuel cost of the power system, active/reactive power losses, and emission, by comparing with recent OPF researches. Considering the applicability of the proposed approach and the results achieved, one can confirm that it might be a different alternative method for solving OPF problems. One of the important results of the paper in the IEEE 30-bus test system is that the cost of fuel is calculated as 798.9105 $/h with classical HHO, while it is calculated as 798.66 $/h with the HHO modified with SD function.