The nonlinear and stochastic characteristics of loads in the distribution system result in the uncertainty of injected harmonic current at load buses

and then lead to the harmonic distribution uncertainty in the power system. To deal with the uncertainties of harmonic sources in harmonic power flow calculation

an interval is used to replace the point value to develop a complex affine model of the constant-current source for the harmonic source. Taking the harmonic source with a typical spectrum as an example

the influence of load uncertainties on the harmonic current produced by the harmonic sources is analyzed

and the modeling method is described as well. On this basis

a complex affine calculating method based on backward/forward sweep for three-phase uncertain harmonic power flow in the distribution system is proposed. The method proposed is tested on a typical 33-bus distribution system

and the results obtained are compared with those from Monte Carlo’s method of harmonic power flow analysis. Simulation results show the effectiveness of the method proposed in calculating harmonic distribution in the distribution system with uncertain harmonic sources. This work is supported by National High Technology Research and Development Program of China (863 Program) (No. 2011AA05A114) and National Natural Science Foundation of China (No. 51361135704

No. 51377115).