In islanded ac microgrids with heterogeneous distributed generations (DGs), secondary frequency control (SFC) can restore the frequency that deviates from the nominal level due to the primary P-f droop control. Traditionally, to realize SFC, the instantaneous frequency needs to be directly measured or estimated to produce frequency compensations, which increases system cost and complexity. In this paper, a new spatial load power forecasting for distributed secondary frequency control (SLPF-DSFC) based on artificial neural networks is proposed. Without frequency measurement, it can effectively eliminate frequency deviations and autonomously cope with various load changes by optimizing active power outputs from DGs. The distributed average and pinning protocols based on graph theory are also included. Comprehensive case studies demonstrate that the proposed SLPF-DSFC method shows superior performance over conventional SFC approaches in terms of frequency stabilization and voltage harmonics reduction during load variations, SFC startup/shutdown, as well as communication delays.