Grid-connected renewable energy conversion systems (RECSs) are usually required by grid codes to possess the low voltage ride through (LVRT) and reactive power support capabilities so as to cope with grid voltage sags. During LVRT, RECS's terminal voltage becomes sensitive and changeable with its output current, which brings a great challenge for the RECS to resynchronize with the grid by means of phase-locked loops (PLLs). This paper indicates that loss of synchronism (LOS) of PLLs is responsible for the transient instability of grid-connected RECSs during LVRT, and the LOS is essentially due to the transient interaction between the PLL and the weak terminal voltage. For achieving a quantitative analysis, an equivalent swing equation model is developed to describe the transient interaction. Based on the model, the transient instability mechanism of RECSs during LVRT is clarified. Furthermore, a transient stability enhancement method is proposed to avoid the possibility of transient instability. Simulations performed on the New England 39-bus test system verify the effectiveness of the method.