Conventional three phase shunt reactive power compensation systems eliminate only the reactive power but do not contribute to the elimination of neutral current or voltage and current unbalance in three phase four wire systems. A hybrid wye and delta shunt compensation can be a solution for eliminating neutral current and unbalance besides compensating the reactive power. The compensator is composed of shunt capacitors and parallel connected thyristor controlled reactors (TCR) by two three-phase circuits, delta and wye. In this work, a mathematical model is presented based on symmetrical components theory and three compensation strategies are derived. The models are validated with MATLAB simulation. The three strategies of compensation are discussed and compared in terms of size and cost.