Wave energy converters together with flexible breakwaters not only provide shelter to the energy devices against wave attacks but also offer improved performance, longer survivability and lower costs. Thus, in the present work we are interested to investigate the interaction of linear water waves with an array of three thin vertical plates, comprising of two plate wave energy converters and one flexible breakwater, submerged in water of finite depth in a two dimensional space. The plate in the middle of the setup is a flexible plate of variable thickness, and on either side of it are piezoelectric plate wave energy converters with constant thickness. The problem is solved by converting the associated boundary value problem into a system of coupled integral equations. A modified form of the energy balance equation is derived, which results due to the presence of the two piezoelectric plates. We investigate how the structural properties of the piezoelectric plates like their submergence depths, plate lengths, distance from the breakwater and different edge conditions can affect the wave attenuation and wave power absorption efficiency. Further, it is also examined how the presence of the non-uniform flexible plate with different flexibility and lengths can improve the performance of the system. It is analysed that shorter sized piezoelectric plate wave energy converters in the presence of non-flat flexible plate offer higher wave power absorption efficiency at lower frequencies.