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We consider the problem of joint optimal placement of phasor measurement units (PMU) and conventional measurements to ensure full observability in power systems. The formulation is initially posed as a nonlinear integer programming problem and then transformed in to an equivalent integer linear programming (ILP) problem by introducing auxiliary variables and constraints. The resulting ILP problem is solved for the optimal solution on IEEE 14-, 57-, and 118-bus systems considering zero-injection buses. To extend the formulation to large-scale systems, two heuristics are proposed where the nonlinear problem is decomposed into two separate problems of lesser complexity. The heuristics are evaluated on standard IEEE test cases and a large 2383-bus Polish system. The heuristics yield solutions close to optimal (difference of 1 PMU) solutions on standard IEEE systems, while substantially reducing problem complexity and run time. The placement results obtained with the proposed formulation require fewer PMUs for observability compared to systems with fixed locations of conventional measurements. The results thus potentially provide a more economical solution to system observability compared to those obtained solely with PMU placement.