Final answer:
To solve the load flow problem manually using the Newton-Raphson method for the given transmission system, one must construct and solve the power mismatch equations iteratively. The Jacobian matrix is key to this process, and iterations are carried out until the power mismatches are below the set convergence criteria. The power dissipated in the lines can be calculated and compared to the total power transmitted to evaluate the efficiency.
Step-by-step explanation:
To solve this PowerWorld Simulator case using the Newton-Raphson method, with each transmission line having an impedance of 0.05+ j0.1 p.u. on a 100-MVA base, we begin by identifying that there's a load of 180MW at bus 3 and generation of 80MW with a set voltage of 1.0 p.u. at bus 2. Bus 1 is the slack bus with a 1.0 p.u. voltage setpoint.
Since the question requires manual calculation, we'd proceed by setting up the power mismatch equations based on the specified bus types (load, generation, slack) and impedance values for the transmission lines. For the Newton-Raphson iteration, we construct the Jacobian matrix from the partial derivatives of the real and reactive powers with respect to voltage magnitude and angle at each bus except the slack. The iteration continues until the power mismatches for P and Q are below the convergence criteria of 0.1 MVA.
It's important to note that the power dissipated in the transmission lines can be calculated using the formula P = I²R, where I can be found by rearranging P = IV and solving for I. Then, by comparing the power dissipated in the lines to the total power transmitted, we can evaluate the efficiency of the power transmission.
In this specific problem, the resistance R of the lines is not given directly within the provided details. Rather, it is expressed as a series impedance in per unit, which includes both resistive (R) and reactive (X) components. Thus, the correct approach for power loss computation in the network would be related to the current through and the impedance of each line.