  Power flow calculation plays an important role in planning, operation, and
control of the power system. The quantum HHL algorithm can achieve theoretical
exponential speedup over classical algorithms on DC power flow calculation.
Since the qubit resources in the Noisy Intermediate-scale Quantum (NISQ) era
are limited, it is important to discuss the performance considering this
limitation. The coefficient matrix of the linear systems of equations in DC
power flow problems cannot be represented perfectly by finite binary number
strings, which leads to imperfect phase estimation. This work is carried out
under the assumption of imperfect phase estimation. The performance of the HHL
algorithm is systematically investigated with different accuracy and redundant
qubits. In order to further reduce the required qubit resources, a hybrid
quantum-classical algorithm is proposed. By comparing errors of the HHL and
hybrid algorithms in the DC power flow calculation of the IEEE 5-bus test
system, it is found that the hybrid algorithm can achieve comparable precision
with fewer qubits than HHL by increasing the number of phase estimation
modules, which may make the hybrid algorithm a feasible route in the NISQ era.
