Power System Analysis: Real Power Balance Equations

Power System Flow and Control

• When analyzing power systems, we know neither the complex bus voltages nor the complex current injections, but rather the complex power being consumed by the load and the power being injected by the generators plus their voltage magnitudes.

Real Power Balance Equations

• The power balance equations are used to analyze power systems, which are composed of complex power injected by the generators (Si) and the power consumed by the load (Pi + jQi).
• The complex power injected by the generators (Si) is equal to the sum of the product of the voltage magnitude at bus i (Vi) and the complex conjugate of the current injection at bus i (Ii*).
• The real power balance equation is resolved into the real part (Pi) and the imaginary part (Qi), which are expressed as a function of the voltage magnitude, conductance (Gik), and susceptance (Bik).

Power Flow Requires Iterative Solution

• When solving for the complex bus voltages (V's) in the power flow, we assume we know the complex power injected by the generators (Si) and the admittance matrix (Ybus).
• The power flow equation has no closed form solution, and therefore, we must use an iterative approach to solve for the complex bus voltages.
• The iterative approach involves resolving the complex power injected by the generators into the real and imaginary parts, and then solving for the complex bus voltages using the power balance equations.

Test your knowledge of real power balance equations and power system analysis. Understand how to analyze power systems using power balance equations rather than complex bus voltages and current injections.