Need for load flow and slack bus

Load flow analysis finds the steady-state bus voltages (magnitude and angle), line power flows and losses of a power system for given generation and load.

Why load flow analysis is needed

• Voltage profile: checks that all bus voltages stay within allowed limits (typically 0.95 to 1.05 pu).
• Line loading: shows whether any line or transformer is overloaded, so that rerouting or reinforcement can be planned.
• Losses: gives the real and reactive power loss of the network, needed for economic operation.
• Planning: tests future load growth and new lines or generators before they are built.
• Operation: used daily to schedule generation, set transformer taps and switch capacitor banks.
• Contingency studies: shows the effect of losing a line or generator.
• Base for other studies: fault, stability and economic dispatch studies all start from a load flow solution.

Significance of the slack bus

The slack (swing or reference) bus is the bus where $|V|$ and $\delta$ are specified and $P$ and $Q$ are left unknown.

1. Supplies the losses. Network losses ($I^2R$ and $I^2X$) are not known until the voltages are found. So the real and reactive power at all buses cannot be fixed in advance. One bus must be left free to "take up the slack":

$$P_{G,slack} = \sum P_{L} + P_{loss} - \sum_{\text{other}} P_{G}$$

2. Angle reference. Only angle differences matter, so one bus angle is fixed (usually $\delta = 0^\circ$). All other angles are measured from it.
3. Voltage reference. Its fixed $|V|$ sets the voltage level of the network.
4. Makes the problem solvable. It gives exactly two known and two unknown quantities at every bus, so the number of equations equals the number of unknowns.
5. Practical choice. It is normally the largest generating station (or the strongest grid connection), which can absorb the mismatch.

After the solution converges, the slack bus power is found from $P_1 - jQ_1 = V_1^{*}\sum_k Y_{1k}V_k$.