PV Curve / Nose Curve

A PV curve (also called a nose curve due to its characteristic shape) is a plot of bus voltage magnitude on the vertical axis against active power transfer (or system loading level) on the horizontal axis. It is the primary graphical tool for assessing voltage stability and determining how much additional power a system can deliver before reaching the point of voltage collapse.

Key Aspects of PV Curves:

• Nose Shape: As active power transfer increases from light load, voltage initially remains nearly flat on the upper portion of the curve. Beyond a critical loading level, voltage drops steeply, creating the distinctive nose shape. The upper portion represents stable operating points, while the lower portion (below the nose) represents unstable equilibria that cannot be maintained in practice.
• Nose Point (Critical Point): The tip of the nose corresponds to the maximum power that can be transferred through the network to the load. Beyond this point, no steady-state equilibrium exists, and any further increase in demand triggers voltage collapse. The distance from the current operating point to the nose point defines the voltage stability margin, typically expressed in MW or as a percentage of current loading.
• Continuation Power Flow: Because standard Newton-Raphson cannot solve past the nose point (the Jacobian becomes singular), PV curves are traced using continuation power flow methods. These techniques parameterize the loading level and use predictor-corrector steps to follow the curve smoothly around the nose, mapping both the stable upper branch and the unstable lower branch.
• Influencing Factors: The shape and position of the PV curve depend on network topology, generator reactive capability, load characteristics (constant power, constant current, or constant impedance), and the status of reactive compensation devices. A contingency that removes a line or generator shifts the curve inward, reducing the maximum transferable power.
• Practical Application: System operators use PV curves to set transfer limits between areas, evaluate the impact of planned outages, determine how much additional load an area can accommodate, and quantify the benefit of proposed reactive power investments. They are a standard deliverable in transmission planning studies worldwide.