Constant S and Constant Z Loads

Electrical power systems engineers, especially those working on systems at the distribution level, are generally required to complete load flow calculations for their projects. Load flow (also known as power flow) studies are used to analyze the steady-state voltage, currents, and complex powers that are present in an electrical system. The power flow calculation shows the designer how the system will behave under various conditions, like light and heavy loading. Engineers can use these results to ensure that there are not dangerous overvoltage or undervoltage conditions.

Load flow studies rely on two main types of load models: Constant S and Constant Z. Constant Z models should be familiar for all electrical engineers, because it is just an application of Ohm's Law. In other words, a constant Z model assumes that the impedance of the load does not change over time, so the steady-state current drawn by the load is proportional to the voltage applied to the load. Constant Z loads are representative of devices like heaters, capacitors, and inductors. Mathematically, for a three-phase system:

I = In * V / Vn

Where:

• I is the line current of the load in Amperes

• V is the line-to-line voltage applied to the load in Volts

• In is the rated current of the load in Amperes

• Vn is the rated line-to-line voltage of the load in Volts

Constant S loads are used to model devices which draw a constant complex power. For these loads, as the voltage drops the current increases. Constant S loads often represent motors near their full-load conditions. This model is simplified and obviously reaches a point of inaccuracy as the voltage at the load approaches zero. Mathematically, for a three-phase system:

I = Sn / (√3 V )

Where the variables I and V are defined the same as above. The variable Sn is the rated three-phase complex power of the load. All discussions above are purely based on a discussion of magnitudes. Full complex numbers and load power factors should be used for detailed load flow modeling to ensure accuracy.

As you can see, the current flowing to a load increases with higher voltages for an impedance load (Constant Z) while the current decreases with higher voltages for a motor load (Constant S). When both types of loads are present together on a bus, the results can be non-trivial.