Short Answer:
Per-unit system calculations are a method used in power system modeling to simplify the analysis of electrical quantities like voltage, current, power, and impedance. In this method, all values are expressed as fractions (or multiples) of selected base values, usually set for voltage, power, current, and impedance.
Using the per-unit system helps standardize different components like transformers, generators, and lines that operate at various voltage levels. It makes calculations easier, avoids confusion with unit conversions, and simplifies comparisons across the power system.
Detailed Explanation:
Per-unit system calculations in power system modeling
In electrical power systems, different components operate at different voltage and power levels. Comparing values across these varying scales can be difficult, especially when performing system-wide analysis involving transformers, buses, generators, and loads. To overcome this, engineers use a per-unit (pu) system, which is a normalized way of expressing electrical quantities based on common reference (base) values.
In the per-unit system, all electrical quantities are scaled against predefined base values, and the resulting numbers are dimensionless. This technique reduces calculation complexity and provides consistency in power system analysis.
Purpose and Benefits of Per-Unit System
- Simplifies complex power system calculations
- Avoids confusion with units like kV, MVA, ohms, etc.
- Standardizes different components in a multi-voltage system
- Simplifies transformer modeling (impedances remain unchanged)
- Improves accuracy and understanding in fault and stability analysis
How Per-Unit System Works
To perform per-unit calculations, the following base quantities must be selected:
- Base Power (S_base) – usually in MVA
- Base Voltage (V_base) – in kV
From these, the remaining base quantities are calculated:
- Base Current (I_base) = S_base / (√3 × V_base)
- Base Impedance (Z_base) = V_base² / S_base
Then, the actual quantity is divided by its base value to get the per-unit value:
Per-unit value=Actual valueBase value\text{Per-unit value} = \frac{\text{Actual value}}{\text{Base value}}Per-unit value=Base valueActual value
Example of Per-Unit Conversion
Suppose a transformer has an actual impedance of 3 ohms, and the base impedance is calculated as 12 ohms. Then:
Zpu=312=0.25 puZ_{pu} = \frac{3}{12} = 0.25 \, \text{pu}Zpu=123=0.25pu
This means the transformer’s impedance is 0.25 per-unit.
Applications in Power System Modeling
- Transformer Modeling:
Impedances on both sides of a transformer can be represented in a single per-unit value without converting to a common side. - Power Flow Analysis:
Voltage and power values are normalized to keep calculations within consistent and simple ranges. - Short Circuit and Fault Studies:
Fault currents and system impedances are easier to calculate and compare using per-unit values. - Stability Studies:
Generator and load models become uniform, aiding in accurate simulation of dynamic behavior. - System Protection Design:
Relay settings and protection coordination are based on per-unit values to maintain consistency across varying voltage levels.
Advantages of Using Per-Unit System
- Uniformity: Makes models easier to build and understand across different voltage levels.
- Simplicity: Reduces the size and complexity of numerical values.
- Scalability: Helps in comparing system components of different ratings.
- Transformer Neutrality: Eliminates the need to refer all parameters to one side of the transformer.
Conclusion
Per-unit system calculations are a powerful and widely used technique in power system modeling. By converting electrical quantities into normalized units based on selected base values, engineers can simplify analysis, maintain consistency, and reduce errors across large and complex electrical networks. The per-unit method is essential for efficient power flow studies, fault analysis, stability simulations, and transformer modeling in modern power systems.