Math Software for Electrical Power Systems Engineers

# Math Software for Electrical Power Systems Engineers

From load flow analysis of power systems to transmission line simulation, Maple provides a complete environment for tasks performed by electrical power systems engineers.

### Electrical power systems engineers use Maple for calculations, technical analyses and report generation

Power systems engineers are critical to power supply and generation. They work at utility companies, wind turbine manufacturers, as well as aerospace and defence companies. Electrical power systems engineers find fault failures in power networks, design substations, work on power system protection, do load flow analysis, protect against arc flashes and more.

These engineers need validated tools that help them solve complex problems – and a mathematics tool is central to this work. Math and data analysis tools may be used for simple design calculations, data analysis, and more intensive mathematical tasks.

Maplesoft has developed Maple with features that specifically address the needs of electrical power systems engineers, such as:

# Hands-on Workshop Electrical Power Systems Engineering with Math Software

A Maple document combines live math, text, images and plots in a single document. In effect, Maple captures the inherent assumptions and thought process behind an analysis, as well as the calculations.

## High-Level Symbolic and Numeric Math

Maple offers practical high-level tools for numeric and symbolic math, data analysis, and programming. These tools are designed for both simple and complex engineering problems.

• Numerically solve equations for transmission line voltage and current transients
• Symbolic and numeric methods for load flow analysis of power systems
• Power swing analysis for out-of-step protection with symbolic derivation and numeric solutions

The symbolic and numeric math engines are seamlessly connected; parameters, equations and calculations can fluidly flow between the two. This means you can derive and numerically evaluate your equations in a single cohesive workflow.

Moreover, Maple’s programming language benefits from an interactive development environment and can use any of Maple’s high-level math tools.

• Code is faster to develop, debug and verify
• Can use Maple’s high level math functions, and
• Is easier to read by humans

## Reduce Calculation Risk with Units

Almost all quantities encountered by power systems engineers – whether it’s a resistance, voltage, or a length – has a unit. Units are fluidly integrated into Maple, and can be used in simple calculations as well as numeric equation solving, optimization and visualization.

volt := 5.2V :
curr := 3.2A :
power := curr volt= 16.64 W

Using units in calculations removes the risk of introducing unit conversion errors, and also acts as a check on the physical validity of the equations.

## Cable Ampacity using the Nehers-McGrath Method

Heat is generated when current flows through a cable. The ampacity of a cable is the amount of current a cable can carry without exceeding its temperature rating. Accurately estimating ampacity is critical to minimizing the total lifetime cost of a cable installation.

This application implements the Nehers-McGrath equations and cross-checks the results against those tabulated in the National Electrical Code (2017); the good agreement means that this worksheet can be the basis of more complex cable ampacity calculations.

Using numeric and symbolic techniques, this application uses Maple’s built-in units system to show standard units throughout the calculations.

## Load Flow Analysis of a Five-Bus Power System

This application uses Maple to analyze a five-bus power system, and calculate the voltages and powers (real and reactive) at each bus.

For larger power systems, there can potentially be thousands of buses, and efficient numerical techniques are needed to solve the system nonlinear equations. Dedicated tools are available to define and simulate larger power flow systems.

Smaller systems can be modeled and studied in Maple, to reinforce theory, investigate numerical techniques, or to try out different topologies.

This Maple application demonstrates two approaches to numerically solving the load flow equations:

• The symbolic real and reactive load flow equations are generated, and solved with fsolve (a powerful numerical equation solver). This is quick to set up, but may be slower for larger systems. This approach also symbolically generates the real and reactive power flow equations.
• The system Jacobian is constructed, and solved with Newton-Raphson iteration (this method requires more initial setup, but may be faster for larger systems).

## Cross-Section of Metallic Tape for Substation Earthing

Substation earthing systems are a grid of buried conductors, known as an earth mat. The grounding of substations is very important for both personnel safety and to provide a discharge route for the overall power system.

This application calculates the cross-section of metallic tape to earth a conductor for a 110/30 kV substation.

Using Maple, the application follows EN 50522:2010 and IEC 60287-3-1, and features natural math notation and units throughout the calculations.

The Maple worksheet can also be converted to an interactive application with buttons and sliders, and can be deployed free of charge using the Maple Player.

## Transmission Line Simulation via Numerical Inversion of Laplace Transforms

Using Maple, you can numerically invert the Laplace transforms that describe the voltage and current in a transmission line. This requires fast, efficient numerical algorithms, fluidly connected to a broader toolset of plots and documentation.

The Laplace transforms are based on the Telegrapher’s Equations, which are a pair of coupled partial differential equations.

The results describe the transient variation of current and voltage at any point on the transmission line.