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What numerical errors should you avoid in electrical systems?

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Numerical errors are inevitable in any computational process, but they can have serious consequences in electrical systems. If you are not careful, you can end up with inaccurate results, unstable behavior, or even damage to your equipment. In this article, we will discuss some common numerical errors that you should avoid in electrical systems, and how to prevent or correct them.

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Luis J. Rodríguez

? Ingeniero Electricista | ??? Profesor | ?? Investigador | Especialista en Transitorios Electromagnéticos: ATP, EMTP?,…
Shayan Razaghi

可再生能源专家， Victron Energy，技术和实践培训课程和研讨会讲师
ígor Botelho

Perícias e Avalia??es | Engenheiro Eletricista, Civil e de Seguran?a do Trabalho | Seguran?a Eletr?nica | SDAI |…

1 Round-off errors

Round-off errors occur when you represent a real number with a finite number of digits, such as in a floating-point format. This can introduce small errors in your calculations, which can accumulate over time or propagate through your system. For example, if you use a 32-bit floating-point number to store the voltage of a circuit, you can only represent about seven decimal digits of precision. This means that if the voltage is very small or very large, you will lose some accuracy. To avoid round-off errors, you should use a higher precision format, such as a 64-bit floating-point number, or a fixed-point format, which can preserve the exact value of an integer or a fraction. You should also avoid subtracting two numbers that are very close in magnitude, as this can cause a loss of significant digits.

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Luis J. Rodríguez

? Ingeniero Electricista | ??? Profesor | ?? Investigador | Especialista en Transitorios Electromagnéticos: ATP, EMTP?, PSCAD
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Numerical instabilities are a main concern on alternative version of EMTP. A very deep engineering judgement must be present in order to identify such oscillations and to correct them via different methods (Snubbers, special requests, etc.) otherwise, this numerical-non-real behavior would lead to wrong conclusions.

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Muhammad Maaz

PEC Registered Electrical Engineer | Major in Computer Engineering |
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Round-off errors are particularly critical in control systems and digital signal processing where precision is paramount. In these fields, even small errors can significantly affect system stability and performance. Engineers often use extended precision or error correction algorithms to mitigate these effects. Additionally, careful algorithm design can minimize the impact of round-off errors, such as by reordering operations to maintain the highest possible precision throughout computations.

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ígor Botelho

Perícias e Avalia??es | Engenheiro Eletricista, Civil e de Seguran?a do Trabalho | Seguran?a Eletr?nica | SDAI | Instala??es Prediais | HVAC | Estágios no IPT (Geotecnia) e Polícia Federal (Perícias)
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Evite erros de arredondamento em sistemas elétricos, pois podem impactar a precis?o das medi??es. Arredondar excessivamente pode levar a perda de informa??es importantes, enquanto arredondar insuficientemente pode introduzir imprecis?es. Utilize uma quantidade adequada de casas decimais para manter a precis?o, considerando padr?es da indústria e requisitos específicos do sistema. Evite acumular erros ao longo de cálculos extensos. Ao adotar práticas cuidadosas de arredondamento, é possível preservar a precis?o numérica crucial para o funcionamento confiável de sistemas elétricos.

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Mauricio dos S.

Professor Mestre, Pesquisador e Autor do livro Elementos de Automa??o Aplicados em Supervis?o de Potências Elétricas.
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Erros numéricos ocorrem durante o cálculo de valores numéricos executados no desenvolvimento do projeto. Eles podem ser causados por uma variedade de fatores, incluindo arredondamento, truncamento, erros de medi??o e erros de algoritmo. Em sistemas elétricos, os erros numéricos podem levar a resultados imprecisos ou incorretos.

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2 Truncation errors

Truncation errors occur when you approximate a continuous function with a discrete one, such as in a numerical integration or differentiation method. This can introduce errors in your estimates, which can affect your system performance or stability. For example, if you use a finite difference method to approximate the derivative of a current in a circuit, you will introduce an error proportional to the step size that you use. To avoid truncation errors, you should use a smaller step size, or a higher-order method, which can reduce the error by using more information from the function. You should also avoid using a method that is not suitable for your problem, such as using a forward difference method for a stiff differential equation.

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ígor Botelho

Perícias e Avalia??es | Engenheiro Eletricista, Civil e de Seguran?a do Trabalho | Seguran?a Eletr?nica | SDAI | Instala??es Prediais | HVAC | Estágios no IPT (Geotecnia) e Polícia Federal (Perícias)
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Evite erros de truncamento em sistemas elétricos ao descartar dígitos após a vírgula. Truncar excessivamente pode resultar em perda de informa??es cruciais para precis?o. Ajuste a quantidade de dígitos truncados com base na relevancia da aplica??o e na precis?o requerida. Ao acumular opera??es, considere o impacto do truncamento, pois isso pode levar a resultados imprecisos em cálculos subsequentes. Gerencie cuidadosamente os erros de truncamento para preservar a acurácia numérica necessária em sistemas elétricos.

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3 Overflow and underflow errors

Overflow and underflow errors occur when you exceed the range of values that your numerical format can represent. This can cause your calculations to fail, or to produce incorrect results. For example, if you use a 16-bit signed integer to store the current of a circuit, you can only represent values between -32768 and 32767. If the current exceeds this range, you will get an overflow error, which can cause your system to crash or behave unpredictably. To avoid overflow and underflow errors, you should use a numerical format that can accommodate the expected range of values for your problem, or scale your values to fit within the range. You should also check for potential overflow or underflow conditions before performing arithmetic operations, and handle them appropriately.

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Muhammad Maaz

PEC Registered Electrical Engineer | Major in Computer Engineering |
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Overflow and underflow errors are critical in electrical engineering, particularly in digital signal processing and control systems where numerical precision is paramount. Using data types with appropriate bit-widths is essential, and implementing saturation logic can prevent system instability by capping values at their maximum or minimum. Moreover, in real-time systems, such errors can lead to catastrophic failures, hence rigorous testing and validation are necessary to ensure robustness against extreme inputs or unexpected operational conditions.

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4 Quantization errors

Quantization errors occur when you convert a continuous signal to a discrete one, such as in an analog-to-digital conversion (ADC) or a digital-to-analog conversion (DAC). This can introduce errors in your measurements or outputs, which can affect your system quality or efficiency. For example, if you use an 8-bit ADC to sample the voltage of a circuit, you can only represent 256 discrete levels of voltage. This means that if the voltage varies between these levels, you will introduce an error equal to the difference between the actual value and the nearest level. To avoid quantization errors, you should use a higher resolution ADC or DAC, which can represent more levels of voltage. You should also use a sampling frequency that is at least twice the highest frequency of your signal, according to the Nyquist theorem, to avoid aliasing errors.

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Muhammad Maaz

PEC Registered Electrical Engineer | Major in Computer Engineering |
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Quantization errors are inherent in digital systems and can significantly impact precision. To mitigate these errors, engineers often employ dithering, which adds a small amount of noise to the signal before quantization. This process can help to randomize the quantization errors, making them less correlated with the signal and reducing distortion. Additionally, oversampling can be used to increase the resolution effectively, allowing for digital filtering to reduce noise and improve the signal-to-noise ratio.

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5 Numerical instability errors

Numerical instability errors occur when you use a numerical method that amplifies small errors or perturbations in your system, making them grow exponentially over time. This can cause your system to diverge from the expected behavior, or to oscillate wildly. For example, if you use an explicit Euler method to solve a differential equation that models a resonant circuit, you will introduce an error that depends on the step size and the natural frequency of the circuit. If the step size is too large, or the frequency is too high, the error will grow faster than the solution, and your system will become unstable. To avoid numerical instability errors, you should use a numerical method that is stable for your problem, or a smaller step size, or a damping factor, which can reduce the growth of errors. You should also monitor your system for signs of instability, such as large fluctuations or deviations from the expected values.

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Shayan Razaghi

可再生能源专家， Victron Energy，技术和实践培训课程和研讨会讲师
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Set a defined guideline in the project's design and engineering working standards. This could be implemented within the organization or project-based. Rounding up or down might be a common and useful strategy to simplify calculations and speed up the design process, while making sure not all of them have the same results in oversizing or undersizing. A good strategy could be to do these simplifications in a way that mitigate the results of each other in a way that the final calculations are neither oversized or undersized.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What numerical errors should you avoid in electrical systems?

1

2

3

4

5

6

1 Round-off errors

2 Truncation errors

3 Overflow and underflow errors

4 Quantization errors

5 Numerical instability errors

6 Here’s what else to consider

Electrical Engineering

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What numerical errors should you avoid in electrical systems?

1

2

3

4

5

6

1 Round-off errors

2 Truncation errors

3 Overflow and underflow errors

4 Quantization errors

5 Numerical instability errors

6 Here’s what else to consider

Electrical Engineering

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