Параметризация СДПМ на основе измерений¶
В этом примере показано, как определить параметры синхронного двигателя с постоянными магнитами (СДПМ) на основе экспериментальных измерений.
Для того чтобы определить параметры двигателя СДПМ, мы проведем три эксперимента. Искомые значения параметров двигателя известны нам заранее, и мы сравним их со значениями, полученными из экспериментов.
Данные из документации на двигатель:¶
Тест 1. Определение R и L при неподвижном роторе¶
Первый эксперимент проводится на двигателе c заблокированным ротором. Между фазами подается ступенька напряжения и изучается переходный процесс отклика. Результирующая постоянная времени τ определяется значениями сопротивления и индуктивности статора:
$$τ = \frac{R}{L}$$

Зададим начальный угол поворота ротора:
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SimulationResult(
"ia" => WorkspaceArray{Float64}("PMSMFromMeasurement1/ia")
,
"uab" => WorkspaceArray{Float64}("PMSMFromMeasurement1/uab")
)
Рассчитаем сопротивление из значений, установившихся напряжения и тока.
Обмотки a и b в эксперименте соединены последовательно, поэтому разделим полученное сопротивление на 2:
$$R_e = \frac{1}{2}\frac{u_{ab}}{i_a}$$
Найдем постоянную времени цепи - это время, за которое ток достигает значения $1-\frac{1}{e}=0.63$ от установившегося:
Из формулы $τ = \frac{R}{L}$ выразим и рассчитаем индуктивность L:
Ожидаемый переходный процесс:
На графике ниже можно сравнить измеренный ток из модели и график тока, полученный из расчетов.
Тест 2. Определение постоянной противо-ЭДС¶
Во втором эксперименте двигатель вращается без электрической нагрузки. Это позволяет оценить постоянную противо-ЭДС.
Обратите внимание, что постоянная противо-ЭДС, выраженная в единицах СИ, равна постоянной момента двигателя, поэтому в этом примере рассчитывается только одна константа.

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SimulationResult(
"uab" => WorkspaceArray{Float64}("PMSMFromMeasurement2/uab")
)
Определение константы противо-ЭДС¶
Константу противо-ЭДС $K_e$ можно рассчитать по формуле:
$$K_e= \frac{V_{a, pk}}{\omega},$$
где $V_{a,pk}$ – падение напряжения на фазе a двигателя,
$\omega$ – угловая скорость вала двигателя.
Постоянная момента равна постоянной противо-ЭДС, выраженной в единицах СИ.
На графике ниже показана противо-ЭДС, возникающая при движении экспериментального двигателя на номинальной скорости.
Количество пар полюсов можно определить, подсчитав количество периодов изменения тока за один оборот ротора.
3. Определение коэффициентов трения и момента инерции¶
В третьем эксперименте ненагруженный двигатель управляется контроллером.
В прошлом эксперименте была получена постоянная момента. C её помощью, путем преобразования токов статора, могут быть рассчитаны коэффициенты трения.
Переменные, требуемые для моделирования контроллера:
Измерим механический крутящий момент, необходимый для поддержания постоянной частоты вращения на четырех различных скоростях.
Момент, необходимый на более низких скоростях, в первую очередь направлен на преодоление сухого трения, на более высоких скоростях - вязкого трения.
На графике показаны измеренные моменты для четырех скоростей. Через эти точки проведена прямая. Пересечение нулевой скорости дает коэффициент сухого трения, а наклон - коэффициент вязкого трения.
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На втором графике показан тест замедления двигателя. Для этого теста требуемый крутящий момент устанавливается равным нулю или двигатель отключается.
Используя измеренное замедление, при заданных значениях моментов трения и демпфирования, можно определить момент инерции ротора двигателя.
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SimulationResult(
"ia" => WorkspaceArray{Float64}("PMSMFromMeasurement3/Controller/Sensing_iabc/ia")
,
"rpm" => WorkspaceArray{Float64}("PMSMFromMeasurement3/Controller/Encoder/rpm")
)
В этом примере мы определили параметры синхронного двигателя с постоянными магнитами на основе экспериментальных измерений.
Для этого мы провели три теста. В первом тесте мы нашли сопротивление и индуктивность обмотки двигателя, во втором определили константу противо-ЭДС, а в третьем – коэффициенты трения и момент инерции.
Найденные экспериментально значения сопоставимы с параметрами двигателя из документации.
Блоки, использованные в примере¶
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