Some control strategies (like : DPC, MPC...) suffers from the presence of active/reactive power ripples, which requires some additional methods to be taken to reduce those ripples. But to judge the efficiency of those methods we need to calculate/quantify the value of the active and reactive power ripples, how can we do that ?

In his paper : Low Complexity Model Predictive Control—Single Vector-Based Approach, Yongchang Zhang & WeiXie wrote :

Table II lists the quantitative comparison of both methods in terms of active power ripple, reactive power ripple, and current THD at two operating points. The power ripple is calculated using the standard deviation function, which is expressed as :


where N is the sampling number of active power and reactive power in a period of 0.1 s.

I didn't understand this method of calculation,

what is this standard deviation function ? what is pi and qi ? how can we implement this calculation in an experimental setup ?

  • \$\begingroup\$ it's really weird that you understand control strategies, but you have not heard of deviation. So, here is the wiki article to start en.wikipedia.org/wiki/Standard_deviation. pi, qi are samples of the original pq power and N the number of samples \$p_{rip}\$ and \$q_{rip}\$ are equal to s = \$ \sqrt{ \frac{1}{N} Σ (x_i - \bar{x})^2} \$ \$\endgroup\$
    – thece
    Aug 3, 2018 at 19:07

1 Answer 1


Check out the wikipedia entry for standard deviation:

enter image description here

The equations above are the same calculation, but different notation

\$p_i\$ and \$q_i\$ are the samples, coming from a sampled vector (like data from an analog to digital converter)

$$ \mu = \frac{1}{N}\sum_{i=1}^{N} x_i$$ means to average the values toghether once you've computed the average, then you plug that into the other equation

If I have a vector of four values [1 5 2 3] the mean (using the above equation) would be 2.75

The standard deviation would be

$$ \sigma = \frac{1}{N}\sum_{i=1}^{N}([1,5,2,3 ]-2.75)=1.707$$

excel or any math package have the mean and std functions, or you could do this with a for loop and code.


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