[Tex/LaTex] Different vertical position of summation limits in consecutive \sum

Question

When I use different summation indices in a double sum the limits are not vertically aligend, for instance:

\begin{equation}
\Delta K_T^i = \sum_{t=1}^{T}\sum_{k=1}^{m}{\Delta K_t^{i,k}} = \sum_{t=1}^{T} {\Delta K_t^k}
\end{equation}

and

\begin{equation}
\Delta K_T^k =\sum_{t=1}^{T}\sum_{i = 1}^{n}{\Delta K_t^{i, k}} = \sum_{t=1}^{T}{\Delta K_t^i}
\end{equation}

The limits below the summation symbol are misaligned vertically while the superscripts seem ok. Also the misalignment is bigger in the first example than in the second one.

If I use the same letter as subscript index the alignment works as expected.

\begin{equation}
\Delta K_T^i = \sum_{t=1}^{T}\sum_{t=1}^{m}{\Delta K_t^{i,t}} 
\end{equation}

I use the following packages, could any of these be the cause, or is this a bug/feature that could be handled in any way? I am using MikTex 2.9

\documentclass[a4paper,twoside,10pt]{article}
\usepackage[swedish]{babel} 
\usepackage[T1]{fontenc}
\usepackage[ansinew]{inputenc}
\usepackage{lmodern}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}

Answer 1

The reason is the different height of the subscripts, t is smaller than k. One way to fix this (not beautiful, I know) is to put an invisible k below the first sum via \vphantom:

\begin{equation}
\Delta K_T^i = \sum_{\vphantom{k}t=1}^{T}\sum_{k=1}^{m}{\Delta K_t^{i,k}} = \sum_{t=1}^{T} {\Delta K_t^k}
\end{equation}