Variables Notation, Meaning, and Introduction
Symbol	Meaning	Definition
$B_{Akj}$	Global benefit of increasing $U_{Akj}$ towards the total objective function	(11)
$B_{Bkj}$	Global benefit of increasing $U_{Bkj}$ towards the total objective function	(12)
$B_{PAkj}$	Benefit of increasing $U_{Akj}$ towards the power and ripple objective function	(8)
$B_{PBkj}$	Benefit of increasing $U_{Bkj}$ towards the power and ripple objective function	(9)
$B_{Vkj}$	Benefit of increasing $U_{kj}$ towards the voltage objective	(4)
$C_{kj}$	DC-Link capacity of the k-th phase j-th module	Figure 1
$f$	Global objective function	(10)
$f_P$	Objective function for the power regulation and ripple reduction alone	(7)
$F_V$	Function to measure the (pondered) quadratic DC-Link voltage deviation	(1)
$f_V$	Objective function for DC-Link voltage regulation alone	(3)
$G_{Pkj}$	Power and ripple gain for the k-th phase j-th module	(8) and (9)
$G_{Vkj}$	Voltage regulation gain for the k-th phase j-th module	(1)
$i_{\alpha } \& i_{\beta }$	Power-invariant α and β components of the phase currents 2 (2 The sign criteria from Figure 1 is selected for the voltages and currents there defined.)
$i_d \& i_q$	Power-invariant d and q components of the phase currents 2 (2 The sign criteria from Figure 1 is selected for the voltages and currents there defined.)
$i_k$	Current of the k-th phase 2 (2 The sign criteria from Figure 1 is selected for the voltages and currents there defined.)	Figure 1
$j$	Subscript 1 indicating the module inside the phase, $j\in \left\{1, 2, 3\dots N\right\}$ (1 Subscripts other than $j$ and $k$ do not represent any numerical values.)
$k$	Subscript 1 indicating the phase, $k\in \left\{1, 2, 3\right\}$ (1 Subscripts other than $j$ and $k$ do not represent any numerical values.)
$L$	Phase inductance	Figure 1
$N$	Number of modules on each phase
$p_k^{*}$	Balance power reference for the k-th phase 3 (3 $p_k^{*}$ and $v_0$ belong to the method from [28] and are introduced on Section 3.2.2.)
$P_{kj}$	Actual active power received by the k-th phase j-th module
$P_{kj}{}^{*}$	Desired active power received by the k-th phase j-th module
$U_{Akj}$	Positive output voltage deviation of the k-th phase j-th module from $U_{kj}{}^{*}$	(6)
$U_{Bkj}$	Negative output voltage deviation of the k-th phase j-th module from $U_{kj}{}^{*}$	(6)
$U_{kj}$	Voltage output selected for the k-th phase j-th module 2 (2 The sign criteria from Figure 1 is selected for the voltages and currents there defined.)	Figure 1
$U_{kj}{}^{*}$	Voltage output for the k-th phase j-th corresponding to its desired power	(5)
$U_{Tk}{}^{*}$	Total voltage reference for the k-th phase given by the current regulator
$U_{Tk}{}^{’}$	$U_{Tk}{}^{*}$ after discounting the voltage corresponding to the desired power	(14)
$v_0$	Zero-sequence voltage 3 (3 $p_k^{*}$ and $v_0$ belong to the method from [28] and are introduced on Section 3.2.2.)	(17)
$V_{Gk}$	Voltage 2 of the grid k-th phase (2 The sign criteria from Figure 1 is selected for the voltages and currents there defined.)	Figure 1
$V_{kj}$	Actual DC-Link voltage of the k-th phase j-th module	Figure 1
$V_{kj}{}^{*}$	Desired DC-Link voltage of the k-th phase j-th module