Method and apparatus for calculating insertion indices for a modular multilevel converter
View Patent ↗A method for calculating insertion indices for a phase leg of a DC to AC modular multilevel converter. Each phase leg includes two serially connected arms, wherein each arm includes a number of submodules, wherein each submodule can be in a bypass state or a voltage insert mode. The insertion index includes data representing the portion of available submodules that should be in the voltage insert mode. The method includes the steps of: calculating a desired arm voltage for an upper arm connected to the upper DC source common bar and a lower arm connected to the lower DC source common bar, obtaining values representing actual total arm voltages in the upper arm and lower arm, respectively, and calculating modulation indices for the upper and lower arm, respectively, using the respective desired arm voltage and the respective value representing the total actual arm voltage. A corresponding apparatus is also presented.
1. A method for calculating insertion indices for a phase leg of a DC to AC modular multilevel converter via a control apparatus, said control apparatus having at east one controller, the converter comprising one phase leg between upper and lower DC source common bars for each phase, each phase leg comprising two serially connected arms, wherein an AC output for each phase leg is connected between the two serially connected arms, wherein each arm comprises a number of submodules, wherein each submodule can be in a bypass state or a voltage insert mode, the insertion index comprising data representing a portion of available submodules that should be in the voltage insert mode for a particular arm, the method comprising the steps of:
calculating, in said controller, a desired arm voltage for an upper arm connected to the upper DC source common bar and a lower arm connected to the lower DC source common bar,
obtaining, in said controller, values representing actual total arm voltages in the upper arm and lower arm, respectively, and
calculating, in said controller, insertion indices for the upper and lower arm, respectively, using the respective desired arm voltage and the respective value representing the total actual arm voltage;
wherein the step of calculating desired arm voltages for a phase leg comprises calculating
u CU ( t )= u D /2 −e V ( t )− u diff ( t )
for the upper arm, and calculating
u CL ( t )= u D /2 +e V ( t )− u diff ( t )
for the lower arm, where u CU (t) represents desired upper arm voltage where u CL (t) represents desired lower arm voltage, u D represents a voltage between the upper and lower DC source common bars, e V (t) represents a reference inner AC output voltage and u diff (t) represents a control voltage to control a current passing through the whole phase leg, and calculating
u diff ( t )= u diff1 ( t )+ u diff2 ( t )
where u diff1 (t) represents a voltage obtained by summing energy in the arms of the leg and u diff2 (t) represents a voltage obtained by calculating a difference in energy between the arms of the leg.
2. The method according to claim 1 , wherein the step of obtaining a value representing actual arm voltage comprises calculating
u diff2 ( t )= û diff2 cos(ω 1 t +ψ)
where û diff2 represents a difference between total upper arm energy and total lower arm energy, ω 1 represents the angular velocity of the network frequency and ψ represents the angle given by ψ=∠(R+jω 1 L) where R represents the resistance of the converter arm and L represents the inductance of the converter arm.
3. The method according to claim 1 , wherein the step of obtaining a value representing actual total arm voltage comprises measuring voltages of the submodules of the arm and summing these measured voltages.
4. The method according to claim 1 , wherein the insertion index comprises data representing a direction of the inserted voltage.
5. A method for calculating insertion indices for a phase leg of a DC to AC modular multilevel converter via a control apparatus, said control apparatus having at least one controller, the converter comprising one phase leg between upper and lower DC source common bars for each phase, each phase leg comprising two serially connected arms, wherein an AC output for each phase leg is connected between the two serially connected arms, wherein each arm comprises a number of submodules, wherein each submodule can be in a bypass state or a voltage insert mode, the insertion index comprising data representing a portion of available submodules that should be in the voltage insert mode for a particular arm, the method comprising the steps of:
calculating, in said controller, a desired arm voltage for an upper arm connected to the upper DC source common bar and a lower arm connected to the lower DC source common bar,
obtaining, in said controller, values representing actual total arm voltages in the upper arm and lower arm, respectively, and
calculating, in said controller, insertion indices for the upper and lower arm, respectively, using the respective desired arm voltage and the respective value representing the total actual arm voltage;
wherein the step of calculating desired arm voltages for a phase leg comprises calculating
u CU ( t )= u D /2 −e V ( t )− u diff ( t )
for the upper arm, and calculating
u CL ( t )= u D /2 +e V ( t )− u diff ( t )
for the lower arm, where u CU (t) represents desired upper arm voltage where u CL (t) represents desired lower arm voltage, u D represents a voltage between the upper and lower DC source common bars, e V (t) represents a reference inner AC output voltage and u diff (t) represents a control voltage to control a current, iV(t), passing through the whole phase leg,
wherein the step of obtaining values representing actual arm voltages comprises:
calculating u CU Σ (t), actual total voltage for the upper arm, using C arm , capacitance for the upper arm, î diff0 , DC current passing through the two serially connected arms of the phase leg, W CU Σ (t), desired average energy in the upper arm, ê V , amplitude of reference for the inner AC output voltage, î V , amplitude of AC output current, φ, a phase difference between i V (t) and e V (t), and
calculating u CL Σ (t), actual total voltage for the lower arm, using C arm , capacitance for the lower arm, î diff0 , DC current passing through the two serially connected arms of the phase leg, W CL Σ (t), desired average energy in the lower arm, ê V , amplitude of reference for inner AC output voltage, î V , amplitude of AC output current, φ, a phase difference between i V (t) and e V (t).
6. The method according to claim 5 , wherein the step of obtaining a value representing actual arm voltage comprises calculating
i
^
diff
0
=
e
^
v
i
^
v
cos
φ
u
D
+
u
D
2
-
4
R
e
^
v
i
^
v
cos
φ
where φ represents a phase difference between i V (t) and e V (t), u D represents a voltage between the upper and lower DC source common bars and R represents the resistance of the converter arm.
7. The method according to claim 6 , wherein the step of obtaining a value representing actual arm voltage comprises calculating
u
CU
Σ
(
t
)
=
2
W
CU
Σ
(
t
)
C
arm
where W CU Σ (t) is calculated as follows:
W
CU
Σ
(
t
)
=
W
CU
0
Σ
-
e
^
v
i
^
diff
0
ω
1
sin
ω
1
t
+
(
u
D
2
-
R
i
^
diff
0
)
i
^
V
2
ω
1
sin
(
ω
1
t
+
φ
)
-
e
^
V
i
^
V
8
ω
1
sin
(
2
ω
1
t
+
φ
)
and calculating
u
CL
Σ
(
t
)
=
2
W
CL
Σ
(
t
)
C
arm
where W CL Σ (t) is calculated as follows:
W
CL
Σ
(
t
)
=
W
CL
0
Σ
+
e
^
v
i
^
diff
0
ω
1
sin
ω
1
t
-
(
u
D
2
-
R
i
^
diff
0
)
i
^
V
2
ω
1
sin
(
ω
1
t
+
φ
)
-
e
^
V
i
^
V
8
ω
1
sin
(
2
ω
1
t
+
φ
)
where ω 1 represents the angular velocity of the network frequency.
8. An apparatus for calculating insertion indices for a phase leg of a DC to AC modular multilevel converter, the converter comprising one phase leg between upper and lower DC source common bars for each phase, each phase leg comprising two serially connected arms, wherein an AC output for each phase leg is connected between the two serially connected arms, wherein each arm comprises a number of submodules, wherein each submodule can be in a bypass state or a voltage insert mode, the insertion index comprising data representing a portion of available submodules that should be in the voltage insert mode for a particular arm, the apparatus comprises:
a controller arranged to calculate a desired arm voltage for an upper arm connected to the upper DC source common bar and a lower arm connected to the lower DC source common bar, to obtain values representing actual total arm voltages in the upper arm and lower arm, respectively, and to calculate insertion indices for the upper and lower arm, respectively, using the respective desired arm voltage and the respective value representing the total actual arm voltage;
wherein the calculating of desired arm voltages for a phase leg comprises calculating
u CU ( t )= u D /2 −e V ( t )− u diff ( t )
for the upper arm, and calculating
u CL ( t )= u D /2 +e V ( t )− u diff ( t )
for the lower arm, where u CU (t) represents desired upper arm voltage, u CL (t) represents desired lower arm voltage, u D represents a voltage between the upper and lower DC source common bars, e V (t) represents a reference inner AC output voltage and u diff (t) represents a control voltage to control a current passing through the whole phase leg, and calculating
u diff ( t )= u diff1 ( t )+ u diff2 ( t )
where u diff1 (t) represents a voltage obtained by summing energy in the arms of the leg and u diff2 (t) represents a voltage obtained by calculating a difference in energy between the arms of the leg.
9. An apparatus for calculating insertion indices for a phase leg of a DC to AC modular multilevel converter, the converter comprising one phase leg between upper and lower DC source common bars for each phase, each phase leg comprising two serially connected arms, wherein an AC output for each phase leg is connected between the two serially connected arms, wherein each arm comprises a number of submodules, wherein each submodule can be in a bypass state or a voltage insert mode, the insertion index comprising data representing a portion of available submodules that should be in the voltage insert mode for a particular arm, the apparatus comprises:
a controller arranged to calculate a desired arm voltage for an upper arm connected to the upper DC source common bar and a lower arm connected to the lower DC source common bar, to obtain values representing actual total arm voltages in the upper arm and lower arm, respectively, and to calculate insertion indices for the upper and lower arm, respectively, using the respective desired arm voltage and the respective value representing the total actual arm voltage;
wherein the calculating of desired arm voltages for a phase leg comprises calculating
u CU ( t )= u D /2 −e V ( t )− u diff ( t )
for the upper arm, and calculating
u CL ( t )= u D /2 +e V ( t )− u diff ( t )
for the lower arm, where u CU (t) represents desired upper arm voltage, u CL (t) represents desired lower arm voltage, u D represents a voltage between the upper and lower DC source common bars, e V (t) represents a reference inner AC output voltage and u diff (t) represents a control voltage to control a current, iV(t), passing through the whole phase leg,
wherein the step of obtaining values representing actual arm voltages comprises:
calculating u CU Σ (t), actual total voltage for the upper arm, using C arm , capacitance for the upper arm, î diff0 , DC current passing through the two serially connected arms of the phase leg, W CU Σ (t), desired average energy in the upper arm, ê V , amplitude of reference for the inner AC output voltage, î V , amplitude of AC output current, φ, a phase difference between i V (t) and e V (t), and
calculating u CL Σ (t), actual total voltage for the lower arm, using C arm , capacitance for the lower arm, î diff0 , DC current passing through the two serially connected arms of the phase leg, W CL Σ (t), desired average energy in the lower arm, ê V , amplitude of reference for inner AC output voltage, î V , amplitude of AC output current φ, a phase difference between i V (t) and e V (t).
10. The apparatus of claim 9 , wherein the step of obtaining a value representing actual arm voltage comprises calculating
i
^
diff
0
=
e
^
v
i
^
v
cos
φ
u
D
+
u
D
2
-
4
R
e
^
v
i
^
v
cos
φ
where R represents the resistance of the converter arm.
11. The apparatus of claim 10 , wherein the step of obtaining a value representing actual arm voltage comprises calculating
u
CU
Σ
(
t
)
=
2
W
CU
Σ
(
t
)
C
arm
where W CU Σ (t) is calculated as follows:
W
CU
Σ
(
t
)
=
W
CU
0
Σ
-
e
^
v
i
^
diff
0
ω
1
sin
ω
1
t
+
(
u
D
2
-
R
i
^
diff
0
)
i
^
V
2
ω
1
sin
(
ω
1
t
+
φ
)
-
e
^
V
i
^
V
8
ω
1
sin
(
2
ω
1
t
+
φ
)
and calculating
u
CL
Σ
(
t
)
=
2
W
CL
Σ
(
t
)
C
arm
where W CL Σ (t) is calculated as follows:
W
CL
Σ
(
t
)
=
W
CL
0
Σ
+
e
^
v
i
^
diff
0
ω
1
sin
ω
1
t
-
(
u
D
2
-
R
i
^
diff
0
)
i
^
V
2
ω
1
sin
(
ω
1
t
+
φ
)
-
e
^
V
i
^
V
8
ω
1
sin
(
2
ω
1
t
+
φ
)
where ω 1 represents the angular velocity of the network frequency.