TEMPUS ENERGY: AC-GRIDS AND DC-GRIDS
1: Historical evolution from AC-grids to DC-grids
Although in the early years of electricity production a lot of electrical grids were DCgrids, nowadays the great majority of the electrical grids are AC-grids. This switch
from DC-grids to AC-grids has a number of technical reasons.
 Due to the need for a commutator, it is very difficult to build DC-generators
generating high voltages. Especially when generating higher voltages (of for
instance 24 kV), it is easier to construct alternators (AC-generators).
 An additional advantage arises when considering electrical motors. In general,
constructing AC-motors (like the three phase induction motor) is easier and
cheaper than constructing DC-motors. Moreover, a lot of AC-motors require
less maintenance.
 When using AC, it is possible to use transformers. Due to these transformers, a
generated voltage level can be transformed to a higher voltage level of 70 kV,
220 kV or even 380kV. These transformers have a long life expectancy (more
than 30 years) and they have a high efficiency (even more than 99.9%).
Transformers have a straightforward construction and they require almost no
maintenance (no moving parts).
 When using a high voltage grid to inject power into a medium or a low voltage
grid, transformers can be used to transform the voltage level to a lower level
(for instance from 380 kV to 70 kV or from 11 kV to 400 V).
 By using transformers, it is possible to supply power at a low voltage level of
230 V and/or 400 V to a customer (reducing the risks related with electricity)
and to use high voltage grids to transport large amounts of power over larger
distances (reducing the losses in the grid).
 It is easier to interrupt AC-currents since these currents have two zero-crossings
in one single period whereas a DC-current has no zero-crossings. When
opening an electrical contact, the zero-crossing can be used to extinct the arc
and it is sufficient to prevent re-ignition of the arc.
When considering AC voltages, the insulation level of cables, appliances and
machines must withstand the peak value and not only the RMS value. This peak value
equals √2 or 1.41 times the RMS value.
2: HVDC-grids as an emerging technology
Although all these technical aspects explain why nowadays the large majority of the
grids are AC-grids, it is wrong to conclude that using DC to transport electrical energy
is old-fashioned and the use of DC only has disadvantages. Using DC, can be an
emerging and useful technological challenge.
2.1: Losses in AC and DC grids
In order to understand why DC-grids still exist, it is useful to calculate and compare
the energy losses in a single phase AC-grid, in a three phase AC-grid and finally in a
DC-grid.
A single phase grid contains two conductors each having a cross section S1. The three
phase grid contains three conductors each having a cross section S3. The DC-grid
contains two conductors each having a cross section S0. In order to make an
appropriate comparison, assume these three types of grids use the same amount of
copper (or aluminum). This implies
2 𝑆1 = 3 𝑆3 = 2 𝑆0 .
(1)
In order to have the same production cost when considering the conductors of a grid,
also assume these three types of grids have the same type of insulation withstanding
the same voltage level. V1 is the RMS value of the voltage of the AC-grid. V3 is the
RMS value of the phase voltage of the three phase grid. V0 is the DC-voltage of the
DC-grid. This implies
√2 𝑉1 = √2 √3 𝑉3 = 𝑉0 .
(2)
Assuming these three grids transport the same power implies
𝑉1 𝐼1 = 3 𝑉3 𝐼3 = 𝑉0 𝐼0 .
(3)
Here, I1 is the RMS value of the current in the single phase AC-grid. I3 is the RMS
value of the current in the three phase AC-grid. I0 is the DC-current in the DC-grid. By
combining (2) and (3), one obtains that
𝐼1 = √3 𝐼3 = √2 𝐼0 .
Based on this information, it is possible to calculate the Joule losses in the three grids.
Here, R1 is the ohmic resistance of a conductor of the single phase AC-grid. Based on
the law of Pouillet, R1 is inversely proportional with S1. R3 is the ohmic resistance of a
conductor of the three phase AC-grid and R3 is inversely proportional with S3. R0 is
the ohmic resistance of a conductor of the DC-grid and R0 is inversely proportional
with S0.
The Joule losses equal:
-
in case of the single phase grid:
in case of the three phase grid:
in case of the DC-grid:
𝑃𝐽1 = 2 𝑅1 𝐼12 .
𝑃𝐽3 = 3 𝑅3 𝐼32 .
𝑃𝐽0 = 2 𝑅0 𝐼02 .
Verify that 𝑃𝐽3 = 0.75 𝑃𝐽1 . The Joule losses in a three phase grid are only 75% of the
Joule losses in a similar single phase grid transporting the same power. This explains
why three phase grids instead of single phase grids are used when transporting
electrical energy.
Finally, compare the Joule losses of a DC-grid and a three phase AC-grid. Verify that
𝑃𝐽0 = 0.67 𝑃𝐽3 . The Joule losses in a DC-grid are only 67% of the Joule losses in a
similar three phase AC-grid. This explains why DC-grids are sometimes used when
transporting large amounts of electrical energy over large distances (more than 750
km).
2.2: Investment costs related with HVDC-grids
A disadvantage related with the use of DC-grids to transport electrical energy is the
lack of transformers allowing to increase or decrease the voltage level. In practice, the
situation visualized in Figure 1 combines the use of DC-grids and AC-grids.
transformer
rectifier
inverter
transformer
DC
Figure 1: Basic structure of a HVDC-grid
Starting from a classical three phase AC-grid, the voltage level is increased using a
transformer. A very high AC-voltage is obtained which will be rectified giving a very
high DC-voltage (originally mercury-vapor rectifiers were used, nowadays
semiconductor rectifiers are used). The very high DC-voltage will be used to transport
the electrical energy over a long distance (HVDC: High Voltage Direct Current). At
the other side of the DC-grid, an inverter converts this DC-voltage back to an ACvoltage. Using a transformer, the AC-voltage level is decreased and the power is
injected into a classical three phase AC-grid.
It is not only possible to transport active power from the left side to the right side. In
case the left power electronic converter does not operate as a rectifier but as an
inverter and in case the right power electronic converter does not operate as an inverter
but as a rectifier, active power is transported from the right side to the left side.
This is an emerging technology since it is not obvious to construct a rectifier and an
inverter dealing with such high voltages. Such a rectifier and such an inverter require a
considerable investment. This investment can only be justified when the energy is
transported over a very long distance and the transported power is sufficiently large
(for instance 2000 MW). Indeed, when preconceiving the energy losses, less copper
(or aluminum) is required when using a HVDC-grid instead of a three phase AC-grid.
However, only for sufficiently long distances the reduced use of copper is able to
justify the installation cost of the rectifier and the inverter.
This situation is visualized in Figure 2 (information provided by ABB). The DC
terminal cost is much higher than an AC terminal cost but the DC line cost is lower
implying a lower total investment when the distance is sufficiently large.
Figure 2: Comparison investment of a HVDC grid and an AC grid
Figure 3: Rectifiers and inverters used in a HVDC installation
3: Applications of HVDC-grids
HVDC-grids are used to transport large powers over large distances. For instance, a
HVDC-grid in Brazil transports power of the Itaipu hydroelectric power plant to the
region of Sao Paulo. This installation contains two ± 600 𝑘𝑉 bipoles having a total
rated power of 6300 MW and transporting the power over a distance of 780 km.
Using HVDC-grids, it is also possible to connect two AC-grids having a different
frequency. For instance in Japan (as visualized in Figure 4), the eastern and northern
parts of Honshu and Hokkaido have a grid frequency of 50 Hz whereas the western
Honshu, Shikoku, Kyushu and Okinawa operate at 60 Hz. The boundary between
these two regions contains four back-to-back HVDC-substations operating as
frequency converters (in case the rectifier and the inverter which are visualized in
Figure 1 are located in the same station, a back-to-back HVDC-system is obtained).
For instance the Higashi-Shimizu frequency converter operates with a DC voltage of
125 kV and has a maximum power of 300 MW.
Figure 4: HVDC-grids in Japan
Moreover, DC-grids also allow to interconnect grids having the same nominal
frequency but which are not synchronized with each other. For instance, there is a DCcable interconnecting the British grid and the continental European grid. This HVDC
Cross-Channel is a 2000 MW system and has a total length of 73 km containing 46 km
submarine cables (an operating voltage of 270 kV).
3.1: DC-grids and renewable energy generation
HVDC allows to transport large amounts of electrical energy over large distances. This
is useful to transport the energy of large remotely located hydroelectric power stations
(for instance the Three Gorges Dam in China, the Itaipu dam in Brasil) to the
industrialized world.
More recently and focused to the transportation of powers which are not that
extremely high, is the use of HVDC light (http://www.abb.com/hvdc) which is used to
transport the energy coming from onshore and offshore wind turbine parks.
When considering the Thornton Bank (offshore, actually farshore wind turbine park)
in Belgium, a three phase AC-grid having a voltage level of 150 kV is used to
transport the power to land. For instance the Gotland project in Sweden (onshore wind
energy) uses the HVDC light technology to transport the generated power.
4: HVDC-technology
4.1: A basic HVDC-installation
Figure 5 visualizes a basic HVDC-installation. Converter 1 is a three phase six pulse
thyristor rectifier and having a firing angle 𝛼1 smaller than 90°, the DC-voltage 𝐸𝑑1 is
positive. Since the DC-current 𝐼𝑑 is positive, converter 1 behaves as a DC power
source implying power is transported from the AC-line 1 to the DC-link.
Figure 5: HVDC-installation
Converter 2 is also a three phase six pulse thyristor rectifier but the thyristors are
mounted upside down in comparison with converter 1. Notice however the anodes
have a firing angle 𝛼2 larger than 90° implying the DC-voltage 𝐸𝑑2 is also positive.
Since the DC-current 𝐼𝑑 is positive, converter 2 behaves as an inverter implying power
is transported from the DC-link to the AC-line 2.
In case 𝛼1 is larger than 90°, 𝐸𝑑1 is negative but 𝐼𝑑 remains positive. This implies
converter 1 behaves as an inverter since power is transported from the DC-link to the
AC-line 1. Since 𝛼2 is smaller than 90°, also 𝐸𝑑2 is negative. This implies converter 2
behaves as a rectifier since power is transported from the AC-line 2 to the DC-link.
When using the HVDC-installation visualized in Figure 5, a power reversal occurs by
changing the sign of the DC-voltage since it is not possible to reverse the sign of the
DC-current.
4.2: Modeling the HVDC-grid and the power flow
In Figure 5, the entire DC-line is modeled as a resistor. In general, a high voltage line
can be modeled as a transmission line where an infinite number of infinitesimal small
parts are cascaded. Figure 6 models such an infinitesimal small part of a transmission
line.
It is quite common to neglect the parallel resistances (1/𝐺 ). 𝑑𝑥 (especially when
considering overhead lines). When considering AC transmission lines, the series
inductances and the parallel capacitances must be taken into consideration. Due to this
series inductances, a voltage drop occurs. Due to the parallel capacitances, a capacitive
current is flowing which can reduce the transport capacity for active power of the
transmission line. When considering a DC-line, the inductances and the capacitances
have no impact on the steady state behavior implying the DC-line can indeed be
modeled as a lumped resistor as visualized in Figure 5. No voltage drop across the
inductance occurs and the transport capacity is not reduced by reactive power.
Figure 6: Infinitesimal small part of a transmission line
When considering Figure 5, the DC-current equals
𝐼𝑑 =
𝐸𝑑1 − 𝐸𝑑2
.
𝑅
By changing the firing angles 𝛼1 and 𝛼2 , the voltages 𝐸𝑑1 and 𝐸𝑑2 change. This
implies 𝐼𝑑 changes and the transported power can be changed rapidly. Not only the
magnitude of the transported power can be changed, by changing the sign of the
voltages also a reversal of the sign of the power can be obtained. This is useful when
using a HVDC-grid to interconnect two AC-grids in order to maintain the power
equilibrium.
4.3: The DC-voltage
In case the rectifier is a three phase six pulse rectifier with a firing angle 𝛼 = 15°, the
DC-voltage is visualized in Figure 7 (neglecting the commutation overlap). This
voltage is not constant, this voltage is a six pulse voltage.
Figure 7: DC-voltage obtained by the rectifier
Using smoothing inductors 𝐿1 and 𝐿2 as visualized in Figure 8, a ripple-free DCvoltage 𝐸𝑑 is obtained. The voltage ripple of 𝐸1𝐺 appears across 𝐿1 and the voltage
ripple of 𝐸2𝐺 appears across 𝐿2 .
Figure 8: HVDC-installation having inductors at DC-side
4.4: Impact on the AC-grid
Notice converter 1 and converter 2 in Figure 5 and Figure 8 can only operate when the
AC-grids line 1 (or network 1) and line 2 (or network 2) are available. The grid
voltages are needed to obtain thyristor commutation. The grid voltages are needed
when firing the gate of a thyristor and these grid voltages are also needed to turn off a
previously conducting thyristor (due to the high voltages, each “thyristor” is composed
of several thyristors connected in series and such a group of thyristors is called a valve,
these series connected thyristors are triggered simultaneously at their gates behaving
as one single super-thyristor).
Notice converter 1 and converter 2 consume reactive power which has to be provided
by the AC-grid (irrespective of the direction of active power flow i.e. irrespective
whether the converter behaves as a rectifier or as an inverter). Moreover, the AC-grid
current is not a sine. The grid current not only contains a 50 Hz fundamental current, it
also contains harmonics.
4.5: Monopole and bipolar HVDC-implementations
The HVDC-implementation of Figure 5 and Figure 8 contains a DC-grid having two
conductors each having a cross section 𝑆0 . In order to obtain a further reduction of the
required amount of copper (or aluminum), it is also possible to use a ground return as
visualized in Figure 9 by connecting the converters with the earth using electrodes.
Figure 9: HVDC monopole system with earth return
Especially for long-distance transmission, using the earth and/or the sea as a return
conductor is cheaper than using a dedicated neutral conductor. Notice however using
the ground and/or sea as a return conductor also has its disadvantages:
-
there is electrochemical corrosion of long buried metal objects like pipelines,
underwater earth-return electrodes in seawater may produce chlorine or otherwise
affect water chemistry,
the current path may result in a magnetic field affecting magnetic navigational
compasses for ships passing over an underwater cable.
In order to reduce the earth and/or sea current, bipolar transmission lines can be used
as visualized in Figure 10. Bipolar transmission lines possess a positive and a negative
line having a common ground return. The positive line is connected with converter 1
and converter 2. The negative line is connected with converter 3 and converter 4. Since
converter 1 and converter 3 are mounted upside down and since 𝛼1 = 𝛼3 , the voltages
𝐸𝑑1 and 𝐸𝑑2 have an opposite sign. Also converter 2 and converter 4 are mounted
upside down and they have the same firing angles 𝛼2 = 𝛼4 .
Figure 10: Bipolar HVDC transmission line
As visualized in Figure 10, converter 1 and converter 3 act as rectifiers since 𝐸𝑑1 𝐼𝑑1
and −𝐸𝑑2 𝐼𝑑2 are positive. Converter 2 and converter 4 act as inverters. Power is
flowing over both lines from AC-network 1 to AC-network 2.
The total ground current equals 𝐼𝑑1 − 𝐼𝑑2 which is usually small since the converters
maintain equals currents in the positive and negative lines. Consequently, corrosion of
underground pipes … is minimized. Moreover, the same transmission line towers can
carry two lines which doubles the transported power with a limited increase in capital
investment. Finally, if the power flow in one line is interrupted, the other line can
continue to function (delivering half the normal power).
Figure 11: Bipolar HVDC transmission line
Figure 11 shows the same bipolar HVDC transmission line as Figure 10 but using
different firing angles, the direction of active power flow is reversed.
4.6: Practical implementation of a HVDC-connection
Figure 12 visualizes a practical implementation of a HVDC-connection (a monopole
system). Notice AC-network 1, AC-network 2, transformers T1 and T2, the two
converters, the single wire HVDC-connection and the two ground electrodes. Finally,
notice a microwave communications link useful to communicate about the power that
must be transported from one side to the other side.
Figure 12: Practical implementation of a HVDC-connection
As already mentioned, converter 1 and converter 2 each consume reactive power at
AC-grid side. In order to limit the reactive power supplied by the grid, reactive power
sources 𝑄1 and 𝑄2 are needed. In principle, these reactive power sources can be
capacitors. However, taking the high voltage level and the large number of required
MVAR’s into account, the use of a synchronous capacitors is more common. A
synchronous capacitor is an overexcited synchronous motor generating reactive power.
Such a synchronous motor is mechanically unloaded i.e. the consumed active power is
as small as possible. By controlling the excitation current, the generated reactive
power can also be controlled.
In both AC-grids, three phase series-resonant LC-filters are placed in parallel with the
grid voltage. These series-resonant filters reduce the harmonic components in the grid
current. Indeed, by supplying (part of) the harmonics required by the rectifier/inverter
(e.g. 5th, 7th, 11th, 13th harmonics), these harmonics need not be supplied by the ACgrid anymore.
Since the DC-voltage at the DC-side of the rectifier/inverter has a ripple (as visualized
in Figure 7), also at DC-side passive filters are placed to obtain a constant voltage 𝐸𝑑 .
To obtain this goal, in Figure 8 two inductors (L1 and L2) are placed. In Figure 12,
more complex passive filters are used. A first series-resonant LC-filter tuned at 300 Hz
(C6 and L6) and a second series-resonant LC-filter tuned at 600 Hz (C12 and L12) are
used to short circuit the 300 Hz and the 600 Hz components in the DC-voltage. These
series LC-filters in combination with inductors L provide a constant voltage 𝐸𝑑 .
Figure 13: HVDC electricity pylon
5: HVDC-light technology
The classical HVDC technology connects two AC networks each having a stable grid
voltage. These grids allow the natural line commutation of the thyristor-controlled
converters and they supply the reactive power consumed by the converters.
5.1: The use of a static generator
Figure 14 visualizes a static three phase generator. At the DC-side, two capacitors 𝐶1
are connected in series. The main part is a self-commutated converter containing six
IGBT’s and six diodes. Using this converter, the DC-voltage can be converted into a
PWM voltage. Using inductances 𝐿1 and carrier-frequency series filters (𝐿2 , 𝐶2 and
𝑅2 ), a sine voltage is obtained.
The self-commutating converter of Figure 14 is able to transmit active power from the
DC-side to the AC-side and vice versa. Moreover, the converter is able to supply
reactive power to the AC-grid or to consume reactive power from the AC-grid (which
is not the case when considering the line commutated converters visualized in Figure
12).
At DC-side, the total voltage 𝐸𝐻 is the sum of two voltages 𝐸𝑑 = 𝐸𝐻 ⁄2. There is a
neutral point N between the two capacitors 𝐶1 . PWM voltages appear between the
terminals a, b, c and N. These PWM voltages fluctuate between +𝐸𝑑 and −𝐸𝑑 at the
carrier frequency 𝑓𝐶 . The fundamental of the line to neutral voltage (usually 50 Hz or
60 Hz) is available between the terminals d, e, f and N. The carrier frequency 𝑓𝐶 and
the harmonics are filtered out by 𝐿1 , 𝐿2 , 𝐶2 and 𝑅2 .
Figure 14: Static generator
5.2: A basic HVDC-light installation
Figure 15 visualizes a HVDC-light installation. Reactors 𝑥, corresponding with
inductances 𝐿1 in Figure 14, connect a three phase power grid with converter 1. A DClink, modeled as a resistance 𝑅, connects converter 1 and converter 2. Converter 2
supplies power to the load by way of reactors 𝑥 (corresponding with inductances 𝐿1 in
Figure 14). In Figure 15, the carrier-frequency series filters are omitted to simplify the
circuit. In case the load in Figure 15 is replaced by e.g. wind turbine park, a reversal of
the active power flow occurs and power is flowing from converter 2 to converter 1.
Figure 15: HVDC-light installation
5.3: Power control in a HVDC-light installation: steady state
[a]
[b]
Figure 16: Phasor diagrams of a HVDC-light installation
Figure 16 [a] visualizes the phasor diagram of the voltages and the line current for
phase 𝑎 in Figure 15 at grid side. Suppose voltage 𝐸1𝑁 leads voltage 𝐸4𝑁 by 𝜃1
degrees. The active power consumed by one single phase of converter 1 equals
𝑃=
𝐸1𝑁 𝐸4𝑁
𝑠𝑖𝑛𝜃1 .
𝑥
Here, P is the power for one single phase, 𝐸1𝑁 and 𝐸4𝑁 are RMS values of phase
voltages. The magnitude and the phase of 𝐸1𝑁 are imposed by the grid. Since 𝑥 is
fixed, it is possible to adjust the magnitude of 𝐸4𝑁 and the angle 𝜃1 in order to obtain
the required P. Since there are two degrees of freedom (𝐸4𝑁 and 𝜃1 ), it is possible to
operate at unity power factor i.e. the grid current 𝐼1 is in phase with 𝐸1𝑁 (as visualized
in Figure 16).
Since the power of one single phase equals
𝑃 = 𝐸1𝑁 𝐼1 ,
the magnitude of 𝐼1 is known implying also
2
𝐸4𝑁 = √𝐸1𝑁
+ 𝑥 2 𝐼12
is known. To obtain the required 𝑃, also 𝜃1 is known.
Figure 16 [b] visualizes the phasor diagram of the voltage and the line current at load
side for phase 𝑎 in Figure 15. Suppose the current 𝐼𝑎 in phase a lags an angle 𝜃𝑎 with
respect to 𝐸𝑑𝑁 . The voltage drop across the reactance 𝑥 equals 𝑗𝑥𝐼𝑎 implying
𝐸𝑎𝑁 = 𝐸𝑑𝑁 + 𝑗𝑥𝐼𝑎 .
In Figure 16 [b], 𝐸𝑎𝑁 leads 𝐸𝑑𝑁 by 𝜃𝑏 degrees implying the active power P flows from
converter 2 to the load. The power P for one single phase equals
𝑃=
𝐸𝑎𝑁 𝐸𝑑𝑁
𝑠𝑖𝑛𝜃𝑏 = 𝐸𝑑𝑁 𝐼𝑎 𝑐𝑜𝑠𝜃𝑎 .
𝑥
𝐸𝑎𝑁 and 𝐸𝑑𝑁 are phase voltages. Since the losses in the converters (and also all other
losses) are neglected, a total power 3 𝑃 is transported along the DC-connection. This
implies
𝐼𝑑 =
3𝑃
.
𝐸𝐻
Summarizing, when considering a steady state condition and neglecting all losses,
3𝑃 =3
𝐸1𝑁 𝐸4𝑁
𝐸𝑎𝑁 𝐸𝑑𝑁
𝑠𝑖𝑛𝜃1 = 𝐸𝐻 𝐼𝑑 = 3
𝑠𝑖𝑛𝜃𝑏 .
𝑥
𝑥
In order to prevent clipping of the peaks of the sinusoidal waveshapes, the peak value
of the line-to-neutral voltage must never exceed 𝐸𝐻 ⁄2. In case the peak value of this
line-to-neutral voltage equals 80% of 𝐸𝐻 ⁄2, the effective value of the line-to-line
voltage equals
𝐸𝐿𝐿 = √3
1 0.8
𝐸𝐻
√2 2
implying
𝐸𝐻 ≈ 2 𝐸𝐿𝐿 .
5.4: Power control in a HVDC-light installation: transient behavior
Under steady-state conditions, the active power of the load is constant. When losses
are neglected, the same power is transported by the DC-connection (implying a
constant 𝐸𝐻 and a constant 𝐼𝑑 ) and this power is consumed by converter 1.
In case the power consumed by the load decreases while 𝐸4𝑁 and 𝜃1 remain constant,
the power input to the DC-cable will be larger than the power output. The excess of
energy will be stored in the capacitors 𝐶1 implying a fast increase of the voltage 𝐸𝐻 .
The control system of converter 1 will detect this increase of 𝐸𝐻 and will adjust 𝐸4𝑁
and 𝜃1 in order to decrease the active power extracted from the AC-grid by converter
1. Finally, the DC-voltage 𝐸𝐻 will remain close to its nominal value.
This way of controlling the active power flow avoids the need for a communication
link between the two converters as it is the case for the classical HVDC-approach of
Figure 12.
5.5: Practical applications of the HVDC-light technology
HVDC-light mainly has the same applications as the classical HVDC technology. It is
possible to transport power over large distances, it is possible to connect AC-grids
having a different frequency, it is possible to connect grids which are not synchronized
with each other. Notice however, the HVDC-light technology has a lower power
rating.
The first commercial HVDC-light transmission system connects an onshore wind
power plant in Gotland (a Swedish island in the Baltic Sea) to the city of Visby. This
approach allowed to use underground cables instead of overhead transmission lines.
This HVDC-light project is commissioned in 1999 (so much more recent than the
classical HVDC-technology) having a power rating of 50 MW using a DC voltage of
±80 𝑘𝑉 over a distance of 70 km (ABB Gotland HVDC light).
Figure 17: HVDC-light cable