Alternative University

High Voltage Direct Current (HVDC)

Page 4:  AC / DC Conversion

Alternating Current (AC)

Direct current (DC) is a steady stream of electricity. Alternating current (AC), on the other hand, fluctuates rapidly, reversing direction many times per second.

Alternating current (AC) is generated in sine waves, because of the circular motion of generators, and the need to be able to power motors (which are basically generators in reverse). If one (single phase) generator is used to generate the AC electricity, the generated electricity has particular instants of time in which there is no voltage, when the voltage (to push current) is changing directions.

Figure 1: Single phase AC voltage.

But if three generators are used that are slightly out of phase (one-third cycle apart each), or if a three-phase generator is used (with three separate windings that are one-third cycle apart), then there is always voltage between different conductors.

Figure 2: Three phase AC voltage.

Figure 2 above shows the oscillating voltage of three AC phases on the time scale of the first phase ‘A’. The following graph shows that time scale:

Figure 3: AC phase voltage cycle.

The AC phase voltage is zero at Time = 0. The sine of zero is zero (Time = 0 corresponds to a “phase angle” of zero).

The AC phase voltage rises to maximum at Time = 1/4th cycle (which corresponds to phase angle 90 degrees or π/2 radians). Then it goes down to zero at Time = 1/2 cycle (phase angle 180 degrees or π radians).

After it is half way through a cycle, the AC phase voltage becomes negative (points in the opposite direction, creating pressure for the current to change direction).

Two-thirds way through the cycle (phase angle 270°), voltage is the most negative (reverse direction flow pressure is maximum).

At 360° the cycle is complete and will start over (no flow pressure, reverse flow pressure stopped, will resume forward flow pressure).

Phase ‘B’ is 120 degrees out of phase with phase ‘A’, and phase ‘C’ is 120 degrees out of phase with phase ‘B’. Each phase is 120 degrees and 240 degrees out of phase with the other two phases, since each phase starts 1/3 way (2/3 way) through another phase.

Three Phase AC Connections

There are two types of three phase AC systems: Delta and Wye. With delta systems, any two conductors span a phase. For wye systems, any two conductors span two phases, with allowance for a fourth wire to use one phase. The fourth wire is neutral / ground, and only used for single phase loads. If there are no single phase loads, the neutral / ground is not needed.

Figure 4: Three phase AC Delta and Wye schematic.

The different systems, delta and wye, result from how the wire windings are wound in generators and transformers. As shown above, for delta systems the windings are relative to each other, one winding skipping to another one which goes back to the intervening one and starts again, while for wye the start of each winding joins at a common neutral with the other end at the terminal for each phase.

To convert a delta system to a wye system, a transformer may be used, by simply winding one side of the transformer with the phase windings feeding each other sequentually (delta side), and the other side windings (wye side) separate for each phase and each connected to a neutral / ground.

An important difference between delta and wye transmission is that they are slightly out of phase (by 30°) for the same power. That will be discussed later in this page.

Diode / Rectifier

A diode is a semiconductor device that only allows electricity to travel in one direction. The symbol for a diode is a triangle pointing in the direction that electricity is conceptually allowed to flow:

Figure 5: Diode symbol.

The diode denoted in Figure 5 would allow electricity to travel from left to right, but not from right to left.

Converting AC to DC is called rectification, and a device that converts AC to DC is called a rectifier. If we use a single diode as a rectifier, only half the electricity is converted, because AC reverses directions and the diode will not let electricity come back in the other direction, losing half of the power (referred to as half wave rectification):

Figure 6: Half wave rectification.

To convert all of the AC power to DC requires more than one diode, and two conductors on the DC side, for electricity to flow in one direction in one of the DC conductors and flow in the opposite direction in the other DC conductor.

One of the DC conductors is labeled plus ‘+’, the other labeled minus ‘–’, signifying that electricity flows in opposite directions (one direction in one conductor, the other direction in the other conductor).

Full wave rectification converts all of the fluctuating AC power to two-conductor DC, and requires four diodes connected in a “bridge”:

Figure 7: Full wave rectifier, diode bridge. Two AC wires left, two DC conductors right.

The AC circuit pushes current onto one of the DC conductors, and pulls current from the other DC conductor, then changes to pulling and pushing, then pushing and pulling again, etc. The resulting DC voltage is shown in this graph:

Figure 8: Full wave rectification.

This resulting DC voltage is not constant. It consists of pulses that drop very low twice per cycle. These pulses correspond to the absolute values of the AC voltage.

This example was for only one AC phase. When rectification is done for all three phases, the pulsing evens out more and does not drop low.


Diodes that have a gate are called thyristors (or valves). The gate turns “on” the thyristor. Normally, a diode automatically lets any electricity through that flows in one direction. A thyristor also only lets electricity flow in one direction, but it must be turned “on” to do that.

While a diode has two leads (or conducting surfaces) for the electrical flow, a thyristor additionally has a third lead to receive a signal to instruct it to open. The electrical symbol for a thyristor is therefore the same as for a diode but with a line sticking out of the diode. That line may be transverse or diagonal, and may be bent. There is no single convention for how to draw that line that sticks out of the thyristor.

Like a diode, a thyristor will only let electricity flow in one direction. But unlike a diode, it must be turned on. If a thyristor is not turned on, no electricity will flow through it, no matter what direction the electricity is trying to flow.

Figure 9: Thyristor and the electronic circuitry that fires it. [NIST/Tang 2007]

Thyristors are made of layers of semiconductor materials that are “triggered” to turn on (allow electricity to flow through it) when a relatively weak electrical or optical signal is transmitted to the thyristor. Sending the electrical or optical signal to the thyristor is referred to as “firing” the thyristor (like spark plug ignition in a gasoline engine, but with less signal power).

Figure 10: Thyristor that is triggered by optical fiber. Five dollar Hong Kong coin (27 mm) shown for scale. [Siemens 2005]

Figure 11: Optical thyristor showing how optical fiber cable is attached to the thyristor. Arrows show direction of optical laser signal. Downward arrow shows where the optical signal will leave the fiber and strike semiconductor material to open thyristor gate, which stays open (without further signalling required) until negative voltage (reversal of electricity that flows through the thyristor). [Siemens 2011]

Figure 12: Material cross section of the thyristors pictured above.

Once the thyristor is fired, it allows electricity to pass through it in the predefined direction until voltage drops to zero and turns negative, at which point the thyristor automatically turns “off”. Then, it will not allow any more electricity through until it is fired again.

Note that while it is possible to turn “on” a thyristor, turning “off” the thyristor can only happen automatically by voltage becoming negative. Thus a thyristor can be turned on with a gate signal, but cannot be turned off. It can only turn off by itself, when voltage turns negative in the predefined (allowable) direction.

Thyristors are used instead of diodes for rectification of three phase AC. Following is a bridge of six thyristors to convert 3 phase AC to  DC:

Figure 13: Six pulse thyristor bridge.

This illustrates three phase AC from the left converted to DC (two conductors) on the right. First the AC power goes through a transformer that sets the proper voltage, then each phase of the AC that is at the proper voltage is connected to two of the six thyristors.

Figure 14: HVDC line using a six pulse bridge at each end. [Hingorani]

In this diagram, three phase AC enters from the left, goes through a transformer that steps up the AC voltage, then each AC phase is connected to two thyristors. A high voltage DC line carries the electric power to the thyristors on the right, which invert the DC electricity back to AC, then the AC electricity goes through a transformer that steps down the AC voltage, producing AC at the desired voltage on the right.

Notice that the inductance symbol (a coiled line segment) is used for the DC line in that figure, indicating the DC line has inductance (using a choke reactor to smooth and clamp the DC power, discussed later).

The thyristors are fired just in time, by suitable electronics, like the electronics of an automobile engine fires spark plugs at the right time, so that the resulting power flow may be largely continuous.

However, while firing of the thyristors works well, automatic turning “off” of the thyristors does not quite work well. Thyristors do not account for leaking inductance from the transformer that prevents the thyristor from automatically turning off in time, which causes some chirping of the power curve.

In order to reduce this chirping of the DC power, two six pulse bridges may be used (instead of one six pulse bridge) by converting some of the AC into three-phase wye and some into three-phase delta, forming a 12-pulse bridge:

Figure 15: Twelve pulse bridge rectifier. [Siemens 2008]

This diagram shows that the AC line to rectify is three phase wye. Two transformers are used, one keeping the wye configuration, the other tranformer changing the configuration to delta. Delta and wye are slightly out of phase, causing some smoothing of the chirping. This can also be done with a single tranformer that has multiple windings to output three wye phases and three delta phases from a single tranformer. Likewise, a diagram that shows one transformer doing this could actually be two or more transformers.

Firing Angles

The thyristors are signaled to turn on (fire) each AC cycle. Firing frequency and time delay are adjusted for a variety of conditions, including correction of AC input power perturbation, frequency drift, phase imbalance (prevent reverse flow), reduction of reactive power consumption, etc.

As illustrated earlier, a time within a cycle may be expressed as an angle (of a sine wave). Hence, the delay from the beginning of a cycle to when a thyristor is fired is called the “firing angle”, denoted alpha (α).

A firing angle of zero indicates the thyristor is fired right away each cycle without delay, which is equivalent to a diode. A diode allows electricity that is in the correct direction to flow immediately without delay. However, firing angles of a thyristor need to be greater than zero, to assure there was enough current to keep the valve open, and to avoid having too much current too long if above the rating of the thyristor (which would degrade the thyristor). Thyristors are very durable, if used within their ratings.

A firing angle less than 90° is used to rectify the AC current (convert AC to DC).

A firing angle of 90° would theoretically result in no electrical power flow.

A firing angle greater than 90° reverses direction of the electric power, making the bridge an inverter instead of a rectifier (to convert DC to AC instead of converting AC to DC). In that case, power flow is reversed, but current flow does not need to reverse (current is already flowing in both directions – bipolar). Power flows from the station at higher voltage to the station at lower voltage (rectifier and inverter respectively, which must set their firing angles accordingly as just described).

Capacitor Commutation

Commutation is the transfer (change) of current flow from one thyristor to another thyristor on the same row. Ideally, the other thyristor starts conducting (turns “on”) right when the previous thyristor stops conducting (turns “off”). However, there is overlap, because of the previous thyristor not turning off in time (due to the problem of thyristors not turning off in time, mentioned above). The commutation overlap period may be as high at 60 degrees, but is usually 20 to 25 degrees.

A further difficulty is that weak AC systems may not provide enough voltage to turn off a thyristor. For example, the AC grids on each end of a DC line would need to be energized already for the DC line to start conducting.

These HVDC systems, which we have been discussing so far, are said to be “line commutated” because each converter station relies on its AC line to provide reverse voltage for the commutation of thyristors.

Another way to provide voltage for commutation is to install capacitors (voltage accumulators) between the transformer and valves:

Figure 16: Capacitor Commutated Converter (CCC). [Fellah]

The symbol for a capacitor is parallel plates, which is how a capacitor is constructed. The symbol for a thyristor bridge is a diode or thyristor symbol enclosed in a rectangle:

Figure 17: CCC HVDC supplying a weak AC grid. [Fischer]


 1.  Le Tang, “Enhanced Power Reliability and Efficiency in new HVDC and FACTS development”, 2007.

(1.1 MB)

 2.  “Cross Border Electricity Transmission with HVDC – Executive Exchange Dhaka”, Siemens 2011.

(5.9 MB)

 3.  Khatir, Dahou, Zidi, Fellah, Hadjeri, “Comparison of Line and Capacitor Commutated Converter (CCC) for HVDC Power Transmission”, 2006.

(260 K)

 4.  Andersson, Cai, Yang, “Black start of a passive AC network using bipolar LCC HVDC”, 2014.

(646 K)

 5.  Fischer, Angquist, Nee, “A new control scheme for an HVDC transmission link with capacitor-commutated converters having the inverter operating with constant alternating voltage”, 2012.

(526 K)

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2021–May–14  04:53  UTC