4. ESTRUCTURA OPERACIONAL
4.1 ACTIVIDADES PREVIAS AL INICIO DE LA OPERACIÓN
2.3.1 Need for voltage control
One of the most crucial aspects of the operation of an HVDC grid is the control of the DC voltage. This is achieved by controlling the power balance in the HVDC grid [Rau14]. To demonstrate this relation between power balance and DC voltage, let us consider an HVDC system of arbitrary topology, shown in Fig.2.12.
∼
∼
∼
∼
∼
∼
∼
∼
=
=
=
=
2.3. DC voltage control 27
Focusing on the DC side of the VSCs and replacing the VSCs and the cables with their equivalent models (shown in Fig.2.4and2.3, respectively), the model of the MTDC grid shown in Fig.2.13 is derived. It consists of the DC capacitors of the VSCs, the shunt DC capacitances of the branches, and the series resistances of the cables. The series inductances have been neglected, as discussed in Section2.2.1.
∼
=
=
∼
∼
=
=
∼
Figure 2.13: Model of MTDC grid (inductances neglected)
If the resistances are also neglected, then all the DC capacitances can be lumped into one equiva- lent capacitanceCdctot, leading to the simplified representation of the MTDC grid of Fig.2.14, in which the DC grid is represented by a single DC bus. Therefore, in case of an imbalance between
∼
=
=
∼
∼
=
=
∼
Ctot dc
Figure 2.14: Simplified model of MTDC grid
grid by all inverters,Ctot
dc will charge or discharge and, thus, the DC voltage will deviate from its
desired value. Its rate of change is given as follows: VdV dt = Pr− Pi 2Htot dc . (2.32)
Hdctot is the electrostatic constant of the DC grid in seconds, given by Hdctot= 1 2C tot dc V2 b Pb (2.33) wherePb is the base power of the DC grid andVb the base DC voltage. These bases are used to
convertV , PrandPiin per unit.
This expression is similar to the one for AC system frequency when there is an imbalance between the mechanical powerPmgiven by all turbines and the active powerPeproduced by all generators.
Similarly, the rate of change of angular frequency in response to a power imbalance is dictated by the total mechanical inertiaHtot
ac of the machines connected to the grid [KBL94] as follows:
ωdω dt = Pm− Pe 2Htot ac . (2.34)
Large excursions ofω or V could lead to equipment tripping or damage. Hence the AC frequency and the DC voltage should be kept near their nominal values. However, while a typical value of the individual mechanical inertia constant of a conventional power plant is in the range of 2− 5 s, the electrostatic constant of an individual VSC is much smaller, namely in a range of 10−100 ms (including the DC branch contribution). However, while there is usually a big number of conventional power plants in an AC interconnection, MTDC grids are expected to include a limited number of terminals. As a result, the total electrostatic inertia in the MTDC grid will be several orders of magnitude smaller than the mechanical inertia of AC systems. This necessitates having to control the power balance in an MTDC grid rapidly and tightly by adjusting the powers the VSCs inject and/or extract from the grid.
To this purpose, several control schemes have been proposed in which there is always at least one VSC adjusting its power to control the DC voltage. The strategies for a point-to-point link and for an MTDC grid are described hereafter.
2.3.2 Control of a point-to-point HVDC link
The most common control for a VSC point-to-point link is the Master-Slave scheme, which is also used in LCC connections. In this strategy one VSC is chosen to act as the Slave converter
2.3. DC voltage control 29 AC grid 2 AC grid 1 '= =' V P Pset + − Vset + − Master Slave
Figure 2.15: Master-Slave control of a point-to-point HVDC link
and the other as the Master. A simplified depiction of the Master-Slave scheme of a point-to-point HVDC link is given in Fig.2.15. The Slave controls the power transfer in the link by controlling the powerP to its setpoint Pset (i.e. by choosing α1 = −1 and β1 = 0 in (2.25)). The Master
adjusts its power to control the power balance in the DC grid by controlling the DC voltageV to its referenceVset(i.e. by settingα1= 0 and β1=−1 in (2.25)).
As far as the reactive current control strategy is concerned, it can be selected independently in both ends, i.e. AC voltage control, reactive power control, etc. can be contemplated.
2.3.3 Control of an MTDC grid
The DC voltage control of an MTDC grid is not as straightforward as that of a point-to-point link, and several methods have been proposed in the literature. The most obvious option is to apply the same control as for a point-to-point link, i.e. the Master-Slave scheme. Assuming an MTDC grid consisting of N VSCs, one is selected as Master and the rest N − 1 as Slaves. However, this configuration raises security concerns since a failure of the Master VSC would lead to the shut-down of the whole MTDC grid.
Alternatives to Master-Slave control have been proposed that provide redundancy in case of failure of the Master VSC. The voltage margin method [Hai12] uses a back-up Master VSC. The back- up VSC is normally operating as Slave, switching to Master only if the DC voltage exceeds a threshold. However, this method has poor dynamic performance and might require some commu- nication in order to work properly. To solve this, the work in [TP14] proposes the use of multiple “master” converters, which control the voltages at different points in the grid.
The DC voltage droop method and its variants has received the most attention in the literature [DSR+12,Hai12,ACML+15,Rau14,BLM14,Vra13,EBVG15,BGG+14]. It is directly inspired by the AC frequency control practice and allows multiple converters to share any power imbalance in the HVDC grid. Namely, in a droop-controlled HVDC grid some of the VSCs are given aP−V
characteristic defined by a power setpoint (Pset), a voltage setpoint (Vset) and a droop gain (K V).
The power of the VSC then follows the relation:
P = Pset− KV(V − Vset) (2.35)
where positive value of P corresponds to rectifier operation2. This characteristic is shown in
Fig.2.16. Following a change in the power injected into the MTDC grid (e.g. change of WF power or tripping of a VSC), the DC capacitors will instantaneously cover this change. This leads to a change of the DC voltage and the adjustment of the VSC power following its characteristic (2.35). For instance, an increase of the DC voltage indicates a surplus of power, hence the VSC power decreases to restore the balance.
V P Pset Vset − 1 KV
Figure 2.16: VSC droop characteristic
The magnitude of the DC voltage change is mainly determined by the droop gains of the VSCs [Hai12]. For example, let us assume an MTDC grid consisting ofN VSCs (with same nominal power for simplicity), each VSCi with its own P − V characteristic. If the losses are neglected then all VSCs have the same DC voltageV and the sum of their powers is equal to zero, i.e.:
N X i=1 Pi = N X i=1 Piset− KV i(V − Viset) = 0 (2.36)
Assuming the outage of VSCj injecting power Pj before the disturbance, the remaining VSCs
should adjust their power so that the power balance is again satisfied in the post-disturbance situ- ation.
The total deviation of the post-disturbance powersPi0 from the initial powers will be equal to the
2