Abstract
For the safe and fast recovery of line commutated converter based high-voltage direct current (LCC-HVDC) transmission systems after faults, a DC current order optimization based strategy is proposed. Considering the constraint of electric and control quantities, the DC current order with the maximum active power transfer is calculated by Thevenin equivalent parameters (TEPs) and quasi-state equations of LCC-HVDC transmission systems. Meanwhile, to mitigate the subsequent commutation failures (SCFs) that may come with the fault recovery process, the maximum DC current order that avoids SCFs is calculated through imaginary commutation process. Finally, the minimum value of the two DC current orders is sent to the control system. Simulation results based on PSCAD/EMTDC show that the proposed strategy mitigates SCFs effectively and exhibits good performance in recovery.
LINE commutated converter based high-voltage direct current (LCC-HVDC) transmission systems are widely applied owing to the geographical separation of primary energy resources and load centers. To lower the influence of commutation failure (CF), the mechanism and influencing factors of CF have been widely investigated. With control-modification-based methods [
Reference [
Thus, a DC current order optimization based strategy for recovery performance improvement of LCC-HVDC transmission systems is proposed, which considers the operating boundary and the SCF mitigation. The first DC current order is calculated by the TEPs and the quasi-steady state equation of LCC-HVDC transmission systems to ensure the maximum active power transfer and the operating boundary. Then, the second DC current order is calculated by imaginary commutation process, which can guarantee the maximum DC current order without SCFs. Finally, the minimum value of the two DC current orders is sent to the control system.
The DC current order in this letter consists of two different parts. The first DC current order Idord1 ensures the maximum active power while keeping certain electric and control quantities within the operation boundary. The second DC current order Idord2 ensures the maximum active power while preventing the LCC-HVDC transmission systems from SCFs.
The equivalent circuit of a generic LCC-HVDC transmission system is shown in
Fig. 1 Equivalent circuit of a generic LCC-HVDC transmission system.
Under the quasi-steady state, the inverter of LCC-HVDC transmission system is controlled by either constant current (CC) controller or CEA controller. The control aims of the CC controller and CEA controller can be described as (1) and (2), respectively.
(1) |
(2) |
where and are the extinction angle (EA) and its rated value, respectively; Idord is the DC current order generated by the control system; and IM is the DC current margin between the rectifier and inverter, which is generally 0.1IdN (IdN is the rated DC current).
The power flow equation of AC grid can be expressed as:
(3) |
The compensated reactive power can be calculated as:
(4) |
where Xc is the reactance of the reactive power compensator.
The DC power can be calculated as:
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
where N is the number of six-pulse bridges of the converter; is the power factor; kT is the transformer ratio; and XT is the equivalent commutation reactance.
The AC power can be calculated as:
(11) |
The AC bus voltage can be calculated as:
(12) |
(13) |
(14) |
(15) |
(16) |
Since we focus on the fault occurs in the inverter-side AC grid, the TEPs of the rectifier-side AC grid is assumed to be constant. Thus, substituting (3)-(10) into (12) leads to:
(17) |
where and are the transcendental equations of Ui and Ur, respectively.
Additionally, the following constraints of the LCC-HVDC transmission system should be added:
(18) |
where UiN and UrN are the rated values of Ui and Ur, respectively; and is the minimum value of FA at the rectifier, which is generally 5°.
For certain TEPs, when the DC current and the EA are controlled at the rated values, the corresponding Ui and Ur can be solved by the transcendental
For the application of the proposed strategy, the practicality of TEP estimation method should be firstly evaluated. Both the response speed and the accuracy of the real-time tracking and identification of TEPs during the AC fault transient process can be ensured during the implementation of the proposed strategy. This is firstly because some methodologies have been proposed to obtain and update network parameters with the data from supervisory control and data acquisition (SCADA) systems and phasor measurement units (PMUs) [
However, since the first DC current order is calculated by the quasi-steady state equation, the SCFs during the transient process are not fully guaranteed. Therefore, the second DC current order is needed to avoid SCFs.
The imaginary commutation process [
Fig. 2 Imaginary commutation process at different time instants. (a) Normal process. (b) Process after fault and before CF. (c) Recovery process from CF.
During the imaginary commutation process when t ranges from ts to te, the imaginary supply voltage time area can be expressed as:
(19) |
where Uc is the commutated voltage.
The imaginary demand voltage time area can be expressed as:
(20) |
where Xci is the equivalent commutated reactance.
Once the inequality (21) holds, the imaginary commutation process is completed, and the corresponding time instant is te.
(21) |
By neglecting the phase shift during the deionization process, the imaginary EA can be calculated as:
(22) |
where is the FA shift at ts; and is the phase shift at te.
Meanwhile, the imaginary deionization area can be calculated as:
(23) |
Since the imaginary commutation process can start at any sample time, we can obtain a series of imaginary deionization areas that start at different sample time, which could provide real-time changing data of the imaginary deionization area after fault.
The rated deionization area can be expressed as:
(24) |
where UcN is the rated commutated voltage.
For imaginary commutation process with the rated deionization area and the second DC current order, we can obtain:
(25) |
where Ade,new is the demand voltage time area with the second DC current order.
Assuming that the DC current variation is added to the original DC current when the second DC current order is applied, substituting (20) into (25) yields:
(26) |
can be expressed as:
(27) |
Thus, the second DC current order Idord2 can be calculated as:
(28) |
As observed from
It is worth noting that, the second DC current order can only mitigate SCFs and cannot keep certain electric and control quantities within their boundaries. Thus, the minimum value of the first DC current order and the second DC current order is selected and sent to the control system. Moreover, to avoid DC current fluctuation during the recovery, the method proposed in [
The block diagrams of control system of the CIGRE HVDC benchmark model (CIGRE control) and the proposed strategy are shown in Figs.
Fig. 3 Block diagram of CIGRE control.
Fig. 4 Block diagram of proposed strategy.
To validate the effectiveness of the proposed strategy, several simulations are performed using the CIGRE control based on PSCAD/EMTDC. The simulation step is , and the sampling step and control step are both .
In this study, A-G and ABC-G AC faults are applied in a typical case to verify the effectiveness of the proposed strategy in terms of the SCF mitigation. With different grounding inductance Lf, the faults are applied at the inverter-side AC bus to simulate different fault severity levels. Herein, the initial time of faults varies from 2.000 s to 2.009 s with a step size of 0.001 s and a fault duration of 0.4 s.
In the simulation of the A-G fault, Lf varies from 0.2 to 1.2 H. The simulation results of the A-G fault are shown in
Fig. 5 Simulation results for AC faults with different grounding inductance and different initial time of faults. (a) A-G fault with CIGRE control. (b) A-G fault with proposed strategy. (c) ABC-G fault with CIGRE control. (d) ABC-G fault with proposed strategy.
In the simulation of the ABC-G fault, Lf varies from 0.2 to 1.6 H. The simulation results of the ABC-G fault are shown in
The simulation results when the ABC-G fault occurs at 2.0 s for a duration of 0.4 s and Lf of 0.9 H are shown in
Fig. 6 System response with CIGRE control and proposed strategy under different faults. (a) ABC-G fault. (b) Faults with changing TEI. (c) Faults with changing TE voltage.
As observed from
To verify the applicability of the proposed strategy under different kinds of conditions, faults with changing TEPs are applied in the inverter-side AC grid.
Firstly, the TEI is changed from 1.0 p.u. to 1.5 p.u. from 2.0 s to 2.4 s, i.e., the short circuit ratio (SCR) changes from 2.5 to 1.67. As observed from
Secondly, the TE voltage is changed from 1.0 p.u. to 0.93 p.u. from 2.0 s to 2.4 s, i.e., the SCR changes from 2.5 to 2.16. As observed from
In this letter, a recovery strategy for the safe and fast recovery of LCC-HVDC transmission systems after faults is proposed, which achieves the SCF mitigation as well. By analyzing the simulation results, it is verified that by using the proposed strategy, the active power can recover fast and the operating point can be kept within the limits as much as possible. Meanwhile, the proposed strategy can mitigate the SCFs effectively under different kinds of fault.
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