Smooth Regulation of DC Voltage in VSC-MTDC Systems Based on Optimal Adaptive Droop Control

: DC voltage stability and power balance are the key conditions for stable operation of DC transmission systems. The droop control does not depend on inter-station communication and has the advantage of multi-station cooperative unbalanced power dissipation, which has been widely used in the voltage source converter based multi-terminal direct current (VSC-MTDC) system. However, its control will cause DC voltage deviation, and there are a series of problems such as unstable system control and overload operation of the VSC-station due to improper setting of droop coefficient. In this paper, the infeasibility of DC voltage error-free correction under droop control mode is theoretically analyzed, and a VSC-MTDC cooperative optimization droop control strategy with DC voltage "quasi-error-free" adjustment ability is proposed. The strategy adjusts the droop coefficient in real-time by monitoring the DC voltage deviation and the power margin of the VSC-station to solve the problem of voltage deviation caused by unbalanced power consumption. At the same time, an additional DC voltage stabilizer is designed to automatically adjust the power reference value and restore the DC voltage. Finally, a five-terminal VSC-MTDC system is built under PSCAD/EMTDC to verify the feasibility of the proposed strategy.


INTRODUCTION
With the continuous adjustment of energy structure, the penetration rate of large-capacity power electronic devices in the power grid has gradually increased, and the trend of power electronics has been shown in the four fields of source, network, load and storage [1][2][3].In terms of transmission system, voltage source converter based multi-terminal direct current (VSC-MTDC) system is suitable for grid connection and consumption of large-scale renewable energy, and has been widely used [4][5].Inter-station coordination control of VSC-stations is one of the key controls for stable operation of the VSC-MTDC system.The current inter-station coordination control methods of the VSC-MTDC system are mainly master-slave control, voltage margin control and droop control.Among them, droop control is currently the most applied method of inter-station coordination control by virtue of the advantage of cooperative imbalance power dissipation by multiple stations [6].However, the essence of droop control is to change the DC voltage to achieve tidal redistribution to dissipate the unbalanced power, and the deviation of DC voltage will affect the normal operation of the system.
The problem of DC voltage deviation inherent in the use of droop control to dissipate unbalanced power in VSC-stations has been extensively studied by scholars.In [7], the error input in the proportional form is changed to the proportional-integral (PI) form by using a Washout filter instead of a droop coefficient to eliminate the control static difference and achieve DC voltage stabilization control.In [8], the DC voltage deviation is superimposed on the droop control, and the zero-error adjustment of the DC voltage is realized by using the zero-error characteristics of the PI controller.However, this control method transforms the droop control station into a DC voltage control station and loses the ability of the droop control station to coordinate the unbalanced power dissipation of multiple stations.Ref. [9][10][11] proposes an adaptively adjusted droop control method, which achieves a reasonable distribution of unbalanced power and suppresses the dynamic deviation of the DC voltage by adjusting the droop coefficient.In [12][13], the unbalanced power of the system is superimposed on the active power loop in the droop control, and the VSC-station is operated near the DC voltage rating by moving the droop curve.Ref. [14] proposes to calculate the system unbalanced power by DC voltage deviation and then adjust the droop control active power reference value.However, this method is sensitive to the droop coefficient and DC voltage, and the amount of power deviation needs to be obtained indirectly from the DC voltage deviation.
Aiming at the problem of DC voltage deviation in droop control, this paper proposes an optimized droop control with DC voltage dynamic correction.The main contributions are as follows: (1) Through theoretical analysis, this paper demonstrates that when the VSC-station with droop control dissipates the unbalanced power to reach the steady state, it is impossible to restore the DC voltage to the initial state with constant power.
(2) By introducing the power margin and DC voltage of the VSC-station into the droop coefficient, it ensures that the droop VSC-station with smaller power margin bears less unbalanced power, and the droop control station with larger power margin bears more unbalanced power, which optimizes the tidal current distribution of the system and reduces the DC voltage deviation.
(3) Aiming at the problem that the optimal droop control can only adjust the DC voltage after the stability of the VSC-station, a DC voltage stabilizer is designed.The DC voltage variation is used as the input to simulate the inertia response of the synchronous generator, and the active power reference value is automatically adjusted during the power disturbance process to restore the DC voltage.
Finally, the simulation results in PSCAD/EMTDC verify the effectiveness of the proposed coordinated control strategy.The rest of the paper is organized as follows.Section 2 briefly describes the basic structure of VSC-MTDC systems and the working principle of the conventional droop controller.Section 3 proves by mathematical derivation that it is infeasible to restore the DC voltage to the initial state when the output active power of the VSC-station keeps constant after the system is disturbed.On this basis, an adaptive droop control strategy considering the VSC-station real-time power margin is proposed to restore the DC voltage to the state closest to the initial value.The presented approach is verified on PSCAD/EMTDC in Section 4. The conclusions of this paper are outlined in Section 5.

MTDC SYSTEM STRUCTURE AND CONTROL
The structure diagram of the parallel type five-terminal VSC-MTDC systems is shown in Fig. 1.The DC sides of the five VSC-stations are connected in parallel through the DC network.The active power transmitted by each VSCstation in this system is injected into the AC grid as the reference positive direction.

Converter Modeling
The physical structure of VSC is shown in Fig. 2, in a two-phase rotating coordinate system, the mathematical model of VSC may be stated as follows.
where i sd and i sq represent the d and q components of the current flowing from the AC system to the converter side.U sd and U sq represent the d and q components of the VSC output AC voltage.U d and U q represent the d and q components of the AC voltage at the point of common coupling.ω represents the angular frequency of the AC system [15].

Figure 2 The topology of VSC-station
The overall control structure of the system includes the outer loop control and the inner loop control.The outer loop controller contains two types of control: active power control and reactive power control, and the tracking of the control quantity to the reference value is realized.The inner loop control mainly tracks the current reference value output by the outer loop and converts it into a voltage signal to generate a PWM pulse, thereby controlling the onoff of the device in the VSC-station [16][17].The doubleloop control structure of VSC-MTDC is shown in Fig. 3.

Analysis of the Droop Control Characteristics
The droop control stabilizes the DC voltage through multiple VSC-stations with power regulation capabilities.The structure of the DC voltage droop controller is shown in Fig. 4. P sref and P s represent the active power command value and measured value.U dcref and U dc represent the DC voltage command value and measured value.k is the droop coefficient and PI is the proportional-integral controller [18][19].In Fig. 4, the following is the relationship between active power and DC voltage.
It is assumed that there are NVSC-stations in the VSC-MTDC systems with droop control strategy, the i (1 ≤ i ≤ N) VSC-station's unbalanced power P i and the DC voltage variation U dc have the following relationship.
To ensure the power balance of the DC network, the sum of the active power shared by each VSC-station should be equal to the power disturbance value P in the DC network. 1 Combing Eq. ( 3) and Eq. ( 4), we get: Technical Gazette 30, 4(2023), 1234-1240 It can be seen from Eq. ( 5) that when each VSC-station's droop coefficient is fixed, the unbalanced power assumed by the VSC-station during the adjustment process is inversely proportional to its droop coefficient.That is to say, the larger the droop coefficient of the VSC-station, the smaller unbalanced power it bears.When the system is disturbed, the DC voltage is bound to have deviations due to unbalanced active power distribution.This provides a research direction for adaptive droop control based on DC voltage deviation-free correction in Section 3.

MTDC SYSTEM STRUCTURE AND CONTROL
The degree of active power and DC voltage departure from the rated value at the VSC-station is an essential measure of stability for VSC-MTDC systems.When using the conventional droop control method, as the measured power approaches the reference power, the gap between the measured DC voltage and the reference DC voltage should decrease [20].

DC Voltage Deviation-free Correction Feasibility Analysis
In the VSC-MTDC systems, the output active power of the VSC-station can also be expressed as: where R ij is the line resistance between the VSC-stations, 1 ≤ i≤ N, 1 ≤ j ≤ N. U dcj1 is the initial DC voltage of VSC j connected to VSC i .As shown in Fig. 5, we can obtain.
Combing Eq. ( 6) and Eq. ( 7), we get: Combing Eq. ( 8) and Eq. ( 9), we get: From Eq. ( 10), P 1 is equal to 0, and as known from Fig. 5, P 1 is not equal to 0 due to the existence of unbalanced power.Therefore, it is impossible to realize the DC voltage deviation-free correction under the condition that the output power of the VSC-station remains constant.On the contrary, at the expense of the change of the output power of the VSC-station, the DC voltage can be restored to a state close to the initial value, and the "difference-free" regulation of the DC voltage can be achieved approximately [21][22].

Optimal Adaptive Droop Coefficient Optimization Strategy
Section 3.1 proves that deviation-free correction of DC voltages without power variations is impossible.The control strategy in this paper is as follows, which can approximate the deviation-free correction of DC voltage based on the rational allocation of unbalanced power.Define the available real-time power margin of the VSC-station as P can , and the DC voltage variation as U can , which can be expressed as: where P max represents the maximum power allowed to be transmitted by the VSC-station.U dcmax and U dcmin represent the maximum and the minimum value of DC voltage allowed by the system.The droop coefficient for optimal adaptive adjustment can be expressed as: where α represents the voltage deviation factor, which is to keep the DC voltage fluctuation within the allowable range of the system.α can be expressed as: When the deviation between the DC voltage measured value and commanded value is more minor, the voltage deviation coefficient α is closer to 0.5, which is the same as decreasing the fraction of the adaptive droop control's DC voltage regulation.As the DC voltage deviation decreases, α increases accordingly, which provides a sufficient adjustment amount for the update of the droop coefficient when the system is in a transient state.
Substituting Eq. ( 13) into Eq.( 5), we get: It can be seen from Eq. ( 15) that the unbalanced power assumed by each VSC-station is determined by its real-time power margin.The larger the real-time power margin of the VSC-station, the larger the unbalanced power it bears, which effectively avoids the problem of overloading the VSC-station caused by the excessive unbalanced power of the system.

Droop Control Strategy with Additional DC Voltage Stabilizer
Aiming at the problem that the optimal droop control can only perform DC voltage regulation after the VSC-station is stabilized, a DC voltage stabilizer is designed to reduce the DC voltage deviation in the dynamic process.Analog to the inertia method of synchronous generator, take ∆U dc as input, and reduce the DC voltage change value by adjusting the power reference value during power disturbance [23].Taking Eq. ( 11), Eq. ( 12), Eq. ( 13), and Eq. ( 14) into consideration, the optimal adaptive droop control with an additional DC voltage stabilizer is depicted in Fig. 6.As shown in Fig. 6, to avoid frequent fluctuations in the system due to DC voltage fluctuations, a dead zone is added after U dc .At the moment of power disturbance, U dc is large enough to provide sufficient regulation for the update of the active power command value.At the end of the dynamic process, U dc is zero and no longer participates in regulation.

ANALYSIS OF SIMULATION RESULTS
To verify the effectiveness of the proposed control strategy, a five-terminal flexible DC system is built on the simulation software PSCAD/EMTDC platform as shown in Fig. 1.The comparative experimental control method used in this paper is as follows: CM1: Conventional droop control.CM2: The control method proposed in [19].CM3: The control strategy proposed in this paper.

VSC3
Active Power Occurs inSteps t = 5 s, the active power command value of VSC3 rises from 0.575 (p.u.) to 0.9 (p.u.), the comparative analysis of the simulation results under the three control strategies is shown in Fig. 7 and Tab. 2. As can be seen from Fig. 7, in the initial state, due to system losses, the actual power of VSC1 and VSC2 under the three control strategies is close to the power command value, but there is a slight difference.The DC voltage gradually decreases after the VSC3 power command value is changed.For CM1, VSC1 and VSC2 dissipate the unbalanced power according to a fixed ratio, and the transmitted power changes from −1.098 (p.u.) and −0.500 (p.u.) to −1.204 (p.u.) and −0.720 (p.u.), respectively, and the DC voltage decreases from 0.999 (p.u.) to 0.983 (p.u.).For CM2, the droop coefficient is calculated from a fixed power margin, and the system power distribution is optimized, the transmitted power varies from −1.092 (p.u.) and −0.506 (p.u.) to −1.174 (p.u.) and −0.750 (p.u.), respectively, and the DC voltage is reduced from 0.999 (p.u.) to 0.987 (p.u.).
For the droop coefficient is automatically adjusted according to the real-time power margin of the VSC-station to further optimize the system power distribution.The transmitted power changes from −1.098 (p.u.) and −0.498 (p.u.) to −1.162 (p.u.) and −0.763 (p.u.), respectively, and the DC voltage decreases from 0.999 (p.u.) to 0.997 (p.u.).As can be seen from Fig. 7d, the DC voltage deviation rates are 1.66%, 1.25% and 0.27% for the three control strategies, respectively.Compared with the other two control strategies, the DC voltage deviation under CM3 is the smallest, and an additional DC voltage stabilizer dynamically adjusts the power value, the system enters the DC voltage recovery state at t = 5.06 s.

VSC4 Active Power Occurs in
Steps t = 4 s, the active power command value of VSC4 rises from 0.425 (p.u.) down to 0.075 (p.u.), the comparative analysis of the simulation results under the three control strategies is shown in Fig. 8 and Tab. 3.
For CM3, the droop coefficient is automatically adjusted by the real-time power margin of the VSC-station, and the power reference value is adjusted during the power disturbance to reduce the amount of DC voltage variation.The transmitted power changes from -1.098 (p.u.) and −0.499 (p.u.) to −0.917 (p.u.) and −0.334 (p.u.), respectively, and the DC voltage decreases from 0.9998 (p.u.) to 0.9993 (p.u.).From Fig. 8d, it can be seen that the DC voltage deviation rates are 1.75%, 0.49% and 0.21% for the three control strategies, respectively.According to the above analysis, when the system power fluctuates, the control strategy in this paper can reasonably distribute the unbalanced power according to the system status, reduce the DC voltage deviation, and improve the stability and reliability of the VSC-MTDC system operation.

The VSC2 Exits when the System is Running Normally
VSC-MTDC system should satisfy the N − 1 principle, any VSC-station in the system is out of operation, and the rest of the VSC-stations in the system should have the power regulation capability to stabilize the DC voltage.t = 3 s, the operation of the VSC2 exit, the comparative analysis of the simulation results under the three control strategies is shown in Fig. 9  From Fig. 9b, it can be seen that VSC1 and VSC2 jointly maintain the power balance of the DC network before the fault occurs.With VSC2 out of operation, its power transfer value drops to 0. The unbalanced power appearing in the DC network causes the DC voltage to drop rapidly.For CM1, VSC1, as the only power balancing point, undertakes the power balancing task of the system, and its delivered active power soon changes to −1.250 (p.u.), reaching full load and switching to constant power operation, losing the ability to control DC voltage.Eventually, the DC voltage continues to drop below the limit value of 0.925 (p.u.), and the whole DC system will become unstable and stop operating.
For CM2, when the DC voltage is not lower than 0.950 (p.u.), VSC1 acts as the only power balancing point and undertakes the power balancing task of the system, and its transmitted power changes to −1.250 (p.u.), switching to constant power operation and losing the ability to control the DC voltage.Since there is still some unbalanced power in the DC network causing a continuous decrease in DC voltage, VSC3 and VSC4 shift their control mode to take up the task of dissipating unbalanced power and stabilizing DC voltage.When the system reaches steady state, the DC voltage drops to 0.944 (p.u.).
For CM3, since the power margin of VSC1 is not sufficient to dissipate the unbalanced system power, VSC3 shifts control mode to cooperate with VSC1 to dissipate the unbalanced system power.When the system reaches steady state, VSC1 does not reach full load and still has the ability to stabilize the DC voltage.From Fig. 9e, it can be seen that the DC voltage deviation rates are 31.5%,5.54% and 1.28% for the three control strategies, respectively.

CONCLUSION
Droop control does not require inter-station communication, but its ability to control DC voltage and active power is fixed and difficult to adapt to various complex operating conditions.Therefore, this paper proposes a droop control optimization strategy to adjust the droop coefficient according to the power margin of the converter station in real time to optimize the system current distribution and reduce the DC voltage deviation.A five-terminal flexible DC transmission model is developed using PSCAD/EMTDC.Comparing the control strategy proposed in this paper with the other two strategies, the results demonstrate that the control strategy of this paper can effectively enhance the power distribution capability with minimum DC voltage deviation when power fluctuation occurs in the DC system.It is also verified that the control strategy can run stably in N-1 mode, which proves the reliability of the control strategy running in the system.

Figure 1
Figure 1 Structure diagram of the five-terminal VSC-MTDC transmission system

Figure 3
Figure 3 Dual-loop control block diagram of VSC-MTDC systems

Figure 4
Figure 4 DC voltage droop controller

Figure 5
Figure 5 Droop control operating point change

Figure 6
Figure 6 Block diagram of optimal adaptive droop control with additional DC voltage stabilizer

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(a) Active power of VSC1 (b) Active power of VSC2 (c) Active power of VSC3, VSC4 and VSC5 (d) System DC voltage Figure Simulation results of VSC3 power variation Ping HE et al.: Smooth Regulation of DC Voltage in VSC-MTDC Systems Based on Optimal Adaptive Droop Control 1238 Technical Gazette 30, 4(2023), 1234-1240

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(a) Active power of VSC1 (b) Active power of VSC2 (c) Active power of VSC3, VSC4 and VSC5 (d) System DC voltage Figure Simulation results of VSC4 power variation and Tab. 4. 1239 (a) Active power of VSC1 (b) Active power of VSC2 and VSC5 (C) Active power of VSC3 (d) Active power of VSC4 (e) System DC voltage Figure 9 VSC2 exit operation simulation

Table 1
Main parameters of the VSC-MTDC systems

Table 2
Simulation results of DC voltage deviation

Table 3
Simulation results of DC voltage deviation

Table 4
Simulation results of DC voltage deviation