A modified droop control structure for simultaneous power-sharing and DC voltage oscillations damping in MT-HVDC grids

Received: 27 August 2021 Revised: 30 December 2021 Accepted: 21 January 2022 IET Generation, Transmission & Distribution DOI: 10.1049/gtd2.12427 ORIGINAL RESEARCH PAPER A modified droop control structure for simultaneous power-sharing and DC voltage oscillations damping in MT-HVDC grids Neda Azizi1Hassan Moradi CheshmehBeigi1Kumars Rouzbehi2 1Department of Electrical Engineering, Razi University, Kermanshah, Iran 2Department of System Engineering and Automatic Control, University of Seville, Seville, Spain Correspondence Hassan Moradi CheshmehBeigi, Tagh-e-Bostan, University St., Kermanshah, Iran. Email: [email protected].ir Abstract With increasing energy demand, the use of renewable energy resources is increasing. Renewable energy sources require power electronic converters to get integrated into power grids. Multi-terminal high voltage direct current (MT-HVDC) systems are a promising solution for their grid integration. Using droop-based controller strategies in power converter stations of MT-HVDC grid, in addition, to providing power-sharing, can support the frequency of the connected AC grids. However, power changes lead to direct voltage deviations, thereby disrupting the stability of the MT-HVDC system. Here, a new control structure for the droop controller of the voltage source converter (VSC) controller is proposed which is named modified droop controller (M-Droop). This method, in addition to power-sharing, uses an appropriate control action to provide the required voltage stability. Here, analytical studies of the modified control strategy are reported. Moreover, through a developed MATLAB Simulink platform, its performance is verified in the events of transients, consisting of fault, variable load, and change in power generation. 1 INTRODUCTION One of the most important challenges on the road of multiterminal HVDC grid development is protecting the system against DC faults. The capacitive behaviour of HVDC cables and their relatively low impedances leads to a significant increase in fault currents. DC circuit breakers (DCCBs) are one of the most effective tools for fast fault isolation [1]. Despite developments in DCCB technology, still they need to large DC reactors to reduce the rate of rising fault currents [2]. Capacitor and DC reactor connected to HVDC grid and inductance and capacitance of HVDC transmission lines make a kind of LC filter, which seriously affects the dynamic response of DC link voltage and its instantaneous power in MT-HVDC grid, especially in the long lines [3]. The main contest in control of MT-HVDC grids is direct voltage regulation with low capacitance [3]. The available control methods for solving this challenge include two options. The first option is based on the central controller and the second option is known as the decentralized method. In the first option, the entire system is monitored through an external communications link and the controller delivers the This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2022 The Authors. IET Generation, Transmission & Distribution published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology optimal power flow for the system’s resources and load. The advantage of this method is that it is optimal, and its major disadvantage is its dependence on external communications [4]. In addition, the implementation of the proposed method in the MT-HVDC grid reduces transient voltage oscillations. However, the control strategy of the second option includes methods such as droop [5], masterslave [6], and DC bus signalling method [7]. In [8], droop control methods are proposed based on the decentralized methods, but most of them cannot deliberate the influence of the resistance of cable and errors of sensor gain. Moreover, there is a trade-off between voltage regulation and current sharing in these methods. Adaptive or nonlinear droop is proposed in [8, 9], in which the trade-off between load sharing and voltage regulation is minimal, but these methods also perform poorly when the power converter current is negative or the power is reversed. Alongside with this methods, there are strategies include the combination of both centralized and decentralized methods as different control layers, which in addition to the advantages, include disadvantages of two methods [10]. 1890 wileyonlinelibrary.com/iet-gtd IET Gener. Transm. Distrib. 2022;16:1890–1900. AZIZI ET AL.1891 In DC grids, the DC voltage has a similar role as the power balance sign that the frequency has in AC grids [11]. That is, the DC voltage dynamics are determined by the energy stored as electrostatic potential energy in the capacitors in the grid [12]. However, conventional droops cannot increase the capacitance. Therefore, a new control method for MMC, called virtual capacitor control, is proposed in [13], which makes it possible to reduce the DC grid oscillation by simulating the dynamic response of a physical capacitor. To perform automatic synchronization using the DC-link capacitor dynamics, the authors in [14] employed a virtual synchronous control, which mimics the synchronization feature of a synchronous generator. The most important advantage of this method is that it is operated without a phase-locked loop (PLL), and therefore avoids instability caused by the PLL when connecting the VSC to a weak grid. The Inertia Emulation Control (INEC) algorithm proposes a method for the inertia emulation that uses the energy stored in the DC-link capacitor to mimic the inertial response of an SG, but this may need the large capacitors to be added to the system. The addition of these capacitors increases costs and will affect the dynamics of the controllers. Combined strategy is another method for emulated inertia, which utilizes both DC-link capacitor and wind turbine kinetic energy, this method is used only in a point-to-point HVDC system and requires some modifications to operate on a DC network [15]. Though for appropriate voltage regulation and power-sharing, a proper strategy is needed to enable the converter to increase DC capacitance. This paper proposes a modified droop controller (M-Droop) that provides capacitance using the energy stored in the grid where the fault occurred. The M-Droop can provide the capacitance requirement of the HVDC grid without depending on frequency measurement and PLL. The contributions of this study are: ∙This paper proposes a successful method for simultaneous power-sharing and oscillations of DC voltage damping ∙The proposed method does not require increasing the value of DC-link capacitors ∙As the conventional DC-PSS can only neutralize a small part of the voltage fluctuations, while, given the presence of the droop controller on the system, it has no proper effect on the volatility of the power. This study shows that the M-droop controller also provides a part of the capacitance required by the system in addition to damping of the direct voltage oscillations. The rest of this paper is organized as follows: Conventional droop controller performance is expressed in Section 2. Section 3is built based on the proposed control strategy. The understudy network and its modelling are discussed in Section 4. The optimization approach is investigated in Section 5. Dynamic performance analysis is analysed in Section 6. Simulations verify and confirm the analytical analysis described in Section 7. Finally, conclusions are given in Section 8. V DC P Operation point V DC,ref P ref Operation re g ion Operation region VDC,min VDC,max Pmax P min αV DC +βP DC +γ=0 FIGURE 1 Generalized characteristics of the proposed droop controller VDC PWM V DC P i DC i *DC V DC* M-droop PCC Power controller P * Current controller e c VC L T R T DC BUS V DC C iDC FIGURE 2 Control structure of the proposed controller for a VSC station 2PERFORMANCE OF A CONVENTIONAL DROOP CONTROLLER Figure 1demonstrates the general characteristics of the droop controller. Usually, P* as the active power reference is manipulated by the voltage droop controller (V–P), so, the active power control scheme acts as part of the plant of droop control model. The coefficient of the droop characteristics can be calculated according to the power flow results [4, 16] or grid condition and stability [17]. 3PROPOSED CONTROL STRATEGY The main contest in control of MT-HVDC grids is direct voltage regulation with low capacitance [3]. This paper suggests a method to provide the transient damping for direct voltages of the HVDC grid during the transient conditions. In this structure, the M-droop controller supplementary signal is being used instead of the conventional V–P droop controller to increase the stability of the HVDC grid. Figure 2shows a general structure of a proposed controller for a VSC station. The configuration of the proposed M-droop controller is revealed in Figure 3. Since the measured local voltage is known as the power balance indicator in the HVDC grid, in this structure, the locally measured voltage is used as the input signal. This M-droop provides an auxiliary capacitance. In 1892 AZIZI ET AL. FIGURE 3 M-droop control structure A0 Ba-A0 Ba-A1 Cb-A1 Bb-A1 B0 Ba-B0 Ba-B2 Ba-B1 Cb-B2 Cb-B1 Bb-B2 Bb-B4 Bb-B1 B0-C2 B0-D1 C2 D1 Bb-E1 Bb-D1 Bb-C2 DC bipole (+/-400 kV) AC onshore (380 kV) AC offshore (145 kV) Cable Overhead line FIGURE 4 Cigre DCS3 test MT-HVDC grid addition, to filter noises in the measured output power of the V–P droop controller, a low pass filter is usually added to the structure. 3.1 Virtual capacitor control Inertia in an AC system is defined as the system’s ability to prevent sudden events of frequency. In general, Hsis defined as the ratio of stored kinetic energy (Ek) and the rated power (Sn), as presented in (1): Hs=Ek Sn (1) Inertia constant can be defined as (2)[18]: Hdc =Wk SVSC (2) where Wkis stored energy in capacitors and SVSC is the rated power of VSC. Compared to synchronous generators with the same capacity, the Hdc is small. However, this value can be increased by increasing the capacitance of the DC link capacitor, but this increases the cost and short circuit level and reduces the dynamic characteristics of the DC bus [19]. The dynamic response of a DC capacitor is defined as (3): CDC VDC dVDC dt =Pi−Po=ΔPDC (3) where Pois the output power and Piis the input power. Due to the high speed and flexibility of the VSC controller, the additional power ΔP VSC , considering the range of direct voltage change, can be obtained through the active power control. ΔP VSC =CvirVDC SVSC dVdc dt (4) With the participation of additional power, the DC link capacitor dynamics change as follows. CDC VDC dVDC dt +CvirVDC dVDC dt =Pi(pu)−Po(pu)(5) According to (5), the additional power ΔP VSC obtained through power control can produce a virtual capacitor. This capacitor provides more inertia to support direct voltage. In this study, additional power is obtained through the remaining power of the system after the power-sharing or fault. The operation of the grid controllers is such that after powersharing or at the time of the fault, the grid may be in a situation where the power reference of the converters is not at maximum power. In this case, part of the grid power can be stored as additional power. 3.2 M-Droop controller A design characteristic of the modified droop controller is shown in (6), and (7) indicates the value of the droop coefficient of this new controller. Pw=Pw,re f −k1(VDC −VDC ,re f )+kvcVDC (6) kvc =k2 dVDC dt (7) As shown in (6), if the direct voltage remains constant, the proposed droop controller converts to the conventional droop controller, where Pwis the nominal value of power. P∗ w=Pw,re f −k1(VDC ,re f −VDC )(8) Comparing (6)with(8), Pw=P∗ w+kvcVDC (9) Regardless of the power losses, it can be said that the output power Pout is equal to the injected power Pi. By considering the droop controller in the system, power changes can be written as (10), where, Pcis the power of the AZIZI ET AL.1893 converter without droop controller effect. Pi=Pout =Pc−kw(Pw−Pw,re f )(10) Substituting (9)into(10) yields: Pi=Pc−kw(P∗ w−Pw,re f )−kWkvcVDC (11) According to (3), (12) can be written as follows: CDC VDC dVDC dt =Pc−kw(P∗ w−Pw,re f ) ⏟⎴⎴⎴⎴⎴⏟⎴⎴⎴⎴⎴⏟ Pin −kWkvcVDC −Po (12) Po−Pin =CDC VDC dVDC dt −kwk2VDC dVDC dt (13) Therefore, the above equations show that using power changes, the droop controller can be designed in a way that to be able to emulate the behaviour of the virtual capacitor. Therefore, the proposed method does not require increasing the value of DC-link capacitors. In addition, according to (13), it can be said that the capacity of the virtual capacitor is equal to (14): Cvir =kwk2(14) 3.3 Effects of delays There are always delays in MT-HVDC grids [20]. Usually, in the structure of a droop control, a low pass filter is added to filter noises in the measured output power. Assuming this delay is first-order lags with a time constant Tdand a gain 1/kp has to be replaced by 1/(1 +Td s) in the small-signal models. 4UNDERSTUDY NETWORK AND ITS MODELING In order to investigate the proposed control strategy, the grid that is shown in Figure 4is selected. In this grid 5-terminal bipolar MT-HVDC grid are connected to four AC areas connected. The test grid is formed by two onshore AC systems, two offshore AC systems, and five VSC-HVDC converters. It is worth noting that the typical test grid (Cigre DCS3) has been selected only as a selective test case, and the proposed scheme can be easily selected in other VSC-based HVDC grids. The main goal in the current paper is to improve the stability of the DC voltage and reduce variations of power in the states of transients, and this standard grid is selected to approve the performance and appropriateness of the proposed control method. In this paper, transmission lines are modelled by the frequency-dependent π(FD-π) section modelling [21]that consists of multiple cascaded πsections which are represented by series RL circuits, and shunt capacitors C[4]. Eigen value-based analysis of small signal dynamics in HVDC transmission systems requires cable models that are compatible with the display of state space. While distributed parameter models that calculate frequency-dependent effects are inherently inconsistent with the display of state space, a typical πmodel can only accurately show cable behaviour at a frequency. Instead, a FD-πmodel, consisting of a lumped circuit representation with multiple parallel RL-branches in each πsection can be utilized to reproduce the frequency dependency of the cable characteristics in a specified frequency range. So, the number of sections and parallel branches are considered as follows: n=10, m=5. Moreover, the rated power of each converter is 1000 MW and the rated voltage is ±320 kV. It is also assumed that the topology of the understudy system is a symmetrical monopole topology. According to the results obtained in [22], Ba-B1 has been selected as the appropriate location for M-droop placement. 5OPTIMIZATION APPROACH The parameters of the M-droop controller must be adjusted to decrease the objective function (15). Error = n ∑ b=1(MVb)(15) where MVbis the maximum peak of direct voltage oscillations from reference value for n DC bus in fault time is visible in (15). It should be noted that in this paper n=5. This equation confirm that, without any fault or malfunction in the system, the Error function will be zero. In this paper, the particle swarm optimization (PSO) algorithm and genetic algorithm (GA) are employed to determine the parameters of M-droop based on (15). The optimum parameters are obtained with 110 repetitions following four scenarios include: ▪Case 1: Three-phase to ground in Ba-A0 with a duration of 15 ms. ▪Case 2: Three-phase to ground in Ba-B0 with a duration of 15 ms. ▪Case 3: Three-phase to ground in Ba-A0 with a duration of 10 ms. Optimization results for the M-droop controller obtained by PSO and GA are shown in Table 1. The procedure of optimization of parameters in this paper is expressed in the following levels. Level 1. The population is set. 1894 AZIZI ET AL. TABLE 1 Optimization results for M-droop controller obtained by PSO algorithms Parameter Optimal valuePSO Optimal valueGA Case 1 k11.9 1.83 k24.3 4.51 kw31.5 30.9 kp0.019 0.0188 Case 2 k11.85 1.9 k24.2 4.16 kw30.1 30.2 kp0.024 0.026 Case 3 k11.81 1.85 k24.4 4.31 kw30.8 31.05 kp0.027 0.023 Level 2. At first, a particle is selected and the value of each parameter is calculated based on this particle. Then, the minimum and maximum limits for each parameter are checked, and finally, the Error criterion is calculated at this level. Level 3. At this level, the position (parameter) of each particle compares with its previous value, and the better particle is selected. Level 4. The degree of adaptive aggregation and the evolution rate is calculated and the speed and position data for each particle is updated. Level 5. In this level, if the repetition of irritation or the desired fitness corresponds to the stop criterion, the criterion stops according to the maximum number of repetitions of irritation or the desired fitness. Otherwise, it goes to the previous level. Level 6. Otherwise, the designed parameters are verified as results. In PSO algorithm, any particle has the situation and the speed that determined by Xand V. Then, the next position and velocity of each particle during the optimization process is calculated according to the current velocity and position and the desired individual position according to (16)and(17). Viter+1 i=wV iter i+c1.r1.(Pbesti −Xiter i)+c2.r2.(Gbest −Xiter i) (16) Xiter+1 i=Xiter i+Viter+1 i(17) where, the ith particle in the swarm is indicated by i.iter, shows iteration. Ps reveals the best position of the ith particle. Gbesti indicates the best general situation among the swarm. wrepresents the weight of inertia and r1and r2are selected as random numbers between one and zero. Start End Initialize population Select first particle of population i=1; Check the limitation of each parameters Constraints violated? Calculate objective function (15) All particle evaluated? Select the best particle with minimum objective function PSO converge? Update the population Remove this particle No Yes No Select a new particle set g=0, ω=0.9, c1=0.2, c2=0.2 evolutionary states estimation (c1, c2) Run simulation file FIGURE 5 Adaptive parameters control process In this algorithm, the updated linear inertia weight is directly related to the linear decrease in inertial weight (LDW) with increasing repetition time. However, the relationships between inertia weight and repetition time are not always the same for different optimization problems. Figure 5shows the flowchart of the PSO algorithm for parameters of the controller. The parameters calculated by both algorithms are almost identical, however, the PSO algorithm reaches the final answer in less time. 6DYNAMIC PERFORMANCE ANALYSIS In this part of the paper, the effect of the proposed method on system stability will be evaluated. Generally, the linearized model AZIZI ET AL.1895 Line (m) Vtr I tr Δu dc(n) Δi dc(n) Δu in l(m) Δi in l(m) Δu dc(1) Line (1) Δu in l(1) Δiin l(1) Δidc(1) FIGURE 6 HVDC grid model integrating line models Δi dc(1) Δi dc(2) Δi dc(n) Δu dc(1) Δu dc(2) Δu dc(n) ΔP *1 ΔP *2 ΔP *n DC Grid model Converter 1 Converter 2 Converter n FIGURE 7 Schematic of a MIMO plant model for the DC voltage control in MT-HVDC grid of the system in the state space form can be expressed as (18) [23]. Δx=AΔx+BΔu(18) where Δuand Bdenote the input vector and input matrix respectively, Δxand Adenote the state vector and the state space matrix respectively. It is necessary to mention, here, the average model of VSC is used to model the power converters and the π-section model is used to model the transmission lines. The number of sections of each transmission line in the π-section model is assumed to be five to achieve the appropriate accuracy. It is also assumed that the proposed controller is located on the Cb-B2 bus. Figure 6displays the construction of a DC network with nconverters and mlines. A schematic of a plant model of the direct voltage control in the MT-HVDC grid for stability investigation in the MT-HVDC grid is shown in Figure 7. This model can be used for studies on a multi-input-multi- output control network (MIMO), and to study the closedloop system following grid conditions. As shown in Figure 7, the input of the controllers of all converters is power. However, for converters equipped with a droop control system, power references in DC voltage control mode are used as the manipulated input. Power changes for converters that are in active power control mode act as a disturbance in DC voltage control. Also, the “reference” of power for each wind farm is the mechanical power taken by the turbine system. Figure 8illustrates the average modelling of a VSC station. As shown in Figure 8, the VSC station is modelled as a + - + - PCC * P P * d i q Li * d e d v 0 C f C i d i sd, sq V s R s L R L sd, sq i d, q v e + - d e s i eq u la i dc i a R a L eq C dc u 2 2 i p k ks + 1 1 s Ts+ 1 1 i p k ks + d, q d, q ω FIGURE 8 VSC-HVDC station model including its control structure controlled voltage source on the AC side and controlled current source on the DC side behind a capacitor based on the power balance principle commonly used for modular multilevel converters (MMCs) [24]. The VSC station is operated in a dq synchronous reference frame. Since in the stiff AC power system, reactive power control and qaxis current have an insufficient effect on the active power, meanwhile the q-axis of the voltage of PCC is generally kept on zero by the phase-locked loop (PLL) [25]. Thus, the analytical model for direct voltage stability study focuses on d-axis related controllers, because the purpose of the analysis is not to deal with weak systems. The dynamics of the system linked to the d-axis current is shown as follow: dΔis−d dt =𝜔Δis−q+1 Ls Δvd−1 Ls Δvs−d−R Ls Δis−d(19) dΔid dt =𝜔Δiq+1 LΔved−1 LΔvd−R LΔid(20) where Δis employed for the linearized operating point, (Rs+jωLs) is the grid impedance, (R+jωL) is equivalent to the impedance of the transformer and the impedance of the reactor arm, also, ωis the velocity angular. The system dynamics of the d-axis filter bus voltage is expressed as (21). In this paper, the q-axis PCC voltage is properly controlled by the PLL, since, the assumption is that the VSC station is connected to a strong system. Consequently, the small-signal method of the inverting power of the VSC can be expressed by way of (22): dΔvd dt =𝜔Δvq+1 cf Δid−1 cf Δisd (21) P=Vdid+Vqiq→ΔP≈vdoΔid+idoΔvd(22) The value of equivalent converter capacitor Ceq is adopted to the total energy stored in the MMC sub-modules. Laas equivalent arm inductance is modeled in the DC side given by Larm =(2/3)Lfor the average model of MMC. It is assumed that the power on the AC side is equal to the power on the DC side in the PCC, the linear dynamic of DC-link capacitance can 1896 AZIZI ET AL. be expressed as: dΔueq dt =Δila Ceq −Po Cequeqo ΔP+Po Cequeqo2Δueq (23) The subscript “o” shows the operating point. The DC voltage udc that across Ceq and Lais the voltage to be controlled voltage. To simplify the sophisticated model, a very small Cocapacitance has been modeled to enable udc to become a state variable. dΔila dt =Δudc La −Δueq La −Ra La Δila Δudc dt =− Δila −Δidc Co (24) The dynamic behaviour of the PI controllers related to the idand active power control is defined in (25), while the state variables of the integrators are the xPand xid. dΔxP dt =−ki2(ΔP−ΔP∗) dΔxid dt =−ki1(Δid−Δid ∗) (25) The reference of ican be indicated in (26), based on the Equation (10) and the structure of the active power controller. Δid ∗=−kp2[(vdoΔid+idoΔvd)−ΔP∗]+Δxp(26) The VSC modulation control is shown by a first-order transfer function with τas a time constant. To facilitate mathematical modeling, (27) is used, which causes the AC voltage edto be converted into a state variable. The dynamics of the state variable shown in (27). 1 𝜏s[Δvd−𝜔LΔiq+kp1(Δid ∗−Δid)+Δxid ] −1 𝜏s Δed=dΔed dt =1 𝜏s (Δed∗−Δed)(27) Here, the reference of voltage ∆ed*based on the current controller construction is deliberated. To achieve the final spacestate formula it is necessary to replace ∆id*in (27)with(26). The equivalent state variables are described as shown in (28). The matrices related to ∆vdc(j) and ∆idc(j) are mined to enable the integration of the VSC model and the HVDC grid model as it shown in (29): xj=[ΔedΔvdΔidΔisd Δxid ΔxpΔueq Δudc Δila] (28) xj=Ajxj+Bdj xdj+[BjG Bj][Δidc(j) ΔP∗ j] Δudc(j)=CjG xj(29) The dominant poles and zeros of the plant model VDC(s)/P*(s) of direct voltage control are shown in Figure 9. Figure 9demonstrations the poles and zeros diagram of the model of small-signal control with the proposed controller and conventional controller. As shown in Figure 9, the understudy grid is stable normally and entire of zeros and dominant poles are on the left side of the complex plane. Also, as shown by the direction of the arrows in the figure, the dominant poles of the system, marked in blue and corresponding to employing the M-droop, are farther away from the origin coordinates, indicating that the grid using M-droop has more stability. However, the predominant red poles associated with the conventional droop system have poles closer to the origin of the coordinates. This figure shows that by employing the M-Droop controller, poles and zeros, move farther from the vertical axis. Therefore, it can be said that the system with the M-droop controller is more stable than the system with a conventional droop controller. Figure 10 compares the frequency response of the system with the M-Droop controller and with the conventional controller. It is clear that M-Droop gives a higher phase margin and it is more flexible. Therefore, this result confirms that the system with the M-droop controller is more stable than the system with a conventional droop controller. 7SIMULATION RESULTS In this section, three different strategies are simulated on the Cigré DCS3 grid to demonstrate the advantages of the proposed M-droop strategy including conventional droop controller and M-droop controller. Three scenarios that are discussed below consist of reducing and increasing the power output of the Cb-A1 bus at 3 s and a three-phase short at the AC side of the Cb-A1 bus for 150 ms (3–3.15 s). In these simulations, the M-Droop controller -40 -30 -20 -10 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2x 10 5 Real axis si x a yranigamI M-Droop Droop FIGURE 9 The dominant poles and zeroes of the open-loop TF VDC(s)/P*(s) AZIZI ET AL.1897 -600 -400 -200 0 )Bd (e dut i ng aM 10-1 100101102103 -360 -180 0 180 360 540 720 Frequency(Hz) )ged ( es ah P M-droop M-droop droop droop 180 1Hz-10Hz FIGURE 10 Frequency response of the open-loop TF VDC(s)/P*(s) TABLE 2 Parameters of VSC-HVDC link Parameter Value Total number of capacitor (N)1 DC capacitor (CDC)7mF Rated DC voltage of VSC (VDCo) 1 p.u. Rated frequency (fo)50Hz Nominal power 1200 KVA Nominal AC voltage 380 kV Nominal DC voltage 400 kV α1 Β0.03 Γ−0.945 Td(s) 1.1 ms is applied to the Cb-B1 bus converter assuming the data are following Table 2. The simulation results for Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 buses are revealed. The VSC controller of the Cb-B1 and Cb-B2 bus is a droop controller and the VSC controller of Cb- C2 and Cb-D1 is a power controller. Figure 11 shows the output direct voltage and power of Cb- A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 following the load reduction scenario at the Cb-A1. As shown in Figure 11, by employing the proposed method, the direct voltage of buses is improved, they decrease more slowly and the much larger enhancement in DC voltage nadir are obtained. Because at the moment of system change, through capacitance improvement, the energy stored in the DC-link capacitor is used to maintain system stability. In addition, this energy in addition to not affecting the M-droop controller performance in power-sharing will increase the overall system stability. Output DC voltage and DC power of all busses include Cb- A1, Cb-B2, Cb-B1, Cb-C2, and Cb-D1 following load increasing scenario at the Cb-A1 is shown in Figure 12.Asshown 1.005 1.01 1.015 ) u.p( 1 A-bC -1000 0 1000 Cb-A1(MW) -500 0 500 Cb-B1(MW) 1 1.005 1.01 ) u . p (2 B -b C -800 -700 -600 Cb-B2(MW) 1.005 1.01 1.015 1.02 )u.p(2C -bC convention M-droop 400 450 500 550 Cb-C2(MW) 3 4 5 1 1.02 1.04 Time(s) (a) )u.p(1D-bC 3 4 5 900 950 1000 Time(s) (b) Cb-D1(MW) 1.005 1.01 1.015 ) u.p(1B-bC FIGURE 11 (a) DC voltage and (b) power of Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 following 250 MW reducing wind farm 2 generation in Figure 11, with the conventional method, the direct voltage of buses, will shock and has keen sharp peaks, from the initial value to the final value. Because with the proposed method, the energy stored in the DC-link capacitor is used to maintain system stability without any affecting the performance of the droop controller. The simulation results following the previous scenario about reducing power production for the Cb-B2 bus are shown in Figure 13 and Figure 14. The results for this bus also confirm that the stability of direct voltage of Cb-A1 and Cb-C2 can be improved by using delay filter compare M-Droop without delay filter, due to lack of drop and a sudden increase in bus voltage. In addition, Figure 14 shows that using M-droop, bus power oscillations are also reduced and do not change abruptly. However, the system with virtual capacitor and delay filter simultaneously has less oscillation and its damping is more rapid. Figure 15 shows the direct voltage of Cb-A1, Cb-B2, and Cb- B1 profiles during a three-phase short circuit to the ground at the AC side of the Cb-A1 bus for 150 ms (3–3.15 s). As shown in Figure 15, with the M-droop method, the direct voltage and power of buses have smaller oscillation than with conventional droop and reach stability fast. Because with the proposed method, the energy stored in the DC-link capacitor is used to maintain system stability without any affecting the performance of the droop controller. 1898 AZIZI ET AL. 1.01 1.015 1.02 ) u .p(1A-bC -700 -600 -500 -400 -300 Cb-A1(MW) 1.01 1.015 1.02 )u.p(1 B -bC -500 0 500 Cb-B1(MW) 1 1.005 1.01 1.015 ) u .p( 2 B- b C -800 -750 -700 -650 Cb-B2(MW) 1.01 1.015 1.02 )u.p(2C-bC 300 400 500 600 Cb-C2(MW) 3 4 5 1.01 1.015 1.02 1.025 Time(s) (a) ) u .p ( 1D- b C 3 4 5 900 950 1000 Time(s) (b) Cb-D1(MW) M-dr oop conventional FIGURE 12 (a) DC voltage and (b) power of Cb-A1, Cb-B1, Cb-B2, Cb-C2, and Cb-D1 following 250 MW increasing wind farm 2 generation 1.01 1.012 1.014 1.016 1.018 )u.p(1A-bC 2.5 33.5 44.5 5 -700 -600 -500 -400 Time(s) )u.p ( 1A-b C with delay w/o delay FIGURE 13 DC voltage and power of Cb-A1 following 250 MW reducing wind farm 2 generation In addition, the frequency of the AC side of Cb-A1 bus is shown in Figure 16. This figure shows the frequency profiles during a three phase short circuit to the ground at the AC side of Cb-A1 bus for 150 ms (3–3.15 s). As shown in Figure 16, with the M-droop method, the frequency oscillations can better damp than with conventional droop and reach stability fast. 1.01 1.015 1.02 1.025 )u. p (2 C - b C 2.5 33.5 44.5 5 350 400 450 500 550 Time(s) )WM(2C-bC with delay w /o delay FIGURE 14 DC voltage and power of Cb-C2 following 250 MW increasing wind farm 2 generation 0.995 1 1.005 1.01 1.015 1.02 1.025 ).u.p ( 1B-bC -400 -200 0 200 400 600 Cb-B1(MW) 3 4 5 0.995 1 1.005 1.01 Time(s) (a) ).u.p(2B-bC 3 4 5 -800 -700 -600 -500 -400 Time(s) (b) Cb-B1(MW) M-droop conventional FIGURE 15 (a) DC voltage and (b) power of Cb-B1 and Cb-B2 following a three-phase short circuit to the ground 8 CONCLUSIONS One of the main contests in control of HVDC grids is direct voltage regulation. This paper proposed a new control structure for the droop controller called the M-droop controller,