HVDC grids stability improvement by direct current power system stabilizer

Received: 13 February 2021 Revised: 2 July 2021 Accepted: 20 August 2021 IET Generation, Transmission & Distribution DOI: 10.1049/gtd2.12295 ORIGINAL RESEARCH PAPER HVDC grids stability improvement by direct current power system stabilizer 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, Postal Code 6714414971, Iran. Email: [email protected].ir Abstract High-voltage direct current breaker is among the essential components of high-voltage direct current grids. Such a breaker generally needs a direct current reactor to reduce the fault currents rate. However, direct current reactors have destructive effects on the multiterminal high-voltage direct current grid dynamic stability, and in such a system, despite the variety of controllers, the system dynamics are highly sensitive to the operating point. Therefore, additional damping control will be needed. This paper proposes a modification to be applied to the traditional droop controller of high-voltage direct current grids to cope with the influence of these large reactors, improving the direct voltage stability and decreasing power variations in the transient events by introducing a direct current power system stabilizer. The proposed method for direct voltage control has been investigated through the analytical model of the system. Stability improvement has been studied following the application of the proposed method by investigating zeros, poles, and frequency response analysis. Moreover, a method is proposed for optimal design and optimal placement of direct current power system stabilizer. The system analysis and time-domain simulations demonstrate a decent damping improvement attained by the proposed method. All simulations and analytical studies are conducted on Cigré DCS3 test high-voltage direct current grid in MATLAB/Simulink. 1 INTRODUCTION The integration of renewable generations and the electrification of oil and gas platforms, as well as the incorporation of different electricity markets, has resulted in a request for new transmission system solutions [1]. Yet, high-voltage direct current (HVDC) transmission technology is used mainly for pointto-point transmission with a sending power converter station and a receiving power converter station [2,3]. In recent years, multi-terminal high-voltage direct current (MT-HVDC) transmission systems have been proposed primarily for use in offshore wind farms along with the classical system [4]. It is identified that the transient stability of such a grid is of serious concern under large disturbances [5] and additional control (to provide adequate damping to HVDC grids) would be necessary [5] and voltage regulation has a crucial role in the control of MTHVDC grids [2]. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. IET Generation, Transmission & Distribution published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology Different strategies have been proposed to control and improve the stability of HVDC networks [6]. These strategies can be categorized into two types of conventional control methods and advanced intelligent control methods. In addition, in terms of stability oscillation, they can be classified into several categories of power/frequency oscillations, subsynchronous oscillations, and direct current (DC) oscillations [7–10]. Mathematical modelling and AC/DC interaction analysis of HVDC systems are studied in [11]. The model of a voltage source converter-based HVDC (VSC-HVDC) system is extracted in [12], and DC voltage control and power-sharing in an HVDC system based on droop control are proposed in [13]. The effect of DC breakers on the stability of the HVDC system is investigated in [14], but the system under study is VSC based, also the effect of the proposed stabilizer on the performance of the droop controller is not investigated. Also, the modelling of overhead transmission lines and cables in [14] 492 wileyonlinelibrary.com/iet-gtd IET Gener. Transm. Distrib. 2022;16:492–502. AZIZI ET AL.493 is based on the π-section model, which is less accurate than modelling based on the model frequency-dependent model (FD-π) model [15,16]. However, addressing the problem of oscillations in HVDC system needs more effort yet [14]and none of them has investigated a combination of droop control and power system stabilizer (PSS) applied to the DC side of modular multi-level converters—based HVDC (MMC-HVDC) stations. The proposed supplementary controller in [17] applied to the DC side of the VSC converter and its parameters tuned by particle swarm optimization (PSO) algorithm considering VSC-HVDC and πline modelling. In [17], the VSC average model is used for converter modelling and the π-section model is used for the line modelling. The main effort of control of DC voltage is to eliminate the imbalance of power in transient conditions and keep the voltage level within an acceptable limit. Therefore, this paper proposes an effective DC-voltage damping controller as direct current power system stabilizer (DC-PSS) to improve the overall system direct voltage/power stability in the presence of large reactors. This controller will have significant impacts on the grid stable operation under grid disturbances and leads to damping of low-frequency fluctuations. Also, to investigate the efficiency of the proposed method alongside the other controllers, several droop controllers are used in the understudy system. By utilizing the proposed controller, fluctuations of voltage and power in HVDC grids are suppressed. It occurs by injecting damping signals into the droop controller loop of the selected power converter stations in case of transient events. Besides, to achieve the proper performance of the DC-PSS, all parameters of DCPSS are optimally tuned at the same time by a mixed-integer non-linear optimization programming and solved by adaptive particle swarm optimization (APSO), which has higher accuracy and speed than the usual PSO algorithm. Besides these, the participation factor (PF) method is used to select the most appropriate location for the DC-PSS installation. Finally, the effects of DC-PSS are studied in small-signal modelling and frequency response analysis. The main differences between this article and [17] are listed as follows. The main purpose of [17] is to introduce a method for optimal location of the stabilizer in a VSC-based grid, which used π-model to transmission line modelling. But here, the FD-πmodel will be used for transmission line modelling. The authors in [17] have proposed a method to improve voltage oscillations that is installed on the DC side of the VSC-HVDC, however here DC-PSS will be used on the DC side of the MMC-HVDC. The proposed controller is compared with the controller based on conventional PI and droop, and the results of this comparison are discussed in detail. The PSO algorithm is used in [17] to optimize the parameters, but here, the APSO algorithm is employed to optimize the parameters. The main contributions of the current study are as follows: ∙introducing an effective direct voltage damping controller as DC-PSS applied to the DC side of MMC-HVDC stations, to deal with negative effects of large DC reactors on direct voltage and power and improve the overall MT-HVDC system direct voltage/power stability; FIGURE 1 Structure of V-P droop controller for an HVDC station FIGURE 2 The general structure of DC-PSS ∙employing direct voltage/power stability alongside the droop controller to make proper power-sharing while improving stability; ∙tuning of the parameters of DC-PSS by the APSO algorithm to eliminate direct voltage fluctuations considering MMCHVDC and FD-πline modelling; ∙selecting the appropriate location for the installation of DCPSS. The remaining sections of the paper are organized as follows. In Section 2, the proposed control strategy is presented and analysed. Section 3discusses the optimization approach. Smallsignal stability analysis is investigated in Section 4. Simulation results are reported in Section 5. 2PROPOSED CONTROL STRATEGY Because of the lack of inertia, the low-frequency oscillatory modes of HVDC grids are less damped out than those in AC power systems. This paper proposes a method, that during the transient conditions, DC voltages of the HVDC grid will be controlled by providing transient damping. In this method, V-P droop control is equipped with a supplementary signal to improve the stability of the HVDC grid which is supplied through DC-PSS. As in the AC power system, the PSS improves the dynamic performance of the power system by adding auxiliary signals to the excitation system [5], a DC-PSS as a damping controller in DC system, operates analogous to a PSS in an AC system and by injecting an additional signal, improves the stability of the HVDC grid. A general control structure of such a controller is presented in Figure 1The structure of the proposed DC-PSS is shown in Figure 2In this structure, the locally measured voltage is used as the input that indicates the power balance index in the HVDC grid. This stabilizer produces an 494 AZIZI ET AL. auxiliary damping signal in the output that is proportional to the input signal. Conventional PSS, as a lead-lag compensator is mainly designed based on using a linear model and considering one operating point [5]. As Figure 2shows, DC-PSS consists of four blocks: a lead compensator block (with T1>T2) to improve the speed response and reduce the transient oscillation peak, a lag block (with T3<T4) to improve steady-state response, a gain block to determine the amount of damping created by DC-PSS, and a washout block. The gain value kDC-PSS determines the amount of damping created by DC-PSS. Ideally, the interest rate is adjusted to a value corresponding to the maximum damping, however, its value is usually limited by other considerations. The washout filter block acts as a high-pass filter with a time constant TWthat allows signals corresponding to voltage fluctuations to pass unchanged. The wash filter only allows direct voltage fluctuations to be transmitted and filter the steady-state offset in the output, without allowing the damping controller to react to a dynamic exceeding a certain frequency threshold. The proposed stabilizer on the active power loop is fed by voltage deviations (ΔV). As is usually the PSS input signal in generator systems is speed deviation, the measured local DC voltage in the DC system, is the DC-PSS input. As a result, its output is proportional to the power oscillations. In the steady-state conditions, an onshore HVDC station equipped with the DC-PSS behaves similarly to a conventional converter with active power control mode. 3OPTIMIZATION APPROACH 3.1 Objective function Parameters of the proposed stabilizer are optimally tuned at the same time by the APSO algorithm. The objective function (1) defines the EDC parameter as an error criterion [18]. This objective function calculates the area under the voltage curve following oscillations and must be minimized. As shown by (1), actually this objective function calculates the error criterion for the sum of the buses from 1 to n. It means that EDC for each DC bus is the region in the plane that is bounded by the graph of DC voltage and proportional to oscillations of direct voltage. Therefore, by minimizing EDC the oscillations can be reduced. In (1), the main reason to include t(time) as the study time limit, in the integration criterion is that the fault severity is considered in the parameter optimization and the parameters can be optimized in such a way that the effect of DC-PSS to be greater in the initial moments of fault. In this equation, nrepresents the number of busses. Accordingly, the goal here is to minimize the EDC parameter as defined in the following: EDC = n ∑ b=1(t ∫ 0 t|||ΔV(t)DC (b)(t)|||dt ).(1) The advantage of this objective function is that minimal dynamic information is required to calculate EDC, and it is only necessary to measure the voltage deviation per bus instead of identifying the model parameters required for the DC-PSS design. However, the problem of optimization of the parameters requires special constraints that are all related to the limits of each of the values and should be taken into account. The objective function, (1), should be minimized considering the maximum and minimum of each parameter. The definition of the objective function in this way indicates that if there is no error or perturbation in the system, the value of this function is zero. 3.2 APSO algorithm An APSO algorithm is used to solve the optimization problem. The APSO algorithm has many advantages over the classic PSO algorithm. These advantages include a global search across the search space at a higher convergence rate [10]. Its details and the solution methodology are presented and discussed in [10]. Since updating the speed and position of each particle is determined based on the objective function, it is very important to select the appropriate objective function. The process of optimizing the parameters here is summarized in the following steps. Step 1. The population is initialized. At the current position, the mean distance of each particle to all the other particles is calculated. The globally best particle is defined as dg. All di’s are compared and determine the maximum and minimum distances dmax and dmin. Then, an ‘evolutionary factor’ fis calculated. Finally, fis classified into one of the several sets. Also, in each subpopulation, a specific set of motion coefficients (c1,c 2) are used, which for each subpopulation change adaptively during optimization. Finally, the most optimal solution that is produced is considered. Several particles are selected as a population using a random probability distribution function in a space with dimensions corresponding to the number of parameters. The weighting or inertia coefficient of the algorithm is adjusted proportionally to the number of iterations of the algorithm to result in an adaptive algorithm and find better answers. In addition, the properties of other algorithms such as genetic algorithms (GAs) are also used in the algorithm to obtain the modified algorithm. The balance between the global and local search capabilities in the PSO algorithm is shown by inertia weight ω, that it can be large in exploration mode and small in exploitation. However, reducing ωovertime is not necessarily correct. Therefore, (2) can be defined in such a way that the value of ω(f), according to the amplitude of changes f, relatively large in the exploration mode and relatively small in the convergence mode [10]. 𝜔(f)=1 1+1.5e−2.6f,∀f∈[0,1].(2) Consequently, ωadapts to the search environment characterized by f. This means that in exploration mode, large fand ωare in favour of global search, and when fis small, an exploitation AZIZI ET AL.495 FIGURE 3 Adaptive parameters control process or convergence mode is detected, and hence, ωis reduced to reduce local search. Figure 3shows the process of adaptive parameter control for step 1. The initial ωis 0.9. To pull each particle to the best position, the c1parameter is considered, and to push the norms to the faster convergence of the region, the c2parameter is considered. Also, gis in the best position in the neighbourhood. It is assumed that the initial of both of these values is 0.2. Step 2. In this step, after randomly selecting a particle and calculating the value of each parameter, the minimum and maximum limits for each parameter are checked, and then the EDC criterion is calculated. FIGURE 4 MMC model including its control structure Step 3. The position (parameter) of each particle compares with its previous value and the better particle is selected. Step 4. The evolution rate and the degree of adaptive aggregation are calculated and the speed and position information for each particle is updated. Step 5. The criterion stops according to the maximum number of repetitions of irritation or desired fitness, if the desired repetition time or fitness does not correspond to the stop criterion, goes to the previous step, otherwise, the calculated parameters are recorded as results. 4STABILITY ANALYSIS OF HVDC GRID WITH DC-PSS 4.1 MMC modelling Figure 4illustrates the arm switching function model of a modular multi-level converter (MMC), to utilize the state-space model of MMC. This model has the most applications in terms of accuracy and velocity of calculations and it is an appropriate model for transient analysis [19]. However, the detailed IGBT-based model of MMC, due to its very low computational speed and high accuracy is used only to investigate and estimate losses. Also, the averaged value model (AVM) MMC model is not used in transient DC studies, since it has an incorrect response to DC side faults [19]. In this type of modelling, considering the concept of a half-bridge converter switching performance, each MMC arm can be assumed average. The dynamics of such a system can be shown as follows. 4.1.1 Internal variables modelling of MMC variables The MMC control system shown in Figure 4consists of two PI control loops that are modelled by only the sum of the energies and the zero-sequence circulation current as of the internal variables of the MMC. The aggregate energy is controlled by a PI controller in an external control loop. This controller 496 AZIZI ET AL. provides zero-sequence circulating current reference as shown in (3), where, kpw,Σ and kiw,Σ are the gains of PI controller. i∗ c,z=kpw,Σ (w∗ Σ−wΣ)+kiw,ΣkΣ, d dt kΣ=w∗ Σ−wΣ. (3) The internal loop PI controller, controls the internal circulating current of the zero sequence, to form a corresponding reference voltage value v∗ c,zin (4). The kffdc as the coefficient of performance of the feedforward loop has a number between zero and one, if the controller has a feedforward loop, the value of kffdc is one and otherwise it is zero. v∗ c,z=−kpc,z(i∗ c,Σ −ic,z)−kic,z𝜉z+kffdcvDC , d dt 𝜉z=i∗ c,z−ic,z. (4) 4.1.2 AC side electrical modelling The current controller loops and phase-locked loop (PLL), relevant to the AC side of the MMC converter, can be modelled like the AC side modelling of VSC converters [19]. In the following equations, icv is the converter side current, iois the grid side current, and vois equivalent capacitor voltage. d dt icv =−⎛⎜⎜⎜⎝ (ra 2+rf)𝜔b La 2+Lf +j𝜔g𝜔b⎞⎟⎟⎟⎠ icv +Avcv −Avo,(5) A=𝜔b La 2+Lf ,(6) d dt vo=−j𝜔g𝜔bvo+𝜔b Cf icv −𝜔b Cf io,(7) d dt io=−(j𝜔g𝜔b+rg𝜔b Lg)io−𝜔b Cf vg+𝜔b Cf vo,(8) where, 𝜔gis the per-unit grid frequency and La,ra,Lf,rf,lg, rg,Cfare the resistances, capacitance, and inductances of the system. The AC side currents of the converter are controlled by decoupled PI controllers corresponding to the d and qaxes. The equations of these controllers are defined by (9–12). kffv vo−v∗ AD +kpc (i∗ cv −icv )+kic𝛾+jLf𝜔PLL icv,(9) d dt 𝛾=i∗ cv −icv,(10) v∗ AD =kAD (vo−𝜑 ),(11) FIGURE 5 PLL linear model d dt 𝜑=𝜔 AD (vo−𝜑 ).(12) The kffv as the coefficient of performance of the feedforward loop has a number between zero and one, if the controller has a feedforward loop of vo, the value of kffv is one and otherwise it is zero. Also, v∗ AD is used to eliminate LC oscillation. In (8), φis the state of a filter. 4.1.3 PLL structure Figure 5exposes the configuration of PLL, which consists of a PI controller. The linear equations of PLL are described in (13) and (14). d dt 𝜃PLL =kp,PLL vo,q+xPLL ,(13) d dt xPLL =vo,q.(14) 4.1.4 DC side electrical modelling State variables of DC side electrical modelling are shown by the next equations. d dt vDC =𝜔b Cdc (idc,s−4icz ),(15) d dt vDC ,f=𝜔 dc,f(vDC −vDC ,f),(16) where the crossover frequency of the low-pass filter is shown by 𝜔dc f . The control system is such that the AC power defined by (17)and(18) passes through the low-pass filter before being used in the power control loop as shown in (15)and(16). Pac =vo,dicv,d+vo,qicv,q,(17) d dt Pac,m=𝜔 pac (Pac +Pac,m).(18) The reference current i∗ cv,dis defined by PI controller of power and a DC voltage droop determines the AC power reference as it is expressed in (19)and(20). i∗ cv,d=kpp,ac (P∗ ac −Pac,m)+kip,ac 𝜌, d dt 𝜌=P∗ ac −Pac,m,(19) AZIZI ET AL.497 FIGURE 6 FD-πmodel of lines P∗ ac =kdroop (v∗ DC −vDC ,f)+Pre f ac .(20) According to the above equations, the matrix of state variables is expressed in (21) and the input matrix is expressed in (22). xj=[vod voq icv,dicv,q𝛾d𝛾qio,dio,q𝜑d𝜑qvDC vPLL ,dvPLL,qvDC ,f𝜌pac,mic,zkΣ𝜉zwz]T,(21) uj=[vre f DC Pre f ac i∗ cv,q|||vg|||idc,sw∗ Σ]T .(22) The equivalent state variables are described as shown in (21). The matrices related to ∆vDC(j) and ∆idc(j) are mined to enable the integration of the MMC model and the HVDC grid model [3]asisshownin(23)and(24). xj=Ajxj+Bdjxdj+[BjG Bj][Δidc(j) ΔP∗ j],(23) ΔvDC (j)=CjG xj.(24) 4.2 DC network model The conventional π-section model of a line accurately shows the cable behaviour only at a single point of the frequency domain. Instead, the frequency-dependent πmodel can be used to modelling the behaviour of cables in a specific frequency range. The FDπmodel consists of a lumped circuit with parallel R-L branches in each section of the πmodel of the line. The accuracy and validity of the FDπmodel are determined by the number of sections of the πmodel and the number of parallel branches in each section. In the π-section model, the number of sections improves hyperbolic factors, but does not necessarily lead to a good approximation of the actual behaviour of the cable because it does not allow the frequency dependence of the distributed parameters to be considered [15]. In order to the modelling of line based on FD-π, firstly the line is divided into n sections. The number of sections is determined by the length of the line and the frequency range to be interested. Then the number of parallel lines is considered and specified. Figure 6shows the line model based on FD-π[16]. The number of the parallel branch is showed by m. Then, the state-space model of the jth FIGURE 7 Closed-loop model of a typical HVDC grid with the proposed supplementary stabilizer line and the related DC breaking reactors: [x]=[Aline j][x]+[Bline j][u],(25) y=[cline j][x],(26) where the input is DC voltages at the two ends and the output is DC currents out of them as output: [x]=[V1V2…Vniin il1…il(n)io]T,(27) [Y]=[iin iout ]T,[u]=[Vin Vout ]T.(28) For an HVDC grid, the models of DC line (25)and(26)canbe unified to make the state-space model of the general DC grid with m separate line [14]. To obtain a proper input vector of the line model, Vtr is employed to convert the vector of the DC voltages of MMC terminal and for obtaining a direct current from the line model outputs, and Itr is employed to attain the direct current vector of the converter from the line model outputs, as exposed in (29)and(30)[3]. [VDC (1)⋯VDc(n)]T =V−1 tr [Vline(1) in Vline(1) out ⋯Vline(m) in Vline(m) out ]T , (29) [idc(1)⋯idc(n)]T=I−1 tr [iline(1) in iline(1) out ⋯iline(m) in iline(m) out ]T . (30) 4.3 Droop controller and DC-PSS modelling Figure 7shows a closed-loop model of a typical HVDC grid with a proposed supplementary stabilizer. As is shown in Figure 7for modelling a droop controller and supplementary stabilizer in converters equipped with this type of controller, it is sufficient to write the reference power according to the droop gain and in terms of DC voltage. 498 AZIZI ET AL. FIGURE 8 Cigré DCS3 test HVDC grids 4.4 MMC modelling alongside DC network modelling DC grid state-space model considering the MIMO plant model of the grid expressed as: xG=AGxG+BGΔVDC Δidc =CGxG.(31) By combing the investigative models of MMCs of all terminals and the HVDC network model, the state-space model can be shown in (31)[3]. Where xjis the state variable of the jth converter, BGj is the jth column of BG,andCGj is the jth row of CG, nis the entire number of the power converters, nGis the number of state variables of xG. 5SIMULATION RESULTS 5.1 Network under study and its modelling Cigré DCS3 test HVDC grid is selected for the investigation of the proposed control strategy [20]. It should be mentioned that the standard test network (Cigre DCS3) is only opted as an illustrative test case and the proposed strategy can also be easily applied to any other selected VSC-based HVDC grids. The main goal is to improve the direct voltage stability and decreasing power variations in the events of transients and this standard grid is selected to confirm the performance and eligibilities of our proposed control strategy. The rated power and voltage for each converter are 1000 MW and ±320 kV. Moreover, it is also assumed that the system has a symmetrical monopole topology. It should be noted that, in line modelling, the number of sections of each line and the number of parallel branches determine the modelling accuracy for each specific frequency range. So, here, it is assuming that number of sections to model a DC line is n=10 and the number of the parallel branch of each section is m=5[15]. See Figure 8illustrates the Cigré DCS3 test HVDC grids. In this study, the transmission lines are modelled by FD-π model [15]. FIGURE 9 The singular value plot of the closed-loop models with all the DC voltages and P1*(kdroop1 =0.3; Cb-B2: kdroop2 =0.42) 5.2 Optimal placement of DC-PSS The PF analysis is used to select the proper location for the DCPSS installation [20]. This method can also be applied to identify the suitable placement of droop control. The singular value technique is the corresponding frequency response in the system with multivariable control systems and offers perceptive evidence about gains among various output and input [21]. Moreover, the method of optimal placement is working to measure the gain among the reference of power related to a specific MMC terminal and direct voltages of all the terminals. A plot of singular value displays the gains amongst the output and that of the input vector in the frequency domain [21]. The suitable terminal for the installation of DC-PSS is a terminal with large single values in the specified frequency range. Figure 9shows the plot of the singular values of the power set-point of the selected terminals and output voltage vector for the closed-loop model with data from [22]. PF method investigation has been accepted for the selected optimal placement of PSS in each multi-machine system [23]. Among the five terminals of the system, two terminals equipped with the droop controller were selected as a candidate for DC-PSS installation. Table 1shows the calculated PFs equivalent to the low-frequency poorly damped modes for the two terminals with droop controller, concerning the voltage of the station. Cb-B1 is selected as the anticipated power converter station for the installation of DC-PSS, due to its significant participation in the most poorly damped mode. Corresponding to this method, the desired power converter station for the installation of DC-PSS is Cb-B1. AZIZI ET AL.499 TABLE 1 Participation factors for the two selected terminals Frequency (Hz) Eigenvalue Cb-B1 Cb-B2 1.96 −12.3 ±0.0132i 0.5679 0.3125 2.16 −13.4 ±0.0131i 0.9679 0.2102 30.7 −17.9 ±30.1i 0.3215 0.2618 35.9 −17.9 ±30.1i 0.2112 0.1894 TABLE 2 Optimal parameters of DC-PSS found by APSO Parameter Minimum Optimal value Maximum KDC 100 123.1 150 T10.01 0.0211 0.1 T20.01 0.01 0.1 T30.01 0.0012 0.1 T40.01 0.01 0.1 5.3 Optimization parameters of DC-PSS APSO algorithm is used to optimize DC-PSS parameters in HVD grid. The parameters T1,T2,T3,T4,andkDC-PSS are optimized by considering the grid stability and minimizing the EDC criterion in (1). Based on the analysis presented in Section 3.2, the proper values of the DC-PSS parameters were obtained from the APSO listed in Table 2 For robustness of the solutions, the obtained values of EDC by employing the calculated parameters of the GA and the APSO algorithm are compared following several faults. The results of this comparison are shown in Table 3As the table shows, the proposed APSO algorithm achieves a better response than the GA algorithm, it also has a faster response and fewer repetitions. 5.4 Dynamic stability analysis The bode plots of the transfer function between voltage reference vj*(s) and the local direct voltage vj(s), which can be straight mined from the MIMO model, without any damping method, with droop controller, and employing DC-PSS beside TABLE 3 Comparison of EDC calculated by the parameters obtained from two algorithm APSO GA EDC Rep. EDC Rep. Three-phase short circuit 0.091 83 0.098 100 Decreasing load 0.283 79 0.297 100 Increasing load 0.287 81 0.296 100 FIGURE 10 Root locus and bode plots of the vj(s)/vj*(s) transfer function with kdroop =0.3 from a single converter droop, are illustrated in Figure 10 This plot shows that the DCPSS and droop controller work at the resonant frequency, but it is clear that DC-PSS gives a higher bandwidth, which improves the transient response and reduces the amount of mutation. Besides, this figure shows that DC-PSS gives a higher phase margin at low frequency. Therefore, the designed compensator will provide more proper damping to the system. 5.5 Investigation of the proposed DC-PSS for the understudy network In this section, the proposed DC-PSS on the HVDC test system is examined. As mentioned before in this study Cigré DCS3 is selected and MATLAB/SIMULINK is used for the simulations. Responses of the DC voltage and DC power of VDC-Cb-A1, VDC-Cb-B2, VDC-Cb-B1 and PDC-Cb-A1, PDC-Cb-B2, PDCCb-B1 under 200 MW reducing of generation in wind farm 2 and during fault happening for 10 ms (3–3.01 s) in Cb-A1 bus with droop controller at Cb-B1 and Cb-B2 (kdroop =0.3, kdroop =0.2) following with and without DC-PSS is shown as follows. However, despite the DC-PSS on the Cb-B1 and the use of power fluctuations to reduce voltage fluctuations, the power of this bus increases slightly in the initial moments of the fault. 5.6 Reducing of generation Figure 11(a) shows that the presence of DC-PSS along with droop controller reduces the oscillation of voltage at the instant of generation decrease and increases the speed of getting the steady-state condition. Furthermore, Figure 11(b) illustrates that the damping of voltage fluctuations has led to a reduction of power oscillations and increases the speed of getting the steady state for power. 500 AZIZI ET AL. FIGURE 11 Frequency, DC voltage and DC power of Cb-A1, Cb-B2 and Cb-B1 following 200 MW reducing of generation in wind farm 2. (a) Frequency and direct voltage of Cb-A1, Cb-B2 and Cb-B1. (b) Power of Cb-A1, Cb-B2 and Cb-B1 5.7 Fault incidence at Cb-A1 Figure 12 shows VDC-Cb-A1, VDC-Cb-B2, and VDC-Cb-B1 profiles during fault occurrence for 10 ms (3–3.01 s) in Cb-A1 bus. The fault at Cb-A1, resulted in a 70% voltage drop. Since it is revealed from Figure 12 throughout the fault, the DC-PSS has been able to minimize the voltage peak and stabilize the bus FIGURE 12 The DC voltage of Cb-A1, Cb-B2, and Cb-B1 following a fault happening at Cb-A1 voltage faster and it means that the peak of voltage has been improved. Figure 12 confirms that without DC-PSS, the peak voltage may be large, so that it goes out of range and the protection system enters operation. In addition, this figure shows that under the same condition proposed, the method with DC-PSS after elimination of the fault has been able to bring back the value of the voltage to the previous value with a smaller peak and less oscillation. The comparison of the simulation results in Figure 12 shows the damping improvement by the proposed DCPSS. Figures 11(a) and (b) in addition to displaying voltage and power fluctuations, show that the damping signal does not affect the performance of the droop controller and does not prevent its proper operation. This means that, despite the washout filter, the injection signal is applied only at the period of disturbances. Figure 11(a) also shows that the use of DC-PSS has an effect on the frequency and DC-PSS can also improve frequency oscillations. Because in the weak systems, usually if the frequency drops reach below 0.98 pu (or 49 Hz in 50 Hz power systems) the load shedding will be activated. As can be seen from Figures 11(a) and (b) the proposed method not only reduces the oscillations but also does not enable load shedding. Additional signals from DC-PSS will reduce power fluctuations and cause a faster decrease in power fluctuations. Table 4shows the improvement of the damping by the results of the analytical study, if DC-PSS is on Cb-B1. The impact of DC-PSS in Cb-B1 on the oscillating frequency and the damping ratio ζof the closed-loop MIMO model for the poorly damped