Low‐frequency oscillation analysis of AC/DC system with offshore wind farm integration via MMC‐based HVDC
2018; Institution of Engineering and Technology; Volume: 2019; Issue: 16 Linguagem: Inglês
10.1049/joe.2018.8534
ISSN2051-3305
AutoresZhongrui Nie, Libao Shi, Yue Zhao, Yixin Ni,
Tópico(s)Superconducting Materials and Applications
ResumoThe Journal of EngineeringVolume 2019, Issue 16 p. 1450-1456 Session – Report Session AOpen Access Low-frequency oscillation analysis of AC/DC system with offshore wind farm integration via MMC-based HVDC Zhongrui Nie, Zhongrui Nie National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorLibao Shi, Corresponding Author Libao Shi shilb@sz.tsinghua.edu.cn National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorYue Zhao, Yue Zhao National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorYixin Ni, Yixin Ni National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this author Zhongrui Nie, Zhongrui Nie National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorLibao Shi, Corresponding Author Libao Shi shilb@sz.tsinghua.edu.cn National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorYue Zhao, Yue Zhao National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this authorYixin Ni, Yixin Ni National Key Laboratory of Power Systems in Shenzhen (Graduate School at Shenzhen, Tsinghua University), Shenzhen, People's Republic of ChinaSearch for more papers by this author First published: 06 December 2018 https://doi.org/10.1049/joe.2018.8534Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In recent years, the low-frequency oscillation (LFO) problem has become increasingly significant with rapid increase in the size of AC/DC interconnected power system containing large-scale wind power. This article aims to conduct the LFO analysis when an offshore wind farm is integrated into the AC power system through module multilevel converter (MMC)-based high-voltage direct current (HVDC). First, the basic mathematical models including the MMC with detailed control strategy and the permanent magnet synchronous generator (PMSG) are described. The eigenvalue analysis is then applied to conduct the LFO study. An interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line is designed as benchmark. To validate the analysis results, the detailed simulation models built under the PSCAD/EMTDCTM environment together with the Prony analysis are carried out. Different simulation scenarios involving the changes of point of common coupling (PCC), wind speed, length of transmission line, and wind penetration level are elaborately studied. Some meaningful conclusions are drawn to provide basic foundation for the future design of damping controller to mitigate LFO. 1 Introduction In recent years, the environment problem has given rise to significant influences on the production and life. Accordingly, the whole world intends to search for the clean and renewable energy resources to implement sustainable development [1]. Currently, all countries are vigorously promoting the development of the renewable energy resources; especially, the wind energy stands out from the crowd due to its inexhaustible, non-polluting, mature, and low-carbon characteristics [2]. In the past few years, offshore wind energy has seen a tremendous growth, and the trend seems to continue. It is known that the permanent magnet synchronous generator (PMSG) is always applied in offshore wind farm for its distinct advantages, such as higher energy yield, higher active/reactive power controllability, low level of acoustic noise, low mechanical stress, and so on [3, 4]. However, the wind farm tends to experience poor stability with voltage oscillation and harmonic resonance during the long-distance wind power transmission. It has been widely accepted that the high-voltage DC (HVDC) transmission technology with voltage source converter (VSC) can be a feasible method for its independent control on real and reactive powers as well as interconnection capability to weak or passive AC network [5]. Nevertheless, the modular multilevel converter (MMC)-based HVDC technique possesses the most well-proven advanced features, such as higher waveform quality, no need for harmonic filters, low switching frequency, and so on. In power system analysis, the small signal stability problem is closely relevant to inadequate damping issue. Meanwhile, the corresponding oscillation also appears. Basically, the oscillation within a frequency between 0.1 and 2.5 Hz is called low-frequency oscillation (LFO), and it can be classified as local modes (0.7–2.5 Hz) and inter-area modes (0.1–0.7 Hz). The local modes reflect the swinging between a generator and a set of generators to the rest of the grid. Inter-area modes are associated with the swinging of many machines in one part of the system against machines in other parts [1]. Once the LFO occurs, it will continue for a long time till it disappears, or continue to result in series of accidents, which will threaten the security and stability of grid [6]. Currently, increasing system damping is the fundamental method to suppress LFO. The HVDC transmission system, flexible alternating current transmission systems (FACTS), power system stabiliser (PSS), thyristor controlled series compensation device (TCSC), and other devices have certain effects on the suppression against LFO. Many researches have been conducted with the control of wind turbines in power system dynamics. A suitable power converter topology and controller for a wind energy conversion system (WECS) with PMSG to serve an isolated load is proposed in [7]. Guo et al. [8] come up with an enhanced voltage control strategy based on model predictive control (MPC) for VSC-HVDC connected offshore wind farms. An enhanced AC voltage and frequency control strategy of the offshore MMC for wind farm integration where an additional frequency loop is used to improve its AC voltage and frequency controllability [9]. In addition, many articles aim to solve the LFO problem with varying degrees of success. The impacts of doubly-fed induction generator (DFIG) location on LFO are studied via eigenvalue analysis and dynamic sensitivity analysis [1]. In [10], a small-signal model of a static synchronous compensator (STATCOM) is presented in a small single machine infinite bus system (SMIB). Liu et al. [11] adopt an improved implicitly restarted Arnoldi (IRA) algorithm in critical eigenvalues searching to avoid eigenvalues missing. In this paper, the LFO analysis of AC/DC system with offshore wind farm integration via MMC-based HVDC is studied elaborately. The detailed models of MMC and PMSG are thoroughly introduced first. Then, based on a modified four-generator two-area hybrid AC/DC test system, the simulations are carried out based on the eigenvalue analysis. Moreover, the PSCAD/EMTDCTM simulation tool combined with the Prony analysis is applied to get the more accurate results. Some useful conclusions and comments are drawn. 2 System modelling 2.1 MMC modelling 2.1.1 MMC topology Nowadays, most of the research concerning MMC adopts the classical half-bridge model [5, 9, 12, 13]. Fig. 1 shows the main circuit topology of three-phase MMC, which is composed of upper and lower arms. Each arm is made up of several sub-modules (SMs) in series, the arm resistance, and arm inductance. All SMs share the same structure as shown in Fig. 2, formed by one capacitor, two IGBTs, and two diodes in inverse parallel. Once taking critical fault and stability into account, the bypass switch and thyristor should be installed in the output port of each SM, building a saver operating environment. Fig. 1Open in figure viewerPowerPoint Main circuit topology of half-bridge MMC Fig. 2Open in figure viewerPowerPoint Structure diagram of half-bridge SM There are three operating states of SM, that is running state, block state, and cutting off state. Fig. 2 shows the first state of SM, which indicates that the shunt capacitors have come into use. At this time, T 1 is on and T 2 is off, then the circuital current will flow through capacitor C by T 1 and D 1. Fig. 3 shows the other two operating states. In Fig. 3 a, T 1 and T 2 remain off, which only happen in fault or state of charge. T 1 becomes off and T 2 becomes on in Fig. 3 b, when the current will not pass through the capacitor C. Fig. 3Open in figure viewerPowerPoint Diagram of operating state of SM (a) Block state, (b) Cutting off state Thus, the output voltage of SM can be controlled by the trigger pulses of two IGBTs, and then the output voltage of MMC will be in control by adjusting the number of insertions of SMs. Also, the number should guarantee that the total voltage of the two converter arms in each phase unit is equal to the DC voltage. 2.1.2 MMC mathematical model and control strategy As shown in Fig. 1, the supply voltage in AC side is u sk (k = a, b, c); the supply current is i sk (k = a, b, c); the resistance and inductance in AC side are RS and LS, respectively; uk (k = a, b, c) is the output voltage of AC side; and the arm currents in the k phase are i pk and i nk (k = a, b, c). U dc and i dc denote the DC side voltage and current. At AC output point, the supply current can be expressed as follows: (1) According to the Kirchhoff voltage law (KVL), the output voltage of AC side can be obtained: (2) (3) Combining (2) and (3), then: (4) where vk can be expressed as follows: (5) In the power supply side, we have the following equation: (6) Then substituting (6) into (4): (7) In (7), Ld can be expressed as follows: (8) For three phase units that meet the strict symmetry, including the same parameters of R and L, there is equal distribution among three phase units, and then the AC current will be distributed equally as well. Accordingly, the upper and lower arm currents can be obtained: (9) (10) In d–q reference frame, (7) can be transformed into the following equations: (11) (12) where ud, uq, id, iq are AC voltage and current in the d−q reference frame. is the angular speed in the AC side. Generally, there are three-level control mode, that is system level, converter level, and trigger level. In system level, the control signal, such as reference of active or reactive power, is passed down from superior instruction. In converter level, the control signal will be transformed to the trigger signal to control the switching devices. At last, the trigger signal will be applied to the specific IGBTs in trigger level. The converter-level control is the main control segment, which consists of constant DC voltage control, constant AC voltage control, constant active power, and constant reactive power. In this paper, the constant DC voltage control is applied during analysis. According to (11) and (12), we have the following equations: (13) (14) Then, the structure diagrams of inner current loop and outer voltage loop can be seen in Figs. 4 and 5. Fig. 4Open in figure viewerPowerPoint Structure diagram of inner current loop Fig. 5Open in figure viewerPowerPoint Structure diagram of outer voltage loop 2.2 PMSG modelling Fig. 6 shows the WECS equipped with PMSG. In renewable energy application, the PMSG is very popular because of its high conversion efficiency with specific structure (no need for brush gear or a gear box) [14, 15]. The mechanical power created by the wind turbine is as follows: (15) where Cp is the power coefficient, and λ is the tip speed ratio. β is the blade pitch angle. vw is the wind speed. Fig. 6Open in figure viewerPowerPoint Diagram of PMSG In d–q reference system, PMSG is generally modelled as follows: (16) (17) where V sd and V sq are d -axis and q -axis stator terminal voltages, respectively. i sd and i sq are the currents in the d–q reference frame. is the electrical rotating speed. and are the flux linkages which can be obtained: (18) (19) where is the flux linkage of the generator. Ld and Lq are the inductances in d–q reference frame. The control of wind turbine can be divided into rotary speed control at low wind speed and pitch angle control. When the wind speed is relatively low, the control block diagram is shown in Fig. 7, where P s is the stator power, and w ref is the reference of wind speed; w r is the rotor speed; and kp and ki are the parameters in proportional integral (PI) control. Based on the deviation between actual wind speed and optimal wind speed, the reference of stator power can be obtained via PI control, and then the maximum power can be achieved through the set of tip speed ratio. Fig. 7Open in figure viewerPowerPoint Control block diagram of rotary speed control In pitch angle control, the deviations of wind speed and stator power are the main control elements. As we can see in Fig. 8, once the actual wind speed or actual stator power increases, β will increase accordingly, resulting in the reduction of wind power. Fig. 8Open in figure viewerPowerPoint Control block diagram of pitch angle control 3 Solution methodology 3.1 Eigenvalue analysis In the small signal stability analysis, the eigenvalue analysis is the most common method, which can get the effective information from the eigenvalues directly [16, 17]. Normally, the linearisation of a power system model can be given as follows: (20) where x is the state vector. A is state matrix whose dimension depends on the number of state variables. In terms of eigenvalue λi, left eigenvector v i, and right eigenvector u i, the state vector can be expressed as follows: (21) Furthermore, the output of the system can be expressed as follows: (22) where C is the output matrix. According to the characteristic of n -order power system, there are always (n − 1) pairs of complex eigenvalues, which denote the electromechanical oscillation modes. Moreover, the participation factor can indicate the position the PSS should be installed, and it can be obtained by u i and v i as described in the following equation: (23) where PF ij means the participation factor of state variable j to the i th mode. 3.2 Prony analysis Prony analysis is a technique which can estimate the specific amplitude Ai, damping , frequency fi, and phase angle according to the sampling value. Thus an approximating signal by finite sum of damped sinusoids can be obtained to fit the output curve described in (22) using the following form: (24) where n is the number of sinusoids. Hence, the i th eigenvalue can be expressed as follows: (25) Prony analysis has been widely applied in LFO field, and it is regarded as a kind of standard method somehow. The biggest advantage of Prony analysis lies in the capacity to analyse simulation results as well as real-time measurement data. Even if the system model is unknown, the reduced-order transfer function can be obtained. 4 Case study 4.1 Simulation system An interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line is established under the PSCAD/EMTDCTM environment. As shown in Fig. 9, the AC part is the classical four-generator two-area system [18]. The system consists of two homogeneous areas (Area 1 and Area 2) connected by double-circuit weak tie line. Area 1 is formed by two 900 MW synchronous generators and one wind farm, while Area 2 is formed only by two 900 MW synchronous generators. The excitation system and governor are taken into account in modelling generator without PSS. The parameters of generator and transmission line are listed in Tables 1 and 2. Fig. 9Open in figure viewerPowerPoint AC/DC test system with wind farm of PMSG type integration Table 1. Parameters of synchronous generator model Symbol Value Symbol Value Xd 1.8 X ″d 0.25 Xq 1.7 X″q 0.25 Xl 0.2 Ra 0.0025 X ′d 0.3 T ′d0 8.0 s X′q 0.55 T ′q0 0.4 s T″d 0 0.03 s H (G 1, G 2) 6.5 T″q 0 0.05 s H (G 3, G 4) 6.175 A sat 0.015 KD 0 B sat 9.6 ΨT 1 0.9 S base 900 MVA U base 20 kV Table 2. Parameters of transmission line Symbol Value r 0.0001 pu/km XL 0.001 pu/km bc 0.00175 pu/km S base 100 MVA U base 230 kV 4.2 Eigenvalue analysis results Taking the aforementioned test system as benchmark, the corresponding eigenvalue analysis is carried out under MATLABTM simulation platform. Generator 3 is regarded as slack machine, and the second-order classical model is adopted during analysis. Generators 1, 2, and 4 adopt the fourth-order model with third-order excitation system model. Here, the wind turbine is treated as negative load. By integrating wind power at BUS 6, the eigenvalue can be solved as follows (Table 3): Table 3. Eigenvalue results Mode Real Imaginary Frequency Damping ratio 1 0.1677 8.0930 1.2880 0.021 2 0.1206 7.8711 1.2527 0.015 3 2.1293 2.6015 0.4140 0.633 The results of eigenvalue analysis are just for the reference of the detailed simulation to be conducted in PSCAD/EMTDCTM due to the simplification. 4.3 Prony analysis results In our work, the detailed simulations are carried out in PSCAD/EMTDCTM environment with different wind speed, wind penetration level, length of transmission line, and point of common coupling (PCC). By comparing the Prony analysis results in different scenarios, the corresponding impacts on LFO can be learnt. Under the normal operation condition, the wind speed is set to be 15 m/s, the installed capacity of wind farm is 120 MW, the length of transmission line is 50 km, and the PCC is located at BUS 6. In order to facilitate the LFO waveform, a three-phase-to-ground fault is set at tie line from 10 to 10.1 s. The responses for the Prony analysis are recorded during 10.5–20 s. 4.3.1 Impacts of wind speed To study the impacts of wind speed on LFO, four kinds of wind speeds are tested, which are 5, 10, 15, and 20 m/s, respectively. Taking the power flow results pertinent to BUS 1 at 15 m/s wind speed for instance, the waveforms simulated in PSCAD/EMTDCTM environment are shown in Fig. 10. Then, the Prony analysis can be conducted based on a Prony analysis tool which can be seen in Fig. 11. By fitting the raw data, the amplitude, frequency, and damping can be obtained. Fig. 10Open in figure viewerPowerPoint Waveforms of the power flow results at BUS 1 Fig. 11Open in figure viewerPowerPoint Results using Prony analysis tool The waveforms of four cases corresponding to different wind speeds are given in Fig. 12. It can be seen that the curves are exactly similar. With the wind speed increasing, the real power presents a trend to reduce, that is because the total real power needs to remain the same, the increase of wind power means the decrease of thermal power output. Fig. 12Open in figure viewerPowerPoint Waveforms of real powers under different wind speeds The analysis results are given in Table 4. It can be seen that when the wind speed is 5 m/s, the local modes are 0.95 and 0.99 Hz, and the inter-area mode is 0.49 Hz. Along with the increase of wind speed, the frequencies of both local mode and inter-area mode will decrease. The damping ratio is of little change in local mode, but the high wind speed will cause small increase in inter-area mode. Table 4. LFO modes in the different wind speeds Case Wind speed, m/s Frequency f, Hz Damping σ Damping ratio ζ 1 5 0.49 0.071 0.0231 0.95 0.59 0.0984 0.99 0.61 0.0976 2 10 0.47 0.083 0.0281 0.94 0.60 0.1011 0.97 0.62 0.1012 3 15 0.45 0.088 0.0311 0.93 0.55 0.0937 0.96 0.61 0.1006 4 20 0.43 0.094 0.0348 0.91 0.61 0.1061 0.95 0.56 0.0934 4.3.2 Impacts of transmission line length The main transmission line lies between MMC and DC/DC converter. The parameters of DC transmission are given as follows: r = 0.0121 Ω/km, l = 0.1056 mH/km, c = 0.2961 μF/km. The initial value of resistance is set to be 0.6 Ω, which represents the length of 50 km. To study the impacts of transmission line length on LFO, the lengths of 5, 50, and 500 km are applied, respectively, for comparisons. The results of Prony analysis are given in Table 5, and the corresponding waveforms of real powers are shown in Fig. 13. Table 5. LFO modes in different lengths of transmission lines Case Length, km Frequency f, Hz Damping σ Damping ratio ζ 1 5 0.43 0.11 0.0407 0.91 0.56 0.0975 0.94 0.63 0.1061 2 50 0.43 0.11 0.0407 0.91 0.56 0.0975 0.94 0.63 0.1061 3 500 0.44 0.091 0.0329 0.92 0.58 0.0998 0.95 0.61 0.1017 Fig. 13Open in figure viewerPowerPoint Waveforms of real power under different lengths of transmission lines It can be seen that the real power value under 500 km length is higher than that of values under 50 and 5 km obviously, while no visible difference can be seen between 5 and 50 km. That is because the line impedance is relatively small both in 5 and 50 km, the impacts cannot be noticed easily. Moreover, the damping ratio of inter-area mode under 500 km is lower. Here, the longer transmission line means more power losses, thus decreasing the actual wind power integrated into the system will lead to the depression on damping of inter-area mode. In a word, the impacts of transmission line length depend on the power loss caused by the line impedance, and then oscillating characteristic will change under the new power flow operating condition. Table 6. LFO modes in different wind penetration levels Case Penetration, MW Frequency f, Hz Damping σ Damping ratio ζ 1 0 0.49 0.075 0.0244 0.96 0.57 0.0941 0.99 0.61 0.0976 2 30 0.48 0.079 0.0262 0.95 0.59 0.0984 0.98 0.61 0.0986 3 60 0.46 0.084 0.0291 0.94 0.61 0.1027 0.97 0.61 0.0996 4 120 0.44 0.11 0.0398 0.91 0.60 0.1044 0.95 0.62 0.1033 5 240 0.38 0.13 0.0544 0.88 0.67 0.1203 0.90 0.57 0.1003 4.3.3 Impacts of wind penetration level To study the impacts of wind penetration level on LFO, the following different penetration levels including 0, 30, 60, 120, and 240 MW are selected during simulations. The corresponding results are listed in Table 6. With the increase of wind penetration level, the frequencies of both local and inter-area modes decrease. The damping ratio of local mode is of little change, while the damping ratio of inter-area mode increases along with the penetration level. Taking BUS 1 for example, the waveforms of real powers are shown in Fig. 14. Fig. 14Open in figure viewerPowerPoint Waveforms of real powers under different wind penetration levels Apparently, the higher the wind power penetration level, the lower the outputs of thermal power located at BUS 1. It is worth noting that when the wind power outputs reach 240 MW, the power fluctuation becomes severer, which indicates that the wind power has a negative effect on local mode. 4.3.4 Impacts of PCC The different PCCs (BUS 6, BUS 8, and BUS 10) for the wind farm integration are selected to study the impacts on LFO. The corresponding simulation results are given in Table 7. Table 7. LFO modes in different point of common coupling Case PCC Frequency f, Hz Damping σ Damping ratio ζ 1 BUS 6 0.44 0.11 0.0398 0.91 0.60 0.1044 0.95 0.62 0.1033 2 BUS 8 0.48 0.09 0.0298 0.93 0.59 0.1005 0.97 0.62 0.1012 3 BUS 10 0.49 0.086 0.0279 0.94 0.55 0.0927 0.97 0.61 0.0996 From Table 7, the differences can be observed including aspects in frequency and damping ratio. Actually, the selection of PCC has indeed certain impact on the LFO mode. However, the specific conclusions cannot be drawn easily because of masses of objective factors, such as system structure, generator operation mode, power distribution in different areas, and so on. For example, the wind farm integrated at BUS 8 will influence the power flow in the inter-area, which is shown in Fig. 15. It can be seen that there is an obvious increase for the power flow when the wind farm is integrated into power system at BUS 8. Fig. 15Open in figure viewerPowerPoint Waveforms of the power flow results at BUS 8 5 Conclusion In this paper, the eigenvalue and Prony analysis methods are applied to study the LFO problem in an interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line. Some different simulation scenarios including the changes of wind speed, length of transmission line, wind penetration level, and PCC are studied elaborately, and the corresponding comparative analysis is given as well. It can be concluded from the simulation results that the higher wind speed or shorter transmission line length will result in the increase in wind power output that will cause higher damping ratio under the inter-area mode with no obvious influence on the local mode. The impacts of PCC vary with different wind farm connection buses. 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