AGGREGATED INVERTERS WIND FARM HARMONIC PROPAGATION ANALYSIS

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1 Anais do XIX Congresso Brasileiro de Automática, CBA AGGREGATED INVERTERS WIND FARM HARMONIC PROPAGATION ANALYSIS CAIO M. PIMENTA1, HEVERTON A. PEREIRA1,2, SILAS Y. LIU1, GABRIEL A. MENDONÇA1, SELÊNIO R. SILVA1 1 Graduate Program in Electrical Engineering - Federal University of Minas Gerais - Av. Antônio Carlos 6627, , Belo Horizonte, MG, Brazil 2 Department of Electrical Engineering - Federal University of Viçosa - Av. P. H. Rolfs, s/n, Campus Universitário, , Viçosa, MG, Brazil s: pimenta@cpdee.ufmg.br, heverton.pereira@ufv.br, silasyl@gmail.com, gforti@gmail.com, selenios@dee.ufmg.br Abstract This work evaluates the harmonic propagation in systems with aggregated inverters, for grid integration studies applied to wind-power generation farms. Frequency-domain theoretical analysis and modeling is developed for the variable speed generation system elements (current-controlled inverters, filters, cables) and their impacts in the overall system resonance is verified. The key points of this work reflect the influence of the control strategy and the aggregation of several units of distributed generation in frequency response of the system. A real case study with resonance problems is shown and the results are analyzed. Keywords Wind Farm, Harmonic Analysis, Frequency Domain Simulation, Static Inverter Modeling and Control. Resumo Este artigo apresenta uma metodologia para a avaliação de propagação de harmônicos em sistemas com inversores agregados, focando em estudos de integração nas redes elétricas de sistemas de geração eólica. É desenvolvido um procedimento de modelamento dos componentes do sistema no domínio da frequência, incluindo elementos internos da tecnologia de sistemas de geração a velocidade variável (inversores controlados em corrente, filtros, cabeamento) e seus impactos sobre a ressonância global do sistema é verificada. Os pontos-chave deste trabalho incluem dois aspectos pouco considerados nestes estudos, a inclusão do efeito do controle e da agregação de unidades de geração na resposta em frequência do sistema. Um estudo de caso real com problemas de ressonância é mostrado e seus resultados são analisados. Palavras-chave Parque Eólico, Análise Harmônica, Simulação no Domínio da Frequência, Modelagem e Controle de Conversores Estáticos. 1 Introduction The adoption of non-conventional sources in electrical power systems is a fact that cannot be neglected in the expansion and operation of national energetic matrices. In particular, the crescent use of wind power generation increases the utilization of static power converters, which are known for injecting harmonic currents in the power grid, thus causing a change of operational scenery. There is also integration of passive filters in the system, which may cause resonances, mainly in low short-circuit ratio cases. The electrical grid equivalent impedance at the point of common coupling is a very important aspect for the performance of the system, due to the fact that the aggregation of a large number of active generation units with their respective passive filters may lead to unexpected situations and relevant operational consequences. In many countries, the regulating agents have changed the grid codes in order to comply with this new scenario and assure the correct behavior of the electric power systems. The existence of harmonic currents and voltages in electric power systems is due to presence of nonlinear loads in the system. The impact of these loads may be evaluated by the frequency dependency of system impedance [1]. Resonance occurrences in presence of harmonic current sources require precautions in the electric system operation. Series resonances may occur, for instance, due to the interaction between the distribution transformer impedance with the power factor correction capacitive filter impedance. The existence of harmonic voltages near this resonant frequency may lead to high currents in the transformer and in the capacitor, reducing their life time and causing possible trips in protection systems. Parallel resonances may cause elevated voltages due to the current in the mesh formed by the inductive and capacitive elements. This current may be low, but it is amplified by the circuit quality factor. Example of series and parallel resonant circuits are shown in Figure

2 Figure 1. Series and Parallel Resonant Circuits The interaction between source and loads can be modeled by Thévenin or Norton equivalents, shown in Figure 2. Figure 2. Source-Load Thévenin and Norton Equivalents Thévenin models are more adequate for evaluating harmonic propagation under a distorted voltage power grid, while Norton models are adequate for modeling non-linear loads that inject harmonic currents. The circuit analysis of these equivalents yields: (1) (2) From (1) and (2) it is possible to observe that the behavior of the electrical variables depend on or magnitudes in frequency domain [2]. In the context of variable-speed wind-power generation, we have two dominant electrical system topologies [3]. These are the permanent magnet synchronous generator (PMSG) with full-power back-toback static converter [4] and the doubly-fed induction generator (DFIG) with rotor-side reduced-power back-to-back converter [5], [6]. These topologies utilize an output high frequency filter, in order to attenuate the harmonic voltage and current injected by the converters. These filters may be L [7], LC or LCL [8] filters, for example. In comparison with traditional power sources, such as hydraulic or thermal, wind turbines are of low-power, thus requiring a large number of generators in order to achieve a high-power output for a generation centre. The aggregation of many units in parallel, each with its power inverter and output filter, may lead to resonance problems [9], [10]. The filters need to be dimensioned in order to achieve low levels of harmonic distortion for each single inverter module and the aggregated effect needs to be evaluated in the technical project of the installation. The objective of this paper is the modeling and analysis of harmonic propagation in the aggregation of units in wind farms. This problem is first addressed theoretically and then the analysis is made in a real case study. In this work it is analyzed a full back-to-back converter wind generator insomuch that the methodology can also be applied to photovoltaic (PV) centres and other systems that use aggregated inverters. This paper is organized as follows. Initially, the real system in the case study is described in section 2. The single converter system is theoretically analyzed in Section 3, showing the assumptions made for the modeling and control strategies. Then, in Section 4, the aggregated system model is derived from the single inverter system. The case study results are shown in Section 5 and the conclusions are made in Section 6. 2 Wind Farm System Description The wind farm considered for the case study is located in the northeastern region of Brazil and it consists of a nominal generation power of 42MW, with 28 generators [11]. These generators are connected in three parallel feeders, the first one having 10 ma-chines and the others 9 machines. All the machines are PMSGs with full-power back-to-back static converters for grid connection, thus allowing the wind turbines to operate at variable speed in order to maximize the energy yield. Furthermore, each generator has an LCL output filter in order to attenuate high-frequency voltages and currents caused by the PWM switching of the converter. This filter is composed of a series 0.15 inductor and a shunt 500 capacitor. The second inductive component of the filter is a transformer, which also raises the voltage of the converter (620V) to the sub-transmission level (34.5kV). 5181

3 Grid connection is done through a substation that raises the 34.5kV voltage to 69kV. The single line diagram of the wind farm, including cabling specifications and transformer reactances, is shown in Figure 3. The wind farm presents harmonic current and voltage levels over the grid code regulation limits when there are 19 or more generators connected. This fact confirms the need of a case study in order to diagnose the real causes of the problem. Figure 3. Wind Farm Single-Line Diagram 3 Single Inverter System Modeling and Control For simplicity purposes, as usual in balanced analysis of three-phase systems, the electric system will be represented by its single-phase equivalent. At this point, it will be also considered that the static converters do not produce harmonic currents, thus modeling them as ideal controlled voltage sources [12]. Later, on Section 4, it will be shown that it is not difficult to include this current injection onto the analysis. The design of the control architecture for the grid current of the LCL filter used a PR controller in this case, with an internal proportional gain loop for the control of the filter capacitor current. With this control strategy, it is possible to achieve zero error in amplitude and phase for the controlled variable, the grid current. The controlled model is shown in Figure 4. Figure 4. Single Inverter Single-Phase Model and Control Scheme The transfer functions of the controllers are expressed by equations (3) and (4) below. In order to achieve a simple notation, the gain, which rep- 5182

4 resents the equivalent gain of the system PWM modulator + inverter is made part of the gain. The parameter is the grid frequency. (3) (4) 4 Aggregated System Modeling Each inverter can be modeled as a current source in parallel with its output impedance. As mentioned on Section 3, this representation also allows harmonic current injection, if desired. The cables are modeled with their pi-model equivalent, shown on Figure 6. Table 1 shows R, L and C parameters for the cables. In order to analyze the harmonic propagation, the system equivalent output impedance is an important factor. This impedance is given by: This expression leads us to: (5) Figure 6. Cable Pi-Model Equivalent Table 1. Cabling Electrical Parameters (XLPE 20/35kV), where, and 1. Controller tuning is done analyzing the transfer function /. The gain primarily determines system stability, is responsible for damping the LCL filter resonant peak and is tuned with the system time response [8]. System response to a sinusoidal step is shown on Figure 5. Parameters used were 1, 100 and 250. (6) Size [ Ω In such manner, each of the three parallel groups of the wind farm is modeled as shown on Figure 7. Figure 7. Parallel Generation Group This system can be easily represented by a matrix, where the buses are each inverter output terminals [12]. Including the other groups and the power grid (represented by its Norton equivalent), it results in a system as shown in Figure 8. Figure 5. Single Inverter Sinusoidal Step System Response Figure 8. Full Wind Farm System Model The matrix can be expressed for each harmonic order, thus yielding a matrix. Inverting it 5183

5 leads us to the matrix, whose diagonal terms express the driving point impedance in each bus. 5 Results and Analysis System simulation is done in three different cases: a. Only the first generating group (10 inverters) is connected, b. Both first and second groups are connected (19 inverters total), and c. All groups are connected (28 inverters total). As described in Section 2, the harmonic current and voltage levels are over the limits in cases (b) and (c) for the real wind farm. This implies that those are the most critical cases. The variation of impedance versus frequency in some buses of the system will be shown. A first result will show the impedance at the point of common coupling (PCC) and at the first generator of each group. The other figures will show the impedance at three buses of each generating group: the first, fifth and last ones. As the second and third groups are identical, only one plot is shown. We can see that the impedance does not vary much from bus to bus. It is possible to identify several series and parallel resonances in these plots. Strong series resonance occurs near the 22 nd harmonic and strong parallel resonances occur near the 9 th and 24 th harmonics. 5.2 Case (b) 19 inverters The results are shown in Figure Case (a) 10 inverters The results are shown in Figure 9. Figure 9. Case (a) Impedance Results Figure 10. Case (b) Impedance Results In this case, we can see that the impedance seen by each bus is increased as we go farther away from the PCC. Once again, several series and parallel resonances occur. For the impedance seen from the PCC, strong series resonance occurs near the 21 st, 36 th and 38 th 5184

6 harmonics and parallel resonances occur near the 23 rd and 37 th harmonics. In the inverter bus, series resonance occurs near the 22 nd and 24 th harmonics and parallel resonances occur near 21 st, 23 rd and 37 th. The incidence of series resonance of the impedance seen from the PCC near the point where parallel resonance occurs from the inverter bus is a critical problem for the system, because we have two phenomena that contribute to increasing harmonic current and voltage levels. At the same time that any grid voltage distortion around that harmonic will cause a high harmonic current level, harmonic current injection by the inverters will also cause high harmonic voltage levels. 5.3 Case (c) 28 inverters The results are shown in Figure 11. In this case we see similar results to case (b). Once again the impedance is increased as we go farther away from the PCC and once again we have several series and parallel resonances. The critical problem explained in section 5.2 is also present. From the PCC, the resonances occur at the same harmonics as the previous case. For the inverter buses of the 1 st group, series resonance occurs between the 22 nd and 23 rd harmonics and parallel resonance occurs near the 21 st and 37 th harmonics. Finally, for the bus of the 2 nd group, series resonance occurs between the 22 nd and 23 rd harmonics and near the 37 th harmonic and parallel resonance occurs near the 21 st, 36 th and 38 th harmonics. 6 Conclusions The main results of this study confirm the importance of preliminary studies on the grid integration of a wind farm or other aggregated installations. These studies should reflect the main features of the facility and the electric power system in the frequency domain. In order to analyze the harmonic propagation, system elements such as inverters, filters, cables and transformers were modeled in the frequency-domain. Inverter control topology was also included and modeled, as it affects the inverter output impedance. Case study results showed that increasing the number of aggregated inverters reflects directly in the impedance seen from each bus of the system, changing the resonant frequencies of the system. Future works comprise the use of three-phase models, the analysis of different generation topologies (such as the DFIG), and the re-tuning of inverter control in order to attenuate resonances. Acknowledgements This work has been supported by the Brazilian agencies CNPq, FAPEMIG and CAPES. References Figure 11. Case (c) Impedance Results 1. IEEE. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis. [S.l.] Cespedes, M.; Sun, J. Renewable Energy Systems Instability Involving Grid-Parallel Inverters. Applied Power Electronics Conference and Exposition, Yazdani, A.; Iravani, R. Voltage-Sourced Converters in Power Systems: Modeling, control, and applications. [S.l.]: WILEY and IEEE PRESS,

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