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, 31270-901, Belo Horizonte, MG, Brazil 2
Department of Electrical Engineering - Federal University of Viçosa - Av. P. H. Rolfs, s/n, Campus Universitário, 36570-000, Viçosa, MG, Brazil
E-mails:
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[email protected] 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 1.
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 1
(1)
1 1 ∙ 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 syn-
chronous 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).
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-
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: ' !" ( !"
* ) " ∗
(5)
+ -
Figure 6. Cable Pi-Model Equivalent
This expression leads us to: ' ( . , .
Table 1. Cabling Electrical Parameters (XLPE 20/35kV)
(6)
where . 0. !1 , ( 0( !1& and 1⁄!2 . 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.
Size [& 6
0 7Ω ∙ 9: 6
1 7 ∙ 9: 6
2 7; ∙ 9: 6
185 95 70
0.130 0.248 0.344
384.62 424.41 445.63
196.10 158.71 143.90
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
