Energy efficient control of a stand-alone wind energy conversion system with AC current harmonics compensation

Control Engineering Practice 93 (2019) 104185

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Energy efficient control of a stand-alone wind energy conversion system with AC current harmonics compensation Mateo Bašić ∗, Dinko Vukadinović, Ivan Grgić, Matija Bubalo Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia

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Keywords: Fuzzy control Hysteresis control Induction generator Maximum power point Total harmonic distortion Wind turbine

ABSTRACT This paper presents a new energy-efficient control strategy for a variable-speed wind energy conversion system (WECS). The considered WECS is designed for dc load supply and battery charging in stand-alone applications. The batteries are charged through a three-phase full-bridge power converter. The WECS contains a vectorcontrolled self-excited induction generator (SEIG) coupled to a wind turbine (WT) for electric power generation on the ac side. The control algorithm proposed in this paper includes three separate optimizations: two fuzzylogic-based optimizations, which ensure that maximum energy is extracted from both the WT and the SEIG, respectively, at all operating conditions, and also the optimization of phase current harmonics through adaptive hysteresis control. In addition, a recently developed algorithm for real-time loss calculation of a hysteresisdriven power converter is utilized to quantitatively assess the power converter losses with respect to different hysteresis bandwidth settings. The performance of the proposed control algorithm is experimentally evaluated and compared with two competing algorithms which do not involve current harmonics compensation, whereas one of them also does not involve optimization of the SEIG output power. This enables evaluation of the gain in system performance due to the introduced optimizations. The evaluation and comparison are made over a wide range of wind speeds, both in steady state and under transient conditions, by using a 1.5 kW experimental setup with the DS1103 controller board (dSPACE).

1. Introduction In the last decades, wind energy conversion systems (WECSs) have emerged as one of the most promising and fastest growing renewable energy alternatives to conventional power generation systems. There are currently over 540 GW of cumulative wind power capacity installed worldwide (as compared to 24 GW in 2001), with an average annual increase of over 50 GW during the last few years. In remote, isolated locations, where connection to a main grid is not viable, small-scale WECSs comprising a self-excited induction generator (SEIG) represent an attractive low-cost solution. This type of generator has many favorable features such as simple and rugged construction, low maintenance, small size and lower cost compared to permanent-magnet synchronous generators (PMSGs). On the down side, it requires external capacitors for excitation and is less efficient than a PMSG of the same rating. In addition, both the amplitude and frequency of the SEIG’s terminal voltage vary with the rotor speed and load, so a power electronics interface to the main grid or to an autonomous load is usually required to control the energy flow in the system. Rotor speed variations are especially pronounced in SEIGs driven by a wind turbine (WT) due to the stochastic nature of wind power. For the same reason, standalone WECSs need to have an energy storage system in order to

ensure continuous power supply. A comprehensive review of energy storage technologies for WECSs is provided in Díaz-González, Sumper, Gomis-Bellmunt, and Villafáfila-Robles (2012). In small-scale WECSs, price and efficiency are crucial, so every effort to improve the overall efficiency is extremely valuable for their cost-effectiveness. Variable-speed WECSs provide the possibility of extracting maximum WT power at different wind speeds by controlling the shaft speed accordingly. This feature makes them more attractive for small-power applications than fixed-speed counterparts. The shaft speed optimization is usually achieved through application of a maximum power point tracking (MPPT) algorithm. Three most common MPPT strategies can be identified as follows: MPPT algorithms based on optimal tip speed ratio (TSR) (Abo-Khalil, 2011; Chen, Hong, & Cheng, 2012; Goel, Singh, Murthy, & Kishore, 2011; Hong, Cheng, & Chen, 2014; Lin, Hong, & Cheng, 2011), those based on power signal feedback (PSF) (Barakati, Kazerani, & Aplevich, 2009; Sowmmiya & Uma, 2017), and perturb and observe (P&O) MPPTs (Ghaffari, Krstić, & Seshagiri, 2014; Mesemanolis, Mademlis, & Kioskeridis, 2012; Nayanar, Kumaresan, & Gounden, 2016; Simoes, Bose, & Spiegel, 1997). Some of these involve application of fuzzy logic or neural networks (Chen et al., 2012; Mesemanolis et al., 2012; Simoes et al., 1997). TSR-based

∗ Corresponding author. E-mail addresses: [email protected] (M. Bašić), [email protected] (D. Vukadinović), [email protected] (I. Grgić), [email protected] (M. Bubalo).

https://doi.org/10.1016/j.conengprac.2019.104185 Received 22 November 2018; Received in revised form 3 October 2019; Accepted 5 October 2019 Available online xxxx 0967-0661/© 2019 Elsevier Ltd. All rights reserved.

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phase currents, as discussed later. In addition, the algorithm for realtime calculation of losses of a hysteresis-controlled power converter, reported in Bašić, Vukadinović, and Grgić (2018), is implemented in order to quantify the impact that different hysteresis bandwidth settings have on these losses. It has to be noted that most existing semiconductor loss estimation methods are inherently inadequate for aperiodic switching schemes – such is the HCC – because they assume a fixed switching frequency (Berringer, Marvin, & Perruchoud, 1995; Bierhoff & Fuchs, 2004; Consoli et al., 1994; Kutkut, Divan, Novotny, & Marion, 1998). Some other methods have the potential for extension to aperiodic switching, but have only been tested for periodic switching (Kimball, 2005; Kouro, Perez, Robles, & Rodriguez, 2008; Xu et al., 2002), whereas the implementation of the method proposed in (Li, Yang, Wang, Agelidis, & Zhang, 2017) is sensitive to initial conditions and implies familiarity with probability and chaos theory concepts. The algorithm proposed in Bašić et al. (2018), on the other hand, is applicable to aperiodic switching schemes, it does not require additional sensors or complex modeling and detailed knowledge of physical characteristics of the power converter switches, and is fairly easy to implement in real time. Given the above, it was recognized as best suited for the purpose considered in this study. In the stand-alone WECS under consideration, a three-phase fullbridge power converter is used to integrate a vector-controlled SEIG with a dc load (e.g., a heater, LED lighting, home appliances, etc.). In addition, the considered WECS contains a battery energy storage system which ensures continuous supply of power, allows capturing maximum available power from the wind, and provides constant voltage on the dc side. Vector control allows for decoupled control of torque and flux and ensures superior dynamic performance compared to scalar control (Abo-Khalil, 2011; Ghaffari et al., 2014; Goel et al., 2011; Hong et al., 2014; Lin et al., 2011; Senjyu et al., 2009; Simoes et al., 1997). This, in turn, allows for decoupled optimization of the WT power – through SEIG torque control – and optimization of the SEIG losses — through SEIG flux control. The proposed control system ensures that maximum energy is extracted from both the WT and the SEIG. It is, in this sense, similar to the systems considered in Mesemanolis et al. (2012), Mesemanolis, Mademlis, and Kioskeridis (2013), Pucci (2015) and Simoes et al. (1997), but there are also a number of fundamental differences. Namely, the system considered here is a stand-alone system designed to supply autonomous dc loads through a single power converter, whereas the systems considered in the above papers comprise two back-to-back converters and are designed primarily to feed the main grid, which implies somewhat different control objectives. Furthermore, the WT optimization strategy proposed in Mesemanolis et al. (2013) uses analytical expressions which require knowledge of the WT and IG parameters and rely on a number of assumptions regarding the variation of these parameters during WECS operation. An experimental testing procedure is proposed to indirectly determine the parameters’ values. This procedure is to be carried out before commissioning and repeated periodically to compensate for the aging and degradation, which can be inconvenient. Similarly, the WT optimization proposed in Pucci (2015) requires knowledge of WT characteristics and wind speed, and utilizes an offline-trained growing neural gas network. As opposed to that, the WT optimization strategy proposed in this study is a nonmodel-based P&O type; it does not require knowledge of the WT or SEIG parameters and it utilizes fuzzy logic (FL) reasoning, so it is more intuitive and able to handle uncertain and noisy signals. Similar approach was suggested in Mesemanolis et al. (2012) and Simoes et al. (1997), but with a significantly greater number of fuzzy rules used for the same purpose, i.e., 27 in Simoes et al. (1997) and 49 in Mesemanolis et al. (2012) as opposed to 14 used here. Note that a smaller number of fuzzy rules implies lower computational requirements, thus making the proposed solution more cost-effective. This reduction is here achieved while preserving good performance in terms of stable operation and fast convergence, as demonstrated later. In addition, in order to achieve

MPPTs require measurement of both the wind speed and the shaft speed, which implies installation of additional sensors. This, in turn, increases the system cost and complexity, while reducing its reliability. In any case, obtaining an accurate wind speed value is rather difficult in practice (e.g., the anemometer has to be insensitive to rapid wind gusts). In addition, the optimal TSR value varies with atmospheric conditions and differs from one WT to another. PSF-based MPPTs require knowledge of the WT maximum power curve, which is obtained through time-consuming and costly aerodynamic tests of individual WTs. The maximum power curve obtained by testing in the end may differ from the actual curve due to the atmospheric conditions or agingrelated decrease in WT efficiency. This curve also differs from one WT to another. Moreover, in order to implement a PSF-based MPPT, either the WT power or shaft speed needs to be measured. This all implies a complicated and expensive implementation of the MPPT algorithm. As opposed to MPPTs from the first two groups, P&O-based MPPTs do not require wind speed measurement or prior knowledge of WT parameters, and can be more generally applied. However, their convergence is somewhat slower. The operating principle relies on observing the effect the perturbation of the minimization variable has on the WT output power and, based on that, the size and direction of the next perturbation are determined. Due to the introduced delay, P&O-based MPPT algorithms are more suitable for small-scale WECSs, which have smaller inertia compared to medium- and large-scale systems. A minimization of the SEIG internal losses is achieved by choosing the appropriate magnetization level. A survey of literature shows that numerous loss-minimization strategies have been proposed. These can be divided into loss-model strategies (Abo-Khalil, 2011; Mesemanolis et al., 2012; Senjyu et al., 2009) and online-search (P&O) strategies (Bašić & Vukadinović, 2016; Simoes et al., 1997). The main advantage of the strategies belonging to the first group is fast convergence. However, they are inherently sensitive to machine parameter variations during operation and their performance largely depends on the accuracy of the applied loss model. Online-search strategies, on the contrary, do not share these problems because the flux adjustment relies on direct online measurement of the generator’s power. However, their performance heavily depends on the measurement accuracy and they are computationally more demanding. They also produce continuous oscillations around the optimum operating point in steady state. As mentioned above, the energy flow in WECS – both stand-alone and grid-connected – is usually controlled by means of power converters. Many voltage and current control strategies for power converters have been reported. The hysteresis current control (HCC), in particular, has found application in various areas where high-performance current control is required. These include active power filters (Durna, 2018; Kale & Ozdemir, 2005; Panda & Patel, 2015; Wang et al., 2015), control systems with induction machines (Bašić & Vukadinović, 2013; Rahman, Khan, Choudhury, & Rahman, 1997), control systems with permanentmagnet synchronous machines (Bose, 1990), aerospace actuators (Fu et al., 2018), etc. The conventional fixed-band HCC is stable and easy to implement, it provides excellent dynamic response and peak current limiting capability, while not being affected by variations of the dc-link voltage (Bašić & Vukadinović, 2013). On the down side, it is characterized by an uneven switching frequency, electromagnetic compatibility problems, high switching losses, and excessive phase current ripple. To overcome these shortcomings, various strategies of hysteresis bandwidth adaptation have been proposed to achieve constant switching frequency (Bose, 1990; Fu et al., 2018; Kale & Ozdemir, 2005; Panda & Patel, 2015), to reduce the switching losses (Durna, 2018; Wang et al., 2015), or to improve the harmonic content of the phase currents (Rahman et al., 1997; Wang et al., 2015). However, many of the existing strategies suffer from computational complexity. Therefore, in this paper, a simple adaptation strategy is proposed which only requires knowledge of the reference phase current amplitude (this information is already contained in the SEIG vector-control algorithm) and is aimed at reducing the total harmonic distortion (THD) of the 2

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high accuracy, the WT speed is here optimized by directly observing the actual WT power rather than observing the grid-side line power as in Simoes et al. (1997) or the calculated approximate value as in Mesemanolis et al. (2012). As for the SEIG loss optimization, flux-weakening strategies proposed in Mesemanolis et al. (2012, 2013) and Pucci (2015) are fundamentally different from the one proposed here since they all rely on analytical expressions involving IG parameters, which need to be determined from the experimental tests conducted prior to commissioning and repeated periodically. In addition, the iron and stray losses were completely neglected in Mesemanolis et al. (2012). The strategy considered here, on the other hand, is quite similar to the previously discussed FL-based P&O strategy. This type of loss optimization was proposed in Simoes et al. (1997), but with almost twice as many fuzzy rules and with yet another FLC employed to enhance speed control against wind vortex and turbine oscillatory torques. Moreover, in Simoes et al. (1997), the search for the optimal flux was initiated from the rated flux value, whereas here it is initiated from the value defined by the rotor speed and dc voltage, thus improving the system stability, as shown in Bašić and Vukadinović (2013), and shortening the search process in most cases. The system proposed in this study also shares several common features with the system proposed in our previous study (Bašić & Vukadinović, 2016), such as the FL-based flux optimization, HCC, and stand-alone configuration. However, the system considered there did not comprise a WT, so it did not involve optimization of the shaft speed. Also, the flux optimization process involved torque measurement and was aimed at achieving the minimum input power of a SEIG (as opposed to the maximum output power in this study), which was there made possible by a load-independent prime mover. There was no battery storage system on the dc side, so the torque control loop had to be employed for maintaining the dc voltage at an assigned level. Hence, in case the WT was employed in such a system, the requirement of dc voltage control would not leave the necessary degree of freedom required for optimization of the WT power. Of all the aforementioned systems, the proposed system is the only one to additionally include a method of reduction of the phase current harmonics. It also includes real-time calculation of the power converter losses. The control algorithm presented in this paper is implemented and tested within a well-known WECS configuration, described in the next section. Still, each of the three employed optimization schemes can be regarded as an improved version of existing similar algorithms with respect to required computational resources, ease of implementation, speed of convergence, or achieved stability, as discussed later. In addition, the proposed control algorithm is, to our best knowledge, the first to combine all the above optimizations within a single WECS, including both stand-alone and grid-connected applications reported in literature. The performance of the proposed control algorithm is experimentally evaluated and compared with two competing algorithms – described in Section 6 – in order to quantitatively evaluate individual contributions of the employed optimizations with regard to the system performance.

Fig. 1. Basic configuration of the considered wind energy conversion system.

for the IGBTs in accordance with the implemented control strategy. It requires five measured signals: the rotor speed 𝜔𝑟 , the mechanical torque 𝑇𝑚 , two phase currents 𝑖𝑠𝑎 and 𝑖𝑠𝑏 , and the dc voltage 𝑢𝑏𝑎𝑡 . The energy-efficient control strategy proposed here is aimed at achieving maximum output power from both the WT and the SEIG at all conditions, while optimizing the harmonic content of the phase currents, as discussed later. 2.2. Induction generator vector controller The schematic diagram of the considered vector controller is shown in Fig. 2 (asterisk denotes reference variables). Note that the stator phase currents in phases a and b are obtained by measurement (Fig. 1), whereas the current in phase c is reconstructed as 𝑖𝑠𝑐 = −𝑖𝑠𝑎 − 𝑖𝑠𝑏 , thus avoiding an additional current sensor. Most of the equations in Fig. 2 belong to the standard IRFO equations derived from the well-known conventional dynamic SEIG model, which can be found in Bašić and Vukadinović (2013). Therefore, particular attention will be given here only to the parts of the algorithm that are in some way specific. When the rotor flux switch in the left end of Fig. 2 is set to position 1, the corresponding reference value is calculated as a function of the rotor speed and dc voltage, thus ensuring stable SEIG operation over wide ranges of speed and load (Bašić & Vukadinović, 2013). Conversely, when this switch is set to position 2, the corresponding reference value is obtained at the output of the rotor flux optimization block, discussed in Section 4. The reference d-axis component of the stator phase current is subsequently calculated as the ratio of the reference rotor flux and the magnetizing inductance, 𝐿𝑚 , which is, in turn, calculated as a function of the magnetizing current magnitude, thus taking into account the magnetic saturation (Bašić & Vukadinović, 2013). The reference q-axis component of the stator phase current is obtained at the output of the PI speed controller, whereas the reference rotor speed is obtained at the output of the rotor speed optimization block, discussed in Section 3. The switching signals are ultimately obtained at the output of the hysteresis current controllers, discussed in Section 5. There are different possibilities at disposal in the IRFO controller in Fig. 2 regarding the optimization of the WT, the SEIG, and the power converter, and these are respectively discussed in the following sections.

2. Basic configuration of the wind energy conversion system 2.1. System components and overall control strategy The WECS under consideration is shown in Fig. 1. The WT-driven SEIG supplies the variable resistive load through the three-phase fullbridge power converter, which, in turn, consists of six insulated-gate bipolar transistors (IGBTs) and corresponding diodes. The capacitor on the dc side provides the reactive power required for SEIG magnetization, whereas the batteries serve as an energy storage device – when there is a surplus energy available – or as a backup — when energy shortage emerges. In addition, the batteries provide constant voltage across the load regardless of the conditions on the ac side. The indirect rotor field oriented (IRFO) controller generates the switching signals

3. Optimal wind turbine control WTs convert the kinetic energy of the wind into mechanical energy handed over to an electric generator shaft. For every wind speed, 𝑣𝑤 , there is a characteristic operating point at which the WT’s output power is at maximum. This operating point is determined by the shaft rotational speed and mechanical load torque of the WT. The WT considered here is a constant-pitch variable-speed WT with the rated power 1.5 kW and the rated wind speed 11 m/s (Bašić, Vukadinović, & Grgić, 2017). Due to the fact that SEIGs have low 3

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Control Engineering Practice 93 (2019) 104185

Fig. 2. Schematic diagram of the proposed IRFO controller.

Fig. 4. Proposed FL-based MPPT algorithm for WT speed optimization.

Table 1 Rule base for the proposed FLC.

Fig. 3. Mechanical torque vs. rotor speed of the WT-driven SEIG (maximum torque and power curves are also shown).

𝛥𝑝𝑚

PB PM PS Z NS NM NB

efficiency at low speeds, which are characteristic of such WTs, usually the WT shaft is not coupled directly to the induction generator shaft, but a step-up gearbox is inserted (as in Fig. 1). Fig. 3 shows the mechanical torque vs. rotor speed characteristics at the output of the WT-gearbox system (i.e., at the input of the SEIG) used in this study. The optimal operating point of a WT at any wind speed within the operating range can be achieved by adjusting the WT rotor speed – i.e., by adjusting the SEIG rotor speed – in order to reach the point where d𝑃𝑚 /d𝜔 = 0 (dashed line in Fig. 3). In the IRFO controller shown in Fig. 2, this is achieved by means of a cascade control of the SEIG rotor speed (outer/slower loop) via the torque-related q-axis stator current (inner/faster loop). The reference q-axis current is obtained at the output of the PI speed controller, whereas the reference speed is obtained at the output of the FL-based MPPT algorithm, whose block diagram is shown in Fig. 4. This algorithm works on the following principle: the speed adjustment signal, 𝛥𝜔∗𝑟 , is generated at the output of the FLC based on the change of the SEIG input power, 𝛥𝑝𝑚 , and the sign of the speed adjustment signal from the previous step; the reference speed value, 𝜔∗𝑟 , is then calculated online as the sum of the generated speed adjustment signal and the reference speed value from the previous step. The input mechanical power is obtained as the product of the measured mechanical torque and rotor speed. The input and output scaling factors, 𝐾𝑖𝑛_𝜔 and 𝐾𝑜𝑢𝑡_𝜔 , in Fig. 4 serve to reduce the related variables to the range [−1 1]. In this paper, their values were derived by trial and error from simulation studies as 𝐾𝑖𝑛_𝜔 = 1∕70 and 𝐾𝑜𝑢𝑡_𝜔 = 20. The rule base for the proposed FLC is presented in Table 1: N, P, and Z stand for negative, positive, and zero, respectively, whereas S, M, and B stand for small, medium, and big, respectively. Such rule base ensures that the search process converges towards the maximum power point, regardless of the position of the starting point. Note that the total number of rules is here reduced to 14 as compared to 27 rules in Simoes et al. (1997) and 49 rules in Mesemanolis et al. (2012),

sign(𝛥𝜔∗𝑟 ) N

P

NB NM NS Z PS PM PB

PB PM PS Z NS NM NB

resulting in lower computational requirements. This, in turn, proved to be the minimum number of rules ensuring stable operation and fast convergence. In addition, the FLC membership functions in Fig. 5 ensure that the convergence point is close to the actual maximum and that it is reached reasonably fast. The FL-based MPPT algorithm in Fig. 4 is executed with the rotor flux switch in position 1 and with the sampling time 𝑇𝜔−𝑜𝑝𝑡 = 3 s, so the speed adjustment signal, 𝛥𝜔∗𝑟 , is updated every three seconds. This sampling time was derived from simulation studies by acknowledging the fact that the WT speed should be allowed to stabilize between successive corrections in order to correctly interpret the WT power trend. The search for the optimal speed is paused and the rotor flux switch is set to position 2 when the input power change, 𝛥𝑝𝑚 , reaches a value less than 1 W, thus allowing the SEIG optimization algorithm, which is discussed in the next section, to take over. Similarly, if the signal 𝛥𝑝𝑚 reaches a value greater than 50 W, this is interpreted as the abrupt change in the wind speed. Consequently, the SEIG optimization algorithm is abandoned, the rotor flux switch is set back to position 1, and the WT optimization algorithm is reactivated. Both these values of 1 W and 50 W were derived from simulation studies and are to a certain extent arbitrary (e.g., by increasing the 𝛥𝑝𝑚 steady-state tolerance from 1 W to a higher value, faster convergence would be achieved, but at the cost of lower accuracy due to the increased dead-zone around the MPP). The synchronization of the WT and SEIG optimizations through the rotor flux switch is performed automatically by means of the block ‘‘FLC 4

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Fig. 6. Proposed FL-based MPPT algorithm for rotor flux optimization.

but may significantly cut down the machine’s efficiency due to a nonoptimal distribution of the internal losses. Hence, the proposed SEIG optimization scheme is aimed at finding the rotor flux reference at which the aggregate of the SEIG’s internal losses is at a minimum. The algorithm in Fig. 6 generates the reference rotor flux signal by observing the trend of the SEIG electrical power and the sign of the reference rotor flux adjustment from the previous step. The instantaneous three phase electrical power is calculated from the instantaneous stator phase voltages and currents as follows: 𝑝𝑒 = 𝑢𝑠𝑎 𝑖𝑠𝑎 + 𝑢𝑠𝑏 𝑖𝑠𝑏 + 𝑢𝑠𝑐 𝑖𝑠𝑐

(1)

The stator voltages in Eq. (1), unlike the currents, are not measured, but are reconstructed from the measured dc voltage and switching signals as follows: ( ) 1 𝑢 2𝑆𝑎 − 𝑆𝑏 − 𝑆𝑐 3 𝑑𝑐 ( ) 1 = 𝑢𝑑𝑐 2𝑆𝑏 − 𝑆𝑐 − 𝑆𝑎 3 ( ) 1 = 𝑢𝑑𝑐 2𝑆𝑐 − 𝑆𝑎 − 𝑆𝑏 3

𝑢𝑠𝑎 =

(2)

𝑢𝑠𝑏

(3)

𝑢𝑠𝑐

(4)

The MPPT algorithm in Fig. 6 is executed with the sampling time 𝑇𝜓−𝑜𝑝𝑡 = 2 s, which was derived from simulation studies in a manner similar to 𝑇𝜔−𝑜𝑝𝑡 . When active (the rotor flux switch in Fig. 2 set to position 2), the algorithm runs continuously, so the reference rotor flux never actually takes a definite value. At best, it oscillates within a narrow band around the optimum. This feature is beneficial in terms of compensation of the system parameter variations during operation. However, as mentioned before, the search for the optimal reference rotor flux is active only while the WT optimization is paused. During the inactive period, the reference rotor flux is calculated as a function of the rotor speed and dc voltage (the rotor flux switch in Fig. 2 set to position 1).

Fig. 5. Membership functions of the proposed FLC: (a) first input signal, (b) second input signal, and (c) output signal.

Sync’’ in Fig. 2. Note also that the proposed optimization algorithm does not require knowledge of the wind speed. Hence, an anemometer is omitted from the considered WECS, thus increasing the system’s reliability and decreasing its cost.

5. Optimal power converter control

4. Optimal induction generator control

5.1. Hysteresis current control

The concept of optimization of the SEIG operation is very similar to that of the WT. Indeed, the structure of the block diagram of the FL-based MPPT algorithm in Fig. 6 is identical to that in Fig. 4. The only difference is in the utilized variables: the mechanical power has given way to the electrical power, whereas the rotor speed has given way to the rotor flux. Moreover, the MPPT algorithms in question share the same FLC, which is the central component of them both. Hence, the membership functions given in Fig. 5 and the rule base given in Table 1 are also valid for the MPPT algorithm in Fig. 6, provided that the mechanical power and rotor speed are replaced by the electrical power and rotor flux, respectively. This significantly facilitates the design of the considered system. In addition, the scaling factors’ values in Fig. 6 are 𝐾𝑖𝑛_𝜓 = 4.2∕𝜔𝑟 and 𝐾𝑜𝑢𝑡_𝜓 = 1. They somewhat differ from 𝐾𝑖𝑛_𝜔 and 𝐾𝑜𝑢𝑡_𝜔 in Fig. 4, but were derived in a similar manner from simulation studies. In IRFO controlled SEIGs, the reference rotor flux is commonly determined as a function of the rotor speed and dc voltage (the rotor flux switch in Fig. 2 set to position 1), which ensures stable operation,

Fig. 7 shows the operating principle of the hysteresis current controllers. The objective is to keep the ripple of the phase current i within the fixed hysteresis band H around the sine reference 𝑖∗ (𝑖 = 𝑖∗ ± H ). The phase current error 𝛥i is the input signal for the controller. When the phase current reaches or exceeds the lower hysteresis boundary, the gate switching signals 𝑆𝑢 = 1 and 𝑆𝑙 = 0 are generated for the upper and lower IGBT in the corresponding converter phase leg, respectively, thus leading to an increase in i(t ). Conversely, when the phase current reaches or exceeds the upper hysteresis boundary, the gate switching signals 𝑆𝑢 = 0 and 𝑆𝑙 = 1 are generated, thus leading to a decrease in i(t ). As mentioned before, the conventional fixed-band HCC has many favorable features, but also a number of drawbacks, one of which is an uneven switching frequency. Among other things, this asymmetric switching makes the calculation of the power converter losses more difficult task. 5

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Fig. 8. Power converter losses – measured (a) and calculated (b) – for different hysteresis band values vs. dc voltage at variable stator phase current (𝐼𝑠 = 0.94 A–3.87 A).

Fig. 7. Operating principle of a hysteresis current controller: (a) controller configuration and (b) sine reference and actual phase current waveforms and upper IGBT switching signals 𝑆𝑢 .

5.2. Calculation of power converter losses The algorithm utilized in this paper for calculation of the power converter losses is that reported in Bazzi, Kimball, Kepley, and Krein (2009, 2012) and subsequently adapted for real-time execution in Bašić et al. (2018). Its implementation requires knowledge of the dc-link voltage, phase current and gate switching signals. In the considered IRFO control system, all three required inputs are readily available since the IRFO algorithm itself requires real-time acquisition of these signals (Fig. 1). Hence, the application of the loss-calculation algorithm does not require installation of any additional sensors. In this study, the loss-calculation algorithm was executed in real-time (along with the IRFO control algorithm) by means of DS1103 controller board (dSpace). The sampling frequency for both the hysteresis current controllers and loss-calculation algorithm was set to 𝑓𝑠 = 40 kHz (the rest of the IRFO algorithm, except for the FLCs, was executed with the sampling frequency of 4 kHz). Consequently, due to the digital implementation, the maximum achievable switching frequency of the power converter is limited to half of the sampling frequency, i.e., 𝑓𝑠𝑤_𝑚𝑎𝑥 = 20 kHz. Good accuracy of the utilized loss-calculation algorithm was verified in Bašić et al. (2018) by a number of experiments carried over wide ranges of the dc voltage and phase current RMS values. High-precision power analyzer Norma 4000 (Fluke) was utilized for electrical measurements and spectral analysis. It was shown that by implementing the fixed-band hysteresis switching strategy, the power converter losses decrease with the phase current amplitude, but at the expense of higher THD values. Conversely, improved harmonic content at higher currents comes at the expense of increased power converter losses. This problem is further analyzed in the next section.

Fig. 9. Measured total harmonic distortion of phase currents for different hysteresis band values vs. dc voltage at variable stator phase current (𝐼𝑠 = 0.94 A–3.87 A).

bandwidths (i.e., 𝐻 = 0.1 A, 𝐻 = 0.2 A, and 𝐻 = 0.05 A), as well as for the case of the proposed adaptive-band switching strategy, which is discussed later. The corresponding results are shown in Figs. 8 and 9. Fig. 8 confirms high accuracy of the loss-calculation algorithm for different hysteresis bandwidth settings. In Fig. 9, it can be observed that the harmonic distortion of the phase currents gets significantly increased by widening the hysteresis band (e.g., from 𝐻 = 0.1 A to 𝐻 = 0.2 A), especially at the lower end of the considered dc voltage and phase current RMS values. At the same time, the power converter losses are reduced as a result of this adjustment, but only by a margin of a few watts (Fig. 8). This reduction is even less pronounced in the case of the measured losses than in the case of the calculated losses. It can be concluded that variations of the H value within the considered range have little impact on the power converter losses. Therefore, as far as the hysteresis adaptation strategy is concerned, achieving satisfactory THD value seems like a more reasonable goal than trying to minimize the power converter losses, especially since these are already relatively small. At the higher end of the considered dc voltage and phase current RMS values, i.e., in the rated current region, the initial strategy with the fixed hysteresis bandwidth of 𝐻 = 0.1 A, which is approximately 2% of the rated stator phase current amplitude, provides satisfactory THD value of about 5%. However, for currents below the rated, such a strategy results in increased phase current ripple. Therefore, a simple hysteresis band adaptation strategy is here proposed in which the hysteresis bandwidth is kept at 2% of the reference phase current amplitude at all times as follows: √ (5) 𝐻 = 0.02 𝑖∗𝑠𝑑 2 + 𝑖∗𝑠𝑞 2

5.3. Proposed adaptive-band switching strategy In order to quantify the influence of the selected hysteresis bandwidth on the power converter losses as well as on the phase current THD value, the experiments involving variations of both the dc voltage and phase current RMS values were carried out for three different fixed 6

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Table 2 Load resistance and wind speed variations. Time

0 s

80 s

130 s

250 s

Load resistance Wind speed

∞ 6 m/s

200 Ω 6 m/s

200 Ω 10 m/s

200 Ω 8 m/s

As it can be seen in Fig. 9, by applying such adaptive-band strategy, satisfactory THD values are obtained in the whole considered range at the cost of an insignificant increase in the power converter losses. When viewed in the context of the WECS shown in Fig. 1, such strategy may prove beneficial in terms of SEIG vector control and loss reduction. Namely, all vector control algorithms essentially operate as fundamental harmonic controllers and they tend to perform better when phase currents resemble an ideal sinusoidal waveform. This is exactly what is achieved by reducing the respective THD value, which can be viewed as a measure of this resemblance (i.e., ideally THD = 0%). On the other hand, higher order harmonics in the phase currents are known to increase induction generator losses (e.g., iron core losses and stray load losses). Hence, these losses are reduced as a consequence of improving the harmonic content of the phase currents, thus compensating to some extent the increase of the power converter losses. 6. Results and discussion To validate the proposed control strategy, a number of experiments were carried out with the 4-pole squirrel-cage induction generator of the following rated values: 𝑃 = 1.5 kW, 𝑈 = 380 V, 𝐼 = 3.81 A, and 𝑛 = 1391 rpm. The WT was emulated by utilizing a separately-excited dc motor controlled by SIMOREG DC-MASTER converter (Siemens), as described in Bašić et al. (2017). The dc voltage was set to 316 V (i.e., the battery system voltage). The performance of the proposed control algorithm was assessed and compared with two competing algorithms. Both these algorithms include the WT optimization, but they do not include the harmonics optimization (i.e., fixed-band hysteresis switching strategy with 𝐻 = 0.1 A is implemented), whereas one of them additionally does not include the SEIG optimization (i.e., the rotor flux switch in Fig. 2 is permanently set to position 1).

Fig. 10. Actual and optimal reference rotor speed of the SEIG: (a) inactive flux optimization and constant hysteresis (𝐻 = 0.1 A), (b) active flux optimization and constant hysteresis (𝐻 = 0.1 A), and (c) active flux optimization and adaptive hysteresis (𝐻 = 0.03 A–0.09 A).

approximately five times longer compared to that in Fig. 10b and c. Therefore, the SEIG flux optimization seems to have a beneficial impact on the WT speed optimization as well. As for the steady-state values of the WT output power, there are virtually no differences between the three analyzed cases. However, the effect of the SEIG flux optimization is most notably visible in the steady-state values of the SEIG output power. The differences are especially pronounced in the period t ≈ 100 s–130 s (𝑃𝑒 increase of 80 W due to optimization) and, to a lesser extent, in the period after t ≈ 260 s (𝑃𝑒 increase of 30 W due to optimization). These periods actually correspond to the periods of pronounced differences between the optimized and non-optimized reference rotor flux in Fig. 13a (e.g., at 𝑣𝑤 = 6 m/s the optimized rotor flux value is about twice smaller compared to the non-optimized value). Likewise, insignificant differences between the optimized and non-optimized reference rotor flux in the period t ≈ 170 s–250 s lead to insignificant differences in the achieved SEIG output power. As it can be seen in Fig. 12, adjustment of the reference rotor flux value is directly reflected on the reference d-axis component of the stator phase current (𝑖∗𝑠𝑑 = 𝜓𝑟∗ ∕𝐿𝑚 ). At the same time, the reference q-axis component of the stator phase current, being the torque-related component, is much less affected by this optimization and much more by the WT optimization. In any case, reduction of the reference rotor flux leads to a reduction of the d-axis stator current, which, in turn, leads to a reduction of the stator phase current amplitude (Fig. 13b). This last observation is important from the vector control perspective. Namely, if the stator phase current amplitude is reduced, the induction machine develops less heat, so the increase of the stator and rotor resistances is restrained. Consequently, the disagreement between the actual induction machine parameters and those assumed in the vector control algorithm is less severe (that is, if the latter are assumed to be constant), so a better control performance is achieved.

6.1. Dynamic analysis In the first set of experiments, the dynamic performance of the proposed WECS was put to a test over a time period of 400 s. During this period, the load resistance was varied at 𝑡 = 80 s, whereas the wind speed was varied at 𝑡 = 130 s and again at 𝑡 = 250 s, as presented in Table 2. The WT optimization was initiated at t ≈ 10 s, after the system attained steady-state condition. The corresponding results are shown in Figs. 10–13. Fig. 10 shows the experimental time responses of the actual and optimal reference rotor speed obtained for the three considered algorithms (‘‘FLC 𝜔𝑟 ’’ denotes intervals when the WT speed optimization is active, whereas ‘‘FLC 𝛹𝑟∗ ’’ denotes intervals when the SEIG flux optimization is active). Higher wind speeds imply higher optimal rotor speeds, as per Fig. 3. Hence, in this experiment, the highest optimal rotor speed was achieved for 𝑣𝑤 = 10 m∕s (ideally 1278 rpm), whereas the lowest optimal rotor speed was achieved for 𝑣𝑤 = 6 m∕s (ideally 767 rpm). There is no apparent difference between the rotor speed responses in Fig. 10c (proposed algorithm) and Fig. 10b (fixed-band hysteresis with SEIG flux optimization). In both cases, rather mild transients are initiated by the activation of the rotor flux optimization. In Fig. 10a (fixed-band hysteresis without SEIG flux optimization), as opposed to Fig. 10b and c, there are oscillations initiated by the wind speed change from 6 m/s to 10 m/s at 𝑡 = 130 s. These oscillations are naturally reflected on the WT output power response in Fig. 11a. In addition, upon the wind speed decrease at 𝑡 = 250 s, the convergence of the rotor speed to a new, lower optimal value in Fig. 10a lasts 7

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Fig. 11. WT and SEIG output power: (a) inactive flux optimization and constant hysteresis (𝐻 = 0.1 A), (b) active flux optimization and constant hysteresis (𝐻 = 0.1 A), and (c) active flux optimization and adaptive hysteresis (𝐻 = 0.03 A–0.09 A).

Fig. 12. Stator phase current d- and q-axis components: (a) inactive flux optimization and constant hysteresis (𝐻 = 0.1 A), (b) active flux optimization and constant hysteresis (𝐻 = 0.1 A), and (c) active flux optimization and adaptive hysteresis (𝐻 = 0.03 A–0.09 A).

Fig. 13c shows that there is also a negative side-effect of the rotor flux optimization. Namely, the power converter losses are increased as a consequence. This increase is, expectedly, more pronounced when the proposed adaptive-band switching strategy is implemented due to higher switching losses. Still, the largest recorded increase of the power converter losses in this example, according to the loss-calculation algorithm, amounts to approximately 15 W (t ≈ 100 s–130 s), which is more than five times lower compared to the increase of the SEIG output power due the rotor flux optimization in the same interval.

in the phase currents leads to a reduction of the induction machine losses so more power is transferred to the output. As the wind speed increases, the differences between the optimized and non-optimized reference rotor flux become smaller (Fig. 14c), so the differences in the SEIG output power values obtained with the three considered algorithms become smaller as well. As mentioned before, the rotor flux optimization leads to a reduction of the amplitude of the stator phase current (Fig. 14d), which results in less developed heat and is beneficial for vector control accuracy. However, this amplitude reduction has a negative side-effect on the harmonic content of the SEIG phase currents. Namely, the corresponding THD value increases as the wind speed decreases (Fig. 14e), but with the proposed adaptive hysteresis strategy, this problem is to some extent mitigated. On the other hand, without the rotor flux optimization, the THD tends to increase with the wind speed. For example, at 𝑣𝑤 = 10 m∕s, the THD almost reaches 20%, which implies severe distortion of the phase current waveform. For comparison, with the other two algorithms implemented, the THD value is kept below 5% under the same conditions. Finally, Fig. 15 shows the converter output power as a function of the wind speed. The converter output power curves are obtained by subtracting the power converter losses (Fig. 14f) from the SEIG output power (Fig. 14b) and then extrapolating the obtained results (𝑣𝑤 = 3 m∕s is the cut-in speed for this WT). It can be seen that when either of the two algorithms with the rotor flux optimization is implemented, the battery charging is ensured under no-load condition for all wind speeds above 4.2 m/s. Moreover, for lower wind speeds, the converter output power is approximately zero, which means that the batteries are neither being charged nor discharged. The choice of hysteresis switching strategy, as it appears, does not have a significant

6.2. Steady-state analysis In the second set of experiments, the steady-state performance of the proposed WECS was analyzed. The experiments were carried out with six wind speed settings and the corresponding results are shown in Fig. 14. It can be seen in Fig. 14a that all three considered control algorithms manage to achieve the WT output power that is quite close to the theoretical limit. However, the algorithms with optimization of the reference rotor flux provide somewhat higher electrical power at the SEIG’s output, especially at lower wind speeds (Fig. 14b). In fact, the algorithm without the rotor flux optimization results in negative SEIG output power at 𝑣𝑤 = 5 m∕s. This implies that the SEIG losses are in this case greater than the WT output power, so they have to be covered from the batteries even at no load in order to avoid shutting down of the system. In case there is a load connected, the situation is further aggravated in the sense that the batteries are being more rapidly discharged. When the proposed adaptive-band switching strategy is implemented, slightly more power at the SEIG’s output is obtained as compared to the fixed-band strategy. This may be related to the previously mentioned fact that the reduction of higher order harmonics 8

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Fig. 13. Experimental time responses: (a) rotor flux reference, (b) stator current amplitude, and (c) power converter losses.

influence on the ultimate output power of the converter. This is because an increase in the power converter losses due to hysteresis bandwidth adaptation is compensated by a decrease in the SEIG losses. On the other hand, when the algorithm without the rotor flux optimization is implemented, battery charging becomes possible only for wind speeds above 5.3 m/s, whereas for wind speeds lower than this, the converter output power is negative, which means that the batteries are being discharged. For example, at the cut-in wind speed, the batteries need to provide approximately 110 W of power to cover for the SEIG and converter losses. Additionally, if the load of 500 W – which is the value used in this study – is connected on the dc side, battery charging becomes possible only for wind speeds greater than 8.7 m/s. 7. Conclusions In this paper, a new energy-efficient control strategy was proposed and applied for a stand-alone WECS containing a vector-controlled SEIG and a battery storage unit, integrated through a three-phase full-bridge power converter. The proposed strategy maximizes the power output of the WT and the SEIG at all operating conditions, while improving the phase current harmonic content. The experimental evaluation of the proposed system’s performance has shown that the benefits of the rotor flux optimization are manifold. The most obvious benefit is the increase of the electrical power obtained at the SEIG output (up to 80 W more power at lower wind speeds), thus increasing the operating range in which it is possible to charge batteries. However, there are also less obvious benefits such as reduction of the stator current amplitude – leading to lower heating of the SEIG and better vector control – and also oscillation reduction and faster convergence rate of the WT optimization algorithm. Furthermore, without the rotor flux optimization, the THD value of the SEIG phase currents significantly increases with the wind speed and reaches almost 20% within the

Fig. 14. Steady-state characteristics: (a) WT output power, (b) SEIG output power, (c) rotor flux reference, (d) stator current amplitude, (e) total harmonic distortion, and (f) converter losses.

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Fig. 15. Converter output power vs. wind speed.

tested range, which implies severe distortion. On the down side, the rotor flux optimization increases the power converter losses, but rather insignificantly. The analysis has also confirmed good performance of the WT optimization algorithm in the sense that the achieved WT output power is very close to the theoretical limit for all considered wind speeds. Finally, the proposed adaptive-band hysteresis switching strategy ensures lower THD value of the SEIG phase currents and also slightly more power at the SEIG’s output compared to the fixed-band strategy. This is, however, achieved at the cost of an acceptable increase in the power converter losses (up to 15 W increase within the tested range). In the end, it comes down to choosing one’s priorities. The algorithm for calculation of power converter losses proved to be a powerful tool in this sense because it enabled a better quantitative insight into distribution of WECS’s losses. The expansion of the system through integration of other renewable energy sources and also with regard to the possibility of connection to the main grid will be the subject of future research. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work has been fully supported by Croatian Science Foundation under the project (IP-2016-06-3319). References Abo-Khalil, A. G. (2011). Model-based optimal efficiency control of induction generators for wind power systems. In IEEE international conference on industrial technology (pp. 191–197). Alabama (USA). Barakati, S. M., Kazerani, Mehrdad, & Aplevich, J. D. (2009). Maximum power tracking control for a wind turbine system including a matrix converter. IEEE Transactions on Energy Conversion, 24, 705–713. Bašić, M., & Vukadinović, D. (2013). Vector control system of a self-excited induction generator including iron losses and magnetic saturation. Control Engineering Practice, 21, 395–406. Bašić, M., & Vukadinović, D. (2016). Online efficiency optimization of a vector controlled self-excited induction generator. IEEE Transactions on Energy Conversion, 31, 373–380. Bašić, M., Vukadinović, D., & Grgić, I. (2017). Wind turbine-driven self-excited induction generator: a novel dynamic model including stray load and iron losses. In 2nd International multidisciplinary conference on computer and energy science (pp. 1–6). Split (Croatia). Bašić, M., Vukadinović, D., & Grgić, I. (2018). Real-time loss calculation of a hysteresis controlled power converter. In 3rd International conference on smart and sustainable technologies (pp. 1–6). Split (Croatia). Bazzi, A. M., Kimball, J. W., Kepley, K., & Krein, P. T. (2009). TILAS: A simple analysis tool for estimating power losses in an IGBT-diode pair under hysteresis control in three-phase inverters. In 24th Annual IEEE applied power electronics conference and exposition (pp. 637–641). Washington DC (USA). Bazzi, A. M., Kimball, J. W., Kepley, K., & Krein, P. T. (2012). IGBT and diode loss estimation under hysteresis switching. IEEE Transactions on Power Electronics, 27, 1044–1048. 10