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An adaptive control algorithm for grid-interfacing inverters in renewable energy based distributed generation systems
Energy Conversion and Management 111 (2016) 443–452
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
An adaptive control algorithm for grid-interfacing inverters in renewable energy based distributed generation systems Naji Al Sayari, Rajasekharareddy Chilipi ⇑, Mohamad Barara Department of Electrical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Received 14 September 2015 Accepted 21 December 2015
Keywords: Distributed generation Renewable energy Adaptive notch filter Grid-interfacing inverter Power quality
a b s t r a c t This paper proposes an adaptive control algorithm for grid-interfacing inverters in renewable energybased distributed generation systems. The proposed control algorithm functions in two different modes: basic power generation mode, harmonics compensation mode. In basic power generation mode, the inverter pumps desired amounts of active and reactive powers into the grid at the point of common coupling. In harmonics compensation mode, the control algorithm ensures sinusoidal grid current through load current harmonics mitigation in addition to desired power generation. Moreover, the proposed control algorithm does not use any detection methods for compensation of harmonic currents. Hence, it results in low computational burden. Based on the requirements, the proposed control algorithm can be operated in either of the modes. A proportional–integral controller-based closed loop control is employed for accurate control of the power injected into the grid. A frequency adaptive notch filter is used to synchronize the grid-interfacing inverter with the fundamental component of grid voltage without using any phase locked loop. The effectiveness of the proposed control algorithm in reference active and reactive powers generation, current harmonics compensation is demonstrated successfully by simulation and experimental results. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction On the pathway to address the concerns posed by conventional energy sources such as depletion of fossil fuels and climate changes, many countries are aiming to increase their share of energy generation from clean energy sources. The energy sources such as solar, wind, hydro and bio-fuel are the prime candidates of clean energy. Generally, the energy harnessed from renewables is first used to cater the needs of local community and the remaining energy will be pumped into the grid by means of power electronic interfaces [1]. Voltage source inverter (VSI)-based power electronic interfaces are being widely used for the grid integration of renewable energy sources (RESs) [2]. In [3], a three-level inverter has been used for grid interconnection of a photovoltaic system. Ref. [4] provides a comprehensive review on application multilevel inverters and their control in grid connected photovoltaic systems. Multilevel inverter topologies are increasingly used in distribution generation applications due to their advantages such as low switch losses, less harmonic distortion and reduced filter
⇑ Corresponding author. E-mail address: [email protected] (R. Chilipi). http://dx.doi.org/10.1016/j.enconman.2015.12.076 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.
size. In [5], a multistage stage dc/ac converter has been proposed to improve the overall conversion efficiency. Integration of RESs with the utility network has attracted a great deal of interest due to potential environmental and economic factors. Various control algorithms for grid interconnection RESs via VSIs are discussed [6]. The grid-interfacing VSIs are operated as controlled current source to inject the power generated by the RESs into the grid. In [7], the power injected into the grid is controlled by changing the phase difference between the grid voltage and the inverter voltage. In [8], particle swarm optimization method has been used to control the grid injected power. In [9], an adaptive neuro-fuzzy controller has been used to control a single-phase grid-coupled inverter. In addition to active power injection, the grid-tied inverters can also be used for simultaneous reactive power compensation [10]. A doubly fed induction generator (DFIG) system with reactive power compensation capabilities has been discussed in [11]. Owing to the proliferation of electronically switched nonlinear loads, the amount of harmonic current being released into the power distribution network is growing rapidly and causing degradation of grid voltages. An active power filter [12] can be used to mitigate the harmonics injected by nonlinear loads. Alternatively, the grid connected VSI itself can be controlled to compensate the harmonic and reactive currents drawn by the local loads to improve
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grid power quality. Therefore, inclusion of harmonic currents suppression capabilities in the grid-tied inverters is gaining interest. Mostly, the capacity of the VSIs employed in grid-interfacing of RESs is underutilized due to the intermittent nature of RES. The remaining capacity of the VSIs can be diverted to power quality improvement. Therefore, the control algorithm that is adopted for grid-interfacing VSIs must offer great flexibility to use the remaining capacity of VSIs for power quality improvement through ancillary services. A control scheme for grid-interfacing VSIs with power quality improving ancillary services such as active power filtering and reactive power injection is presented in [13]. In [14], a grid interfaced multi-level inverter with shunt compensation capabilities is discussed. A flexible control algorithm based on recursive least squares has been presented in [15] for power quality improvement in grid interfaced distributed generation systems. In order to accommodate power quality improvement features such as active harmonic filtering and reactive power compensation, detection of harmonic and reactive currents is mandatory. Rapid and accurate detection of the harmonic signal, fast processing of the reference signal, and high dynamic response of the controller are the prime requirements for achieving desired level of compensation. Numerous control methodologies for detection of harmonic and reactive currents have been reported so far. The synchronously rotating d-q frame (SRF) theory [16] and instantaneous p-q theory [17] are the widely used conventional control algorithms to generate reference signals for harmonic currents compensation. In Ref. [18] also, the instantaneous p-q theory has been used for incorporating active harmonic filtering in grid-tied DFIG system. Ref. [19] has proposed a control algorithm for simultaneous active power generation and power quality improvement in wind energy driven DFIG system. In addition to aforementioned conventional methods, the detection methods employing artificial neural networks (ANN) [20] and fast Fourier transforms (FFT) [21] can be found in the literature. In [22], various ANN techniques have been compared for harmonic currents extraction and active power filtering. Nonetheless, the performance of the aforementioned detection techniques is highly affected by grid voltage distortion and frequency variations. To address this issue, a detection method that is independent of grid voltage distortion is developed in [23]. This method employs second order frequency adaptive pre-filters such as second order generalized integrators (SOGIs) [24] and adaptive notch filters. Precise and accurate estimation of harmonic and reactive components of load current would significantly increase the computation burden and therefore demands high speed digital controllers. For a low cost solution and minimizing the computational burden, researchers have proposed harmonics detection free methods [25]. These methods are designed for healthy grid conditions. In case of abnormal grid condition, the performance of VSI varies highly depending on the control algorithm used. In view of the above-stated drawbacks with the existing control algorithms, this article proposes a robust and harmonics detection free control algorithm. The proposed control also offers a flexibility to operate the grid-tied VSI in two different modes such as basic power generation mode and harmonics compensation mode for optimal utilization of VSI rating. Unlike the harmonic detectionfree control algorithms reported, the proposed control algorithm is immune to grid voltage distortions and frequency fluctuations. The proposed control algorithm synchronizes the grid-interfacing VSI with the fundamental frequency component of grid voltage to make its performance independent of grid disturbances such as frequency fluctuations and voltage distortions. The fundamental frequency component of grid voltage is obtained by using a frequency adaptive notch filter (ANF) [23]. Adaptive nature of the ANF allows precise tracking of variations in the frequency and magnitude of the fundamental components and thereby eliminates the use of single-phase phase locked loop (PLL) [26]. This will
further reduce the computational load on the digital processor. Closed-loop control of active and reactive powers with simple proportional-plus-integral (PI) controller based regulation is employed to achieve accurate tracking of reference powers with zero steady state errors. The key benefits of proposed control algorithm are summarized as follows: 1. Detection free harmonic and reactive currents compensation. 2. Accurate control of active and reactive powers. 3. Immune to grid voltage distortions and adaptive to frequency fluctuations. 4. PLL less grid synchronization. 5. Offers flexibility to operate in different modes. The feasibility and the effectiveness of the proposed control algorithm are simultaneously verified through computer simulation studies and hardware-in-the-loop (HIL)-based experimental tests. The rest of the paper is organized as follows: Section 2 discusses the configuration of the grid-interfacing VSI system under study. Section 3 presents the formulation of proposed PLL less frequency adaptive control algorithm and its various modes of operation. Section 4 validates the proposed control algorithm based on simulation and experimental results. Section 5 concludes the paper. 2. System configuration Fig. 1 depicts the basic configuration of grid-interfacing singlephase H-bridge VSI in renewable energy systems consisting of renewable power generation units and different types of loads. Renewable energy sources, such as wind and solar, are typically used to generate electricity for residential users. The power generation units use dc/dc and dc/ac static power electronic converters for voltage conversion and battery banks for energy storage. The battery banks form a constant voltage dc bus. The power electronic converters perform maximum power point tracking and extract the maximum energy possible from wind and solar sources. Thus the energy extracted is fed to the grid via a single-phase VSI after serving the local loads. The grid-interfacing VSI is connected to single-phase distribution network with a coupling inductor (Lf) at the point of common coupling (PCC). The symbols ig, ivsi and il represent the grid current, VSI current, and load current, respectively. The grid voltage and the voltage at PCC are denoted as vg and vpcc, respectively. 3. Proposed control algorithm This section describes the proposed adaptive control algorithm for single-phase grid interfaced VSI. The schematic of proposed control algorithm is shown in Fig. 2. As previously mentioned,
Lg AC
Grid
vg
ig
il
v pcc Lf
AC
ivsi
Local Loads
DC
Energy Storage
Wind Energy
VSI
DC DC
Solar Energy
400V DC Bus
PWM pulses
Fig. 1. Schematic of grid-interfacing single-phase inverter.
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the proposed control algorithm operates in two different modes: (1) basic power generation mode, (2) harmonics compensation mode. These modes are also referred to as mode-I and mode-II, respectively. In both the modes, the VSI is operated as controlled current source. Closed loop control of active and reactive powers injected into by the VSI is maintained in both the modes. The reactive power generated by the VSI is needed to be adjusted by varying the reference value to meet the reactive power demand of local loads and achieve unity power factor operation of grid at the PCC. The control algorithm can be operated in either of the modes by changing the value of the gain parameter Gh. The Gh value can be either ‘0’ or ‘1’. In basic power generation mode, the Gh is set to ‘0’ and in harmonics compensation mode, the Gh is set ‘1’. A frequency adaptive notch filter is used to synchronize the VSI with the fundamental frequency component of PCC voltage. This achieves harmonic rejection capability and frequency adaptability of the proposed control algorithm even under distorted utility conditions. 3.1. Adaptive notch filter As mentioned earlier, an ANF is used in this study to synchronize the VSI with fundamental frequency component of PCC voltage. The structure of ANF is shown in Fig. 3. The ANF processes the PCC voltage signal and produces a set of fundamental frequency orthogonal signals [23]. The outputs of ANF vpccf and vpccfq are having equal amplitudes, but phase displaced by 90° from each other. The ANF is a linear time invariant system whose magnitude response vanishes at a particular frequency called notch frequency and constant elsewhere on the jx axis as defined by the transfer function given in (1).
EðsÞ ¼
ev ðsÞ s2 þ x21 ¼ 2 v pcc ðsÞ s þ kx1 s þ x21
ð1Þ
where x1 is the ANF estimated fundamental frequency and also the resonating/natural frequency in rad/s. From the bode diagram of E(s) shown in Fig. 4, it is observed that the magnitude of E(s) is equal to zero when the input signal frequency is equal to the resonance frequency (x = x1) and it is equal to unity for when the input signal frequency is greater (x > x1) or less (x < x1) than the resonating frequency. The relation between input voltage signal and the output orthogonal signals is characterized by the following transfer functions.
DðsÞ ¼
v pccf ðsÞ kx1 s ¼ v pcc ðsÞ s2 þ kx1 s þ x21
ð2Þ
Pref
ivsi v pcc
Pvsi
Qref
Average Power Estimation
ANF
ð4aÞ
x_ 1 ¼ cx1 ev x
ð4bÞ
ev ¼ v x_
ð4cÞ
where k > 0 is the damping coefficient and c > 0 determines the adaptation speed. These parameters are used to tradeoff between adaptation speed and noise sensitivity. As in all adaptive systems, the estimated frequency x1 reaches the steady state slowly com_ xÞ when c is very small. For a given sinusoidal pared to its states ðx; input signal v = Vm sin xt, the dynamical system represented by (4) has a unique periodic orbit with constant and correct estimated frequency,
2
3 2 V 3 x xm cos xt 6 _ 7 6 7 o,4 x 5 ¼ 4 V m sin xt 5 1 x x
v_ ¼
x_ €x
¼
0
x 0 þ v kx1 x_ kx1 1
x21
_ x_ 1 ¼ cx1 xðv xÞ
ð6Þ ð7Þ
Considering a steady state operating frequency locked condition _ 1 ¼ 0, then (6) boils down to i.e. x = x1 and x
" #
x_ sin x1 t v_ jx¼x1 ¼ ¼ V m €x x1 cos x1 t
ð8Þ
Even if the frequency estimated by ANF is locked intentionally at a different value from the input signal frequency by making c = 0, still the state vector would keep a stable orbit as expressed by (9) and (10)
v_ jx–x1 ¼
" # x_ sinðxt þ /Þ ¼ Að x Þ €x x cosðxt þ /Þ
IP
Vmf
uf ivsi*
u fq
il
PI
ð5Þ
The bar (–) over the variables in (5) represent equilibrium condition. The state space realization of ANF which is required for stability analysis can be obtained from (6) and (7) as,
v pccfq
Qvsi
ð3Þ
€x þ x21 x ¼ kx1 ev
v pccf
v pcc
v pccfq ðsÞ kx21 ¼ 2 v pcc ðsÞ s þ kx1 s þ x21
3.1.1. Local stability The dynamic behavior of ANF structure can be described by a set of continuous time differential equations given in (4).
PI
90° Delay
90° Delay
QðsÞ ¼
IQ
Fig. 2. Schematic of proposed control algorithm.
ivsierr
ivsi Gh
ð9Þ
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kxx1 where AðxÞ ¼ V m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 ðx1 x2 Þ þ k x21 x2 / ¼ arctan
kxx1 x21 x2
ð10aÞ
ð10bÞ
From (9), it is evident that the ANF keeps the following steady state relationship between € x and x when x – x1 as described in (11).
€x ¼ x2 x
ð11Þ
Using (11), the steady state synchronization error, (the difference between v and x) can be deduced as
ev ¼ v x ¼
1 :ð€x þ x2 xÞ kx1
ð12Þ
Using (11) and (12), the frequency error in steady state can be written as,
ef ¼ xx1 ev ¼
x2 ðx21 x2 Þ k
ð13Þ
Therefore, (13) confirms that the signal ef carries the frequency error information and hence used as the control signal in ANF for estimating the system frequency. Now, the local stability analysis can be carried out by assuming x x1 that approximates x21 x2 to 2(x x1)x1, in this condition the dynamics of ANF can be described as,
c c x_ 1 ¼ cef ¼ x2 ðx2 x21 Þ 2 x2 ðx x1 Þx1 k
k
ð14Þ
If we define the frequency estimation error as d = (x x1) and _ 1. its derivative under constant input frequency is given by d_ ¼ x Therefore, the condition given by (15) will always be true for positive values of estimated frequency which is the key for local stabilization.
c
dd_ ¼ 2 x2 d2 x1 6 0: k
ð15Þ
3.1.2. Tuning of ANF Tuning of ANF involves design of its parameters ‘k’ and ‘c’. For a given sinusoidal input signal v = Vm sin xt with constant frequency, the relation between input and output signal is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi kx1 2V m 2 xt 4k e 2 þ V m sin xt x_ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin 2 2 4k
ð16Þ
From (16), the settling time taken by the ANF is given by
t ANF ¼
10 k x1
ð17Þ
Expression (17) affirms that the gain ‘k’ defines the bandwidth and hence the filter response time. A very high value of ‘k’ would result in fast response and reduces its immunity to noise. However, a very low value of ‘k’ leads to sluggish ANF response. In the prepffiffiffi sent study ‘k’ is set to 2 to achieve optimal performance. The other unknown parameter ‘c’ of ANF cannot be estimated directly using linear control system analysis as the frequency adaptation loop is highly nonlinear. Therefore, as illustrated in [24], using averaged dynamics and assuming x x1 the value of gain ‘c’ can estimated as
c¼
kx1 V 2m
s:
ð18Þ
The value of s can be selected based on the settling time (tF) in frequency estimation process as
tF ¼
5
s
:
ð19Þ
3.2. Mode-I: basic power generation mode In this mode, the VSI pumps the reference active and reactive powers into the grid by injecting in-phase and quadrature-phase currents with PCC voltage, respectively. To regulate the powers being injected into the grid, the instantaneous real and reactive powers across the VSI terminal are first measured.
pv si ¼
1 v pcc iv si þ v pccq iv siq 2
ð20Þ
qv si ¼
1 v pccq iv si v pcc iv siq 2
ð21Þ
where vpccq and ivsiq are the quarter cycle delayed signals of vpcc and ivsi, respectively. The grid frequency information required to estimate the quarter cycle delayed signals of vpcc and ivsi is obtained from ANF. The powers estimated in (20) and (21) are fed to moving average blocks to estimate their averages. The estimated average active and reactive powers of the VSI are now compared with reference powers and then the errors are processed through PI controllers. The regulation law is defined as,
IP ¼
k2 k1 þ ðPref Pv si Þ s
IQ ¼
k3 þ
k4 ðQ ref Q v si Þ s
ð22Þ
ð23Þ
where k1, k2, k3 and k4 are the proportional and integral gain constants of the PI controllers, Pvsi and Qvsi are the averages of pvsi and qvsi, respectively. Ip and IQ represent the magnitudes of active and reactive currents to be injected by the VSI for reference powers generation. The Pref is decided by the power extracted from the RESs. Unlike the open-loop methods, use of PI controllers for active and reactive powers control takes care of power errors caused due to the interactions between VSI harmonic current and PCC harmonic voltage. From (22) and (23), the reference current signal for generating Pref and Qref is computed as
iv si ¼ IP uf þ IQ ufq
ð24Þ
where uf and ufq are the in-phase and quadrature-phase unit templates of PCC voltage at fundamental frequency, respectively. From (24) it is evident that the envelope of the reference VSI current iv si is decided by the unit templates (uf and ufq) of fundamental component of PCC voltage. The unit templates of fundamental PCC voltage are obtained as,
uf ¼
v pccf V mf
ufq ¼
v pccfq V mf
ð25Þ ð26Þ
where vpccf and vpccfq are the orthogonal signals generated by the ANF employed over PCC voltage as shown in Fig. 3 and Vmf is their amplitude. 3.3. Mode-II: harmonics compensation mode For Gh = 1, the control algorithm offers compensation of harmonic and reactive currents drawn by the local loads. Unlike the basic power generation mode, in this case, the outputs of PI controllers are multiplied with fundamental in-phase and quadrature-phase unit templates of PCC voltage to yield reference grid current instead of reference VSI current.
ig ¼ IP uf þ IQ ufq
ð27Þ
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
x
k v pcc = v
ω1x
ev
ef
-γ
ω1
v pccf
x
∫ x
∫
v pccfq
4.1. Performance under step change in active power generation The performance under a step change in active power has been examined and the corresponding results are depicted in Figs. 5–7. A nonlinear load of 2.5 kW is connected to the system. Fig. 5 (a) and (b) shows the simulation and experimental recordings of vpcc, ig, ivsi and il in mode I, respectively. During Pvsi = 0, the current ivsi is absent and ig is seen to be identical to il. Change in wave shape of ig and ivsi can be noticed as the Pref changes from 0 to 5 kW. In this mode, the grid current ig carries harmonics as the VSI offers no harmonics compensation. Fig. 6 shows the waveforms of vpcc, ig, ivsi and il under Pref change in mode II. Both simulation and experimental results exhibit identical transient performance. In Fig. 6, the current ig is maintained sinusoidal since the VSI offers compensation along with reference power generation in this mode. In mode II, during Pref = 0, the VSI acts as simple compensator as it provides only the compensation of harmonic currents to keep grid current distortion free at the PCC. Further, the active power injected by the VSI tracks the reference power very accurately and it reaches steady state within 20 ms as illustrated in Fig. 7(a) and (b).
Fig. 3. Structure of adaptive notch filter.
ω> ω
1
1
Magnitude (abs) Phase (deg)
1
0.5
0
0 90
-90 0.01
0.1
1
10
50
1000
10000
Frequency (Hz) Fig. 4. Magnitude and phase response of E(s).
4.2. Performance under step change in reactive power generation
From ig of (27), the load current il is subtracted from ig to obtain reference current of VSI.
iv si ¼ ig il
ð28Þ
In addition to harmonic currents suppression, the VSI injects pre-set values of active and reactive powers into the grid. In order to achieve unity power factor, the IQ in (27) should be brought to zero by adjusting the Qref value in (23) which makes the unity power factor operation of the grid manual. Now, the reference VSI current iv si estimated in (24) or (28) is compared with actual current ivsi and the error is defined as, err
iv si ¼ iv si iv si
variables such as PCC voltage (vpcc), grid current (ig), VSI current (ivsi), load current (il), reference power (Pref) and the injected power (Pvsi) are displayed on a digital oscilloscope via onboard D/A converter for the illustration of system performance. The experimental results obtained are presented alongside the simulation results for simultaneous evaluation of the results.
ω1
∫
ω< ω
447
ð29Þ
The current error in (29) is fed to a hysteresis current controller to generate the firing pulses for the grid-interfacing VSI.
The performance of the proposed control algorithm is also verified under step change in reactive power generation and it is illustrated in Figs. 8–10. Keeping the active power generation at 5 kW, the reactive power supplied by the VSI is changed from 0 to 2.5 kVAr. The positive value of Qvsi indicates the inductive nature of the supplied reactive power. The waveforms of vpcc, ig, ivsi and il during the reactive power change in mode I and II are shown in Figs. 8 and 9, respectively. During Qref = 0, the currents ig and ivsi are exactly out-of-phase with vpcc. As the Qvsi rose to 2.5 kVAr, change in magnitude of ivsi and ig and their phase displacement with respect to vpcc can be seen. Transient behavior of Qvsi and Pvsi during Qref change is shown in Fig. 10. It is observed that the Qvsi is perfectly following its reference value, whereas the Pvsi is exactly maintained at 5 kW except the small oscillations during Qvsi sudden change. 4.3. Performance under step change in load
4. Results and performance evaluation The feasibility of the proposed control algorithm for grid-tied inverters is verified through simulation and experimental studies. The system configuration presented in Fig. 1 and the proposed control algorithm are modeled in MATLAB/Simulink environment using power system tool box. The simulation is carried at a fixed step size of 10 ls. The proposed control algorithm is tested for an active power generation system of 5 kW. A local nonlinear load of 2.5 kW is considered for performance evaluation. The system parameters are presented in appendix. The performance of the control algorithm is verified in both the modes. A dSPACE-based digital signal processor DS1202 is employed to implement the proposed control algorithm. A sampling frequency of 40 kHz is used in processing the control algorithm. The system under study consisting of single-phase grid, H-bridge inverter and local loads is realized in a hardware-in-the-loop (HIL) system. The system parameters and the loading conditions are kept identical to those used in computer simulations. All the necessary
The performance under load step change is demonstrated with the power generation keeping at Pvsi = 5 kW and Qvsi = 0. The load connected to the system is nonlinear in nature. The results obtained in mode I and II are presented in Figs. 11 and 12, respectively where the load on system is increased from 1.25 kW to 2.5 kW. Since the net active power is being drawn from the grid is negative, any increase in the load causes reduction in ig. The VSI current is seen to be constant since Pvsi is constant. In mode II, the VSI current magnitude slightly changes as the load changes due to the increase in harmonic compensation current. 4.4. Performance with harmonic grid Fig. 13(a) and (b) shows the simulation and experimental results obtained with harmonic grid conditions, respectively. These results demonstrate effective harmonics compensation capabilities of the proposed control algorithm even under highly distorted grid voltages. These results are obtained for active power generation of
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
il(A)
ivsi(A)
ig(A) vpcc(V)
448
200 0 -200 20 0 -20 40 20 0 -20 -40 20
P = 5 kW vsi
P =0 vsi
0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
200 0 -200 20
P = 5 kW vsi
0 -20
ivsi(A)
ig(A) vpcc(V)
Fig. 5. Performance during a step change in active power generation in mode-I: (a) simulation results and (b) experimental results.
P =0
20 0 -20
vsi
il(A)
20 0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
Fig. 6. Performance during a step change in active power generation in mode-II: (a) simulation results and (b) experimental results.
6
Pvsi= 5 kW
5
P(kW)
4
Actual Power
3
Reference Power
2 1
Pvsi= 0
Pvsi= 0
0 -1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Time(s)
(a)
(b)
Fig. 7. Illustration of accurate control of active power generation. (a) Simulation results. (b) Experimental results.
5 kW and zero reactive power. The performance in mode II only is considered. The grid voltage distortion is realized by injecting 3rd and 9th harmonics of magnitude 0.1 p.u. in the single-phase ac source. The grid current is seen to be harmonics free and its wave shape is close to sinusoidal despite the nonlinear loads and grid voltage harmonics as demonstrated in simulation and experimental results. To realize distortion free grid current, the grid-interfacing VSI is always synchronized with fundamental frequency component of the PCC voltage.
4.5. Performance under grid frequency fluctuations The performance of the VSI system under frequency fluctuations in mode II is illustrated through Figs. 14 and 15. The behavior during grid frequency drop is shown in Fig. 14. The grid frequency is reduced to 45 Hz from its nominal value (i.e. 50 Hz). The performance of the VSI is found to be unaffected as it is able to carry out its tasks such as harmonics compensation and active power injection even under frequency fall. Similarly, the performance during
449
ig(A) vpcc(V)
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
200 0 -200 20 0
ivsi(A)
-20 30 0 -30 20
il(A)
Qvsi= 2.5 kVAr
Qvsi= 0
0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
200 0 -200 20
Qvsi= 2.5 kVAr
0 -20 30
ivsi(A)
ig(A) vpcc(V)
Fig. 8. Performance during a step change in reactive power generation in mode-I: (a) simulation results and (b) experimental results.
0
Qvsi= 0
il(A)
-30 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
Fig. 9. Performance during a step change in reactive power generation in mode-II: (a) simulation results and (b) experimental results.
6
Pvsi= 5 kW
5
Q(kVAr)
4
Qvsi= 2.5 kVAr
3 2
Actual Power
Reference Power
1 0 -1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Time(s)
(a)
(b)
Fig. 10. Illustration of accurate control of reactive power generation. (a) Simulation results. (b) Experimental results.
grid frequency rise can also be understood from the waveforms shown in Fig. 15. Further, the simulation and experimental results are found to be in good agreement and demonstrate the immunity of the proposed control algorithm to grid frequency fluctuations. 4.6. Performance comparison of ANF with single-phase PLL in frequency estimation The performance of ANF in frequency estimation is compared with the well-known SOGI-based single-phase PLL [26] under different operating conditions. The comparative results are shown in
Fig. 16 for various testing scenarios such as frequency step change, phase-angle jump, voltage sag and voltage harmonics. The performance under frequency step change is illustrated in Fig. 16(a). It can be seen that both ANF and single-phase PLL are having equal response time of 30 ms. However, the frequency estimated by the single-phase PLL seem to have high overshoot and undershoots compared to those of ANF method. The performance under phaseangle jump of 40° is shown in Fig. 16(b). The SOGI-based PLL is found to have more frequency deviation compared to that of ANF method. However, the settling times for both the methods are found be to equal during the phase angle jump. The performance
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
il(A)
ivsi(A)
ig(A) vpcc(V)
450
200 0 -200 20 0 -20 30 0 -30 20
Load Change
0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 11. Performance under load application in mode-I: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20 20 0 -20 20
Load Change
0 -20 0.26
0.28
0.3
0.32
0.36
0.34
0.38
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 12. Performance under load application in mode-II: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20 20 0 -20 20 0 -20 0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
0.44
Time (s)
(a)
(b)
Fig. 13. Performance with harmonic grid: (a) simulation results; (b) experimental results.
comparison under a voltage sag of 0.4 p.u. is illustrated in Fig. 16 (c). In this case, the ANF estimated frequency is observed to have more deviation from the actual value. In Fig. 16(d), the performance under PCC voltage distortion is demonstrated. The frequency estimated by the single-phase PLL contains severe oscillations whereas the frequency estimated by the ANF contains very low amplitude oscillations which can be ignored.
4.7. Brief comparison of proposed control scheme The proposed control scheme is compared with the reported control algorithms such as neural networks and instantaneous p-q theory [19]. Various aspects such as complexity, settling time and harmonics compensation under grid voltage distortion have been considered and illustrated in Table 1. Both the reported
451
il(A)
ivsi(A)
ig(A) vpcc(V)
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200 0 -200 20 0 -20
Frequency Drop
20 0 -20 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 14. Performance during grid frequency drop: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20
Frequency rise
20 0 -20 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
Fig. 15. Performance during grid frequency rise: (a) simulation results; (b) experimental results.
56
ANF SRF
54 53 52 51
0.2
0.25
0.3
0.35
0.4
0.45
52
48 0.15
0.5
0.2
(a)
(b)
50 49 48 47
0.35
54
ANF SOGI
51
0.3
0.25
Time(s)
ANF SOGI
53
Frequency (Hz)
Frequency (Hz)
54
Time (s)
52
46 0.15
56
50
50 49 0.15
ANF SOGI
58
Frequency(Hz)
Frequency (Hz)
55
52 51 50 49 48 47
0.25
0.2
0.3
0.2
0.25
0.3
0.35
Time (s)
Time (s)
(c)
(d)
0.4
0.45
0.5
Fig. 16. Performance comparison of ANF-based frequency estimation with SOGI-PLL [26] based frequency estimation under various operating conditions (a) step change in frequency, (b) phase-angle jump, (c) voltage sag and (d) voltage harmonics.
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Table 1 Comparison of the proposed method with the existing methods. Control scheme
Is PLL required?
Sampling frequency (kHz)
Complexity
THD of ig under distorted voltages (%)
Settling time for ig under load step change (ms)
Proposed control Neural network [20] Instantaneous p-q theory [19]
No Yes Yes
40 30 30
Low Moderate Moderate
3.04 4.69 4.82
w10 w30 w30
References Table 2 System parameters. Grid rated voltage and frequency (f) VSI rating Coupling inductance (Lf) Nonlinear load
240 V(L-L), and 50 Hz 7.5 kVA 4 mH Single-phase diode bridge rectifier with series connected Rl = 20 X and Ll = 400 mH on dc side
methods require load harmonics extraction and an advanced single-phase PLL which leads to a lot of computations. Therefore, these methods need to be executed at higher sampling times i.e. lower sampling frequencies. The sampling frequencies used in those methods have also been listed in Table 1. Further, since the reported control algorithms require harmonic estimation, they possess larger settling times during the load disturbances. In addition to sampling frequency and settling time, the performance of the proposed control algorithm is compared for effective harmonic compensation under distorted conditions. Though all the methods ensure less than 5% THD for ig, in case of the proposed method, the ig have least THD. This is due to the fact that the frequency estimated by the ANF contains low amplitude oscillations compared to that of SOGI-based single-phase PLLs used in the reported ones. 5. Conclusion A simple and frequency adaptive control algorithm has been proposed for the control of single-phase grid-interfacing inverter in distributed generation applications. The main advantage of the proposed control algorithm is its low computational burden as it does not use any PLL block and harmonic current estimation unit. Further, the control algorithm uses closed loop control of power injected by the VSI to ensure accurate control. The different modes of operation of the proposed control algorithm have been discussed in detail. A variety of tests have been performed to demonstrate the accurate power control and load compensational capabilities. The performance of the proposed control algorithm has been analyzed through simulation and experimental results in basic power generation mode and harmonics compensation mode. It is shown that the proposed control algorithm achieves sinusoidal grid current irrespective of the loading and grid conditions in harmonics compensation mode. The robustness of the proposed control algorithm has been demonstrated as it is able to successfully inject the power and provide harmonics compensation even under distorted grid and frequency varying condition. Therefore, the proposed control algorithm acts as good alternative for existing control algorithms of gird-tied inverter as it offers better flexibility and less computations. Appendix A See Table 2.
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
An adaptive control algorithm for grid-interfacing inverters in renewable energy based distributed generation systems Naji Al Sayari, Rajasekharareddy Chilipi ⇑, Mohamad Barara Department of Electrical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Received 14 September 2015 Accepted 21 December 2015
Keywords: Distributed generation Renewable energy Adaptive notch filter Grid-interfacing inverter Power quality
a b s t r a c t This paper proposes an adaptive control algorithm for grid-interfacing inverters in renewable energybased distributed generation systems. The proposed control algorithm functions in two different modes: basic power generation mode, harmonics compensation mode. In basic power generation mode, the inverter pumps desired amounts of active and reactive powers into the grid at the point of common coupling. In harmonics compensation mode, the control algorithm ensures sinusoidal grid current through load current harmonics mitigation in addition to desired power generation. Moreover, the proposed control algorithm does not use any detection methods for compensation of harmonic currents. Hence, it results in low computational burden. Based on the requirements, the proposed control algorithm can be operated in either of the modes. A proportional–integral controller-based closed loop control is employed for accurate control of the power injected into the grid. A frequency adaptive notch filter is used to synchronize the grid-interfacing inverter with the fundamental component of grid voltage without using any phase locked loop. The effectiveness of the proposed control algorithm in reference active and reactive powers generation, current harmonics compensation is demonstrated successfully by simulation and experimental results. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction On the pathway to address the concerns posed by conventional energy sources such as depletion of fossil fuels and climate changes, many countries are aiming to increase their share of energy generation from clean energy sources. The energy sources such as solar, wind, hydro and bio-fuel are the prime candidates of clean energy. Generally, the energy harnessed from renewables is first used to cater the needs of local community and the remaining energy will be pumped into the grid by means of power electronic interfaces [1]. Voltage source inverter (VSI)-based power electronic interfaces are being widely used for the grid integration of renewable energy sources (RESs) [2]. In [3], a three-level inverter has been used for grid interconnection of a photovoltaic system. Ref. [4] provides a comprehensive review on application multilevel inverters and their control in grid connected photovoltaic systems. Multilevel inverter topologies are increasingly used in distribution generation applications due to their advantages such as low switch losses, less harmonic distortion and reduced filter
⇑ Corresponding author. E-mail address: [email protected] (R. Chilipi). http://dx.doi.org/10.1016/j.enconman.2015.12.076 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.
size. In [5], a multistage stage dc/ac converter has been proposed to improve the overall conversion efficiency. Integration of RESs with the utility network has attracted a great deal of interest due to potential environmental and economic factors. Various control algorithms for grid interconnection RESs via VSIs are discussed [6]. The grid-interfacing VSIs are operated as controlled current source to inject the power generated by the RESs into the grid. In [7], the power injected into the grid is controlled by changing the phase difference between the grid voltage and the inverter voltage. In [8], particle swarm optimization method has been used to control the grid injected power. In [9], an adaptive neuro-fuzzy controller has been used to control a single-phase grid-coupled inverter. In addition to active power injection, the grid-tied inverters can also be used for simultaneous reactive power compensation [10]. A doubly fed induction generator (DFIG) system with reactive power compensation capabilities has been discussed in [11]. Owing to the proliferation of electronically switched nonlinear loads, the amount of harmonic current being released into the power distribution network is growing rapidly and causing degradation of grid voltages. An active power filter [12] can be used to mitigate the harmonics injected by nonlinear loads. Alternatively, the grid connected VSI itself can be controlled to compensate the harmonic and reactive currents drawn by the local loads to improve
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grid power quality. Therefore, inclusion of harmonic currents suppression capabilities in the grid-tied inverters is gaining interest. Mostly, the capacity of the VSIs employed in grid-interfacing of RESs is underutilized due to the intermittent nature of RES. The remaining capacity of the VSIs can be diverted to power quality improvement. Therefore, the control algorithm that is adopted for grid-interfacing VSIs must offer great flexibility to use the remaining capacity of VSIs for power quality improvement through ancillary services. A control scheme for grid-interfacing VSIs with power quality improving ancillary services such as active power filtering and reactive power injection is presented in [13]. In [14], a grid interfaced multi-level inverter with shunt compensation capabilities is discussed. A flexible control algorithm based on recursive least squares has been presented in [15] for power quality improvement in grid interfaced distributed generation systems. In order to accommodate power quality improvement features such as active harmonic filtering and reactive power compensation, detection of harmonic and reactive currents is mandatory. Rapid and accurate detection of the harmonic signal, fast processing of the reference signal, and high dynamic response of the controller are the prime requirements for achieving desired level of compensation. Numerous control methodologies for detection of harmonic and reactive currents have been reported so far. The synchronously rotating d-q frame (SRF) theory [16] and instantaneous p-q theory [17] are the widely used conventional control algorithms to generate reference signals for harmonic currents compensation. In Ref. [18] also, the instantaneous p-q theory has been used for incorporating active harmonic filtering in grid-tied DFIG system. Ref. [19] has proposed a control algorithm for simultaneous active power generation and power quality improvement in wind energy driven DFIG system. In addition to aforementioned conventional methods, the detection methods employing artificial neural networks (ANN) [20] and fast Fourier transforms (FFT) [21] can be found in the literature. In [22], various ANN techniques have been compared for harmonic currents extraction and active power filtering. Nonetheless, the performance of the aforementioned detection techniques is highly affected by grid voltage distortion and frequency variations. To address this issue, a detection method that is independent of grid voltage distortion is developed in [23]. This method employs second order frequency adaptive pre-filters such as second order generalized integrators (SOGIs) [24] and adaptive notch filters. Precise and accurate estimation of harmonic and reactive components of load current would significantly increase the computation burden and therefore demands high speed digital controllers. For a low cost solution and minimizing the computational burden, researchers have proposed harmonics detection free methods [25]. These methods are designed for healthy grid conditions. In case of abnormal grid condition, the performance of VSI varies highly depending on the control algorithm used. In view of the above-stated drawbacks with the existing control algorithms, this article proposes a robust and harmonics detection free control algorithm. The proposed control also offers a flexibility to operate the grid-tied VSI in two different modes such as basic power generation mode and harmonics compensation mode for optimal utilization of VSI rating. Unlike the harmonic detectionfree control algorithms reported, the proposed control algorithm is immune to grid voltage distortions and frequency fluctuations. The proposed control algorithm synchronizes the grid-interfacing VSI with the fundamental frequency component of grid voltage to make its performance independent of grid disturbances such as frequency fluctuations and voltage distortions. The fundamental frequency component of grid voltage is obtained by using a frequency adaptive notch filter (ANF) [23]. Adaptive nature of the ANF allows precise tracking of variations in the frequency and magnitude of the fundamental components and thereby eliminates the use of single-phase phase locked loop (PLL) [26]. This will
further reduce the computational load on the digital processor. Closed-loop control of active and reactive powers with simple proportional-plus-integral (PI) controller based regulation is employed to achieve accurate tracking of reference powers with zero steady state errors. The key benefits of proposed control algorithm are summarized as follows: 1. Detection free harmonic and reactive currents compensation. 2. Accurate control of active and reactive powers. 3. Immune to grid voltage distortions and adaptive to frequency fluctuations. 4. PLL less grid synchronization. 5. Offers flexibility to operate in different modes. The feasibility and the effectiveness of the proposed control algorithm are simultaneously verified through computer simulation studies and hardware-in-the-loop (HIL)-based experimental tests. The rest of the paper is organized as follows: Section 2 discusses the configuration of the grid-interfacing VSI system under study. Section 3 presents the formulation of proposed PLL less frequency adaptive control algorithm and its various modes of operation. Section 4 validates the proposed control algorithm based on simulation and experimental results. Section 5 concludes the paper. 2. System configuration Fig. 1 depicts the basic configuration of grid-interfacing singlephase H-bridge VSI in renewable energy systems consisting of renewable power generation units and different types of loads. Renewable energy sources, such as wind and solar, are typically used to generate electricity for residential users. The power generation units use dc/dc and dc/ac static power electronic converters for voltage conversion and battery banks for energy storage. The battery banks form a constant voltage dc bus. The power electronic converters perform maximum power point tracking and extract the maximum energy possible from wind and solar sources. Thus the energy extracted is fed to the grid via a single-phase VSI after serving the local loads. The grid-interfacing VSI is connected to single-phase distribution network with a coupling inductor (Lf) at the point of common coupling (PCC). The symbols ig, ivsi and il represent the grid current, VSI current, and load current, respectively. The grid voltage and the voltage at PCC are denoted as vg and vpcc, respectively. 3. Proposed control algorithm This section describes the proposed adaptive control algorithm for single-phase grid interfaced VSI. The schematic of proposed control algorithm is shown in Fig. 2. As previously mentioned,
Lg AC
Grid
vg
ig
il
v pcc Lf
AC
ivsi
Local Loads
DC
Energy Storage
Wind Energy
VSI
DC DC
Solar Energy
400V DC Bus
PWM pulses
Fig. 1. Schematic of grid-interfacing single-phase inverter.
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the proposed control algorithm operates in two different modes: (1) basic power generation mode, (2) harmonics compensation mode. These modes are also referred to as mode-I and mode-II, respectively. In both the modes, the VSI is operated as controlled current source. Closed loop control of active and reactive powers injected into by the VSI is maintained in both the modes. The reactive power generated by the VSI is needed to be adjusted by varying the reference value to meet the reactive power demand of local loads and achieve unity power factor operation of grid at the PCC. The control algorithm can be operated in either of the modes by changing the value of the gain parameter Gh. The Gh value can be either ‘0’ or ‘1’. In basic power generation mode, the Gh is set to ‘0’ and in harmonics compensation mode, the Gh is set ‘1’. A frequency adaptive notch filter is used to synchronize the VSI with the fundamental frequency component of PCC voltage. This achieves harmonic rejection capability and frequency adaptability of the proposed control algorithm even under distorted utility conditions. 3.1. Adaptive notch filter As mentioned earlier, an ANF is used in this study to synchronize the VSI with fundamental frequency component of PCC voltage. The structure of ANF is shown in Fig. 3. The ANF processes the PCC voltage signal and produces a set of fundamental frequency orthogonal signals [23]. The outputs of ANF vpccf and vpccfq are having equal amplitudes, but phase displaced by 90° from each other. The ANF is a linear time invariant system whose magnitude response vanishes at a particular frequency called notch frequency and constant elsewhere on the jx axis as defined by the transfer function given in (1).
EðsÞ ¼
ev ðsÞ s2 þ x21 ¼ 2 v pcc ðsÞ s þ kx1 s þ x21
ð1Þ
where x1 is the ANF estimated fundamental frequency and also the resonating/natural frequency in rad/s. From the bode diagram of E(s) shown in Fig. 4, it is observed that the magnitude of E(s) is equal to zero when the input signal frequency is equal to the resonance frequency (x = x1) and it is equal to unity for when the input signal frequency is greater (x > x1) or less (x < x1) than the resonating frequency. The relation between input voltage signal and the output orthogonal signals is characterized by the following transfer functions.
DðsÞ ¼
v pccf ðsÞ kx1 s ¼ v pcc ðsÞ s2 þ kx1 s þ x21
ð2Þ
Pref
ivsi v pcc
Pvsi
Qref
Average Power Estimation
ANF
ð4aÞ
x_ 1 ¼ cx1 ev x
ð4bÞ
ev ¼ v x_
ð4cÞ
where k > 0 is the damping coefficient and c > 0 determines the adaptation speed. These parameters are used to tradeoff between adaptation speed and noise sensitivity. As in all adaptive systems, the estimated frequency x1 reaches the steady state slowly com_ xÞ when c is very small. For a given sinusoidal pared to its states ðx; input signal v = Vm sin xt, the dynamical system represented by (4) has a unique periodic orbit with constant and correct estimated frequency,
2
3 2 V 3 x xm cos xt 6 _ 7 6 7 o,4 x 5 ¼ 4 V m sin xt 5 1 x x
v_ ¼
x_ €x
¼
0
x 0 þ v kx1 x_ kx1 1
x21
_ x_ 1 ¼ cx1 xðv xÞ
ð6Þ ð7Þ
Considering a steady state operating frequency locked condition _ 1 ¼ 0, then (6) boils down to i.e. x = x1 and x
" #
x_ sin x1 t v_ jx¼x1 ¼ ¼ V m €x x1 cos x1 t
ð8Þ
Even if the frequency estimated by ANF is locked intentionally at a different value from the input signal frequency by making c = 0, still the state vector would keep a stable orbit as expressed by (9) and (10)
v_ jx–x1 ¼
" # x_ sinðxt þ /Þ ¼ Að x Þ €x x cosðxt þ /Þ
IP
Vmf
uf ivsi*
u fq
il
PI
ð5Þ
The bar (–) over the variables in (5) represent equilibrium condition. The state space realization of ANF which is required for stability analysis can be obtained from (6) and (7) as,
v pccfq
Qvsi
ð3Þ
€x þ x21 x ¼ kx1 ev
v pccf
v pcc
v pccfq ðsÞ kx21 ¼ 2 v pcc ðsÞ s þ kx1 s þ x21
3.1.1. Local stability The dynamic behavior of ANF structure can be described by a set of continuous time differential equations given in (4).
PI
90° Delay
90° Delay
QðsÞ ¼
IQ
Fig. 2. Schematic of proposed control algorithm.
ivsierr
ivsi Gh
ð9Þ
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kxx1 where AðxÞ ¼ V m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 ðx1 x2 Þ þ k x21 x2 / ¼ arctan
kxx1 x21 x2
ð10aÞ
ð10bÞ
From (9), it is evident that the ANF keeps the following steady state relationship between € x and x when x – x1 as described in (11).
€x ¼ x2 x
ð11Þ
Using (11), the steady state synchronization error, (the difference between v and x) can be deduced as
ev ¼ v x ¼
1 :ð€x þ x2 xÞ kx1
ð12Þ
Using (11) and (12), the frequency error in steady state can be written as,
ef ¼ xx1 ev ¼
x2 ðx21 x2 Þ k
ð13Þ
Therefore, (13) confirms that the signal ef carries the frequency error information and hence used as the control signal in ANF for estimating the system frequency. Now, the local stability analysis can be carried out by assuming x x1 that approximates x21 x2 to 2(x x1)x1, in this condition the dynamics of ANF can be described as,
c c x_ 1 ¼ cef ¼ x2 ðx2 x21 Þ 2 x2 ðx x1 Þx1 k
k
ð14Þ
If we define the frequency estimation error as d = (x x1) and _ 1. its derivative under constant input frequency is given by d_ ¼ x Therefore, the condition given by (15) will always be true for positive values of estimated frequency which is the key for local stabilization.
c
dd_ ¼ 2 x2 d2 x1 6 0: k
ð15Þ
3.1.2. Tuning of ANF Tuning of ANF involves design of its parameters ‘k’ and ‘c’. For a given sinusoidal input signal v = Vm sin xt with constant frequency, the relation between input and output signal is given by
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi kx1 2V m 2 xt 4k e 2 þ V m sin xt x_ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin 2 2 4k
ð16Þ
From (16), the settling time taken by the ANF is given by
t ANF ¼
10 k x1
ð17Þ
Expression (17) affirms that the gain ‘k’ defines the bandwidth and hence the filter response time. A very high value of ‘k’ would result in fast response and reduces its immunity to noise. However, a very low value of ‘k’ leads to sluggish ANF response. In the prepffiffiffi sent study ‘k’ is set to 2 to achieve optimal performance. The other unknown parameter ‘c’ of ANF cannot be estimated directly using linear control system analysis as the frequency adaptation loop is highly nonlinear. Therefore, as illustrated in [24], using averaged dynamics and assuming x x1 the value of gain ‘c’ can estimated as
c¼
kx1 V 2m
s:
ð18Þ
The value of s can be selected based on the settling time (tF) in frequency estimation process as
tF ¼
5
s
:
ð19Þ
3.2. Mode-I: basic power generation mode In this mode, the VSI pumps the reference active and reactive powers into the grid by injecting in-phase and quadrature-phase currents with PCC voltage, respectively. To regulate the powers being injected into the grid, the instantaneous real and reactive powers across the VSI terminal are first measured.
pv si ¼
1 v pcc iv si þ v pccq iv siq 2
ð20Þ
qv si ¼
1 v pccq iv si v pcc iv siq 2
ð21Þ
where vpccq and ivsiq are the quarter cycle delayed signals of vpcc and ivsi, respectively. The grid frequency information required to estimate the quarter cycle delayed signals of vpcc and ivsi is obtained from ANF. The powers estimated in (20) and (21) are fed to moving average blocks to estimate their averages. The estimated average active and reactive powers of the VSI are now compared with reference powers and then the errors are processed through PI controllers. The regulation law is defined as,
IP ¼
k2 k1 þ ðPref Pv si Þ s
IQ ¼
k3 þ
k4 ðQ ref Q v si Þ s
ð22Þ
ð23Þ
where k1, k2, k3 and k4 are the proportional and integral gain constants of the PI controllers, Pvsi and Qvsi are the averages of pvsi and qvsi, respectively. Ip and IQ represent the magnitudes of active and reactive currents to be injected by the VSI for reference powers generation. The Pref is decided by the power extracted from the RESs. Unlike the open-loop methods, use of PI controllers for active and reactive powers control takes care of power errors caused due to the interactions between VSI harmonic current and PCC harmonic voltage. From (22) and (23), the reference current signal for generating Pref and Qref is computed as
iv si ¼ IP uf þ IQ ufq
ð24Þ
where uf and ufq are the in-phase and quadrature-phase unit templates of PCC voltage at fundamental frequency, respectively. From (24) it is evident that the envelope of the reference VSI current iv si is decided by the unit templates (uf and ufq) of fundamental component of PCC voltage. The unit templates of fundamental PCC voltage are obtained as,
uf ¼
v pccf V mf
ufq ¼
v pccfq V mf
ð25Þ ð26Þ
where vpccf and vpccfq are the orthogonal signals generated by the ANF employed over PCC voltage as shown in Fig. 3 and Vmf is their amplitude. 3.3. Mode-II: harmonics compensation mode For Gh = 1, the control algorithm offers compensation of harmonic and reactive currents drawn by the local loads. Unlike the basic power generation mode, in this case, the outputs of PI controllers are multiplied with fundamental in-phase and quadrature-phase unit templates of PCC voltage to yield reference grid current instead of reference VSI current.
ig ¼ IP uf þ IQ ufq
ð27Þ
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
x
k v pcc = v
ω1x
ev
ef
-γ
ω1
v pccf
x
∫ x
∫
v pccfq
4.1. Performance under step change in active power generation The performance under a step change in active power has been examined and the corresponding results are depicted in Figs. 5–7. A nonlinear load of 2.5 kW is connected to the system. Fig. 5 (a) and (b) shows the simulation and experimental recordings of vpcc, ig, ivsi and il in mode I, respectively. During Pvsi = 0, the current ivsi is absent and ig is seen to be identical to il. Change in wave shape of ig and ivsi can be noticed as the Pref changes from 0 to 5 kW. In this mode, the grid current ig carries harmonics as the VSI offers no harmonics compensation. Fig. 6 shows the waveforms of vpcc, ig, ivsi and il under Pref change in mode II. Both simulation and experimental results exhibit identical transient performance. In Fig. 6, the current ig is maintained sinusoidal since the VSI offers compensation along with reference power generation in this mode. In mode II, during Pref = 0, the VSI acts as simple compensator as it provides only the compensation of harmonic currents to keep grid current distortion free at the PCC. Further, the active power injected by the VSI tracks the reference power very accurately and it reaches steady state within 20 ms as illustrated in Fig. 7(a) and (b).
Fig. 3. Structure of adaptive notch filter.
ω> ω
1
1
Magnitude (abs) Phase (deg)
1
0.5
0
0 90
-90 0.01
0.1
1
10
50
1000
10000
Frequency (Hz) Fig. 4. Magnitude and phase response of E(s).
4.2. Performance under step change in reactive power generation
From ig of (27), the load current il is subtracted from ig to obtain reference current of VSI.
iv si ¼ ig il
ð28Þ
In addition to harmonic currents suppression, the VSI injects pre-set values of active and reactive powers into the grid. In order to achieve unity power factor, the IQ in (27) should be brought to zero by adjusting the Qref value in (23) which makes the unity power factor operation of the grid manual. Now, the reference VSI current iv si estimated in (24) or (28) is compared with actual current ivsi and the error is defined as, err
iv si ¼ iv si iv si
variables such as PCC voltage (vpcc), grid current (ig), VSI current (ivsi), load current (il), reference power (Pref) and the injected power (Pvsi) are displayed on a digital oscilloscope via onboard D/A converter for the illustration of system performance. The experimental results obtained are presented alongside the simulation results for simultaneous evaluation of the results.
ω1
∫
ω< ω
447
ð29Þ
The current error in (29) is fed to a hysteresis current controller to generate the firing pulses for the grid-interfacing VSI.
The performance of the proposed control algorithm is also verified under step change in reactive power generation and it is illustrated in Figs. 8–10. Keeping the active power generation at 5 kW, the reactive power supplied by the VSI is changed from 0 to 2.5 kVAr. The positive value of Qvsi indicates the inductive nature of the supplied reactive power. The waveforms of vpcc, ig, ivsi and il during the reactive power change in mode I and II are shown in Figs. 8 and 9, respectively. During Qref = 0, the currents ig and ivsi are exactly out-of-phase with vpcc. As the Qvsi rose to 2.5 kVAr, change in magnitude of ivsi and ig and their phase displacement with respect to vpcc can be seen. Transient behavior of Qvsi and Pvsi during Qref change is shown in Fig. 10. It is observed that the Qvsi is perfectly following its reference value, whereas the Pvsi is exactly maintained at 5 kW except the small oscillations during Qvsi sudden change. 4.3. Performance under step change in load
4. Results and performance evaluation The feasibility of the proposed control algorithm for grid-tied inverters is verified through simulation and experimental studies. The system configuration presented in Fig. 1 and the proposed control algorithm are modeled in MATLAB/Simulink environment using power system tool box. The simulation is carried at a fixed step size of 10 ls. The proposed control algorithm is tested for an active power generation system of 5 kW. A local nonlinear load of 2.5 kW is considered for performance evaluation. The system parameters are presented in appendix. The performance of the control algorithm is verified in both the modes. A dSPACE-based digital signal processor DS1202 is employed to implement the proposed control algorithm. A sampling frequency of 40 kHz is used in processing the control algorithm. The system under study consisting of single-phase grid, H-bridge inverter and local loads is realized in a hardware-in-the-loop (HIL) system. The system parameters and the loading conditions are kept identical to those used in computer simulations. All the necessary
The performance under load step change is demonstrated with the power generation keeping at Pvsi = 5 kW and Qvsi = 0. The load connected to the system is nonlinear in nature. The results obtained in mode I and II are presented in Figs. 11 and 12, respectively where the load on system is increased from 1.25 kW to 2.5 kW. Since the net active power is being drawn from the grid is negative, any increase in the load causes reduction in ig. The VSI current is seen to be constant since Pvsi is constant. In mode II, the VSI current magnitude slightly changes as the load changes due to the increase in harmonic compensation current. 4.4. Performance with harmonic grid Fig. 13(a) and (b) shows the simulation and experimental results obtained with harmonic grid conditions, respectively. These results demonstrate effective harmonics compensation capabilities of the proposed control algorithm even under highly distorted grid voltages. These results are obtained for active power generation of
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
il(A)
ivsi(A)
ig(A) vpcc(V)
448
200 0 -200 20 0 -20 40 20 0 -20 -40 20
P = 5 kW vsi
P =0 vsi
0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
200 0 -200 20
P = 5 kW vsi
0 -20
ivsi(A)
ig(A) vpcc(V)
Fig. 5. Performance during a step change in active power generation in mode-I: (a) simulation results and (b) experimental results.
P =0
20 0 -20
vsi
il(A)
20 0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
Fig. 6. Performance during a step change in active power generation in mode-II: (a) simulation results and (b) experimental results.
6
Pvsi= 5 kW
5
P(kW)
4
Actual Power
3
Reference Power
2 1
Pvsi= 0
Pvsi= 0
0 -1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Time(s)
(a)
(b)
Fig. 7. Illustration of accurate control of active power generation. (a) Simulation results. (b) Experimental results.
5 kW and zero reactive power. The performance in mode II only is considered. The grid voltage distortion is realized by injecting 3rd and 9th harmonics of magnitude 0.1 p.u. in the single-phase ac source. The grid current is seen to be harmonics free and its wave shape is close to sinusoidal despite the nonlinear loads and grid voltage harmonics as demonstrated in simulation and experimental results. To realize distortion free grid current, the grid-interfacing VSI is always synchronized with fundamental frequency component of the PCC voltage.
4.5. Performance under grid frequency fluctuations The performance of the VSI system under frequency fluctuations in mode II is illustrated through Figs. 14 and 15. The behavior during grid frequency drop is shown in Fig. 14. The grid frequency is reduced to 45 Hz from its nominal value (i.e. 50 Hz). The performance of the VSI is found to be unaffected as it is able to carry out its tasks such as harmonics compensation and active power injection even under frequency fall. Similarly, the performance during
449
ig(A) vpcc(V)
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200 0 -200 20 0
ivsi(A)
-20 30 0 -30 20
il(A)
Qvsi= 2.5 kVAr
Qvsi= 0
0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
200 0 -200 20
Qvsi= 2.5 kVAr
0 -20 30
ivsi(A)
ig(A) vpcc(V)
Fig. 8. Performance during a step change in reactive power generation in mode-I: (a) simulation results and (b) experimental results.
0
Qvsi= 0
il(A)
-30 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
Fig. 9. Performance during a step change in reactive power generation in mode-II: (a) simulation results and (b) experimental results.
6
Pvsi= 5 kW
5
Q(kVAr)
4
Qvsi= 2.5 kVAr
3 2
Actual Power
Reference Power
1 0 -1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Time(s)
(a)
(b)
Fig. 10. Illustration of accurate control of reactive power generation. (a) Simulation results. (b) Experimental results.
grid frequency rise can also be understood from the waveforms shown in Fig. 15. Further, the simulation and experimental results are found to be in good agreement and demonstrate the immunity of the proposed control algorithm to grid frequency fluctuations. 4.6. Performance comparison of ANF with single-phase PLL in frequency estimation The performance of ANF in frequency estimation is compared with the well-known SOGI-based single-phase PLL [26] under different operating conditions. The comparative results are shown in
Fig. 16 for various testing scenarios such as frequency step change, phase-angle jump, voltage sag and voltage harmonics. The performance under frequency step change is illustrated in Fig. 16(a). It can be seen that both ANF and single-phase PLL are having equal response time of 30 ms. However, the frequency estimated by the single-phase PLL seem to have high overshoot and undershoots compared to those of ANF method. The performance under phaseangle jump of 40° is shown in Fig. 16(b). The SOGI-based PLL is found to have more frequency deviation compared to that of ANF method. However, the settling times for both the methods are found be to equal during the phase angle jump. The performance
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
il(A)
ivsi(A)
ig(A) vpcc(V)
450
200 0 -200 20 0 -20 30 0 -30 20
Load Change
0 -20 0.26
0.28
0.3
0.32
0.34
0.36
0.38
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 11. Performance under load application in mode-I: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20 20 0 -20 20
Load Change
0 -20 0.26
0.28
0.3
0.32
0.36
0.34
0.38
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 12. Performance under load application in mode-II: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20 20 0 -20 20 0 -20 0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
0.44
Time (s)
(a)
(b)
Fig. 13. Performance with harmonic grid: (a) simulation results; (b) experimental results.
comparison under a voltage sag of 0.4 p.u. is illustrated in Fig. 16 (c). In this case, the ANF estimated frequency is observed to have more deviation from the actual value. In Fig. 16(d), the performance under PCC voltage distortion is demonstrated. The frequency estimated by the single-phase PLL contains severe oscillations whereas the frequency estimated by the ANF contains very low amplitude oscillations which can be ignored.
4.7. Brief comparison of proposed control scheme The proposed control scheme is compared with the reported control algorithms such as neural networks and instantaneous p-q theory [19]. Various aspects such as complexity, settling time and harmonics compensation under grid voltage distortion have been considered and illustrated in Table 1. Both the reported
451
il(A)
ivsi(A)
ig(A) vpcc(V)
N. Al Sayari et al. / Energy Conversion and Management 111 (2016) 443–452
200 0 -200 20 0 -20
Frequency Drop
20 0 -20 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
il(A)
ivsi(A)
ig(A) vpcc(V)
Fig. 14. Performance during grid frequency drop: (a) simulation results and (b) experimental results.
200 0 -200 20 0 -20
Frequency rise
20 0 -20 20 0 -20 0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
Time (s)
(a)
(b)
Fig. 15. Performance during grid frequency rise: (a) simulation results; (b) experimental results.
56
ANF SRF
54 53 52 51
0.2
0.25
0.3
0.35
0.4
0.45
52
48 0.15
0.5
0.2
(a)
(b)
50 49 48 47
0.35
54
ANF SOGI
51
0.3
0.25
Time(s)
ANF SOGI
53
Frequency (Hz)
Frequency (Hz)
54
Time (s)
52
46 0.15
56
50
50 49 0.15
ANF SOGI
58
Frequency(Hz)
Frequency (Hz)
55
52 51 50 49 48 47
0.25
0.2
0.3
0.2
0.25
0.3
0.35
Time (s)
Time (s)
(c)
(d)
0.4
0.45
0.5
Fig. 16. Performance comparison of ANF-based frequency estimation with SOGI-PLL [26] based frequency estimation under various operating conditions (a) step change in frequency, (b) phase-angle jump, (c) voltage sag and (d) voltage harmonics.
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Table 1 Comparison of the proposed method with the existing methods. Control scheme
Is PLL required?
Sampling frequency (kHz)
Complexity
THD of ig under distorted voltages (%)
Settling time for ig under load step change (ms)
Proposed control Neural network [20] Instantaneous p-q theory [19]
No Yes Yes
40 30 30
Low Moderate Moderate
3.04 4.69 4.82
w10 w30 w30
References Table 2 System parameters. Grid rated voltage and frequency (f) VSI rating Coupling inductance (Lf) Nonlinear load
240 V(L-L), and 50 Hz 7.5 kVA 4 mH Single-phase diode bridge rectifier with series connected Rl = 20 X and Ll = 400 mH on dc side
methods require load harmonics extraction and an advanced single-phase PLL which leads to a lot of computations. Therefore, these methods need to be executed at higher sampling times i.e. lower sampling frequencies. The sampling frequencies used in those methods have also been listed in Table 1. Further, since the reported control algorithms require harmonic estimation, they possess larger settling times during the load disturbances. In addition to sampling frequency and settling time, the performance of the proposed control algorithm is compared for effective harmonic compensation under distorted conditions. Though all the methods ensure less than 5% THD for ig, in case of the proposed method, the ig have least THD. This is due to the fact that the frequency estimated by the ANF contains low amplitude oscillations compared to that of SOGI-based single-phase PLLs used in the reported ones. 5. Conclusion A simple and frequency adaptive control algorithm has been proposed for the control of single-phase grid-interfacing inverter in distributed generation applications. The main advantage of the proposed control algorithm is its low computational burden as it does not use any PLL block and harmonic current estimation unit. Further, the control algorithm uses closed loop control of power injected by the VSI to ensure accurate control. The different modes of operation of the proposed control algorithm have been discussed in detail. A variety of tests have been performed to demonstrate the accurate power control and load compensational capabilities. The performance of the proposed control algorithm has been analyzed through simulation and experimental results in basic power generation mode and harmonics compensation mode. It is shown that the proposed control algorithm achieves sinusoidal grid current irrespective of the loading and grid conditions in harmonics compensation mode. The robustness of the proposed control algorithm has been demonstrated as it is able to successfully inject the power and provide harmonics compensation even under distorted grid and frequency varying condition. Therefore, the proposed control algorithm acts as good alternative for existing control algorithms of gird-tied inverter as it offers better flexibility and less computations. Appendix A See Table 2.
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