Decoupled control of grid connected inverter with dynamic online grid impedance measurements for micro grid applications

Electrical Power and Energy Systems 68 (2015) 1–14

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Decoupled control of grid connected inverter with dynamic online grid impedance measurements for micro grid applications A. Vijayakumari a,⇑, A.T. Devarajan a, N. Devarajan b a b

Amrita Vishwa Vidyapeetham University, Coimbatore 641 112, India Government College of Technology, Coimbatore 641 013, India

a r t i c l e

i n f o

Article history: Received 8 October 2013 Received in revised form 20 October 2014 Accepted 5 December 2014

Keywords: Current control of inverter Synchronous reference frame d–q decoupling Micro grid Grid impedance measurement

a b s t r a c t This paper presents a decoupled control of grid connected inverter using dynamic online grid impedance measurements for a micro grid application. The proposed controller is implemented in synchronous reference frame (SRF) and controlled using linear PI controllers. The mutual coupling introduced between the d and q control loops due to the transformation into SRF is accurately decoupled using the dynamically measured grid impedance using a feed-forward control. The decoupling allows independent control of active and reactive powers against step changes in the active/reactive power references. The online measurement of the actual impedance and its use further for decoupling is proposed in this paper for making the decoupling accurate inspite of the network configuration being altered like in micro grids. Here the grid resistance and inductance are measured during the operation using a non-characteristic frequency current continuously injected into the grid, and subsequently calculating the impedance using discrete Fourier transforms. The continuous injection of non-characteristic current at 75 Hz avoids the injection of sub-harmonics into the grid during measurements. The control loop is updated periodically with the estimated grid impedance, thus enabling the independent control of active and reactive powers delivered by the inverter. The proposed decoupled controller with grid impedance measurement is tested through simulation studies and hardware experiments. The experiments are conducted with the proposed controller on a scaled down laboratory model of micro-grid with a 1 kVA solar inverter, and the performances are presented for step changes in the power references and the results are presented. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction The exponential growth of energy demand with deteriorating environment has lead to the research on renewable energy generation systems like wind power, solar photo voltaic power, etc. Renewable energy sources are connected to the grid through inverters [1,2] with one or more of the following control requirements viz. (i) Independent control of active and reactive powers (ii) synchronization to grid, (iii) meeting the harmonics standards, (iv) control under healthy and fault grid conditions and (v) islanding detection and isolation. The power delivered by the inverter is controlled either by PWM voltage control [1] or by current control [3,4]. PI control is commonly used and recently the PR control is advocated [5,6].

⇑ Corresponding author at: Department of Electrical and Electronics Engineering, Amrita Vishwa Vidyapeetham University, Amrita Nagar, Coimbatore 641 112, India. Tel.: +91 4222656422, mobile: +91 9942999952. E-mail addresses: [email protected], [email protected] (A. Vijayakumari). http://dx.doi.org/10.1016/j.ijepes.2014.12.015 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

The selection of controller is based on the steady state and transient state performance requirements to meet the power quality standards. PR controllers operate, both with the stationary reference frame quantities or directly with time varying abc quantities. PR controller, proposed in [5,6] for grid connected applications tracks the ac reference quantities with zero steady state error without introducing any phase delay. Also it does not require synchronous d–q transformation of the three phase quantities. However, PR controller is very sensitive to the grid frequency fluctuations, as it introduces infinite gain at grid frequency. If the frequency is outside the band, the system may go to unstable conditions [7] unless the band is wide enough, which in turn causes increased steady state error. With linear PI regulators, the ac quantities are transformed into dc quantities using synchronously rotating reference frame transformations [1,2,8–12]. This makes it possible to derive a dc control loop to track the ac quantities with zero steady state error. The information about the phase, the form and magnitude of the grid voltage is necessary for the abc ? dq transformation. This transformation

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introduces mutual coupling terms linking the d and q axis control loops due to the presence of the impedance between inverter and grid [1,2,7]. Consequently, a step change in the active power reference causes change in the reactive power delivered, in spite of the reactive power reference being kept constant. Similar change is felt with step change in reactive power reference as well. Thus independent control of active and reactive powers is not possible. Both feed forward and feedback based controllers have been suggested in literature to cancel the mutual coupling effect [13,15–18,20–23]. They use a constant value of impedance in the decoupling terms. However, in practice, the impedance will vary from system to system. It also varies depending on the operating conditions of the system. For e.g. in a micro grid, several renewable energy sources and conventional energy sources operate together. The switching in and switching out of any distributed generator will cause variation in the impedance seen by the grid connected inverters [19]. So, it becomes necessary to measure the grid impedance in an actual application to make the decoupling independent of the system and the operating conditions. Measurement of grid impedance magnitude has been done in [24–28], by burst of non characteristic frequency current injection and discrete Fourier transform (DFT) based calculations. This paper proposes continuous injection of a non characteristic frequency component for online measurement of grid impedance and periodic update of these impedance values into the control loop for the removal of cross coupling. The briefing of the modeling and design of a generic PI based current controller for grid connected VSI is done in Section ‘Modeling of synchronous reference frame current controllers for grid connected VSI’. The concept of removal of cross coupling between the d and q axis control loops with grid impedance for a typical micro-grid is explained in Section ‘Existence of cross-coupling and its effect of on active–reactive power control’, and the effect of variation of source inductance on decoupling is presented in Section ‘Decoupling the dependency of active and reactive powers on each other’. Section ‘Configuration changes in micro grids and its effect on decoupling’ explains the measurement of grid impedance. Section ‘Grid impedance measurement’ describes the proposed decoupled control of grid connected VSI with online grid impedance measurement and its performance evaluation. Finally Section ‘The proposed decoupled control of grid connected VSI with on-line grid impedance measurement’ presents the conclusions and the future scope for the proposed system. Modeling of synchronous reference frame current controllers for grid connected VSI There have been several methods proposed [4,6–13] for current control of grid tied inverters. Control of grid connected inverters is done with variables in synchronous reference frame (SRF), in which they appear as dc quantities. The control action is performed with simple PI controllers. Fig. 1 shows the circuit diagram of a three phase grid connected VSI. ua, ub and uc are the inverter pole voltages, ea, eb and ec are the grid phase voltages, Li is the filter

S1

S3

S5 R

ua Vdc

ub uc

S2

S4

Li

Lg i e a a ib

eb

inductance and Lg is the grid inductance. The currents injected into the grid in each phase are ia, ib and ic. The differential equation for the system shown in Fig. 1 is

  di L ¼ ½uabc  ½eabc  R½iabc dt abc

ð1Þ

where L is the total inductance from the inverter to the mains, i.e. L = Li + Lg. If x = 2pf, where f is the grid frequency, then Eq. (1) is written in synchronously rotating reference frame [13,14] as

udq ¼ L

didq þ ðR þ jxLÞidq þ edq dt

ð2Þ

Resolving (2) to its real and imaginary parts results

ud ¼ L

did þ Rid  xLiq þ ed dt

ð3Þ

uq ¼ L

diq þ Riq þ xLid þ eq dt

ð4Þ

Based on Eqs. (3) and (4) the general block diagram for current control of grid connected VSI in synchronous reference frame is obtained as shown in Fig. 2, where id⁄, iq⁄ are d and q axes reference currents respectively. A PLL gives the necessary phase information of the grid voltage to the abc–dq transformation blocks. The voltage drop due to the line impedance is compensated using a PI controller in each loop. The control equations for ud and uq are given as

  ki  ðId  Id Þ ud ¼ ed  xLiq þ kp þ s

ð5Þ

  ki uq ¼ eq þ xLid þ kp þ ðI  Iq Þ s P q

ð6Þ

Also the active power P and reactive power Q in the SRF using dq quantities are given as

P¼

3 ðud id þ uq iq Þ 2

ð7Þ

Q¼

3 ðud iq  uq id Þ 2

ð8Þ

But, Eqs. (7) and (8) exhibits a mutual coupling between the d and q axis quantities thus, makes it impractical to control P and Q independently. It is obvious that when the d axis voltage and currents are varied to vary the active power delivered, there is no grip to maintain the reactive power delivered unvarying. This dependency can be eliminated by setting uq = 0. It can be achieved by aligning the space-vector on the d-axis making the projection of it on the q-axis zero. Now the active and reactive powers expressions are modified as

P ¼ 3=2ud id

ð9Þ

Q ¼ 3=2ud iq

ð10Þ

Eqs. (9) and (10) revels that the active power is carried by d-axis current alone and the reactive power is carried by the q-axis current alone. This makes the active and reactive powers being controlled by controlling the respective currents independently. Existence of cross-coupling and its effect of on active–reactive power control

ic ec

S6

Fig. 1. Three phase grid connected VSI.

Even though independent active–reactive power control is successful, still there exists an interaction between the two axis variables when looking back Eqs. (3) and (4) thus the dependency persist between the control loops. With reference to Eqs. (3) and

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ed id*

PI Controller

id

+

+

Vdc

ωL

ud

ωL

3φ

SVPWM MODULATOR

INVERTER

uq R

+

*

iq

PI Controller

iq

+

+

L

eq

id

dq abc

iq

θ

ia ib ic eabc

PLL

ed eq

θ

dq

abc

eabc

Grid Fig. 2. General block diagram of current control of VSI in synchronous reference frame.

(4), under steady state the d-axis applied voltage results in q-axis current and the q-axis applied voltage results d-axis current with the assumption xL  R. For instance, the q-axis voltage is changed in order to change the d-axis current intending to change the power from say P1 to P2. As an upshot, there will be a change in the q-axis current which in turn will result a change in Q. But, this change in Q will not be entertained by the closed loop feed back, and corrects it back to the set value under steady state. However, during a considerable transient period, consisting of the measuring delays, inverter switching delays etc., the interaction between the d and q control loops exists. This interaction makes the inverter system and its control vulnerable to model changes. So, whenever the active power reference changes the reactive power delivered will change during the transient period and then comes back to its set value. The converse is also true with reactive power reference change. This dependency can again be cancelled by adapting a simple control system compensation method which is elaborated in the next section.

   of the plant G(s) from  RL þ jx to  RL in synchronous reference frame and by adding a real zero using the compensator. This is achieved by selecting a control voltage udq as

udq ¼ udq þ jxLidq

By substituting udq from Eq. (11) in Eq. (2) a control equation for the decoupled system is obtained as

L

didq ¼ udq  Ridq  edq dt

ð12Þ

It is evident that there is no cross coupling in Eq. (12) as there are no complex valued coefficients. Eq. (11) is modelled as the inner feedback loop and a current regulator having its output as u-dq ⁄ is designed as an outer loop for the decoupled system. The block diagram of the decoupled control system with the new control voltage as in Eq. (11) is given in Fig. 3, where idq is the reference vector expressed as

Decoupling the dependency of active and reactive powers on each other With reference to Eqs. (5) and (6), ud and uq are the control voltages in d and q axes respectively, and will get updated upon a change in the reference quantities which in turn will change the active or reactive power delivered by the inverter. The cross coupling exists in the form of the term jxLi in Eq. (2). Here, the d axis control voltage ud not only depends on the d axis current but also on the q axis current and vice versa, i.e. two first order systems, are interacting with each other resulting a cross coupling. The removal of cross coupling [14,15,20,21] is done by cancelling the complex drop due to the inductance by moving the pole

ð11Þ

Plant

e

jωL

idq*

+ +

F(s) -

+ +

udq

*

+ -

1 d L dt R jωL

Fig. 3. Current control with an inner decoupling loop.

idq

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idq ¼ id þ jiq

ð13Þ

The transfer function of the decoupled system from udq⁄ to idq is expressed as

G0 ðsÞ ¼

1 sL

ð14Þ

Now this first order complex valued system with no interacting terms can be regulated using PI controller with transfer function as F(s) = kp + ki/s. Configuration changes in micro grids and its effect on decoupling When converters are feeding power to large utility network the control is relatively simple compared to when it feeds into a microgrid. In micro-grids energy sources are intermittent in nature as they are driven by wind, solar etc., so, any generator may come into or go out of generation at any point of time during the operation. Such a switching in and switching out of one or more generators will cause the configuration of the network to get altered frequently. Whenever the configuration is altered, the electrical equivalent circuit and the grid impedance of the network will also be altered. An attempt is made to study the variation in the configuration and grid impedance of a micro-grid due to switching in and switching out of generators and load. Studies and experiments are carried out on a scaled down model of a micro-grid available in the department laboratory to investigate the source impedance variation as seen at solar inverter

output. The micro-grid model has various distributed generators and loads represented in a single line diagram with the indicated parameters of the transmission lines as shown in Fig. 4. The results of the measurements are listed in Table 1. The entry ‘‘1’’ in Table 1 represents the presence of the respective generator/load and a ‘‘0’’ entry represents its absence. It is observed that the inductive reactance varies between j4.531 X and j9.742 X, which is +63% and 73% from its average value of j7.135 X. In the SRF-PI control, the dependency of active and reactive powers is cancelled using the impedance value seen by the inverter’s output as given in Fig. 3. Furthermore, the effectiveness of decoupling solely depends on the accuracy of impedance used in the control loop. i.e. how close the actual line impedance seen by the inverter is to the impedance value used in the control loop. A nominal value of L is used in the control loop for obtaining the decoupling in grid connected inverter systems in [1,2,13,20,21]. The grid being a stiff power source, the line impedance is relatively constant; however, if the same control is adapted for micro-grid the decoupling may fail as the grid impedance of micro-grid varies in a large extent during the operation as presented in Table 1. To demonstrate the effect of source inductance variations on decoupling, the system shown in Fig. 2 has been set up in MATLAB/Simulink. In Fig. 2 references are shown in terms of id and iq but in the study, the references are given in terms of P and Q. The required values of current references are obtained using Eq. (9). Taking the average value of j7.135 X for xL in the control loop, the decoupled system is simulated for two extreme values of actual inductive reactance j4.531 X and j9.742 X, two of the extreme values from Table 1. Step changes in the active (Pref) and reactive (Qref)

4.592 + j5.3088 Ω

5 km

Solar Plant

1

j 6+

9.184 + j10.617 Ω

5 km

1.5 kW

Radial Feeder

500 W

4Ω

26 5.9

77

13.

7.5 km 13.776 + j15.9264 Ω

2.5 km

5

7.

km

4.592 + j5.3088 Ω

5 km

9.184 + j10.617 Ω

9.184 + j10.617 Ω

2.5 km

GRID

13.776 + j15.9264 Ω

7.5 km

Radial Feeder

1 kVA

Wind Generator

Hydro generator

Fig. 4. A scaled down laboratory model of micro-grid.

Table 1 The impedance presented by the micro grid at the solar port. State

Grid

Wind generator

Hydro generator

Feeder 1

Feeder 2

Impedance seen at solar inverter (X)

1 2 3 4 5 6 7

1 0 1 1 1 0 1

1 1 0 1 0 0 0

1 1 1 0 0 1 0

1 1 1 1 1 1 0

1 1 1 1 1 1 1

3.094 + j4.531 3.262 + j4.731 3.144 + j4.59 5.334 + j7.192 7.041 + j9.288 3.61 + j5.146 7.486 + j9.742

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A. Vijayakumari et al. / Electrical Power and Energy Systems 68 (2015) 1–14

Pref (W)

power references are introduced and the results of the active and reactive power delivered by the inverter are presented in Figs. 5a and 5b. It is observed from Figs. 5a and 5b that during steady state Pactual and Qactual corresponds to Pref and Qref respectively. When there is a step change introduced in Pref at any time, there is a transient in Qactual at that time finally settling at its reference value. Similarly, when step change is introduced at any time in Qref, there is a transient in the Pactual for duration of about 30–50 ms at that time. Moreover, during these transient periods, the magnitude and phase of the current delivered will not be following the reference values. For instance, one of the step change point is presented in

an expanded scale in Fig. 5c, wherein the Pref is kept at 280 W from the start at 0 s and given a step change at 0.4 s to 500 W and the simulation is run till 2 s. The first waveform of Fig. 5c shows the instantaneous current delivered by the inverter from 0 to 2 s. It is observed that a steady state current of 0.6 A peak is delivered upto 0.4 s and is increased to 1 A peak after the increase in the power reference at 0.4 s. But during the transient period, the current magnitudes are reaching several folds higher than its normal value which is presented in the last waveform of Fig. 5c. So, it is apparent that the system exhibits a cross coupled behavior with the active and reactive power controls interacts with each other. Thus it can be concluded that the variations in source inductance lead to improper decoupling resulting in poor dynamic response

600 400 200 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pactual (W)

Qref (VAr)

30 20 10 0

600 400 200

Qactual (VAr)

0

20 0 -20

time (s) Fig. 5a. Effect of step change in Pref on reactive power delivered.

Pref (W)

1 0

Qref (VAr)

-1 0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

600 400 200

Qactual (VAr)

Pactual (W)

0

10 0 -10

600 400 200 0

time (s) Fig. 5b. Effect of step change in Qref on active power delivered.

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10 0

0

-10

i (A)

0

0.5

1

1.5

2

-2

0

0.1

0.2

time (s)

0.3

time (s)

2 10 0

0 -10

-2

0.5

0.6

0.7

0.8

0.9

1

0.35

0.4

time (s)

0.45

0.5

time (s)

Fig. 5c. The instantaneous current delivered by the solar inverter.

for reference quantity changes. Though the feedback controller regulates these quantities at their reference values, it requires a considerable transient period as comprehended from the responses and thus the system is not dynamics free. It is evident from the previous discussions that the grid impedance varies during operation in micro grids and due to this the SRFPI controller loop’s decoupling fails during transient periods. The loss of independency of power control and demands a dynamic controller which can track these configuration changes and modifies the controller capabilities accordingly when used in microgrids. If the grid impedance is accurately measured continuously during the operation, then the decoupling can be made perfect every time. An attempt is made to measure the impedance during the operation of micro-grid using a non characteristic harmonic current injection into the grid, a method used for islanding detection [24–27].

Table 2 Parameters for simulation and hardware experiments.

Grid impedance measurement

Table 3 Grid Impedance obtained from simulation.

Values

DC bus voltage Inverter PWM frequency Grid impedance

400 V 20 kHz (i) 5 X, 4.5 mH (ii) 4 X, 12 m (iii) 5 X, 8 mH For simulation 3 mH

Output filter inductance Lf

Load power Grid voltage Grid frequency Sampling frequency of ADC Microcontroller

Method of measurement

v g ðxk Þ

Zgrid (obtained) (X)

4.2266 + j2.5124 3.3386 + j4.1635 4.116 + j3.2452

4.328 + j2.5821 3.4277 + j4.279 4.2085 + j3.3149

formed. The general DFT equation for any variable ‘x’ is expressed as,

XðkÞ ¼

N1 X j2pkn xðnÞe N

ð16Þ

n¼0

ð15Þ

ig ðxk Þ

¼

To extract the amplitude and phase of the applied harmonic voltage and the resulting current discrete Fourier Transformation is per-

  X   N1 N1 X 2pkn 2pkn þ j xðnÞ sin xðnÞ cos N N n¼0 n¼0

ig(ωh) PCC

Rg

Lg

vg(ωh) Grid RL Test Voltage

PV Array

For hardware (i) 0.14 X, 3 mH (ii) 0.1 X, 4.7 mH

1 kW 230 V(rms) 50 Hz 2 kHz dsPIC30f4011 (from Microchip)

Zgrid (actual) (X)

The impedance is measured by injecting a known voltage at a known frequency and measuring the grid response [24–27]. A non-characteristics frequency, which is not present in the network, is injected for this work. Fig. 6 shows the block diagram for grid impedance measurement. Through the inverter a voltage vg(xk), at non-characteristic frequency is injected into the grid and the current ig(xk) through the grid is measured. The impedance is calculated as

zg ð xk Þ ¼

Parameters

Load LL C Impedance

Inverter Fig. 6. Block diagram of grid impedance measurement.

ð17Þ

A. Vijayakumari et al. / Electrical Power and Energy Systems 68 (2015) 1–14

7

Inverter Board

CT s & PTs

dsPIC30f4011 Processor Board

(b)

(a)

(c)

(d)

Fig. 7. (a) Experimental set up for grid impedance measurement, (b) snapshot showing the measured grid impedance, (c) gating signals from microcontroller for 50 + 75 Hz output and (d) voltage at PCC showing the 50 + 75 Hz components.

¼ X k;real þ jX k;img

ð18Þ

where X(k) is the complex number representing the amplitude and phase of the harmonic component of the input signal x(n); k is the harmonic order; n is the time index (multiple of DFT sampling period); N is the number of samples of the input signal x(n), needed for the DFT; Xk,real and Xk,imag are the real and the imaginary parts of the DFT. DFT can be implemented through an iterative procedure and summation terms are realized with simple accumulators (running sum approach) as in [25–28]. At execution time tn, real and imaginary parts of DFT output are iteratively calculated as

X k;real ðtn Þ ¼ ACC k;real ðtn1 Þ þ v ðtn Þ cos

X k;img ðtn Þ ¼ ACC k;img ðt n1 Þ þ v ðtn Þ sin





2pkn N

2pkn N



 ð19Þ

where ACCk,(tn1) is the accumulated value of the running sum at time instant tn1. When the last sample is acquired and the last sum is executed, then algorithm output provides the real and imaginary parts of the DFT correspond to the input signals vg(xk) and ig(xk). The output voltage and current of the inverter are converted to digital values by using the ADC module. Each sample is used for the calculation of the DFT. The contents of the accumulators at the end of the window period denote the real and imaginary components of voltage and current. Using these values the grid impedance at the harmonic frequency is estimated [24]. Subsequently, the required

impedance at the fundamental frequency xgrid is obtained by scaling the reactive component as

zgridðxgrid Þ ¼ Rgrid þ jX gridðxkÞ

xgrid xik

ð20Þ

Frequency, magnitude and duration of harmonics injected Continuous injection of 75 Hz is proposed in this work, after a harmonic analysis conducted on the inverter outputs of [19,25– 27]. In [19,25] an 8% non characteristic frequency 75 Hz component is injected for 40 ms once in every 80 ms, which leaves a repeating frequency of 12.5 Hz for the injections. A Fourier analysis is performed on the inverter output voltage to estimate the influence of the repeating low frequency injections. It is found that this choice results in a considerable low frequency harmonics at 12.5 Hz of about 1% and its odd multiples approximately about 7.81% into the 50 Hz system. Also, the harmonic injected and the DFT calculations have to be in synchronism with the zero crossing of the grid frequency, which has practical difficulty. Hence, continuous injection of the 75 Hz is proposed in this work; this does not introduce any harmonics into the grid other than the 75 Hz and also easier to implement as synchronization is not needed. The magnitude of injection as low as 1% is sufficient to determine the grid impedance with a reasonable accuracy, with only a marginal THD increase in the grid. Implementation of impedance measurement The grid impedance has been measured in MATLAB/Simulink simulation and verified with hardware experiment results. The parameters used for simulation and the experimental set up are

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listed in Table 2. The simulation results are given in Table 3. The fundamental frequency of DFT is taken as 25 Hz and an 80 point DFT is performed. The impedance measured with DFT calculations are found to be within an accuracy of 3%. The experimental set up for grid impedance measurement is shown in Fig. 7(a), which includes a single phase inverter with Sine PWM (SPWM) implemented in microcontroller dsPIC30f4011. The source voltage is stepped down to provide the fundamental reference for the SPWM inverter. The 75 Hz reference signal is generated in the microcontroller by using a sine look up table with a magnitude of 1% of the 50 Hz component as used in the simulation. The 75 Hz signal is then super imposed on the 50 Hz reference and compared with the repeating triangular signal to generate the gating signals. The gating signals so generated are shown in Fig. 7(c), and the resulting voltage at PCC containing both 50 Hz and 75 Hz is shown in Fig. 7(d). The injected voltage and the resulting currents are measured at PCC and given as input to the ADC module of the

microcontroller, where the equations from (16)–(20) are programmed. The DFT extracts only the 75 Hz components and subsequently the DFT calculations are carried out and the line impedance value for 50 Hz is directly returned to the control loop. The results are also displayed in an LCD display and Fig. 7(b) shows the result during one of the measured instant. Prior to the experiment, the local network is manually measured for its source impedance by loading it with R and RL linear loads and the measured data are compared with the proposed experimental results in Table 4. The accuracy is found to be within 3% as in the case of simulations. Thus it is proposed to use this method of grid impedance estimation and is subsequently used in the control loop for perfect decoupling as explained in Sections ‘Decoupling the dependency of active and reactive powers on each other’ and ‘Configuration changes in micro grids and its effect on decoupling’.

Table 4 Grid Impedance measured in Experiment.

System description

Grid impedance from manual measurement (X)

Fig. 8 shows the block diagram of the decoupled control of grid connected VSI with on-line grid impedance measurement for delivering the required active and reactive power. The voltages and currents at PCC eabc and iabc are converted to find their d–q components by the abc–dq transformation blocks. The phase angle

Grid impedance from non-harmonic current injection (X)

1.86 + j3.518 1.833 + j4.06

1.898 + j3.5795 1.858 + j4.1131

ed(75)

ed +

*

id

+

PI Controller

id

-

+

ud

+

Vdc

+

ud*

iq

×

uα *

dq

3φ INVERTER

uq*

ωL

iq*

The proposed decoupled control of grid connected VSI with online grid impedance measurement

αβ

θ

eq

uβ *

SVPWM

+ +

PI Controller

iq

uq

+

-

-

+

eq(75)

ωL

iabc

GRID IMPEDANCE MEASUREMENT

eabc R

id

× ωL

L

id iq

dq abc θ

ia ib ic eabc

PLL

θ θ

ed eq

dq abc

eabc

Grid

Fig. 8. Block diagram of decoupled current control with dynamic grid impedance measurement.

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information for the d–q transformation is provided by the PLL. The grid impedance measurement block with inputs eabc and iabc performs DFT, calculates the impedance for 75 Hz, converts it to 50 Hz and returns the value of xL, which is used to get decoupled control as per Eq. (9), resulting in the control voltages ud and uq as specified in Fig. 8. The d–q components of 75 Hz sinusoidal signal for the grid impedance measurement are added with the control voltages ud and uq to get the reference voltage components ud⁄ and uq⁄ for the inverter. This d–q reference quantities are converted to a–b as required for an SVPWM generation. The d–q to a–b conversion is done with the phase angle information from PLL. The measured grid impedance is updated in the control loop periodically with new impedance values. The measured impedance value is multiplied by the dq current components for dynamic decoupling. This will account for the system configuration variations as

Table 5 Specifications of the power circuit. Inverter specifications

Value

DC input voltage VA rating Output frequency Output phase Voltage Filter inductor Switching frequency

680 V 1 kVA 50 Hz 230 V (rms) 11 mH (rL 0.1 X) 4 kHz

Lg2 rL

+

Lg1

Lf

t = 1.3 s C

Grid

-

explained for the micro grid introduced in Section ‘Decoupling the dependency of active and reactive powers on each other’. Performance of the proposed decoupled controller for step changes in the references The simulation studies are carried out to study the system performance when the operating states of the micro-grid vary. Simulation results The performance of the proposed decoupled controller is evaluated by conducting simulation studies in MATLAB/Simulink environment for the micro-grid of Fig. 4. The system consists of different generators with the ratings as specified in Fig. 4. The solar inverter with online grid impedance based decoupled controller with the power circuit specification as listed in Table 5 is integrated onto the micro-grid. The impedances as seen by the solar inverter as given in Table 1 are used for testing the controller at various operating conditions of the system. An inductance value of 14.42 mH, corresponding to all generators ‘on’ is placed in the circuit. The control loop is loaded with an arbitrary initial xL value of 9.288 X, corresponding to one of the conditions in Table 1. This will ensure that the actual value of grid impedance is not the same as the one present in the control loop, so that the impedance estimation will start at the start of simulation. The impedance measurement block will change the xL value in the control loop from the initial value to j4.531 automatically. Further the simulation is carried out in two ways: (a) Keeping the Qref constant and introducing step changes in Pref, (b) Keeping the Pref constant and introducing step changes in Qref. In both these cases a step change in the grid impedance from 14.42 mH to 29.565 mH is introduced at 1.3 s as depicted in Fig. 9. In Fig. 9 with Lg1 representing the initial grid inductance and by keeping the breaker ‘‘on’’ till 1.3 s the total grid inductance is Lf + Lg1 and when opened adds Lg2 in series with Lg1 introducing a step change. Step change of Pref. First, Qref is kept constant at zero throughout the simulation time, and Pref is given step changes from 580 W to 200 W at 0.5 s and from 200 W to 480 W at 0.8 s. The simulation results in Fig. 10 shows the Pref and the corresponding actual P

Inverter Fig. 9. Realizing step change in grid impedance.

700

Pref (W)

600 500 400 300 200 100 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time (s)

Pactual (W) & Qactual (VAr)

(a) 1500 P Q

1000 500 0 -500 -1000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time(s)

(b) Fig. 10. Active and reactive powers and their corresponding reference quantities for step change in Pref.

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A. Vijayakumari et al. / Electrical Power and Energy Systems 68 (2015) 1–14 400 300

Vph@PCC (V)

200 100 0 -100 -200 -300 -400

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time (s) Fig. 11. Voltage at PCC. 2

iabc (A)

1 0 -1 -2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.52

0.54

0.56

0.58

0.6

time (s)

(a) 2

iabci

1 0 -1 -2 0.4

0.42

0.44

0.46

0.48

0.5

time (s)

(b)

iabc (A)

2 1 0 -1 -2 0.65

0.7

0.75

0.85

0.8

0.9

0.95

1

time (s)

(c) 2

iabci

1 0 -1 -2 1.2

1.22

1.24

1.26

1.28

1.3

1.32

time (s)

(d) Fig. 12. Current delivered at PCC.

1.34

1.36

1.38

1.4

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and Q delivered and Fig. 11 shows the voltage at PCC. It is obvious that the grid impedance based decoupled dq controller exhibits superior performance compared to a decoupled dq controller with mismatched impedance value. Even with an intentional mismatch introduced in xL at the beginning of the simulation, it is observed that the step change in Pref at 0.5 s and at 0.8 s is not introducing any transient changes either in Q, or in the magnitude of voltage at PCC, thus exhibiting a perfect independency in the control of active and reactive powers. Also it is evident from the current delivered by the inverter shown in Fig. 12(a)–(c) that the transition from one Pref value to another happens as a smooth current magnitude change. At 0.5 s, the current magnitude starts falling from 1.2 A peak to 0.4 A peak and finally at 0.8 s starts rising from 0.4 A peak to 0.98 A peak corresponding to Pref. The step change in the grid inductance at 1.3 s does not have any effect on the voltage magnitude at PCC or on the magnitude of current delivered as expected due to the constant Pref. The distortions in the current waveform becomes less after 1.3 s as a result of the increased filtering effect due to increased inductance value as seen from Fig. 12(d). Fig. 13 shows the frequency Fig. 15. The experimental setup of the proposed system.

Pref (W),Qref (VAr)

Fig. 13. Frequency spectrum of current delivered at PCC. 1000

P Q

500 0 -500 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2

1.8

Pactual (W) & Qactual (VAr)

time (s) 1000 P Q

500 0 -500 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time (s) Fig. 14. Active and reactive powers and their corresponding reference quantities for step change in Qref.

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Fig. 16. The scaled down model of micro-grid available in the department laboratory.

Pref

Qref

Fig. 18. Active and reactive power references showing a step change. Fig. 17. Line to line inverter output voltages.

spectrum of the current with THD values as low as 4%, and shows the presence of only the 75 Hz component, not the low repeating frequency components as in the case of discontinuous injection. Step change of Qref. Next, Pref is kept constant at 200 W throughout the simulation time, and the Qref is given step changes from 80 VAr

to 480 VAr at 0.8 s. The simulation results of Pref, Qref and the corresponding actual P and Q delivered are shown in Fig. 14. At 0.8 s when the actual Q starts following its reference, no transients are observed on the P delivered. It is once again evident that with the grid impedance based decoupled dq controller independent control of active and reactive powers is achieved. Here also a step change in the grid inductance at 1.3 s is introduced, but it does not

Fig. 19. Line current (a) showing the change in magnitude due to increase in Pref and (b) same line current in expanded scale.

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introduce any transient in the P and Q delivered respectively, because of the update of the grid impedance due to the continuous measurement.

Pref

Qref

Fig. 20. Active and reactive power references showing another step change.

Fig. 21. Line current showing a change in magnitude due to a change in Pref.

Experimental results The experimental set up shown in Fig. 15 includes a three phase inverter controlled by the proposed current controller implemented in a 16 bit microcontroller dsPIC30F4011. The grid impedance calculations are also programmed in the same controller. To reduce the calculation time of the co-ordinate transformations the following strategies are followed: (1) Float calculations are avoided in the microcontroller by multiplying the sampled quantities with a suitable scale, (2) Cosine values required for Park’s transform is fetched from the stored lookup table, (3) A custom algorithm with squaring and shifting is developed for calculating the square root instead of the built in function, (4) A custom algorithm is developed for calculating the angles using lookup tables in which 128 values corresponding to 0–90° are provided for tan1. These strategies reduced the calculation time, thus the sampling time of ADC is selected as 0.025 ms, which is far greater than the calculation times. The inverter is synchronized to the scaled down laboratory model of micro-grid referred in chapter III and shown in Fig. 16. An arbitrary xL value is loaded into the microcontroller as an initial value for decoupling. Before introducing the power reference change of Fig. 18, the micro-grid is configured as the first state of Table 1 and is altered to second configuration during operation. Fig. 17 shows two line to line inverter output voltages. Fig. 18 shows a step change in the Pref from 620 W to 760 W introduced in the control circuit. Fig. 19(a) shows the line current corresponding to the above step change in phase ‘a’. It is seen that the current changes from 0.9 A to 0.36 A for the active power reference change. The same current waveform in an expanded time scale is presented in Fig. 19(b). It is observed as in the case of simulation that there are no transients during the reference step changes. There are no abnormal magnitudes of currents witnessed during the transition periods, exhibiting no transients in the power delivered. A power reference change from 480 W to 275 W is introduced and the consequential line current change from 0.7 A to 0.4 A is shown in Figs. 20 and 21 respectively. Once again there are no transients observed in the current magnitudes during the transition periods. The voltage at Point of common coupling and the line current injected with a Pref of 280 W, Qref of zero is shown in Fig 22 (a) inorder to show the steady state performance of the controller.

v

v i

(a)

i

(b)

Fig. 22. Voltage and current at PCC (a) current delivered at UPF and (b) current delivered at 0.81 PF lag.

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Under steady state the current delivered is proportional to the Pref also the current is delivered at UPF and the Qref is zero. For the same active power reference when the Qref is made 200 VAr a current of 0.5 A is delivered at 0.81 PF lagging as shown in Fig. 22(b). Conclusions A decoupled current controller using dynamic grid impedance measurements for control of grid connected inverter for a typical micro grid application has been presented. The proposed grid impedance based decoupled current controller has a better d–q axis decoupling capability because of the use of the correct impedance value for decoupling. This is achieved by continuously measuring the grid impedance and updating the control loop with new values every time. This decoupling allowed independent control of active and reactive powers against step changes in their active/reactive power references even during a change in the network configuration. This makes the control insensitive to the system parameter uncertainties in the micro grid. Here the grid inductance is measured during the operation using a non-characteristic frequency current continuously injected into the grid, which avoided the injection of sub-harmonics into the grid during measurements. The decoupled controller with grid impedance measurement is tested through simulation studies and hardware experiments and the results are presented separately. The influence of source inductance mismatch on decoupling and the active/reactive power delivered is presented. Experiments are conducted with the decoupled current controller using dynamic grid impedance measurements controlling a 3 phase 1 kVA inverter synchronized to the scaled down laboratory model of micro-grid. The hardware experimental set up is tested by introducing step changes in the active and reactive power references, and concluded that these step changes from one level to another does not introduce any transients in the delivered P and Q. Also they truly follow their references. Acknowledgement The authors would like to acknowledge the Indo-Swedish, DSTVINNOVA Research project on ‘‘Energy Management on Smart Grid using embedded systems’’ at Amrita Vishwa Vidyapeetham University, Coimbatore, for the use of their scale down micro grid laboratory model for performance validation of this paper. References [1] Kadri R, Gaubert JP, Champenois Gerard. An improved maximum power point tracking for photovoltaic grid-connected inverter based on voltage-oriented control. IEEE Trans Ind Electron 2011;58(1):66–74. [2] Haque ME, Negnevitsky M, Muttaqi Kashem M. A novel control strategy for a variable speed wind turbine with a permanent magnet synchronous generator. IEEE Trans Ind Electron 2010;46(1):331–9. [3] Blaabjerg F, Teodorescu R, Liserre M, Timbus AV. Overview of control and grid synchronization for distributed power generation systems. IEEE Trans Ind Electron Oct. 2006;53(5):1398–409.

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