A Simple Active-Power Control Technique for Grid ... - IEEE Xplore

4th International Conference on Power Engineering, Energy and Electrical Drives

Istanbul, Turkey, 13-17 May 2013

A Simple Active-Power Control Technique for Grid-Connected Three-Phase Inverters at Unity Power Factor *

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A. Elserougi , A. S. Abdel-Khalik , S. Ahmed , and A. Massoud Alexandria University_Egypt ,**Texas A&M University at Qatar, ***Qatar University

Abstract –This paper presents a simple active-power control technique for low voltage grid-connected three-phase inverters with zero injected reactive power (unity power factor at grid). Two versions of the proposed controller are introduced, namely, open-loop and closed loop controllers. The proposed controller is characterized by lower computational burden and reduced number of sensors, which are desired features for low-cost systems. The performance of the proposed controllers is studied during normal as well as abnormal operating conditions. Key words- boost inverter, grid connected inverters, distributed power, unity power factor.

P, Q Pref , Qref Id , Iq Idref , Iqref va, vb,vc Vd vai, vbi, vci ia, ib, ic Vdc , Idc Vdi , Vqi Kac, Kdc ߜ D Vg Vi X

NOMENCLATURE Actual grid active and reactive power injected Reference grid active and reactive power d- and q- components of the grid current Reference d- and q-components of the grid current Grid three phase voltages Direct component of the grid voltage Inverter output three phase voltages Grid Three phase currents DC-Link voltage, DC-Link current d- and q- components of the inverter voltages AC and DC components of the boost inverter Phase shift between inverter and grid voltage Duty cycle RMS value of the grid voltage Inverter voltage magnitude Interfacing reactance I.

INTRODUCTION

The renewable energy is recognized as an important energy source and its application as an independent home generation system is now increasing. The conventional voltage source inverter (VSI) is the most common power conversion topology in several applications. One of the main characteristics of the conventional VSI is that the peak of output voltage is always lower than the input DC voltage. To consider the VSI topology in the grid-connected renewable energy applications, the low output voltage of the renewable sources requires proper boosting in order to meet grid interface requirements. A two stage power conversion process is thus typically used; it has mainly two most common configurations.

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(a) (b) Fig.1. Two stage power conversion process (a) Using DC-DC boost inverter, (b) Using output transformer.

C

L

Vdc

Fig.2 Three-Phase Boost Inverter

The first configuration uses an intermediate DC-DC boost converter before the DC-AC grid interface inverter (as in Fig.1a). This adds significant complexity and hardware to the power conversion system [1-7]. Alternatively, the second configuration uses an output transformer to boost the inverter output voltage (as in Fig.1b), but with this configuration the inverter will not be lighter, more compact, and more affordable. Single-stage boost inverters were proposed in [8-10], it can generate an output AC voltage larger than the input DC voltage depending on the duty cycle. The system consists of three DC to DC bi-directional boost converters with a common point (as shown in Fig.2). These converters produce a DC biased sine wave output. The AC component of each converter is 120 degrees out of phase with the other. In this paper the single-stage boost inverter is used. Current control of the grid-connected VSIs [11–15] is needed to control power injected into the grid network. The most common current control techniques proposed in the literature are:

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Hysteresis current control [11], Predictive current control [12, 13], Proportional-integral (PI) current control in stationary or synchronous reference frame [14–18]. Direct control of the converter instantaneous current based on direct power control [19]. Power-synchronization control is proposed in [20].

Since the proportional-integral (PI) current control in synchronous reference frame is the most common approach which is used for active and reactive power control in gridconnected inverters (as shown in Fig.3), it will be used to assess the performance of the proposed controller in this paper. The proposed simple control technique enables controlling the injected active power with zero injected reactive power to the grid (unity power factor). The main advantages of the proposed controller are: It has lower computational burden (no need for same number of abc-to-dq or dq-to-abc transformations), It uses one current sensor (DC-Link current measurement). The performance of the grid-connected three-phase single-stage boost inverter with the proposed new control is investigated for normal as well as abnormal operating conditions. This paper is divided to five sections, section I introduces the introduction about grid-connected converters and its control schemes. Section II shows the basics of three-phase single-stage boost inverter topology, section III illustrates the proposed controller. Section IV introduces the simulation results and its discussion. Section V describes the conclusion of this work. II.


v AOref = K dc + K ac sin(ωt + δ ) 2π ) 3 2π = K dc + K ac sin(ωt + δ + ) 3

vBOref = K dc + K ac sin(ωt + δ − vCOref

(1)

For leg of phase-A (can be considered as DC-DC boost converter), the following voltage relation for the continuous conduction mode can be obtained: v AO (t )

V dc

= 1

(1 − D A (t ) )

(2)

To obtain (vAOref) across the capacitor of phase A, the instantaneous value of reference duty cycle for this phase can be obtained from (3). PWM signals are generated by comparing the reference duty cycle by carrier waveform with frequency of fs; where fs is the inverter's switching frequency. This can be done similarly to phases B and C, the duty cycle variation of phases B and C are given by (4) and (5) respectively. Generation of PWM signals for boost inverter is shown in Fig. 4. §V · D A ( t ) = 1 − ¨ dc v AOref ( t ) ¸¹ ©

· §V D B ( t ) = 1 − ¨ dc v BOref ( t ) ¸¹ © §V · D C ( t ) = 1 − ¨ dc v COref ( t ) ¸¹ ©

(3) (4) (5)

PRINCIPLE OF BOOST INVERTER OPERATION

Each phase in the three-phase boost inverter consists of two IGBTs, one inductor and one capacitor (Fig.2). There is a common point for capacitors (O) which connected with the negative terminal of the DC supply. The load is connected to inverter terminals and creates another common point (N) δ which should not be connected to the capacitors common point. The reference voltage of output capacitors is given by Fig.4 Generation of PWM signals for boost inverter (1). III.

θ PLL

θ PLL

Fig. 3 Conventional proportional-integral (PI) current control

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PROPOSED CONTROLLER FOR GRID CONNECTEDINVERTERS

Referred to Fig. 5, the power flow into the grid is described as in (6), (7). For zero injected reactive power (Q=0), i.e. unity power factor at grid, equation (8) should be verified. In this case, the per-phase active power and the corresponding ߜ are given by (9) and (10) respectively. The open-loop version of the proposed active power controller with zero injected reactive power is shown in Fig.6. It has to be noted that in all of the following formulas the parasitic resistance of the interfacing inductance is negligible.

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Vg2 (9) tanδ X § · δ = tan −1 ¨¨ PX 2 ¸¸ (10) Vg ¹ © The main drawbacks of the open-loop controller based system are: 1- The system will be very sensitive to the noise. 2- The system response will be affected by any variation in any parameter in the system (steady state error). 3- Voltage dependent power order limiter (VDPOL) is needed, to avoid large fault currents. When VDPOL is used, if the grid voltage is lowered due to remote faults in the grid, the injected active power order will be limited to zero. To enhance the system response, closed-loop version will be recommended. In the proposed controller, to reduce number of current sensors, DC-Link current measurement will be used to extract the direct components of the grid currents instead of measuring the three-phase currents. Current controller here will be for direct component only (i.e. one PI controller is needed). With respect to the quadrature component, equation (8) will guarantee forcing its value to be zero (zero injected reactive power). The closed loop version of the proposed controller is shown in Fig.7. P=

Vg ∠0

Vi ∠δ Fig.5 Single line diagram for Grid connected inverter

Referred Fig.6, Equation (10) is used to calculate suitable phase shift between inverter and grid voltages. Rate limiter is used to avoid any abrupt change in ߜ, to avoid high transient currents. Then equation (8) is used to determine corresponding inverter voltage magnitude, this value guarantee zero quadrature component of the grid current, i.e. unity power factor at the grid. After estimating the inverter voltage magnitude and phase difference, the inverter reference voltages are generated as in Fig.4. The dc component of the boost inverter output voltage (Kdc) must be selected to ensure that (Kdc-Kac >Vdc) to avoid operating at zero duty cycle. P =

Q=−

Vg X

2

+

ViV g X

ViV g X

cos δ = Vi =

sin δ

Vg

Vg

X

( −V g + Vi cos δ )

cosδ

(6) (7) (8)

Fig.6 Open-loop version of the proposed controller

Fig.7 Closed-loop version of the proposed controller

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DC-Link current measurement can be used to extract the direct component of the grid currents as follows: Pdc ≅ P (11) Where; Pdc is the Pumped power from the DC link =Vdc Idc(ave) P is the injected power to the grid =3/2 (IdVd) By substituting with previous values into (11) yields, Vdc .I dc ( ave ) =

3 I dVd 2

(12)

By Rearranging (12), the estimated direct component of the grid current from the DC-Link current measurement is given by (13), 2V I I d = dc dc ( ave ) (13) 3Vd Referred to closed-loop version of the proposed controller (Fig.7), the reference of active power and the grid voltage is used to calculate the reference direct component of the grid current. The actual value of grid current direct component is estimated from measuring the DC-Link current using Equation (13). The difference between reference and actual value is fed to proportional-integral controller to obtain the suitable phase shift between inverter and grid voltages. Then equation (8) is used to determine the inverter voltage magnitude. Then, the inverter reference voltages can be simply generated. Tunnig of PI controller is very important to get proper performance.

IV. SIMULATIONS Three control schemes for grid-connected single-stage three-phase boost inverter (with similar parameters, as in table-I) have been built using MATLAB; first one uses the conventional PI current control in synchronous reference frame with Qref =0. Second one uses open-loop version of the proposed controller with voltage dependent power order limiter to avoid high fault currents, finally the third one uses the closed-loop version of the proposed controller. Following scenarios are applied to each model to compare between their responses. The scenarios can be summarized as follows: Change of power order, Faulty condition at grid. TABLE I. GRID-CONNECTED BOOST INVERTER PARAMETERS Parameter Value Vdc (assuming bi-directional DC 200 V supply in the simulation) L , C, fs 1 mH, 40 μF, 3 kHz Kp and Ki (for current control in 0.1 and 1 synchronous reference frame) Kp and Ki (for closed-loop version 0.01 and 0.5 of the proposed controller) for ߜ in degree Vg (phase) 220 Volt (r.m.s) Interfacing reactance 0.5 Parasitic resistance 0.05

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Scenario 1: Change in power order during normal operating condition. In this scenario the three-phase power order is changed as follows: Interval I: 0 kW for 0