978-1-4799-5115-4/14/$31.00 ©2014 IEEE

Three-Phase VSI Supplied by Renewable Energy Sources and Controlled in Voltage and Power Modes

For Grid-Tie Operation

Amilcar F. Q. Gonçalves, Renan F. Bastos, Cassius R. Aguiar, Ricardo Q. Machado Department of Electrical Engineering and Computation - SEL

University of São Paulo – EESC/USP São Carlos, Brazil

amilcarquerubini@gmail.com

Abstract— This paper presents a strategy to control the terminal voltage produced by the voltage source inverter (VSI) as well as, the power delivery or absorbed from the grid independently of the local load. The terminal voltage is controlled by means of double cascade PI controllers. The resonant controller is placed in parallel to the classical voltage PI to improve its performance. To enhance the resonant structure dynamic response, an adaptive resonant controller based on the modification of their coefficients is used. Additionally, the paper exhibits the reactive power control at the grid changing the voltage amplitude synthetized by the VSI, and the active power control by means of the management of the angle of displacement between the grid voltage and the VSI terminal voltage. To the power control operates adequately two controllers in decoupled mode of operation (one with faster dynamic response and other with slower time response) are employed. To prove all statements proposed in this paper a set of experimental results are presented.

Keywords— AC-DC power converters; VSI; Distributed Generation; Power Quality; Alternative Sources.

I. INTRODUCTION The use of distributed generation (DG) sources is currently

being considered as a solution for the growing problems of energy demand [1]. Apart from the consequent reduction in the size of the generating plants and the possibility of modular implementation, DG systems based on renewable energy sources [2] (photovoltaic, fuel cells and storage systems such as ultracapacitors and batteries [1]) have received great interest due to their low environmental impact [3] as well as, their technical advantages. Furthermore, DG systems can promote co-generation [4] and improve the overall efficiency [5]. Regarding the most important technical advantages for using this kind of power plants, it can be inferred that there are improvements in the power quality of the DG system, and reduction in power losses mainly in radial lines [6].

Actually the increasing presence of nonlinear loads, such as variable-speed drives, light-emitting diode (LED) lamps, compact fluorescent lamps (CFLS), etc., will degrade the distribution system power quality [7]. In this sense, recent researches in DG are promoting as solution the use of modified

active filters in order to improve the power quality and produce energy from renewable energy sources to be injected into the grid.

In this context, shunt, series or unified power quality conditioner (UPQC) are the most important topologies where the first of all is employed to compensate the harmonic current at the grid. The series active filter have been used to reduce the harmonic on the voltages at the point of common coupling (PCC) whereas, the UPQC structure integrates the characteristics of both active filters what is adequate for DG systems.

However, in UPQC filter two power converters are employed what increases the losses, reduced level of reliability, increasing the coast as well. In [8, 9 and 12] an alternative structure whose, the power flow control is determined by regulating the amplitude and the angle of displacement between the voltage produced by the VSI and the grid voltage [10] are presented. The voltage control gives to the DG system capability to supply different kinds of loads at the DG system terminals. However great part of these systems do not use power control in closed-loop to determine exactly the level of power that will be transferred to the grid neither high level of voltage control (VSI voltage free of distortion independently of the local load) [11].

In this paper an analysis of the capability of DG system to compensate its terminal voltage, independently, if the local load is linear or a nonlinear load is presented. Additionally, the power flow control through the grid is also evaluated by means of a closed-loop control structure where the active and reactive power are regulated changing the angle of displacement between the DG and grid voltage, and the amplitude of the DG terminal voltage, respectively. To improve the voltage control dynamics and adaptive resonant control that uses the frequency of synchronism produced by the phase-locked loop (PLL) algorithm has been used.

In section II a general description of the analyzed system is presented with the control structures. The first is related to the PLL algorithms, in the second level are de cascade voltage and current controls. In levels three and four are mentioned the resonant filter and power control through the feeder.

This work was supported by the São Paulo Research Foundation (FAPESP).

Fig. 1. General scheme of control.

In the section III are illustrated the experimental results in

order to prove all statements developed in this paper. Finally, the main points of the paper are discussed in the conclusion.

II. CHARACTERISTICS OF THE DG SYSTEM The proposed system is shown in Fig. 1 whose the main

idea consist in produce a terminal voltage free of distortion and instabilities when different sort of loads are connected to the DG terminals (stand-alone operation) or when it operates in a grid-tie mode. In this kind of system the topology employed is a VSI with a LCL filter used to connect the DG to the grid.

In order to avoid disturbances by the interaction between grid and generation, a PLL algorithm was inserted to synchronize the connection between the DG system and the grid [12]. To obtain a stable voltage controller a cascade PI structures are used to regulate both the terminal voltage and current of the VSI. To improve the voltage controller response an adaptive resonant filter compensating the 1st, 3rd, 5th, 7th and 9th is placed in parallel.

Fig. 1 shows a general scheme of control (green line) and physical structure in red line. In case of stand-alone mode ∆ and ∆ are zero. The filter used to reduce the harmonics level, connect the VSI to the grid, adapt the voltage level between the DG system and the grid in case of represents the DG transformer disperse inductance. In the same figure, , , and , , are the instantaneous phase-to-neutral voltages and currents produced by the VSI whereas, the gains of the AC current and voltage sensors at the DG terminals and at the grid are , _ , and _ , respectively.

A. Synchronization Algorithm To connect the DG to the grid it is essential to synchronize

both systems. This is done by means of a PLL algorithm that computes the average of the internal product between and the synchronous voltage ( ) [12, 13]. If it is equal to zero, in steady-state regime, and are perpendicular and synchronized [14]. When it is achieved, the integration of the angular frequency ( ) defines the angle θ ( ) used as argument to produce . Due to the high sampling and

switching frequency 0, the delay block can be dismissed in the PLL closed-loop transfer function (1).

(1)

In this way, comparing the characteristic equation of the prototype transfer function with the PLL closed-loop transfer function (2), the PI constants (3) and (4) can be adjusted choosing the more appropriate values for the natural undamped frequency ( ) and the damping ratio (ξ). To avoid problems of stability, it is usual that is greater than 1 or 2 periods of the fundamental frequency and the maximum overshoot is lower than 30%.

A general description of the PLL algorithm is found in Fig. 2, where , are the fundamental angular frequency ( 2 60), and the adjusted angular frequency, respectively.

In Fig. 2, is the transfer function of the low-pass filter in the PLL algorithm. The low-pass filter is implemented as a moving window in discrete-time. 2

(2)

2 (3)

(4)

B. PI Controllers Design To maintain the converters operating in a stable mode,

proportional-integral (PI) controllers were used as a control technique to stabilize the current and AC voltage at the DG terminals, and on the capacitance (Fig. 1).

A method based on phase-margin (mf) and cut-off frequency ( ) was used to obtain the PIs gains (5) and (6) [2, 8] where the open-loop gain ( ), angular frequency ( )

and margin of phase (mf) define the PIs gains ( and ) for each kind of controller (current or voltage) [8].

1 (5)

k k ωFCLtan mf (6)

In this context, Table I and II displays the main parameters

to design the PIs gains of the VSI, respectively. TABLE I

CURRENT PI PARAMETERS OF THE DC-AC CONVERTER

CLF (rad/s) mf (º) DCV (V) convL (mH)

7,539.82 70 300 2 1/10

TABLE II

VOLTAGE PI PARAMETERS OF THE DC-AC CONVERTER

CLF (rad/s) mf (º) DCV (V) (µF)

753.98 70 300 10 1/360

C. Resonant Filters In literature a great numbers of authors have used resonant

filters (RES) to improve the PI dynamic behavior in αβ to produce voltages free of distortions at the VSI [15-17]. An advantage of this technique is to add filters in specific frequencies as odd harmonics as well, what reduces the VSI impedance making all distortion circulates through the VSI. To improve the RES response an adaptive mode of operation is used to alter the resonant frequency in order to make the RES algorithm follows all variation when the grid frequency changes within the boundaries established by international standards of power quality

The mathematical model of the resonant filter in s domain is given by (7). Wherein h represents the harmonic order and n is the harmonic with highest order. In practice, it is necessary to apply an appropriate discretization method in order to obtain an adequate resonant response [16]. According to the discretization method and frequency sample used, some methods may have a limited gain in resonant frequencies resulting low capability to compensate high harmonic orders, because of the low resolution of the coefficients what does not guarantee selectivity at narrow band [17].

In (8) is shown the discrete mode used to calculate the resonant filter constants. Wherein is, in general, a high gain that can be adjusted according to (9) where, is the number

of periods whereas, represents the period of the fundamental frequency [18].

In the mathematic models, the filter coefficients are calculated on each interruption of the microprocessor as the grid frequency is altered due to the oscillation present on the main generation [15]. In this way, when a frequency grid variation occurs the frequency of resonance will be changed together in order to avoid gains in the inter harmonics.

(7)

11 2 (8)

2.2 (9)

D. Power Control Through the Feeder The power control is employed due to the distribution

system operation be susceptible of any parametric alteration on the grid reactance ( ), making them indispensable. Following these ends, controlling the average active power at PCC, it is possible to transfer, exactly, the power used as reference [8,10]. In the method applied, the power measurement uses instantaneous power calculation [12] adjusting the Δ angle and Δ amplitude.

The instantaneous three-phase active ( ) and reactive ( ) power at the grid is calculated as (10) and (11) where, , , and , , are the instantaneous phase-to-neutral grid voltages and currents [12]. To avoid grid disturbances only the average reactive (12) ( ) and active power (13) ( ) per phase are controlled.

(10)

√3 √3 √3 (11)

13 1 (12)

13 1 (13)

Two controllers are used to manage the power transfer from GD to the grid. The first controller adjust the angle displacement (∆ ) of displacement between and (Fig. 1)

Fig. 2. PLL algorithm.

in case of active power control whereas to regulate the reactive power is used ∆ that is the variation on the amplitude.

The control structure uses proportional (P) controllers in order to obtain the incremental amplitude and angle of displacement. The controllers gain can be determined with a large time constant. The reactive control has to be faster than the active control, what is necessary for a decoupling in the power control loop, avoiding interference and destabilization between active and reactive controllers but both must be slower than the voltage, current or PLL controllers.

To design the gain for active and reactive power the same method employed to design the VSI voltage and current controllers are used. In (14) is the open-loop gain of the plant for active and (15) for reactive power.

_ (14)

√2 _ (15)

Based on these aspects, it is possible to determine the amount of average power that can be exchanged with the grid. To obtain such performance, it is essential takes into account the maximum variation allowed on the DG voltage amplitude and the minimum ∆ angle, between and , necessary to transfer the rated power. To maximize the DG operation, a minimal level of power losses on [8, 10] is expected, as well as it is fundamental that at the PCC the short-circuit power must not be altered when the DG is inserted to the grid. This will avoid reliability and stability restriction as well as power quality problems.

According to the international standards, it is also important that the DG voltage be ranked from 0.95 to 1.1 p.u. [19] with regard to its rated value in order to avoid problems in case the DG supplies sensitive loads, such as data processing systems, hospitals, defense systems and etc. This kind of imposition makes the reactive power (16) [2], [20] exchanged with the grid achieve at most 15% of the rated power (Fig. 3a). However, when the ∆ angle changes from the minimal to the maximum value, 100% of the active power (17) [2], [20] can be controlled at the grid, Fig. 3b.

_ _ (16)

_ (17)

III. Experimental Results A setup was built in laboratory to evaluate the performance

of DG experimentally as can see in Fig. 5. In this figure the voltage and current sensors, the microprocessor, filter, the VSI as well as, the relay to grid connection are illustrated. The proposed control algorithm was embedded in a

150-MHz float point microprocessor TMS320F28335 from Texas Instruments. The power converter is an IGBT commercial module from Semikron with 750 V of maximum dc-link, 25 A of maximum output current and 15 kHz of maximum switching frequency.

In terms of operation isolated and connected operation mode were analyzed in order to prove the system capability. To represent the grid a three-phase California Instruments 4500LX AC power supply was used.

In the experimental results were analyzed three cases to evaluate the proposal of this work. First case was a step of frequency to verify the dynamic of resonant controllers. The second case shows a transfer of power to the grid using the algorithm discussed in the section II. Additionally, in the last case is presented an analysis with transfer of power when there is presence of voltage harmonic distortions on the grid.

A. Variation on the Grid Frequency Because of the frequency deviation caused for instabilities

or nonlinear behavior of generated power plants and due to the narrow bandwidth of resonant filters the system was tested using fixed and adaptive coefficients to the resonant controller. This system is supplying a three-phase non-controlled rectifier with RC load equal to 270 Ω and 470 µF. The test consists of a variation starting from 61 Hz to 60 Hz.

(a)

(b)

Fig. 3. Reactive (a) and active (b) power flow through the grid.

Qg (p

.u.)

In Fig 2a the adaptive controller is active and the compensation of the VSI terminal voltage shown THD lower than 3%. However, when the resonant controller coefficients are not calculated dynamically the adaptive filters are not tracked and the coefficients are keeping constants reducing the controller capability (Fig. 2b), producing a VSI voltage with high level of distortion, i. e., THD higher than 5%.

B. Transfer of Power to the Grid The transfer of power from the primary source to the grid is

analyzed in Fig. 6(a). The system is connected with the grid after the synchronism between grid and GD was stabilized by PLL algorithm at 1.

From 1 until 2, the VSI is operating connected to the grid without the power control be active, it generates a level of the active power (80 VAr) different of zero because of the instantaneous the difference between the VSI and grid voltages. In 2 the power control is turned on, and a ramp of power is applied to take the reactive to zero and the reactive power to set-point determined as reference (420 W) whereas, in 3 stats the steady-state regime.

Additionally, Fig. 6b presents the phases A and B of grid voltage and current to prove the capability of the VSI to operate with unity power factor (currents and voltages in phase) in steady-state regime.

C. Operation Under Harmonic Grid Distortions The Fig. 7 shows the VSI injecting power into the grid as

well as, avoiding the flow of harmonic currents to the local load when 5% of 3rd and 5th harmonics were added to the grid voltage. In this situation, the resistive local load is consuming about 700 W whereas, 600 W is sent to the grid.

In this figure is shown the VSI voltage and load current free of distortion because of the action of the resonant filters. In the same figure, it is possible to observe the flow of harmonics from the grid to the VSI (way of low impedance).

CONCLUSION The use of dynamic resonant filters in voltage

compensators for mitigation of voltage harmonic distortion was

presented. The purpose of this work was evaluated through practical examples. Different types of loads were used to represent a real situation in DG applications. The nonlinear load is the worst case of voltage compensation and the results shows that the voltage control with dynamic resonant filters was satisfactory for this purpose when compared with fixed coefficients.

(a) Vertical: DG voltage 30 V/div, grid voltage 30 V/div, and load current 1 A/div. Horizontal: 5 ms/div.

(b) Vertical: DG voltage 30 V/div; grid voltage 30 V/div; and load current 1 A/div. Horizontal: 5 ms/div.

Fig. 5. Frequency deviation. (a) Control with adaptive resonant filters. (b) Control without adaptive resonant filter.

(a) Vertical; Pg 60W/div and Qg 60 VAr/div. Horizontal 500ms/div.

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P

Q

1 2

3

500 ms/div

Fig. 4 – Prototype developed in laboratory.

(b) Vertical: Voltages 50 V/div, and currents 5 A/div. Horizontal: 5 ms/div.

Fig. 6. Transfer of power. (a) Three-phase active and reactive power. (b) Grid voltages and currents.

Fig. 7. Grid with harmonics. Vertical: Upper traces VSI voltage and load currents. Lower traces grid voltages and currents. Voltages 30 V/div, and currents 5 A/div. Horizontal: 5 ms/div.

A method of power flow control for 3-phase VSI system was tested. The advantage of this method consists in easy manner of power transfer to the grid applied in systems with terminal voltage control. A disadvantage is that only three-phase power is guarantee and is not possible to determine the portion of power transfer for each phase. Otherwise the grid current harmonic is determined by the grid, in this way, the control has no influence on its waveform. Therefore, the principal contribution of this work is a three-phase distributed generation system that ensures low voltage harmonic distortion in the PCC and injects power excess to the grid.

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