International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 2, Jun 2013, 171-184 ÂŠ TJPRC Pvt. Ltd.

A NEW FAST PI CONTROLLER BASED DSTATCOM UNDER BALANCED & UNBALANCED LOADING CONDITIONS USING INSTANTANEOUS SYNCHRONOUS REFERENCE THEORY D. MOHAN REDDY1 & T. GOWRIMANOHAR2 1

Department of EEE, SVIET, Pedana, Machilipatnam, Krishna District, Andhra Pradesh, India 2

Department of EEE, SVUCE, Tirupati, Chittoor District, Andhra Pradesh, India

ABSTRACT In this paper presents a fast new PI controlled DSTATCOM used to compensate for harmonic distortion in threephase system. The DSTATCOM employs a simple Method for the calculation of the reference compensation current based. The presented DSTATCOM is able to operate in balanced, unbalanced and Variable load conditions. Classic filters may not have satisfactory performance in fast varying conditions. But fast PI active power filter gives better results for harmonic minimization, reactive power compensation and power factor improvement. The proposed fast PI- DSTATCOM maintains the THD well within IEEE519 standards.

KEYWORDS: DC-Link Voltage Controller, Fast Transient Response, THD, Power Quality (PQ), Unbalance, VoltageSource Inverter (VSI), Proportional-Integral (PI) Control

INTRODUCTION In recent years, power quality distortion has become serious problem in electrical power systems due to the increase of nonlinear loads drawing non sinusoidal currents Active filters & DSTATCOM have been widely used for harmonic mitigations well as reactive power compensation, load balancing, voltage regulation, and voltage flicker compensation in three-phase systems with nonlinear loads a high level of harmonic currents. Unbalanced loads also results in further declination of the Supply quality. Various harmonic mitigation techniques have been proposed to reduce the effect of harmonics. These techniques include phase multiplication, passive filters, active power filters (APFs), and harmonic injection. One of the most popular APFs is the shunt active power filters & DSTATCOM. It is mainly a current source, Connected in parallel with the non-linear loads. Conventionally, a shunt APF is controlled in such a way as to inject harmonic and reactive compensation currents based on calculated reference currents. The injected currents are meant to cancel the harmonic and reactive currents drawn by the nonlinear loads In a modern electrical distribution system, there has been a sudden increase of nonlinear loads, such as power supplies, rectifier equipment, domestic appliances, and adjustable speed drives (ASD), etc. As the number of these loads increased, harmonics currents generated by these loads may become very significant. These harmonics can lead to a variety of different power system problems including the distorted voltage waveforms, equipment overheating, malfunction in system protection, excessive neutral currents, light flicker, inaccurate power flow metering, etc. They also reduce efficiency by drawing reactive current component from the distribution network. In order to overcome these problems, active power filters (APFs) &DSTATCOM have been developed. The voltage-source inverter (VSI)-based shunt active power filter & DSTATCOM have been used in recent years and recognized as a viable solution of the control scheme, in which the required compensating currents are

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determined by sensing line currents only, which is simple and easy to implement. The scheme uses a conventional proportional plus integral (PI) controller for the generation of a reference current. The shunt-connected custom power devices, called the APF & DSTATCOM, injects current at the point of common coupling (PCC) so that harmonic filtering, power factor correction, and load balancing can be achieved. The APF consists of a current-controlled voltage-source inverter (VSI) which injects current at the PCC through the interface inductor. The operation of VSI is supported by a dc storage capacitor with proper dc voltage across it. One important aspect of the compensation is the extraction of reference currents. Various control algorithms are available in literature [7]–[9] to compute the reference compensator currents. However, instantaneous symmetrical component theory [9] is preferred. Based on this algorithm, the compensator reference currents are given as follows:

and

(1)

where γ = tan φ / √3, and φ is the desired phase angle between the supply voltages and compensated source currents in the respective phases. The term P lavg is the dc or average value of the load power. The term P dc accounts for the losses in the VSI without any dc loads in its dc link. To generate P dc, a suitable closed-loop dc-link voltage controller should be used, which will regulate the dc voltage to the reference value. The transient performance of the compensator is decided by the computation time of average load power and losses in the compensator. In most APF applications, losses in the VSI are a fraction of the average load power. Therefore, the transient performance of the compensator mostly depends on the computation of Plavg. In this paper, Plavg is computed by using a moving average filter (MAF) to ensure fast dynamic response. The settling time of the MAF is a half-cycle period in case of odd harmonics and one cycle period in case of even harmonics presence in voltages and currents. Although the computation of Pdc is generally slow and updated once or twice in a cycle, being a small value compared P lavg to, it does not play a significant role in transient performance of the compensator. In some applications, such as the telecommunications industry uses several parallel-connected switch-mode rectifiers to support dc bus voltage. Such an arrangement draws nonlinear load currents from the utility. This causes poor power factor and, hence, more losses and less efficiency. Clearly, there are PQ issues, such as unbalance, poor power factor, and harmonics produced by telecom equipment in power distribution networks. Therefore, the functionalities of the conventional APF should be increased to mitigate the aforementioned PQ problems and to supply the dc loads from its dc link as well. The load sharing by the ac and dc bus depends upon the design and the rating of the VSI. Here, there are two important issues. The first one is the regulation of the dc-link voltage within prescribed limits under transient load conditions. The second one is the settling time of the dc–link voltage controller. Conventionally, a PI controller is used to maintain the dclink voltage. It uses the deviation of the capacitor voltage from its reference value as its input. However, the transient response of the conventional dc-link voltage controllers is slow, especially in applications where the load changes rapidly. Some work related to dc-link voltage controllers and their stability is reported in (2-5). In this paper, a fast-acting dc-link voltage controller based on the dc-link capacitor energy is proposed. The detailed modeling and simulation verifications are carried out by using MATLAB environment to prove the efficacy of this fast-acting dc-link voltage controller. There is no systematic procedure to design the gains of the conventional PI controller

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used to regulate the dc-link voltage of the APF. But some, mathematical equations are given to design the gains of the conventional controller based on the fast-acting dc-link voltage controllers to achieve similar fast transient response.

Figure 1: Schematic Diagram of Shunt Active Power Line Conditioners

CONTROL METHOD: REFERENCE FRAME POWER THEORY The proposed reference frame-power (p) theory derives from the conventional p-q theory or reference framepower theory concept and uses simple algebraic calculations. It operates in steady-state or transient as well as for generic voltage and current power systems that allowing to control the active power filters in real-time. The active filter should supply the oscillating portion of the instantaneous active current of the load and hence makes source current sinusoidal.

Figure 2: α-β Coordinates Transformation The p-q theory performs a Clarke transformation of a stationary system of coordinates a b c to an orthogonal reference system of coordinates

. In a b c coordinates axes are fixed on the same plane, apart from each other by 1200

that as shown in Figure 2. The instantaneous space vectors voltage and current Va , ia are set on the a-axis, Vb , ib are on the b axis, and Vc , ic are on the c axis. These space vectors are easily transformed into instantaneous source voltages vsa, vsb, vsc are transformed into the

coordinates. The

coordinate’s voltage V, Vβ by Clarke

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transformation as follows:

(2) Similarly, the instantaneous source current isa, isb, isc also transformed into the

coordinate’s current i i β

by Clarke transformation that is given as:

(3) Where and

axes are the orthogonal coordinates. They V, iare on the α-axis, and V iare on the β-axis.

Real-Power (P) Calculation The orthogonal coordinates of voltage and current v,iare on the instantaneous real-power calculated from the

-axis and v, iare on the-axis. Let the

-axis and - axis of the current and voltage respectively. These are given

by the conventional definition of real-power as :

(4) This instantaneous real-power Pac is passed to first order Butterworth design based 50 Hz low pass filter (LPF) for eliminating the higher order components; it allows the fundamental component only. These LPF indicates ac components of the real-power losses and it’s denoted as Pac. The DC power loss is calculated from the comparison of the dc-bus capacitor voltage of the cascaded inverter and desired reference voltage. The proportional and integral gains (PI Controller) are determining the dynamic response and settling time of the dc-bus capacitor voltage. The DC component power losses can be written as

(5) The instantaneous real-power (P) is calculated from the AC component of the real-power loss Pac and the DC power loss PDC(Loss) ) ; it can be defined as follows:

(6) The instantaneous current on the

coordinates of Ic and ic are divided into two kinds of instantaneous

current components; first is real-power losses and second is reactive power losses, but this proposed controller computes only the real-power losses. So the

coordinate currents ic, ic are calculated from the v, vvoltages with instantaneous real power P

only and the reactive power q is assumed to be zero. This approach reduces the calculations and shows better performance

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A New Fast PI Controller Based DSTATCOM Under Balanced & Unbalanced Loading Conditions Using Instantaneous Synchronous Reference Theory

than the conventional methods. The coordinate currents can be calculated as

(7) From this equation, we can calculate the orthogonal coordinate’s active-power current. The

axis of the

instantaneous active current is written as:

(8) Similarly, the -axis of the instantaneous active current is written as:

(9) Let the instantaneous powers p(t) in the

-axis and the - axis is represented as Pand Prespectively. They

are given by the definition of real-power as follows:

(10) From this equation (10), substitute the orthogonal coordinates

-axis active power (8) and - axis active power

(9); we can calculate the real-power p(t) as follows

(11) The AC and DC component of the instantaneous power p(t) is related to the harmonics currents. The instantaneous real power generates the reference currents required to compensate the distorted line current harmonics and reactive power.

DC-LINK VOLTAGE CONTROLLERS The sudden removal of load would result in an increase in the dc-link voltage above the reference value, whereas a sudden increase in load would reduce the dc-link voltage below its reference value. As mentioned before, the source supplies an unbalanced nonlinear ac load directly and a dc load through the dc link of the APF, as shown in Figure 1. Due to transients on the load side, the dc bus voltage is significantly affected. To regulate this dc-link voltage, closed-loop controllers are used. The proportional-integral-derivative (PID) control provides a generic and efficient solution to many control problems. The control signal from PID controller to regulate dc link voltage is expressed as Uc = Kp (Vdc ref – Vdc) +

(12)

In (12), Kp, Ki and Kd are proportional, integral, and derivative gains of the PID controller, respectively. The proportional term provides overall control action proportional to the error signal. An increase in proportional controller

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gain (Kp) reduces rise time and steady-state error but increases the overshoot and settling time. An increase in integral gain (Ki) reduces steady state error but increases overshoot and settling time. Increasing derivative gain (Kd) will lead to improved stability. However, practitioners have often found that the derivative term can behave against anticipatory action in case of transport delay. A cumbersome trial-and-error method to tune its parameters made many practitioners switch off or even exclude the derivative term [8], [9]. Therefore, the description of conventional and the proposed fast-acting dc-link voltage controllers using PI controllers are given in the following subsections. Conventional DC-Link Voltage Controller The conventional PI controller used for maintaining the dc-link voltage is shown in Figure 3. To maintain the dclink voltage at the reference value, the dc-link capacitor needs a certain amount of real power, which is proportional to the difference between the actual and reference voltages. The power required by the capacitor can be expressed as follows: Pdc = Kp (Vdc ref â€“ Vdc) +

(13)

Figure 3: Schematic Diagram of the Conventional Dc-Link Voltage Controller

Figure 4: Schematic Diagram of the Fast-Acting Dc-Link Voltage Controller The dc-link capacitor has slow dynamics compared to the compensator, since the capacitor voltage is sampled at every zero crossing of phase supply voltage. The sampling can also be performed at a quarter cycles depending upon the symmetry of the dc-link voltage waveform. The drawback of this conventional controller is that its transient response is slow, especially for fast-changing loads. Also, the design of PI controller parameters is quite difficult for a complex system and, hence, these parameters are chosen by trial and error. Moreover, the dynamic response during the transients is totally dependent on the values of Kp, and Ki, when Pdc is comparable to Plavg. Fast-Acting DC Link Voltage Controller To overcome the disadvantages of the aforementioned controller, an energy-based dc-link voltage controller is proposed. The energy required by the dc-link capacitor (Wdc) to charge from actual voltage (Vdc) to the reference value (Vdc ref) can be computed as Wdc = Â˝ Cdc (

(14)

In general, the dc-link capacitor voltage has ripples with double frequency, that of the supply frequency. The dc power (Pâ€™dc) required by the dc-link capacitor is given as: (15)

A New Fast PI Controller Based DSTATCOM Under Balanced & Unbalanced Loading Conditions Using Instantaneous Synchronous Reference Theory

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where Tc is the ripple period of the dc-link capacitor voltage. However, due to the lack of integral term, there is a steady-state error while compensating the combined ac and dc loads. This is eliminated by including an integral term. The input to this controller is the error between the squares of reference and the actual capacitor voltages. This controller is shown in Figure 4 and the total dc power required by the dc-link capacitor is computed as follows: Pdc = Kpe (

(16)

The coefficients Kpe and Kie are the proportional and integral gains of the proposed energy-based dc-link voltage controller. As an energy-based controller, it gives fast response compared to the conventional PI controller. Thus, it can be called a fast acting dc-link voltage controller. The ease in the calculation of the proportional and integral gains is an additional advantage. The value of the proportional controller gain (K pe) can be given as Kpe = Cdc / 2Tc

(17)

For example, if the value of dc-link capacitor is 2200 μF and the capacitor voltage ripple period as 0.01 s, then K pe is computed as 0.11 by using (17). The selection of K ie depends upon the tradeoff between the transient response and overshoot in the compensated source current. Once this proportional gain is selected, integral gain is tuned around and chosen to be 0.5. It is found that if Kie is greater than Kpe / 2, the response tends to be oscillatory and if Kie is less than Kpe / 2, then response tends to be sluggish. Hence, Kie is chosen to be Kpe / 2.

DESIGN OF CONVENTIONAL CONTROLLER BASED ON THE FAST-ACTING DC-LINK VOLTAGE CONTROLLER The conventional dc-link voltage controller can be designed based on equations given for the fast-acting dc-link voltage controller as in (11) and can be written as (18) It can also be written as (19) Where

(20) (21) It is observed from the aforementioned equations that the gains of proportional and integral controllers vary with

respect to time. However, for small ripples in the dc-link voltage, Vdc ≈ Vdc ref, therefore, we can approximate the above gains to the following (22) (23) The relations (17)–(18) give approximate gains for a conventional PI controller. This is due to the fact that V dc ref + Vdc is not really equal to 2Vdc ref until variation in Vdc is small during transients. Hence, the designed conventional PI controller works only on approximation. The open-loop gains for the two cases are given by

(24)

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Where

D. Mohan Reddy & T. Gowrimanohar

Eer =

where Er = Vdc ref - Vdc. Since

and

(25)

is the same as Kie / Kpe,the higher gain in the conventional PI controller renders

less stability than that of the proposed energy-based dc-link controller. For nearly the same performance, the conventional PI controller has gains which are 364 (40/0.11 from Table-I) times larger than that of that proposed one. Also, the amplifier units used to realize these gains need more design considerations and are likely to saturate when used with higher gains. Table 1: Simulation Parameters

MATLAB/SIMULINK MODELING AND SIMULATION RESULTS Figure 5 shows the Matlab/Simulink power circuit model of DSTATCOM with balanced linear load. It consists of five blocks named as source block, linear load block, control block, DSTATCOM block and measurements block. The system parameters for simulation study are source voltage of 415v, 50 Hz AC supply, DC bus capacitance 1500e-6 F, Inverter series inductance 10 mH, Source resistance of 0.1 ohm and inductance of 0.9 mH. Load resistance and inductance are chosen as 50 ohms and 60mH respectively.

Figure 5: Matlab/Simulink Power Circuit Model of DSTATCOM with Balanced Linear Load Figure 6 shows the three phase source voltages, three phase source currents and load currents respectively with DSTATCOM having balanced linear load. It is clear that the source current and load current are sinusoidal.

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Figure 6: Source Voltage, Current and Load Current of DSTATCOM with Balanced Linear Load Figure 7 shows the MATLAB circuit of the DSTATCOM having balanced nonlinear load. It consists of five blocks named as source block, non linear load block, control block, DSTATCOM block and measurements block. The system parameters for simulation study are source voltage of 415v, 50 Hz AC supply, DC bus capacitance 1500e-6 F, Inverter series inductance 10 mH, Source resistance of 0.1 ohm and inductance of 0.9 mH. Load resistance and inductance are chosen as 30mH and 60 ohms respectively.

Figure 7: Shows the MATLAB Circuit of the DSTATCOM Having Balanced Non Linear Load Figure 8 shows the DC bus voltage. The DC bus voltage is regulated to 11kv by using PI regulator.

Figure 8: DC Bus Voltage with PI Controller

Figure 9: DC Bus Voltage with Fast PI Controller

Figure 9 shows the DC bus voltage with fast PI controller. From the above Figures, it is clear that with fast PI controller DC link voltage controlled with less time.

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Figure 10 shows the three phase source voltages, three phase source currents and load currents respectively with DSTATCOM having balanced non linear load. It is clear that the load current is non sinusoidal but balanced.

Figure 10: Source Voltage, Current and Load Current of DSTATCOM with Balanced Non Linear Load Figure 11 shows the unity power factor for balanced nonlinear load.

Figure 11: Waveform Showing Unity Power Factor Figure 12 shows the MATLAB circuit of the DSTATCOM having unbalanced linear load. It consists of five blocks named as source block, non linear load block, control block, DSTATCOM block and measurements block. The system parameters for simulation study are source voltage of 415v, 50 Hz AC supply, DC bus capacitance 1550e-6 F, Inverter series inductance 10 mH, Source resistance of 0.1 ohm and inductance of 0.9 mH. Load resistance and inductance are chosen as 30mH and 60 ohms respectively.

Figure 12: MATLAB Circuit of the DSTATCOM having Unbalanced Linear Load

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Figure 13 shows the three phase source voltages, three phase source currents and load currents respectively with DSTATCOM having unbalanced linear load. It is clear that the load current is sinusoidal and balanced.

Figure 13: Source Voltage, Current and Load Current of DSTATCOM with Unbalanced Linear Load Figure 14 shows the unity power factor for unbalanced nonlinear load.

Figure 14: Waveform Showing Unity Power Factor Figure 15 shows the MATLAB circuit of the DSTATCOM having unbalanced non linear load. It consists of five blocks named as source block, non linear load block, control block, DSTATCOM block and measurements block. The system parameters for simulation study are source voltage of 11kv, 50 Hz AC supply, DC bus capacitance 1550e-6 F, Inverter series inductance 10 mH, Source resistance of 0.1 ohm and inductance of 0.9 mH. Load resistance and inductance are chosen as 30mH and 60 ohms respectively.

Figure 15: MATLAB Circuit of the DSTATCOM having Unbalanced Non Linear Load Figure 16 shows the three phase source voltages, three phase source currents with DSTATCOM having unbalanced non linear load. It is clear that the load current is non sinusoidal.

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Figure 16: Source Voltages, three Phase Source Currents with DSTATCOM having Unbalanced Non Linear Load

CONCLUSIONS A Voltage Source Inverter topology for DSTATCOM compensating ac unbalanced and nonlinear loads and a dc load supplied by the dc link of the compensator is presented. The state-space modeling of the DSTATCOM are discussed for carrying out the simulation studies. An energy-based fast-acting dc-link voltage controller is suggested to ensure the fast transient response of the compensator. Mathematical equations are developed to compute the gains of this controller. Finally Matlab/Simulink based model is developed and simulation results are presented.

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AUTHOR’S DETAILS

Mr. D. Mohan Reddy received the B.Tech. Degree in Electrical and Electronics Engineering from the JNT University, Hyderabad, India and he received the M.E Power Systems Engineering from Anna University Chennai and presently pursuing PhD from S.V.University,Tirupati,India. Presently he is working as an Associate Professor in the department of Electrical and Electronics Engineering in Sri Vasavi Institute of Engineering and Technology, Machilipatnam. His research areas of interests are Power Electronic Converters, Electrical Drives and Power Quality.

Dr T. Gowri Manohar received the B.Tech, M.Tech and PhD Degrees in Electrical and Electronics Engineering from the S.V.University, Tirupati, India. Presently he is working as an Associate Professor in the department of Electrical and Electronics Engineering S.V.University, Tirupati, India. He is having 15 years of teaching experience and

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he was published more than 65 numbers of various international and national conferences & journals. He is a senior Member of IEEE and also he is a member in Indian Society for Technical Education. His research areas of interests are Modern Restructured Power Systems, Electrical Drives and Power Quality and harmonics â€“issues & challenges.