A STATCOM-Control Scheme used for Power Factor Improvement of Grid connected weak bus System

A STATCOM-Control Scheme used for Power Factor Improvement of Grid connected weak bus System

P. C. Pradhan*, P. K. Ray **, R. K. Sahu *** and J. K. Moharana****

* Faculty and Research Scholar, Dept. of EE, DRIEMS, Cuttack, ** Dept.of EEE, IIIT, BBSR, *** Dept.of EE, VSSUT, Burla and **** Dept.of EEE,GITA,BBSR

Abstract– Improvement of power factor of long weak distribution lines connected to grid is a challenging problem, particularly when it may not be economic to simply upgrade the network. The STATCOM (STATics synchronous COMpensator) offers an attractive alternative, with their potential to provide both steady state and transient voltage compensation for a limited capital investment. However, operation of these systems with weak networks needs careful attention to achieve a stable and fast response under all supply conditions. This paper proposes a new control strategy in the STATCOM to improve power factor at a distribution weak bus which is more robust and works well under all system conditions. Simulation results are presented to verify the stability of this control strategy across a range of operating conditions. The operation of the STATCOM with supply system makes the rural consumers healthy and wealthy.

Index Terms-: Controller design, PI Controller, STATCOM

1. INTRODUCTION

   Inductive loads and diode rectifiers are widely employed in industrial fields and consumer products thanks to advantages of low cost, simple structure, robustness and absence of control. However, this type of converters results in only unidirectional

   voltage regulation, voltage unbalance, low power factor and harmonics often become a significant problem. As is well known, the current is proportional to the voltage in case of a linear load as shown in Fig.1(a) where as the current is not proportional to the voltage in case of non-linear load (as shown in Fig.1(b)). A linear load draws active power from the grid with only fundamental component being present in the current and absorbs/injects reactive power from/to the grid. However, a non-linear load draws active power from the grid, where the current has fundamental and harmonics. These harmonics do not provide extra power but unnecessarily, yet unavoidably, increase the system volt-ampere (VA). This shows up as an increase in the rms current in the lines and leads to an extra heating of the transmission conductors and system elements. Hence, the compensation of reactive power is necessary for both linear and non-linear loads. Harmonic compensation upto standard values and power factor improvement are the main issues for such loads. The power factor PF is defined as the ratio of the active power P to the apparent power S . Thus

   power flow, low input power factor, high level of harmonic input currents, malfunction of sensitive electronic equipment,

   PF P

   S

   (1)

   increased losses and also contributing to inefficient use of electric energy. And also the inductive loads especially

   For purely sinusoidal voltage and current, the standard expression is obtained as

   inductive motors create low power factor at the electric supply

   system. Recently, many promising power factor correction

   PF cos

   (2)

   (PFC) techniques have been proposed for rectifiers and

   where

   cos

   is popularly known as the displacement factor.

   inductive loads. Apart from application of active and passive filters, the best solution is in using pulse width modulated (PWM) rectifiers. Research interest in three-phase PWM rectifiers has grown rapidly over the last few years due to some of their important advantages, such as power regeneration capabilities, control of dc-bus voltage over a wide range, and low harmonic distortion of input currents. In recent years power systems have become very complex with interconnected long distance transmission lines. The interconnected grids tend to become unstable as the heavy loads vary dynamically in their magnitude and phase angle and hence power factor. Commissioning new transmission systems are extremely expensive and take considerable amount of time to build up. Therefore, in order to meet increasing power demands, utilities must rely on power export/import arrangements through the existing transmission systems. In specially, the distribution networks supplying rural consumers are often quite weak because of the long distances involved and the relatively high R/X ratio of the cables that are used. Hence, as demand increases on these networks, power quality issues such as poor

   The survey of the power factor for a year of the rural consumers is given in Table.I

   Month of the Year	Demand (KW)	Demand (KVA)	Actual Power Factor (%)
   January February	200 150	245 224	81.63% 66.69%

   Month of the Year	Demand (KW)	Demand (KVA)	Actual Power Factor (%)
   January February	200 150	245 224	81.63% 66.69%

   Fig.1: Linear and non-linear loads of consumers connected to supply system

   March	125	175	71.43%
   April	224	256	87.50%
   May	208	289	71.97%
   June	210	299	70.23%
   July	223	289	77.16%
   August	211	278	75.90%
   September	204	265	76.98%
   October	198	245	80.82%
   November	156	198	78.79%
   December	201	265	75.85%

   Table.I: It shows the power factor of the rural consumers

   Power electronic devices are gaining popularity for applications in the field of power transmission and distribution systems. The reactive power (VAR) compensation and control have been recognized [1] as an efficient & economic means of increasing power system transmission capability and stability. The use FACTS (Flexible AC Transmission System) devices in a power system can potentially overcome limitations of the present mechanically controlled transmission systems. By facilitating bulk power transfers, these interconnected networks help minimize the need to enlarge power plants and enable neighboring utilities and regions to exchange power. The stature of FACTS devices within the bulk power system will continually increase as the industry moves toward a more competitive posture in which power is bought and sold as a commodity. As power wheeling becomes increasingly prevalent, power electronic devices will be utilized more frequently to insure system reliability and stability and to increase maximum power transmission along various transmission corridors. The FACTS device, such as STATCOM has been introuced more recently which employs a VSI with a fixed DC link capacitor as a static replacement of the synchronous condenser. In a traditional synchronous condenser, the field current of the synchronous motor controls the amount of VAR absorbed/injected and hence in a similar way, the firing instant of the 3-phase inverter controls the VAR flow into or out of the STATCOM. Large numbers of capacitor banks or inductor banks are no more required. Only a fixed set of capacitor provides the required VAR control, with a rapid control of bus voltage and improvement of utility power factor. It offers several advantages over conventional thyristorised converters [2] in terms of speed of response. The STATCOM is a voltage source inverter (VSI) based device, which regulates distribution bus voltage using reactive power compensation. The potential of STATCOM to improve supply quality and increase line utilization in weak distribution networks is well documented [3, 4]. However, many of the proposed control strategies assume a stiff, balanced grid source, and this is often not the case in practice. Recently, there has been some research focus on the performance of STATCOM devices operating under unbalanced supply conditions. Direct voltage control algorithms used to compensate for supply unbalance in distribution networks were proposed in [5] and [6]. However, the results in [6] show a relatively slow dynamic response because of the filters employed. Also, both algorithms have been developed for a VSI device interfaced to the distribution

   network through a simple inductive filter, and have not been tested for the more complex LCL filter considered in this work. A multi-variable control strategy was proposed in [7] for a STATCOM with a LCL filter interface. Although this strategy is shown to achieve good steady state and dynamic responses under balanced and unbalanced supply conditions, it is complex and sensitive to variations in system parameters. The penalty paid for this improvement is in terms of introduction of some harmonics, which requires separate handling using active filtration techniques. Moran et al [8] have shown in details how the utilization of Sinusoidal Pulse Width Modulation (SPWM) techniques reduces harmonic distortion. It has also been shown that an increase of modulation index reduces the size of the link reactor and stress on switches which are significant issues in practical implementation. The modeling and analysis of STATCOM steady state and dynamic performance with conventional control method have been studied by Schauder and Mehta [9] using non-linear controller. In [10, 11] the dynamic responses and steady state behavior of STATCOM with Space Vector Pulse Width Modulation (SVPWM) has been studied and the advantages of introducing SVPWM inverter with higher values of modulation index are highlighted.

   The controllable reactive power allows for a rapid control of bus voltage and power factor at the system or at the load end. To compensate for the distorted current drawn by the rectifiers from the utility grid, the STATCOM and its current controller must have the capability to track source PWM (Pulse Width Modulation) converters. The linear control is more suitable for STATCOM application reported in [13, 14]. The present paper suggests the design of a linear current controller and voltage controller on the basis of gain and time constant adjustment along with the parameter of the coupling inductor and storage capacitor.

   The present paper goes on to develop closed loop model for investigating transient performance of the STATCOM by using controller parameter. First, in Section 2 focuses on modeling of the power system and Section 3 gives state space model of the STATCOM with the system. Secondly, in Section 4, a current and voltage controllers are designed. The simulated responses with the designed controller parameters are presented in Section 5. This scheme is both an extension and a significant improvement of the scheme suggested by Shauder et al [9] and Sensarma et al [4].The results obtained have been compared and appropriate conclusions have been drawn.

2. MODELING OF THE POWER SYSTEM

   Fig.2: Interconnected Six Bus system

   The 6-bus system is a simple power system network given in Fig.2 and scaled model of a bus is shown in Fig.3.The 6-bus system is intended to illustrate in a simple context notions

   current Fig.5.

   Ica to be injected into the system at PCC as shown in

   of transfer capability and the impact that various actions have on the given transfer capability. Buses 1, 2, 3 of the system diagram are generators and buses 4, 5, 6 of the diagram are loads. The primary flow of power is from the top of the diagram to the bottom of the diagram and also from left to right. Reactive demand by the loads (signified by the empty portion of the load arrows) is large. The network has 10 branches and each branch represents a transmission line. The model is an AC power flow model; it represents real and reactive power flows and power system nonlinearity. Operational limits relating to transmission line flow, voltage magnitude, and voltage collapse are represented. The weak bus no 5 is connected to industrial area and also local consumers. The power factor of this grid (Bus no.5) is poor and hence its power factor can be improved as the model given in Fig.4.

   Fig.3: Scaled distribution network model

   Fig.4: A single Bus connected with STATCOM

3. MODELING OF THE STATCOM AND ANALYSIS

   1. Modeling

      The modeling of the STATCOM, though well known, is reviewed in the lines below, for the sake of convenience. The modeling is carried out with the following assumptions:

      1. All switches are ideal

      2. The source voltages are balanced

      3. Rs represents the converter losses and the losses of the coupling inductor

      4. The harmonic contents caused by switching action are

   negligible

   The 3-phase stationary abc coordinate vectors with 1200 apart from each other are converted into 2-phase stationary coordinates (which are in quadrature). The axis is aligned with a axis and leading axis and both

   converted into dq two-phase rotating coordinates. The Parks abc to dq transformation matrix is

   Fig.5: Schematic diagram of STATCOM

   Fig.6: Phasor diagram for inductive load operation

   1. Operating principle

      As is well known, the STATCOM is, in principle, a static (power electronic) replacement of the age-old synchronous condenser. Fig.5 shows the schematic diagram of the

      Cos(t)

      2

      2

      K Sin(t) 3

      1/ 2

      Cos(t 2 / 3) Sin(t 2 / 3) 1/ 2

      Cos(t 2 / 3)

      Sin(t 2 / 3) (3)

      1/ 2

      STATCOM at PCC through coupling inductors. The

      fundamental phasor diagram of the STATCOM terminal voltage with the voltage at PCC for an inductive load in operation, neglecting the harmonic content in the STATCOM

      The actual proposed circuit is too complex to analyze as a whole, so that it is partitioned into several basic sub-circuits, as shown in Fig.5. The 3-phase system voltage vs,abc lagging with

      terminal voltage, is shown in Fig.6. Ideally, increasing the

      the phase angle to the STATCOM output voltage v

      o,abc

      and

      amplitude of the STATCOM terminal voltage Voa above the

      amplitude of the utility voltage Vsa causes leading (capacitive)

      differential form of the STATCOM currents are defined in (4) and (5).

      vsa

      Sin(t )

      (4)

      the transient responses take about one and half power cycle to reach at their steady state values.

      v v 2V

      2

      Sl	Parameters	Symbol	Values
      1	Frequency	f	50 Hz
      2	Angular Frequency	w	314 rad/sec
      3	RMS line-to-line Voltage	Vs	230V
      4	Coupling Resistance	Rs	1.0
      5	Coupling Inductance	Ls	5.0mH
      6	DC-link capacitor	C	500 F
      7	Modulation Index	M	0.979
      8	Phase angle		50
      9	Load Resistance	RL	52
      10	Load Inductance	LL	126mH
      11	Load Power factor		0.79

      Sl	Parameters	Symbol	Values
      1	Frequency	f	50 Hz
      2	Angular Frequency	w	314 rad/sec
      3	RMS line-to-line Voltage	Vs	230V
      4	Coupling Resistance	Rs	1.0
      5	Coupling Inductance	Ls	5.0mH
      6	DC-link capacitor	C	500 F
      7	Modulation Index	M	0.979
      8	Phase angle		50
      9	Load Resistance	RL	52
      10	Load Inductance	LL	126mH
      11	Load Power factor		0.79

      Sin(t )

      s, abc

      sb

      3 s 3

      vsc

      Sin(t

      2

      L d i

      R i v

      3

      • v

   (5)

   s dt

   c,abc

   s c,abc

   s,abc

   o,.abc

   where , V , , R and L have their usual connotations. The

   s s s

   above voltages and currents are transformed into dq frame

   L d i

   R i

   • wL i

     • v v

     s dt cq

     s cq

     s cd

     sq oq

     (6a)

     d

     Ls dt icd

     wLsicq Rsicd vsd vod

     (6b)

     The switching function S of the STATCOM can be defined as follows

     Sin( wt)

     Table.II: It shows the system parameters

     Sa

     S S

     b

     Sc

     2

     m Sin( wt

     3

     2

     )

     3

     (7)

     Sin( wt

     2 )

     3

     The modulation index, being constant for a programmed PWM, is given by,

     MI

     vo, peak 2

     m

     Vdc 3

     (8)

     Fig.7: Steady state responses of Icq , Icd and Vdc

     The STATCOM output voltages in dq transformation are

     vo,qdo m0 1

     0T v

     (9)

     dc

     dc

     The dc side current in the capacitor in dq transformation

     i m0 1

     0i i

     i T

     (10)

     dc cq cd co

     The voltage and current related in the dc side is given by

     Fig.8: Steady state responses of Pc and Qc

     dvdc m i

     (11)

     dt C cd

     The complete mathematical model of the STATCOM in dq

     frame is obtained as given in (12)

     Rs w 0

     icq

     Ls

     icq

     Sin

     d i

     w

   • Rs

   • m i

   Vs Cos

   (12)

   Fig.9: Transient responses of icq in capacitive and inductive

   dt cd

   L L cd L

   v

   s s v s 0

   dc 0

   m 0 dc

   C

   3.3. Steady State and transient Analysis

   The detailed steady state and transient responses with the Table.II are given in Fig.7-10 and responses suggest the static and dynamic conditions of the STATCOM. It can be seen that

   Fig.10: Transient responses of vdc in capacitive and inductive

4. DESIGN OF CONTROLLERS:

   With the assumption of the system voltage and STATCOM output voltage are in phase and hence the equation (12) can be modified as given in equation (13)

   Gq (s)

   I q (s)

   oq

   oq

   V * (s) Rs

   1

   • sLs

     , Gd (s)

     I d (s)

     od

     od

     V * (s) Rs

     1

   • sLs

     (17)

     Rs

     d icq

     Ls

     icq

     1 vsq

     voq

     dt i

     Rs i

     L v

     v

     (13)

     Fig.12: Current control of inverter of equivalent decoupled SISO systems

     cd

     cd

     Ls

     s sd

     od

     For similar dynamic behaviour of the d and q – axis currents, both the d and q – axis controllers are identical and its transfer

     So the equation (13) is a Multiple Input and Multiple Output

     (MIMO) system and its input and output are given as

     function is given in (21)

     oq cq

     oq cq

     v i

     I cq (s) I cd (s) 1

     u ,y

     (14)

     G (s)

     i * *

     (18)

     vod icd

     Voq (s) Vod (s) Rs sLs

     The block diagram of the STATCOM in d-q transformation as

     The transfer function of a PI controller is

     per (13) is shown in Fig.11.The instantaneous voltage of the system and the STATCOM are independent, but the active and the reactive currents are coupled with each other through the reactance of the coupled inductor. So it is very essential to decouple the active and reactive current from each other and

     G pi (s) K 1

     K

     1

     1

     K p i s i s

     K

     (19)

     design the controller for tracking the required value.

     With

     K p K , Ki

     i

     . The transfer function in open loop of

     PI controller associated with the transfer function on the a.c. system is

     1 R

     G (s).G (s) K 1 1 s

     (20)

     Fig.11: Equivalent Diagram on a.c.side of STATCOM

     pi i

     s

     Ls

     1 s Ls

     i

     i

     Rs

     4.1 Design of current controller:

     The current controller design for the above system can be done

     While taking i

     and on simplification reduces to

     Rs

     using the strategy [8-9] attempts to decouple the d and q axes equations, so that the MIMO system reduces to two independent

     G (s).G (s) K

     (21)

     Single Input Single Output (SISO) system. Hence, the control

     pi i

     sLs

     inputs vod

     and voq

     are configured as

     The closed loop transfer function is

     oq

     oq

     voq v*

     *

     • wLsicq vsq

     (15) T 1

     L

     (22)

     vod

     vod wLsicd

   • vsd

   1 s s

   The equation (16) can be obtained by replacing (13) by (15). Hence each row of (16) is independent of each other and thus defines an independent SISO system. Conventional frequency- domain design methods can now be directly applied for current

   K

   Thus the system behaves like a first order with an apparent time constant as

   controller. Taking the Laplace transformation of both sides of

   (17) and rearranging terms are given by (18) and their

   Ls

   i K/p>

   (23)

   decoupled SISO system is shown in Fig.12.

   The gain of K can be adjusted such a way that if it is increased

   Rs 0

   *

   too high then the system behaves as second order, otherwise

   icq

   Ls icq

   1 voq

   (16)

   responses very slow. Hence the numerical values for

   i

   Rs i

   L *

   K p and Ki are decided from the circuit parameters Ls and Rs

   cd 0

   cd

   Ls

   s vod

   from the required value of K. So the parameters of PI controller are defined as

   K p K , Ki

   KRs

   Ls

   (24)

   where , v

   C

   K * Kdc

   and taking v

   1msecond and with the

   where,

   Ls

   which is taken as 0.3mseconds and with the

   parameters of Table. I, the value of Kdc 1.08

   K

   K

   i

   p

   parameters given in Table-II, value of

   K pi 16.9

   and

   3

   3

   Kii 3.310

   are calculated. These parameters are used

   in d and q – axis current controller. The structure of the effective closed loop system is shown in Fig.13 and is replicated in both the d and q – axis current controllers.

   Fig.14: DC link voltage control loop

   Then Proportional Integral controller is considering for the voltage control. Hence, the transfer function of PI controller in

   (19) is associated with the transfer function on dc side is

   Fig.13: Effective closed loop current control system

   Gv (s).G pi (s)

   ol

   ol

   v

   v

   K 1

   1 1

   (31)

   4.2. Design of voltage controller:

   s sC

   The relation between dc voltage vdc and dc current idc is

   After taking v C

   and on simplification

   v 1 i dt

   (25)

   1 s

   dc C dc

   G (s).G (s) K

   v pi

   v pi

   v

   2 2

   (32)

   The transfer function can be written as

   ol

   s v

   G (s) Vdc 1

   v I sC

   (26)

   The transfer function in closed loop

   dc

   1 s

   Neglecting the power loss in the source resistance and power

   G (s).G

   (s)

   v

   (33)

   losses in the switches, balancing the power on both sides,

   v pi

   cl

   1 s

   s 2 2

   v

   vsdicd

   vdcidc

   (27)

   v K

   From the above equation, we have

   So the system behaves like a second order system. As

   i v V 230 2

   dc sd s

   0.46

   (28)

   v

   and the initial slope in magnitude plot at break

   icd

   vdc

   Vdc

   500 v K

   With Vdc as the reference, the voltage control loop is shown in Fig.14 and it consists of inner d – axis current control loop. The

   active power is supplied by the d -axis current which is nothing but the ripple current of the capacitor. To make the steady state

   point is approximately 20db/decade and hence it reduces to first order system. The value of K can be determined form root locus with approximate settling time as given in (34) and implementation block diagram is shown in Fig.15.

   K

   error of the voltage loop zero Proportional control is adopted here and it produces the reference d -axis current for the control of the d -axis current. The design of voltage controller is as follows:

   The open loop transfer function of DC bus voltage controller is

   K pv K 0.15, Kvi

   200

   C

   (34)

   Gop

   K * Kdc

   sC

   (29)

   The closed loop transfer function with unity feed back gain is

   Gcl

   1

   1 sC K * Kdc

   (30)

   Fig.15: Implementing scheme for linear loads

5. SIMULATION RESULT 5.1: Simulation Result of the load:

   Fig.17: System voltage and system current

   A linear load, simulated with

   R L

   parameters (given in

   Table.II), is connected to the grid at Bus no.5. The waveforms of the grid side phase-a voltage ( vsa ) and current ( isa ) at point of common connection (PCC) (without the STATCOM in operation) are shown in Fig.16. It may be mentioned that here

   and elsewhere (unless otherwise mentioned)

   vsa is plotted to a

   reduced scale of 10:1. Under steady state it is seen that the

   Fig.18: System voltage and STATCOM current

   power angle is

   39.640 (so that power factor is

   0.77 ). The

   STATCOM will now act in closed-loop with this system along with the proposed controllers in order to improve this power factor.

   Fig.16: Grid phase a voltage and current

   5.2. Simulation Results with STATCOM:

   Then after PI controller is applied to control DC link voltage and PI controllers are used to control d and q axis current of STATCOM using the same control block as above. These controllers work and STATCOM functions at initial value of DC link voltage less than 550V. The relevant outputs at initial DC link voltage of 550V are shown in Fig.17 to 23.Fig17 shows the dynamics of system voltage and system current after using PI controller at DC link voltage and it shows the over shoot of only 20A and the same dynamics is obtained in case of STATCOM current as shown in Fig.18. Figs.19 and 20 show the dynamics of DC link voltage and current. Figs.21 and 22 show the change of STATCOM current and DC link voltage due to change of reference current (reactive current of load).The system voltage and the STATCOM voltage are shown in Fig.23 and both are in-phase as it signifies for linear model. These controllers work well without spike at initial voltage of 700V as shown in Fig.24 of system voltage.

   Fig.19: DC link voltage

   Fig.20: DC link current

   Fig.21: Reference current

   Fig.22: DC link voltage due to change of reference current

   Fig.23: System and STATCOM output voltage

   Fig.24: System voltage and system current

6. CONCLUSION

   The investigation of performances of the STATCOM for the power factor improvement with linear loads at weak bus connected to the grid has been carried out. The proposed control strategy has been simulated. The STATCOM works as a power factor compensator. It has also been shown that the interaction between a STATCOM device and a supply system makes the rural consumers healthy and wealthy.

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