Effect of SMES Unit in a Restructured Power System Considering GDB Non – Linearity

Effect of SMES Unit in a Restructured Power System Considering GDB Non – Linearity

V. Rajaguru

Lecturer / ECE, Debre Berhan University

Debre Berhan,, Ethiopia.

1. Shanmugam,

   Assistant Professor / EEE,

   1. Sathya,

      Assistant Professor / EEE, Krishnasamy College of Engg & Tech, Cuddalore, India.

      Krishnasamy College of Engg & Tech, Cuddalore, India.

      Abstract In power system, any sudden change in load leads to the deviation in frequency and the tie-line power flow. Therefore, Load Frequency Control (LFC) is an important issue in power system operation and control for supplying reliable electric power with good quality. This paper presents the effect of Super conducting Magnetic Energy Storage (SMES) unit in a restructured power system considering Governor Dead Band (GDB) non-linearity. The proposed work consist of two area interconnected power system in a restructured environment with SMES unit considering GDB non-linearity has been designed to improve the dynamic performance of the system and Integral Square Error (ISE) technique is used to obtain the optimal Proportional – Integral gain settings. The simulation result shows the load frequency control in a restructured power system with and without SMES unit considering GDB non-linearity for different contracted scenarios.

      KeywordsLoad Frequency Control; Restructured power system; Super conducting Magnetic Energy Storage (SMES) unit; Governor Dead Band (GDB) non-linearity.

      1. INTRODUCTION

         The power system composed of several interconnected control areas, any sudden changes in the load causes frequency deviations. So Load Frequency Control (LFC) plays a vital role in an interconnected power system for supplying reliable and good quality of power supply. The main objective of the LFC is to maintain zero steady state errors for frequency deviation and good tracking load demands in a multi-area restructured power system.

         A lot of studies have been made in this area are as follows. A study of two area Load Frequency Control in deregulated power system is presented and any mismatch between actual and contracted demands will result in a frequency deviation [1]. Automatic Generation Control (AGC) of two area interconnected power system has been studied and the concept of Distribution Company (DISCO) Participation Matrix (DPM) is presented [2]. Usually the Governor Dead Band (GDB) effects are neglected in the load frequency control studies for simplicity. But for realistic analysis of system performance, this should be incorporated. This results in considerable effects on the amplitude and settling time of

         oscillations [3]. A new optimal controller for the automatic generation control problem in deregulated power system is proposed and the performance of a two area power system considering different contracted scenarios has been proposed [4]. A multi stage fuzzy Proportional Integral Derivative (PID) type controller is proposed to solve the LFC problem in a restructured power system and the results of the proposed controller are compared with the classical fuzzy PID type controller and mixed H2 / H controller through some performance indices to illustrate its robust performance [5]. A new approach for the design of decentralized biased controllers for LFC of interconnected power systems is presented and the simulation results proved that the biased controllers provide better transient as well as steady state response [6]. A fuzzy logic controller for AGC in a interconnected power system including SMES units has been studied [7]. A comprehensive digital computer model of a two area interconnected power system including the GDB non-linearity, steam reheat constraints and the boiler dynamics is developed. The improvement in AGC with the addition of a small capacity SMES unit is studied [8]. Fast acting energy storage devices can effectively damp electromechanical oscillations in a power system. A power system with a SMES unit of 4 6 MJ capacity would reduce the maximum deviation of frequency and tie-line power flow by about 40% in power areas of 1000 2000MW capacity is analyzed [9].

      2. SMES MODEL

         The Fig.1 shows the basic configuration of a SMES unit in the power system. The superconducting coil can be charged to a set value (which is less than the full charge) from the utility grid during normal operation of the grid. The DC magnetic coil is connected to the AC grid through a Power Conversion System (PCS) which includes an inverter/rectifier. Once charged, the superconducting coil conducts current, which supports an electromagnetic field, with virtually no losses. The coil is maintained at extremely low temperature (below the critical temperature) by immersion in a bath of liquid helium.

         Fig.1. Configuration of SMES in the power system

         U

         When there is a sudden rise in the demand of load, the stored energy is almost immediately released through the PCS to the grid as line quality AC. As the governor and other control mechanisms start working to set the power system to the new equilibrium condition, the coil charges back to its initial value of current. Similar is the action

         The inductor is initially charged to its rated current, Ido by applying a small positive voltage. Once the current has attained the rated value, it is held constant by reducing voltage ideally to zero since the coil is superconducting. A very small voltage may be required to overcome the commutating resistance.

         The energy stored at any instant,

         d

         WL = (½)(LI 2), MJ (2)

         Where, L = inductance of SMES, in Henry.

         In LFC operation, the Ed is continuously controlled by the input signal to the SMES control logic. The inductor current must be restored to its nominal value quickly after a system disturbance so that it can respond to the next load disturbance immediately. Thus, in order to improve the current restoration to its steady state value the inductor current deviation is used as a negative feedback signal in the SMES control loop. Based on the above discussion, the converter voltage deviations applied to the inductor and inductor current deviations are described as follows:

         during sudden release of loads. The coil immediately gets charged towards its full value, thus absorbing some portion of the excess energy in the system, and as the system returns

         Edi

         (S)

         KSMES

         1 STdci

         1

         SMES i

         1. Kid

            1 STdci

            Idi

            (S)

            (3)

            to its steady state, the excess energy absorbed is released and the coil current attains its normal value.

            Idi (S) SL

            i

            Where

            Edi (S)

            (4)

            The operation of SMES units, that is, charging, discharging, the steady state mode and the power modulation during dynamic oscillatory period are controlled by the application of the proper positive or negative voltage to the inductor. This can be achieved by controlling the firing angle of the converter bridges.

            Neglecting the transformer and the converter losses, the DC voltage is given by

            Ed = 2Vdocos – 2IdRc (1)

            Where, Ed = DC voltage applied to the inductor (KV) = firing angle (degree)

            Id = current through the inductor (KA)

            Rc = equivalent commutating resistance ()

            Vdo= maximum open circuit bridge voltage of each six pulse convertor at =0 degree (KV)

            Edi (s) = Converter voltage deviation applied to inductor in SMES unit

            KSMES = gain of control loop SMES

            Tdci = convertor time constant in SMES unit USMES = control signal of SMES unit

            Kid = gain for feedback Id in SME unit

            Idi (s) = inductor current deviation in SMES unit.

            The ACEi is defined as follows:

            ACEi = BiFi +Ptie,I (5)

            Where

            Bi = Frequency bias in area i.

            Fi = Frequency deviation in area i.

            Ptie,i = Net tie line power flow deviation in area i.

            LS

            Idoi+Idi

            Fig. 2. The block diagram of SMES unit

            The deviation in the inductor real power of SMES unit is expressed in time domain as follows:

            PSMES i Edi Idoi IdiEdi (6)

            Where, PSMESi = Deviation in the inductor real power of SMES unit in area i.

            This value is assumed to be positive for transfer from AC grid to DC. Fig. 2 shows the block diagram of SMES unit.

      3. RESTRUCTURED POWER SYSTEM

         1. Traditional VS Restructured Scenario

            The traditional power system industry has a vertically integrated utility (VIU) structure. In the restructured or deregulated environment, vertically integrated utilities no longer exist. The utilities no longer own generation, transmission, and distribution; instead, there are different entities, viz, GENCOs (Generation Companies), TRANSCOs (Transmission Companies) and DISCOS (Distribution Companies).

            As there are several GENCOs and DISCOs in the restructured structure, a DISCO has the freedom to have a contract with any GENCO for transaction of power. A DISCO may have a contract with GENCO in another control area. Such transactions are called Bilateral Transactions.

            All the transactions have to be cleared through an impartial entity called an Independent System Operator (ISO). The ISO has to control a number of ancillary services, one of which is Load-Frequency Control.

         2. DISCO Participation Matrix

         In the restructured environment, GENCOs sell power to various DISCOS at competitive prices. Thus, DISCOS have the liberty to choose the GENCOs for contracts. They may or may not have contracts with the GENCOs in their own area. This makes various combinations of GENCO-DISCO contracts possible in practice. We introduce the concept of a DISCO participation matrix (DPM) to make the visualization of contracts easier. DPM is a matrix with the number of rows equal to the number of GENCOs and the number of columns equal to the number of DISCOS in the system. Each entry in this matrix can be thought of as a fraction of a total load contracted by a DISCO (column) toward a GENCO (row). Thus, the ijth entry corresponds to the fraction of the total load power contracted by DISCO from a GENCO. The sum of all the entries in a column in this matrix is unity. DPM shows the participation of a DISCO in a contract with a GENCO; hence the name DISCO participation matrix.

         Consider a two-area system in which each area has two GENCOs and two DISCOS in it. Let GENCO1, GENCO2 , DISCO1 , and DISCO2 be in area I and GENCO3, GENCO4, DISCO3, and DISCO4 be in area II as shown in Fig.3.

         		GENCO3 GENCO4 DISCO3 DISCO4
         DISCO1 DISCO2 GENCO1 GENCO2	Tie-Line

         Area 1 Area 2

         Fig. 3. Schematic diagram of a two area system in restructured environment

         The corresponding DPM will become

         cpf11 cpf12

         cpf13 cpf14

         To solve the non-linear problem, it is necessary to make the basic assumption that the variable x, appearing in the above equation is sufficiently close to a sinusoidal equation, that is

         DPM cpf21

         cpf31

         cpf41

         cpf22 cpf32 cpf42

         cpf23 cpf33 cpf43

         cpf24 cpf34 cpf44

         (7)

         x A sin 0t (10)

         Where, x is a variable

         Where cpf refers to contract participation factor. Suppose that DISCO3 demands 0.1 pu MW power, out of which 0.025 pu MW is demanded from GENCO2, 0.03 pu MW from GENCO2, 0.035 pu MW from GENCO4 and

         0.01 pu MW from GENCO4.

         Then column 3 entries in (12) are easily defined as

         A is the amplitude of the oscillation

         0 is the frequency of the oscillations

         cpf13 cpf33

         0.025 0.25,

         0.1

         0.035 0.35,

         0.1

         cpf23 cpf43

         0.03 0.3,

         0.1

         0.01 0.1

         0.1

         (8)

         F(x)

         1

         Other cpfs are defined similarly to obtain the entire

         DPM. It should be noted that i cpfij 1

         . The

         -A -D 0

         diagonal elements of DPM correspond to local demands. Off diagonal elements correspond to the demands of the DISCOS in one area to the GENCOs in another area.

      4. GOVERNOR DEAD BAND

         Governor Dead Band (GDB) is defined as the total magnitude of a sustained speed change with in which there is no resulting change in valve position. The Governors in all areas in a power system have dead bands, which are important for speed control under small disturbances. The dead band affects the stability of the system. One way to improve the stability of the system is to optimize the bias factor B associated with change of frequency (as opposed to tie-line power) in Area Control Error (ACE). In addition, the total ACE can be used to improve stability by proper selection of its integrating factor

         KI in the determination of supplementary control.

         D A X

         2

         Fig. 4. Governor Dead Band non-linearity

         As the variable function is complex and periodic function of time, it can be developed in a Fourier series as follows,

         . N .

         The limiting value of dead band is specified as 0.06%. One of the effects of Governor Dead Band is to

         F (x, x) F°

         N1x 2 x …

         0

         (11)

         increase the apparent steady-state speed regulation R. This can be seen from the fig.4. by joining points 1 and 2 and multiplying the slope of this line with 1/R. The slope of the line K without dead band is 1.The GDB of the form shown in fig.4.exists in real system.

         The hysteresis type of non-linearity is expressed as,

         As the backlash non-linearity is symmetrical about the origin, F° is zero. From the above equation, for simplification, neglect higher order terms. The Fourier co-efficients are derived as N1=0.8 and N2=-0.2. By substituting the values in the above equation, we get the transfer function for GDB as follows,

         . . N .

         2

         Y=F(x, x) rather than as Y=F(x) (9)

         F (x, x) N1x

         0

         x …

         (12)

      5. CONVENTIONAL PI – CONTROLLER

         Kp(optimum) = 0.11 KI(optimum) = 0.09

         Fig.5. Performance index curve for optimal KP Fig.6. Performance index curve for optimal KI

         Kp(optimum) = 0.9 KI(optimum) = 0.43

         Fig.7. Performance index curve for optimal KP Fig.8. Performance index curve for optimal KI

         P-I controller (proportional Integral controller) is a feedback controller which drives the plant to be controlled with a weighted sum of the errors (difference between the output and desired set-point) and the integral of that value.

         The controller output is given by KP+KI dt. (13) Where is the set point error

         KP proportional gain KI Integral gain

         The integral term in a PI controller causes the steady state error to be zero for a step input.

         For conventional PI – controller the gains KP and KI have to be determined by using Integral Square Error (ISE) criterion.

         The objective function used for this technique is

         t

         F1 1

         Where, F1 change in frequency in area 1.

         Ptie change in tie line power.

         On the basis of performance index (J) curve (J VS KP & J Vs KI) the feedback gains are determined to achieve the optimality of system performance. Figs. 5, 6, 7& 8 show optimum values of KP and KI, for with and without SMES unit.

      6. SIMULATION MODEL AND RESULTS

         A two area interconnected restructured power system with SMES unit considering GDB non-linearity s used to illustrate the behavior of the proposed LFC scheme. The data used for simulation is given in the appendix. Both the areas are assumed to be identical. The governor-turbine units in each area are assumed to be identical.

         J (

         0

         2 Ptie2 )dt.

         (14)

         Fig.9 (a). Simulation model of load frequency control in a restructured power system without SMES unit considering GDB non-linearity for case-1

         Fig.9 (b). Simulation model of load frequency control in a restructured power system with SMES unit considering GDB non-linearity for case-1

         Fig.10 (a). Simulation model of load frequency control in a restructured power system without SMES unit considering GDB non-linearity for case-2

         Fig.10 (b). Simulation model of load frequency control in a restructured power system with SMES unit considering GDB non-linearity for case-2

         1. – Frequency deviation in area – 1 (a) – Frequency deviation in area – 1

         2. – Frequency deviation in area – 2 (b) – Frequency deviation in area – 2

         3. – Tie-Line power deviation (c) – Tie-Line power deviation

         Fig.11. Frequency response of a two area interconnected restructured power system considering GDB non-linearity for case-1

         Fig.12. Frequency response of a two area interconnected restructured power system considering GDB non-linearity for case-2

         Case 1 : Base Case

         The GENCOs in each area participate equally in LFC (i.e., ACE participation factors are apf 1=0.5, afp2=1 apf1=0.5; apf3=1-apf2=0.5; apf4=1-apf3=0.5). The load change occurs only in area 1. Thus, the load is demanded only by DISCO1 and DISCO2. Let the value of this load perturbation be 0.1 pu MW for each of them.

      7. CONCLUSION

In this paper, Load-Frequency Control for an interconnected power system with SMES unit considering GDB non-linearity is proposed for the solution of LFC problem in a Restructured Environment. LFC provides a relatively simple, yet effective method of adjusting generation to minimize frequency deviations and regulate

0.5

0.5

DPM

0.5 0 0

0

0.5 0

Tie-line power flow. In addition to this the Integral Square Error (ISE) technique is used to obtain conventional P-I controller gains. Thus, the simulation results show that the

0 0

0

0

0 0

0

0

dynamical performance of the system (such as frequency oscillation, peak over shoot and settling time) is significantly improved when an SMES unit is included in a

The DISCO3 and DISCO4 do not demand power from any GENCOs, and hence corresponding participation factors (columns 3 and 4) are zero. DISCO1 and DISCO2 demand identically from their local GENCOs viz. GENCO1 and GENCO2.

Fig.9(a & b) shows the simulation model of two area interconnected restructured power system with and without SMES unit considering GDB non-linearity for this base case.

Case 2 : Bilateral Transactions

In this case where all the DISCOS contract with the GENCOS for power as per the following Disco Participation Matrix (DPM):

two-area interconnected restructured power system with GDB non-linearity.

APPENDIX

1. Data for the two area interconnected restructured power system without SMES unit considering GDB non-linearity

   TG = 0.08 sec , TT = 0.3 sec , KP = 120 Hz/pu , Tp = 20 sec , T12 = 0.545 pu/Hz ,Kp = 0.11 , KI = 0.09, B = 0.425 Pu/Hz , R = 2.4 Hz/pu, N1=0.8, N2 = -0.06.

2. Data for the two area interconnected restructured power system with SMES unit considering GDB non-linearity

   TG = 0.08 sec , TT = 0.3 sec , KP = 120 Hz/pu, Tp = 20 sec , T12 = 0.545 pu/Hz , KP= 0.9, KI = 0.43, B = 0.425 Pu/Hz, R = 2.4 Hz/pu, N1=0.8, N2 = -0.06.

3. Data for SMES unit

L = 2.65 H

Tdc = 0.03 sec

KSMES = 50 KV/unit MW

Kdi = 0.2 KV/kA

0.5

0.2

DPM

0.25 0 0.3

0.25 0 0

Ido = 4.5 kA

REFERENCES

0 0.25 1 0.7

0.3 0.25 0 0

It is assumed that each DISCO demands 0.1 pu MW power from GENCOS as defined by cpfs in DPM matrix. The off diagonal blocks of the DPM correspond to the contract of a DISCO in one area with a GENCO in another area.

Fig.10(a & b) shows the simulation model of two area interconnected restructured power system with and without SMES unit considering GDB non-linearity for this bilateral transaction case.

The above two different contracted scenarios (i.e., case-1 & 2) are simulated by using MATLAB and the simulation results are shown in Fig.11 & 12.

The fig.11(a,b&c) & fig.12(a,b&c) show the simulation results of Frequency deviation of area 1 (f1), Frequency deviation of area 2 (f2), and Tie-Line power deviation (Ptie) in a restructured power system with and without SMES unit considering GDB non-linearity for different contracted scenarios.

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BIOGRAPHIES

V. Rajaguru received B. E. degree in Electrical and Electronics Engineering in 2006 from Annamalai University, India, and M.E degree in Power Systems Engineering in 2009 from Annamalai University, India. He is currently working as a Lecturer in Electrical and Computer Science Engineering Department at Debre Berhan University, Debre Berhan, Ethiopia.

R. Sathya received B. E. degree in Electrical and Electronics Engineering in 2006 from Annamalai University, India, and M.E degree in Power Systems Engineering in 2009 from Annamalai University, India. She is currently working as a Assistant Professor in Krishnasamy College of Engg & Tech., Cuddalore,TamilNadu, India.

V. Shanmugam received B. E. degree in Electrical and Electronics Engineering in 2001 from Annamalai University, India, and M.E degree in Power Systems Engineering in 2009 from Annamalai University, India. He is currently working as a Assistant Professor in Krishnasamy College of Engg & Tech., Cuddalore,TamilNadu, India.