Power Flow Control and Solutions with Dynamic Flow Controller

2008 IEEE Electrical Power & Energy Conference

Power Flow Control and Solutions with Dynamic Flow Controller Roya Ahmadi*,Student Member,IEEE, Abdolreza Sheykholeslami*,Ali Nabavi Niaki*,Senior Member IEEE Hamidreza.Ghaffari** *Noushirvani Industrial University/Department of Electrical Engineering, Babol, IRAN. ** Sharif University of Technology, IRAN Email: [email protected] Abstract— this paper presents two new methods for power flow calculation of power systems in presence of Dynamic Flow Controller (DFC), which is a new member of FACTS controllers. In first method A new steady state model of DFC is introduced for the implementation of the device in the conventional Newton-Raphson power flow algorithm. The impact of DFC on power flow is accommodated by adding new entries and modifying some existing ones in the linearized Jacobian equations of the same system without DFC. The focus of second method is on the discrete nature of the DFC and including its effects on power flow. This method is based on Nabavi model for FACTS devices. A case study on a power system located in northern of IRAN shows the effectiveness of proposed methods. Keywords—Dynamic Flow Controller; Jacobian Matrix; Power flow

I. INTRODUCTION Application of FACTS controllers has been considered as a satisfied solution especially in regions that it is becoming very difficult to construct a new transmission line in order to avoid a power transmission limit of the existing lines, particularly under heavily loaded system conditions [1]-[7]. A new member of FACTS controllers is considered in this paper. This controller is Dynamic Flow Controller (DFC) [2]. DFC is a hybrid compensator, i.e. provides series and/or shunt compensation. Compared with Unified Power Flow Controller (UPFC)[3], DFC has some salient features like cost effectiveness, simplicity, maturity and ruggedness of the technologies of its subsystems, potentially lower losses and thus higher efficiency , which make it alternative to the UPFC [2]. Structurally a DFC [2] unit is composed of a mechanically-switched phase shifting transformer (PST), a mechanically switched shunt capacitor (MSC), and multimodule thyristor-switched series capacitor (TSSC) and inductors (TSSR)[7]. Fig. 1 shows a schematic diagram of DFC which is connected between buses i and j in a transmission system. Undoubtedly, an important part of power system study is power flow [8], [9], thus for power flow control of a system in presence of DFC, it is very important to include this new FACTS controller in power flow equations. For power flow calculations most researchers and industries use NewtonRaphson method of Iterative solution, and it is although used in this paper. For including DFC in power flow equations, it is very important to consider its discrete nature of operating points. This can be faced with several ways. In this paper first method[10],[11], assumed that step magnitudes are close enough together, thus if the calculated values of internal parameters correspond to a point located between

978-1-4244-2895-3/08/$25.00 ©2008 IEEE

two steps by rounding up the parameters to those of the closest step values, the probable mismatch error can be neglected. To solve the power flow problem with DFC in place, a new power flow model is introduced for DFC, and thus new equations are written, then Jacobian equation is extended and modified to accommodate the added equations. Second method is based on Nabavi model [3], [4] for FACTS Devices. This time Newton Raphson algorithm is modified to include discrete nature of the device. Through this method numbers of iterations increase, but this dose not have an inverse effect on the speed of the algorithm, because there are no extra equations to solve and no change is made on the original Jacobian matrix. The modeling approaches presented in this paper are tested on a 9-bus 230-400KV system located in northern of IRAN and implemented using MATLAB software package. The study results show the effectiveness of introduced methods. II.

PRINCIPLES OF OPERATION OF DFC

Fig. 1 shows a schematic diagram of a DFC that is connected between buses i and j and within a transmission line and comprises[2]:

Fig. 1. Schematic diagram of DFC

• a conventional (mechanically switched) phase-shifting transformer (PST), which can inject a lead/lag quadrature phase voltage; • a series-connected multimodule thyristor-switched series capacitor (TSSC) system that can insert series capacitive reactance in discrete steps to adjust the line series reactance[10];

• a series-connected multimodule thyristor-switched series reactor (TSSR) system that can insert series inductive reactance in discrete steps primarily to prevent over flow in the line; • a shunt-connected mechanically-switched capacitor (MSC) for voltage control or reactive power compensation[7]. Due to their large inherent time-constants, PST and MSC can only provide slow steady-state power flow control, while the TSSC and TSSR modules can provide both dynamic and steady-state power flow control. Since the tap control of PST and the switching actions of TSSC and TSSR are discrete in nature, this must be considered in power flow studies.

The power flow equations for a power system's generic bus (bus i) without DFC is [9]:

Pi = Qi =

∑ ∑

| Vi || Vj || Yij | cos (δ i - δ j - θ ij )

(8)

| Vi || Vj || Yij | sin (δ i - δ j - θ ij )

(9)

Where |Vi|∠δi represents the voltage of Bus i and |Yij| ∠θij represents elements of Y-matrix. Equations (1), (2) are iteratively Solved using linearized Jacobian equation. The equation is given in (10), where the sub Jacobian matrices are defined as J1=∂P/∂δ, J2=∂P/∂|V|, J3=∂Q/∂δ, J4=∂Q/∂|V|.

Based on DFC steady state model [2] a Single-phase equivalent model of the DFC is shown in Fig. 2 The details to reduce the single phase PST of Fig. 2 from that of Fig. 1 , under balance conditions are given in [3].Extraction of perphase representation of the TSSC, TSSR and MSC is given in [1].

Fig. 3.

J1 Fig.2.

J2

Xij = kL. XL + k 2 . XE + XB + XLINE - kcXc Zij = Rij + jXij Ys = Yij = 1 = Gs + jBs Zij

=

(1) (2) (3)

Since the ideal transformers of the PST do not exchange any power with the system:

Ip + Iv = - j.k .Iij

(4)

(1 + j.k ).Vi Vj Iij = − j. Xij j. Xij

(5)

J3

Ii = Ip + Iv + Iij (6) Substituting for Ip+Iv from (4) and Iij from (5) in (6) we deduced: (7)

POWER FLOW CALCULATION IN PRESENCE OF DFC (FIRST METHOD) The block diagram given in Fig. 3 shows a symbolic representation of a power system that includes several generators, loads and a DFC.

J4

∆|V|

∆Q (10)

DFC can actively adjust its internal parameters for controlling active and reactive power flow and regulating the voltage. That means based on power flow solution, parameters P, Q, V, δ at buses which the DFC is located are determined. Thus, the internal control parameters of the DFC can be calculated as follows:

S = Vi.Ii*

(11)

Substituting for Ii from (7) in (11) we deduce

-(1 + k 2 ) 2 (1 + jk ) Si = Vi + .Vi.Vj * j. Xij j. Xij Si =

At bus i

Ii = (1 + k 2 )Yij.Vi - (1- jk )Yij.Vj

∆P

∆δ

Single-line equivalent model of DFC

In Fig. 2 kL.XL and kC.XC represent the reactive and capacitive modules (ohmic losses are ignored). k is the PST voltage ratio which is between -1 and 1, XE, XB, XP and Rv are PST internal parameters. So for the line between busses i and j it can be written:

III.

Symbolic representation of a power system

-(1- jk ) ( XMSC - Xij ) 2 Vi *.Vj + . Vj j. Xij j. Xij . XMSC

(12)

(13)

As mentioned, power flow is analyzed based on the preset values of power and voltage magnitude that the DFC is expected to impose. But since the DFC works in discrete steps, a set of solutions may not exactly match the actual values of DFC parameters. The consequence mismatch may have effects on analyzing iterations, convergence or even speed of calculations, but not in the results of power flow. First method assumes that step magnitudes are close together enough so probable mismatch error can be neglected. For including the DFC in power flow equations with systematical method, its circuit model must be changed. In this way it is much easier to write DFC equations in the

format of power flow equations. This new model (extracted from Fig. 2) is illustrated in Fig. 4. As it shown in Fig. 4, circuit model of DFC is converted to a new model, which only consists of one series and one parallel branch.

To solve the power flow problem with DFC in place, Jacobian equation is extended and modified as shown in (21) to accommodate the added equations (18 to 20) and the modified ones (14 to 17). As it shown in (21) three rows and three columns are added to the original Jacobian matrix (gray color filled in), the added elements are although mentioned in these rows and columns. The elements of original Jacobian matrix which need to be modified are written in grey cells. As it indicated in (21) , 14 elements of original Jacobian matrix must be modified and 31 elements must be added. IV.

Fig. 4.

New circuit model of DFC

Parallel branches of PST in Fig. 2 can be converted to their Thevenin equivalent, after calculating thevenin parameters, parallel branches can be replaced with an admittance of Yp and a voltage source of Ep as it shown in Fig. 4. The power flow equations for all busses of the system with DFC in place are the same as those of the system without DFC, except for buses i and j which are written as follow:

Pi = Pij + ∑ | Vi || Vx || Yix | cos (δ i - δ x - θ ix )

Qi = Qij + ∑ | Vi || Vx || Yix | sin (δ i - δ x - θ ix )

Pj = Pji + ∑ | Vj || Vx || Yjx | cos (δ j - δ x - θ jx )

Qj = Qji + ∑ | Vj || Vx || Yjx | sin (δ j - δ x - θ jx )

In power flow calculations, usually there is no access to the Jacobian Matrix of the system software, So in practical cases it is needed to find a method to include DFC (or FACTS devices in general speaking) in power flow calculations without making any changes in the original program. One of proposed methods for such cases is Nabavi Model. Based on this model when there is no access to Jacobian Matrix the model of FACTS devices can be considered as it shown in Fig. 5:

(14) (15) (16) (17)

The summation terms in the above equations represents the same equations for the system without DFC. The equations for Pij and Qij are found to be: 2

Pij = (Gp +Gs) Vi − Vi . Ep . Yp cos(δi −δ p −θ p) + Vi . Es . Ys cos(δi −δ s −θs) − Vi . Vj . Ys cos(δi −δ j −θ p) (18) 2

Qij = (Bp + Bs) Vi − Vi . Ep . Yp sin(δ i − δ p −θ p) + Vi . Es . Ys sin(δ i − δ s −θ s) − Vi . Vj . Ys sin(δ i − δ j −θ p) (19) The presence of the voltage sources EP and ES introduces four new variables (|EP|, δp, |Es|, δs) to the power flow problem. However |Vi| is known due to preset values of power flow, so one equation will be solved for voltages. Thus three additional equations are needed for solving the power flow problem. Two of these equations are found by equating Pij and Qij to their pre-specified target values. Third equation is found by using the fact that the ideal transformers of the PST of DFC do not exchange any real and reactive power with the system. So it can be written:

PPST = Real [Vp.Iij*]- Real [VE.IE*] = 0

POWER FLOW CALCULATION IN PRESENCE OF DFC WITH NABAVI MODEL

(20)

Thus for implementation of DFC in the conventional Newton-Raphson power flow algorithm these four equations must be taken in consideration.

Fig. 5. Representation of FACTS devices in power flow

Based on Nabavi model, the impact of DFC on power flow can be considered as proposing the busses which DFC is connected between them, using power flow terminology, as P-V and P-Q bus. For the DFC of Fig. 5 which is used to maintain a pre-specified power flow from i-bus to j-bus, and to regulate the j-bus voltage at a specific value, j-bus is a PV bus and i-bus is a P-Q bus. If it was possible to control parameters of DFC continues there would be no problem to use Nabavi model for DFC. But for the discrete nature of these parameters this model most be modified to include the discrete effect of DFC. The algorithm for modifying Newton power flow to include DFC with the use of Nabavi Model is illustrated in Fig. 6. As it indicated in Fig. 6, no change has been made in conventional Jacobian matrix of the system. A function is added to the original algorithm, which in all iterations calculates DFC parameters i.e. number of tap steps and capacitor bank, and chooses best operating point that can satisfy power flow preset requirements. If it is not possible, with a feedback loop preset values may change until an acceptable result achieves. V. CASE STUDY In order to investigate the feasibility of the proposed methods, DFC embedded in power flow studies on the 230400 KV network of a power system which is located in the northern part of Iran. It is predicted that the system will experience unacceptable under-voltage due to increase in load demand, besides there are limits in the area that oppose

Pi/ δi Pj/ δi

Pi/ δj Pj/ δj

Pi/ Ep

Pi/ |Vj| Pj/ |Vj|

Pi/ δp

Pi/ δs Pj/ δs

Pi/ |Es| Pj/ |Es|

Qi/ δi Qj/ δi

Qi/ δj Qj/ δj

Qi/ Ep

Qi/ |Vj| Qj/ |Vj|

Qi/ δp

Qi/ δs Qj/ δs

Qi/ |Es| Qj/ |Es|

PPST/ δi

PPST/ δj

PPST/ Ep

PPST/ |Vj|

PPST/ δp

PPST/ δs

PPST/ |Es|

Pij/ δi

Pij/ δj Qij/ δj

Pij/ Ep|

Pij/ |Vj| Qij/ |Vj|

Pij/ δp Qij/ δp

Pij/ δs Qij/ δs

Pij/ |Es| Qij/ |Es|

Qij/ δi

Qij/ Ep

∆δ

∆P

∆ Ep

×

∆|V| ∆δp ∆δs ∆|Es|

∆Q

= ∆PS ∆Pij ∆Qij (21)

building new transmission lines. A proposed solution to the problem is to connect bus-7 and 8 through a set of transformers. The power flow shown in Fig.7 is based on the presence of hypothetical transformers. This connection can effectively handle the under voltage problem in 230 KV bus. The drawback of proposed connection is that it reduces the loading of the 230 KV line between bus-5 and bus-7 from 382MW to 36MW and it reduces the loading of the 230 KV lines and results in their permanent and uncontrolled underutilization. Installation of a DFC in path between bus-5 and 7 is investigated, to increase the 230 KV line power transfer from 36 MW to about 400 MW while maintaining the voltage at both buses 5 and 7.

Fig. 6. Proposed algorithm for power flow

Fig. 7.

230-400KV power system

C o n v e rg e n c e E rro r

The DFC composed of a 115-MWA PST, which can introduce up to -15° phase shift, a three module TSSC with reactance of 4, 8 and 12Ω and a MSC system (2×25-MVAr). Fig. 8 shows the receiving-end between the busses which the DFC is in service.The phase shifter of the DFC can increase real power transfer from 70 MW to 275 MW through 18 steps. The series capacitor modules can be controlled to increase real power transfer up to 440-MW by seven steps. These modules can be switched in/out at any tap position. In Fig. 8 discrete points cover all operating steps of the PST (18 steps), the TSSC(7 steps), and the MSC (3 steps) of the DFC unit, i.e 3×18×7=378 discrete operating points. Fig. 8 shows that the DFC can maintain active power transfer up to 450 MW, and reactive power up to 40MVAr. As it mentioned before operating point of DFC can change between these points based on scheduled active and reactive power transfer.

2

1.5 1

0.5 0 0 1 2 3 4 5 6 7 8 9 10 Iteration Count

Fig. 10 . the convergence characteristics for the system with DFC( 1ST method) 40

30

2

25 Q ( M V A r)

C o n v e rg e n c e E rro r

1.Without MSC 2.With 25MVAr MSC 3.With 50MVAr MSC

3

35

20 15 10 5 0

2 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 12

1

-5

Iteration Count

-10 50

100

150

200

250 P( M W)

300

350

400

450

Fig. 7: The receiving end P-Q area covering all operating points of the DFC

C o n v e rg e n c e E rro r

Power flow results indicate that in both cases after installing the DFC, objective of increasing active power between bus-5 and 7 to 400MW is achieved, so in both cases DFC can effectively handle power flow requirements. Fig .9-11 show the convergence characteristic for the system without DFC, With DFC included by first method and with DFC included by second method. All these figures indicate very good convergence characteristics.

Fig. 11 . the convergence characteristics for the system with DFC(2ND method)

Besides the acceptable voltage profile in Fig. 11 shows that new algorithms can effectively handle presence of DFC and modification process didn’t destroy the original algorithm.

2 1.5 1 0.5 0

Fig. 12.Voltage profile of the study system

0 1 2 3 4 5 6 7 8 9 Iteration Count Fig. 9 . the convergence characteristics for the system without DFC

VI.

CONCLUSION

In this study two methods are investigated for power flow calculations in presence of Dynamic flow controller (DFC). First method is an improved steady-state mathematical model for implementation of DFC in the conventional Newton-Raphson power flow. In this method conventional

power flow solution systematically modified and extended to include DFC. Impact of DFC on power flow can be accommodated for by introducing a new suitable model for DFC and then making changes in the linearized Jacobian equation of the original system. Second method is based on Nabavi model for FACTS devices. In this method the discrete nature of DFC is considered in power flow calculation, as a results number of iterations increased, but it is still in an acceptable margin. An existing power flow program that uses NewtonRaphson method of solution can be easily modified to include DFC, using methods introduced in this paper. The study results on the 230-400KV power system located in northern of Iran using Matlab software package show the effectiveness of introduced methods for increasing power flow between busses which DFC is installed in, from 36 MW to 400MW. Analysis of voltage profiles in these two cases reveals that both can maintain and even improve voltage profile. The numerical results although show the robust convergence of the presented methods. ACKNOWLEDGEMENTS This work is supported by NOUSHIRVANI Industrial University of Babol, IRAN. We are pleased to acknowledge our thankfulness

REFERENCES [1]

B.Scott, “Review of load flow calculation methods”, ProcIEEE62(7)(1974)916–929 [2] Nabavi Niaki.A, Iravani.R and Noroozian.N”Power Flow Model and Steady State Analysis of the Hybrid Flow Controller" Accepted for publication in IEEE Transaction on Power Delivery 2008 (TPWRD00420-2006) [3] S.A.Nabavi,”Modelling and Application of Unified Power Flow Controller for Power Systems”Ph.D dissertation .Dept.Electrical and Computer Eng, Univ of Toronto, 1996 [4] E. Acha, Claudio R. Fuerte-Esquivel "FACTS, Modeling and Simulation in Power Networks" John Wiley & Sons, 2004 [5] ]Y.H.Song , A.T.Johns, " Flexible A.C Transmission Systems (FACTS)" IEEE 1999 [6] X.-P. Zhang and E. Handschin, “Optimal power flow control by converter based FACTS controllers,” in Proc. 7th Int. Conf. AC-DC PowerTransm., London, U.K., Nov. 28–30, 2001. [7] M. Noroozian," Improving Power System Dynamics by SeriesConnected FACTS Devices" IEEE Transactions on Power Delivery, Vol. 12, No. 4, October 1997 [8] P.Kundur, “Power System Stability and control”. New York, McGrawHill, 1994 [9] H. Saadat,"Power system analysis" McGraw-Hill Primis Custom Publishing,ISBN: 0-07-2847964 [10] S.Y.GE”Optimal Active Power Flow Incorporating Power Flow Control Needs In Flexible AC Transmission Systems” IEEE Transactions on Power Systems, Vol. 14, No. 2, May 2005 [11] Narayana Prasad Padhy∗, M.A. Abdel Moamen, "Power flow control and solutions with multiple and multi-type FACTS devices" Electric Power Systems Research 74 (2005) 341–351