Analysing Powe Flow Solution with Optimal Unified Power.Flow Controller

Abstract— The electric power system function is to maintain the power plants under pool operation and utility centers to supply the active and reactive powers demanded by the loads connected to the system. Now a day’s transmission systems are difficult to operate as well as more stressed due to unscheduled power flows and more losses of growing demand. However many HV systems are operating below thermal rating due to the voltage and stability limit. Later on rapid development in the technology introduces high rating and fast acting switching devices with power electronic components. Flexible AC transmission system (FACTs) controllers equipped with fast acting semi conductor devices designed to control one or more power system parameters for the effective operation of system. In this paper, a novel FACTs controller namely, optimal unified power flow controller (OUPFC) is proposed with its current injection model along with its incorporation procedure. The effect of this device on system parameters is analyzed on standard test systems with its graphical and numerical results. KeywordOptimal unified power flow controller; Current based model; PST; UPFC

supply or absorb reactive power to provide desired reactive shunt compensation for the line moreover controls the bus voltage.

A. Mathematical Model of Phase Shifting Transformer
The Phase Shifting Transformer (PST) is used to advance the phase angle of the bus voltage. It is represented by an ideal transformer as in previous cases but with a turn's ratio which is a complex number. Let the turns ratio be (a s + jb s ). The configuration of phase shifting transformer is shown in Fig.2.

B. Mathematical Model of UPFC
The general structure of UPFC contains "back-to-back" AC to DC voltage source converters through a common DC link capacitor shown in Fig.3. First converter (CONVERTER-I) is connected in shunt and the second one (CONVERTER-II) in series with the line. The shunt converter is primarily used to provide active power demand of the series converter through a common DC link. Converter-I can also generate or absorb reactive power, if it is desired, and thereby provide independent shunt reactive compensation for the line. Converter-II provides the main function of the UPFC by injecting a voltage with controllable magnitude and phase angle in series with the line.

C. Power Injection Model of OUPFC
The complete power injection model for OUPFC is taken from [8]. The power injections at the OUPFC connected buses can be expressed as Similarly, at mth bus can be expressed as

III. CURRENT BASED MODEL OF OUPFC
In current based (CB) model of OUPFC, the injected current in to the transmission line is given by, OUPFC device injecting power at kth bus is, On simplifying the above expression series device injecting real and reactive powers are obtained as, Similarly real and reactive powers injected by series converter at mth bus are calculated as, On simplifying the above expression , Shunt converter injecting power at kth bus is calculated as,

Real power injected at kth bus is
Net active and reactive powers injected by the device at kth and mth bus are, The detailed equations are derived as follows,

IV. DEVICE INCORPORATION PROCEDURE
To analyze the effect of UPFC/OUPFC on a given power system, this device is incorporated in Newton-Raphson (NR) load flow solution. The developed current based model of UPFC/OUPFC is easily incorporated into the system by modifying Jacobian elements and power mismatch equations related to device connected buses [8].
The final steady state network equation in NR load flow in the presence of UPFC can be expressed as Where, 'ΔP, ΔQ' are the vector corresponds to real and reactive power mismatches, 'Δδ, ΔV' are the vector of incremental changes in angles and voltages, 'H, N, J, L' are the partial derivatives of P and Q w.r.to δ and V.
The corresponding Jacobian elements related to OUPFC connected buses are expressed as follows: Jacobian elements related to CBM of OUPFC The elements related to 'H' matrix are obtained from equation (11) The elements related to 'N' matrix are obtained from equation (12 The elements related to 'J' matrix are obtained from (13) ) The elements related to 'L' matrix are obtained from (14) )

V. POWER FLOW SOLUTION IN THE PRESENCE OF OUPFC
The overall computational procedure of Newton-Raphson power flow method with OUPFC is described in the following steps.
 Read bus data, line data and OUPFC data.  Assume flat voltage profile and set iteration count k=0.  Compute active and reactive power mismatch from the scheduled and calculated powers.  Determine Jacobian matrix using power flow equations.  Modify power mismatch and Jacobian elements related to OUPFC connected buses to incorporate OUPFC.  Solve the NR method to find the voltage magnitudes and angles correction vector.
 Update the solution using correction vector.  Increase the iteration count, k=k+1.  Stop the process, if tum mismatch is less than given tolerance and print the output. Otherwise, go to step 3.

VI. RESULTS AND ANALYSIS
In this section, to show the effectiveness of OUPFC over the existing PST and UPFC, the analysis is performed for the following two cases.
Case-1: Analysing the effect of OUPFC on system parameters by varying device control parameters. Case-2: Comparing the effectiveness of OUPFC over the existing PST and UPFC with respective numerical results.
For this analysis, the device control parameter variation for the considered devices is as follows: 1. For PST: The transfer ratio

A. Example-1
In this example, IEEE-5 bus system popularly known as Hale network with two generators, seven transmission lines is considered [9]. The total load on this system is 165 MW. To show effect of these devices, predominantly transmission line connected between buses 4 and 5 (Line-7) with shunt converter placed at bus-4 is considered to install these devices. The reactance of the series converter transformer is considered to be 0.1 p.u.
For Case-1, the OUPFC control parameters k and σ are fixed at 0.08 p.u and 18.028 deg and the parameters r is varied from 0 p.u. to 0.1 p.u and γ is varied from -180 deg to 180 deg. The variation of bus voltage magnitudes with OUPFC is shown in Fig.5, variation of power flow, power losses and number of iterations is shown in Figs.6 and 7. From these figures, it is identified that, value of the system parameters (voltage magnitude, power flow, losses) is increasing as the device control parameters value is varied from minimum setting (r=0 p.u) to maximum setting (r=0.1 p.u). To show more clearly the effect of OUPFC on system parameters, the consolidated variation of system parameters for the variation of device control parameters is shown in Figs. 8 and 9. Fig.8 clearly shows that, voltage magnitude at bus-4 has major variation as the device shunt converter is connected at this bus. Similarly from Fig.9, the power flow in the device connected line (7th line) and nearby line (5th line) has got major variations. It is also observed that, the power flow in line-5 can be varied up to its maximum limit. In Case-2, to show the effectiveness of OUPFC over PST and UPFC, variation of voltage magnitude difference (Vmax-Vmin) at each bus is shown in Fig.10, power flow difference (Pmax-Pmin) in each line is shown in Fig.11 and variation of power losses is shown in Fig.12. The numerical results of the losses with respective PST, UPFC and OUPFC control parameters are tabulated in Table.1. From this table, it is observed that, due to simplified mathematical equations solved with CB of OUPFC, the number of iterations taken to solve load flow is decreased.

B. Example-2
In this example, IEEE-14 bus system with five generators connected at buses 1, 2, 3, 6 and 8, twenty transmission lines, three tap changing transformers (lines 8, 9 and 10 connected between buses 4-7, 4-9 and 5-6) and one shunt compensator (connected at bus-9) is considered. The total load on this system is 259 MW. To show effect of these devices, based on [10], predominantly transmission line connected between buses 7 and 9 (Line-15) with shunt converter placed at bus-7 is considered to install these devices. The reactance of the series converter transformer is considered to be 0.2 p.u.
For Case-1, to show the effect of OUPFC on system parameters, the consolidated variation of system parameters for the variation of device control parameters is shown in Figs. 13-15. Fig.13 clearly shows that, voltage magnitude at bus-9 has major variation as the device is connected at this bus. Similarly from Fig.14, the power flow in the device connected line (15th line) and nearby lines (14th and 16th lines) has got major variations. It is also observed that, the power flow in line-15 can be varied from lower limit to upper limit. From  Fig.15, it is observed that, minimum and maximum power losses are obtained when device is at maximum operating limit. It is also observed that, due to increased mathematical computations with OUPFC, the number of iterations taken to solve load flow is also increased. In Case-2, to show the effectiveness of OUPFC over PST and UPFC, variation of voltage magnitude difference (Vmax-Vmin) at each bus is shown in Fig.16, power flow difference (Pmax-Pmin) in each line is shown in Fig.17 and variation of power losses is shown in Fig.18. The numerical results of the losses with respective PST, UPFC and OUPFC control parameters are tabulated in Table.2. From this table, it is observed that, due to simplified mathematical equations solved with CB of OUPFC, the number of iterations taken to solve load flow is decreased.

C. Example-3
In this example, IEEE-30 bus system with six generators connected at buses 1, 2, 5, 8, 11 and 13, forty one transmission lines, four tap changing transformers (lines 11, 12, 15 and 36 connected between buses 6-9, 6-10, 4-12 and 28-27) and two shunt compensators (connected at buses 10 and 24) is considered. The total load on this system is 283.4 MW. To show effect of these devices, based on [11], predominantly transmission line connected between buses 6 and 7 (Line-9) with shunt converter placed at bus-6 is considered to install these devices. The reactance of the series converter transformer is considered to be 0.2 p.u.
For Case-1, to show the effect of OUPFC on system parameters, the consolidated variation of system parameters for the variation of device control parameters is shown in Figs. 19-21. Fig.19 clearly shows that, voltage magnitude at bus-7 has major variation as the device is connected at this bus. Similarly from Fig.20, the power flow in the device connected line (9th line) and nearby lines (5th, 6th, 7th, 8th, and 10th lines) has got major variations. It is also observed that, the power flow in line-9 can be varied from lower limit to upper limit. From Fig.21, it is observed that, minimum and maximum power losses are obtained when device is at maximum operating limit. It is also observed that, due to increased mathematical computations with OUPFC, the number of iterations taken to solve load flow is also increased. In Case-2, to show the effectiveness of OUPFC over PST and UPFC, variation of voltage magnitude difference (Vmax-Vmin) at each bus is shown in Fig.22, power flow difference (Pmax-Pmin) in each line is shown in Fig.23 and variation of power losses is shown in Fig.24.  Table.3. From this table, it is observed that, due to simplified mathematical equations solved with CB of OUPFC, the number of iterations taken to solve load flow is decreased. VII.

CONCLUSION
In this paper, current based model of OUPFC with supporting mathematical derivation has been presented with its incorporation procedure to solve load flow problem. The effectiveness of OUPFC on system parameters such as bus voltages, power flow in transmission lines and total power losses have been analyzed and compared with the existing PST and OUPFC. From the analysis, it has been identified that, due to controlling of multiple parameters with OUPFC, the voltage magnitude at the device shunt converter connected bus and the power flow in the device series converter connected line have been enhanced to minimize the total power losses. The numerical results along with supporting graphical results have been presented for the considered IEEE-5 bus, IEEE-14 bus and IEEE-30 bus test systems.