a dispatch strategy for an interline power flow controller ... - RPI ECSE

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A DISPATCH STRATEGY FOR AN INTERLINE POWER FLOW CONTROLLER OPERATING AT RATED CAPACITY Xuan Wei, Joe H. Chow, B. Fardanesh, and Abdel-Aty Edris Abstract—The maximum dispatch benefit of an Interline Power Flow Controller (IPFC) often occurs when it operates at its rated capacity and line flow setpoint regulation is no longer possible. This paper uses injected voltage sources to directly model an IPFC and impose the rating limits in a Newton-Raphson loadflow algorithm. A dispatch strategy is proposed for an IPFC operating at rated capacity, in which the power circulation between the two series converters is used as the parameter to optimize the voltage profile and power transfer. Voltage stability curves for two test systems are shown to illustrate the effectiveness of this proposed strategy. Index Terms—Voltage-sourced converters (VSC), Flexible AC Transmission system (FACTS) controllers, Interline Power Flow Controllers (IPFC), Newton-Raphson Algorithm, Voltage stability

operating limits can be readily implemented, but the circulating active power Pc between the series VSCs can also be specified as well to pinpoint the desired operating conditions. The dispatch strategy is illustrated with a 6-bus test system and a 21-bus test system. For both systems, we show the familiar P V curves for the IPFC dispatched below and at rated capacity. In particular, we show systematically how the dispatch of the circulating power between the two VSCs affects the system voltage profile and the power transfer capability. The dispatch computation is performed using VSM of the IPFC, with computer code based on the Power System Toolbox [19]. II. IPFC Loadflow Model

I. Introduction The operating limits of voltage-sourced converter (VSC) based Flexible AC Transmission system (FACTS) controllers must be observed to ensure that the VSCs are not overloaded and the voltages of the adjacent buses are within an acceptable range [1], [2], [18]. For these FACTS Controllers, the maximum dispatch benefit, as often demanded in post-contingency cases, occurs when it operates at its rated capacity, such as maximum current, voltage, and MVA rating. For stand-alone VSC-based FACTS Controllers such as Static Synchronous Compensators (STATCOM) [3] and Static Synchronous Series Compensators (SSSC) [4], dispatch at rated capacities translates to relaxing the setpoint enforcement in an appropriate manner. For multiple VSCs with coupled DC capacitors, such as Unified Power Flow Controllers (UPFC) [5], Interline Power Flow Controllers (IPFC) [6], and Generalized Unified Power Flow Controllers (GUPFC) [7], the dispatch optimization is more complex because of the ability of these controllers to circulate active power. A dispatch strategy for the UPFC operating at rated capacity has been proposed in [18]. In this paper, we establish the methodology and solution technique for dispatching an IPFC operating at rated capacity. Our approach is based on a Newton-Raphson loadflow using an injected voltage source model (VSM) for VSC-based FACTS Controllers [8]-[14]. The VSM is a direct way to represent series FACTS Controllers, without requiring the transformation of series VSCs into power or current injections [15][17]. For example, [14] illustrates the direct computation of FACTS control variable sensitivities using VSM. In this paper, we show that using the VSM, not only the IPFC X. Wei and J. H. Chow are with the Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. B. Fardanesh is with Manhattan College, Riverdale, NY 10471 and New York Power Authority, White Plains, NY 10601. A.-A. Edris is with Electric Power Research Institute, Palo Alto, CA 94303-0813.

An IPFC consists of two series VSCs whose DC capacitors are coupled, allowing active power to circulate between the VSCs. Figure 1 shows the circuit representations of an IPFC 1 , in which the injected series voltage sources model the VSCs, and Xt denotes the equivalent series transformer reactances. Thus the voltage variables of an N -bus power system with an IPFC can be ordered as [Ve1 Ve2 · · · VeN Vem1 Vem2 ]T

(1)

where Vei = Vi ²jθi is the complex bus voltage for the ith bus and Vemj = Vmj ²jαj is the complex injection voltage due to the jth VSC. ~ V3

Z1

~ V1

VSC 1 jXt1

+

Ise1

~ V7

Z3

~ V5

~ Vm1

_

~ V2

Z2

~ V4

Pse1 Pse2 ~ ~ V6 Vm2 _ +

VSC 2 jXt2

Z4

~ V8

Ise2 Fig. 1. Model of an IPFC

By coupling the DC capacitors of the VSCs, an IPFC can operate with the flexibility of circulating active power between the two VSCs. For the IPFC model in Figure 1, the active and reactive powers injected into Line 1-2 by VSC 1 are given by, respectively, Pse1 = Vm1 (V2 sin(θ2 − α1 ) − V1 sin(θ1 − α1 ))/Xt1 (2a) 1 In Figure 1, the IPFC model has two different from-buses (Buses 1 and 5) and two different to-buses (Buses 2 and 6). In most cases, either the from-buses or the to-buses are the same bus.

2

Qse1 = (V1 (Vm1 cos(θ1 − α1 ) − V1 ) −V2 (Vm1 cos(θ2 − α1 ) + V2 ) +2V1 V2 cos(θ1 − θ2 ))/Xt1

(2b)

Similarly, the active and reactive powers injected into Line 5-6 by VSC 2 are given by Pse2 = Vm2 (V6 sin(θ6 − α2 ) − V5 sin(θ5 − α2 ))/Xt2 (3a) Qse2 = (V5 (Vm2 cos(θ5 − α2 ) − V5 ) −V6 (V6 + Vm2 cos(θ6 − α2 )) +2V5 V6 cos(θ5 − θ6 ))/Xt2 (3b) When operating below its rated capacity, the IPFC is in regulation mode, allowing the regulation of the P and Q flows on one line, and the P flow on the other line. In addition, the net active power generation by the two coupled VSCs is zero, neglecting power losses. As a result, the loadflow equations are V2 (Vm1 sin(θ2 − α1 ) − V1 sin(θ2 − θ1 )) Xt1 V2 (V1 cos(θ2 − θ1 ) − Vm1 cos(θ2 − α1 ) − V2 ) Xt1 V6 (Vm2 sin(θ6 − α2 ) − V5 sin(θ6 − θ5 )) Xt2 Pse1 + Pse2

= Pd1 (4a) = Qd1 (4b) = Pd2 (4c) =0

(4d)

where Pd1 and Qd1 are the desired line active and reactive power flowing into Bus 2, respectively, and Pd2 is the desired line active power flowing into Bus 6. Pse1 and Pse2 can be calculated from (2a) and (3a), respectively. We can designate VSC 1 with setpoints Pd1 and Qd1 as the primary VSC, whereas VSC 2, with only setpoint Pd2 , as the secondary VSC. Although by specifying the desired Q flow, the primary VSC can control the voltage at its tobus, the to-bus voltage of the secondary VSC still needs to be coordinated. When any VSC reaches one of its operating limit, the IPFC will operate in rated capacity mode, where the regulation of all the quantities in (4) is no longer possible. III. Newton-Raphson Algorithm

where ∆v` is solved from J(v` )∆v` = ∆S

(8)

with ∆S being the mismatch vector and the Jacobian matrix given by  ∂f  ∂f ∂f ∂f P

 J =

P

∂V ∂fQ ∂V ∂fVSC ∂V

∂θ ∂fQ ∂θ ∂fVSC ∂θ

P

∂Vm ∂fQ ∂Vm ∂fVSC ∂Vm

P

∂α ∂fQ ∂α ∂fVSC ∂α

 

(9)

Thus the NR algorithm formulation (7) to (9) can be readily built into an existing conventional NR algorithm. For large data sets, sparse factorization techniques can be used to achieve an efficient solution. Because the NR algorithm updates all the variables in v simultaneously, it achieves quadratic convergence when the iteration is close to the solution point. IV. IPFC Operating Limits There are a number of limits that need to be imposed on the VSCs [1], [2], [18] for proper operation. For the series VSCs of an IPFC, the operating limits are listed as follows, where the subscripts max and min denote maximum and minimum, respectively, and i=1, 2. 1. Inserted series VSC voltage magnitude: Vmi ≤ Vmimax

(10)

2. Line current magnitude through the series VSC: |Isei | ≤ Iseimax

(11)

3. Series VSC MVA rating:

In an N -bus power network with Ng generators and an IPFC, the loadflow equations can be formulated as N − 1 equations fP for the active power bus injections P , N − Ng equations fQ of reactive power bus injections Q, and 4 VSC equations fVSC of setpoints and power circulation (4) fP (v) = P fQ (v) = Q fVSC (v) = R

is a 2(N + 2) − Ng − 1 vector variable of bus voltage magnitudes and angles, with Ng generator bus voltage magnitudes and the angle of the swing bus removed, and injected VSC voltage magnitudes and angles. To apply the NR algorithm, starting from the solution v` at the `th iteration, the updated solution is, with a step size of β v`+1 = v` + β∆v` (7)

(5a) (5b) (5c)

where R is a 4 × 1 vector of the right-hand side of (4) and ¤T £ v = V T θT VmT αT £ = V1 · · · V N θ 1 · · · θ N ¤T Vm1 Vm2 α1 α2 (6)

|Ssei | ≤ Sseimax

(12)

where Ssei is the complex power injected into the line by the series VSC i. 4. Maximum and minimum line-side voltage Vmin ≤ |Vtoi | ≤ Vmax

(13)

where Vtoi is the to-bus voltage of VSC i. 5. The active power circulation Psei |Psei | ≤ Pcmax

(14)

These limits are included in the NR loadflow program, but are enforced only when it is determined that the IPFC is operating at one or more of the limits. When any one

A DISPATCH STRATEGY FOR AN INTERLINE POWER FLOW CONTROLLER

of the limits is reached, some setpoints for the IPFC cannot be regulated. For example, if the MVA rating of one series VSC is reached, it can no longer keep the active or reactive power flow at the desired setpoint. Thus some of the desired setpoint equations need to be disabled and replaced by appropriate limit constraint equations. Hence, a different dispatch strategy needs to be developed. V. Dispatch Strategy for IPFC Operating at Rated Capacity For an IPFC operated in the regulation mode, the default setpoints are the primary line active and reactive power flows Pd1 and Qd1 , respectively, and the secondary line reactive power flow Qd2 , as determined by (4). Power system planners and operators can usually provide proper values of the active power setpoints Pd1 and Pd2 . The specification of the desired line reactive power flow Qd1 , however, is not obvious, because Qd1 affects the to-bus voltage of the primary VSC, and, through the active power circulation between the two VSCs, affects the to-bus voltage of the secondary VSC. Furthermore, the circulating power Pc comes as a by-product of the Qd1 specification and is not specified directly. When an IPFC reaches any of its limits, it is operated at rated capacity mode, where one or more of the setpoints Pd1 , Qd1 , and Pd2 can no longer be enforced. We propose to specify the circulation power Pc when capacity saturation takes place. Using the maximum current magnitude, injected voltage magnitude, and MVA rating as examples, the new setpoints and constraints used in the dispatch strategy is summarized in Table I. Note that in Table I we omit the situation when only VSC 2 saturates, where the strategy is the similar to that of only VSC 1 saturated. TABLE I Setpoints for Regulation Mode and Rated Capacity Mode for an IPFC

Regulation Only VSC 1 Both VSCs Mode Saturates Saturate VSC Pd1 Sse1 /Ise1 /Vm1,max Sse1 /Ise1 /Vm1,max 1 Qd1 −Pc −Pc VSC Pd2 Pd2 Sse2 /Ise2 /Vm2,max 2 Pse1 +Pse2 =0 Pc Pc Suppose the MVA rating of VSC 1 is reached. Then one of the equations (4a) and (4b) cannot be enforced. We replace (4a) by the limit equation q 2 + Q2 Pse1 (15) se1 = Sse1max where Pse1 and Qse1 are the active and reactive powers injected into the line by VSC 1, given by equation (2). We also replace (4b,d) by specifying the desired circulating power Pc : Pse1 = −Pc Pse2 = Pc ,

(16a) (16b)

3

where Pse2 is the active power injected into the line by the secondary VSC, given by (3a). At the same time, the regulation (4c) for VSC 2 is still maintained. Similarly, if VSC 2 reaches its MVA rating, then (4c) is replaced by the limit equation q 2 + Q2 Pse2 (17) se2 = Sse2max where Qse2 is the reactive power injected into the line by VSC 2, given by equation (3b). In addition, (4b,d) are replaced by the circulating power equation (16a,b), and the regulation (4a) for VSC 1 is still maintained. If both series VSCs reach their MVA ratings, then (4a) and (4c) are replaced by (15) and (17), and (4b,d) are replaced by (16a,b). Similarly, when the IPFC reaches other operating limits, we enforce the active limit equations as in (15) and (17), and specify power circulation (16). For the VSC injected voltage magnitude limits, the limit equations are simply to enforce Vm1 and Vm2 at Vm1max and Vm2max , respectively. For the current magnitude limits, the limit equations are |V1 ²jθ1 − Vm1 ²jα1 − V2 ²jθ2 | = Ise1max Xt1 |V5 ²jθ5 − Vm2 ²jα2 − V6 ²jθ6 | = Ise2max Xt2

(18a) (18b)

To implement this strategy in the NR loadflow algorithm, the operating limits of the IPFC need to be monitored at the end of each iteration. Once it is determined that either one of the VSCs or both VSCs will be operated at rated capacities, the proper limit equations and the power circulation setpoint (16) will be utilized as the VSC equations fVSC (5c), and the corresponding modification in the Jacobian matrix (9) with respect to fVSC will be carried out. This proposed strategy is particularly suitable for computing the maximum power transfer limited by voltage stability where we expect that one or both VSCs of the IPFC will operate at their rated capacities. By specifying the power circulation Pc , we can systematically evaluate the amount of coupling or co-optimization required for achieving the optimal results. If Pc = 0, then the two VSCs are operated separately as two SSSCs. Intuitively, we expect that by increasing the coupling, that is, increasing or decreasing Pc from zero, we would improve the power transfer, until the power circulation provides no further benefit or the loadflow ceases to have a solution. VI. Applications In this section we illustrate the proposed IPFC dispatch strategy for maximizing voltage-stability limited power transfer in a 6-bus test system and a 21-bus test system. Perhaps the most common approach in voltage stability analysis is to increase the system loading Pload and observe the resulting voltage variation V on the critical buses. The analysis is frequently presented in the form of P V curves, which are now being used in many power control centers.

4

1.1

No power circulation 1.05

Power circulates from VSC 1 to VSC 2

1

V6 (pu)

To generate consistent P V curves, we modify the IPFC control strategy slightly by enforcing the desired circulating power Pc at all operating conditions, regardless of whether the VSCs are at their rated capacities or not. That is, if both VSCs are below their rated capacities, then besides requesting a specific power circulation level (16), the series VSCs will regulate line active power flows Pd1 and Pd2 . The reactive power flow Qd1 is no longer enforced.

0.95

VI.1 6-Bus Test System 2

0.9

3

1 A

0.85

4

generator load 1

VSC 1 VSC 2

6

5

Power circulates from VSC 2 to VSC 1

0.8 700

No IPFC Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1) 750

800

850

No Compensation

900 950 Pload (MW)

1000

1050

1100

1150

Fig. 4. Bus 6 Voltage V6 of the 6-Bus System with 100 MVA Rating on the IPFC

B load 2 Fig. 2. The 6-Bus Test System

The 6-bus test system, shown in Figure 2, has one equivalent generator and two equal amount of loads at Bus 3 and Bus 6. There are two transmission paths, each consisting of two parallel lines, with Line 2-3 and 4-3 weaker than Line 2-6 and 5-6. An IPFC is sited at Bus 2, with each VSC on one of the parallel lines on the two transmission pathes. Note that by closing Switch A and B, the IPFC is bypassed, which is referred to as the uncompensated system. The IPFC is in service if Switch A and B are opened. The system parameters are included in the appendix. 1.1

No power circulation 1.05

Power circulates from VSC 2 to VSC 1

V3 (pu)

1

0.95

Power circulates from VSC 1 to VSC 2

0.9

0.85

0.8 700

No IPFC Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1) 750

800

850

No Compensation

900 950 Pload (MW)

1000

1050

1100

1150

Fig. 3. Bus 3 Voltage V3 of the 6-Bus System with 100 MVA Rating on the IPFC

By increasing the loads Pload1 at Bus 3, Pload2 at Bus 6, and the necessary amount of generation at Bus 1, we can investigate the variation of voltage V3 at Bus 3 and V6 at Bus 6, with and without the IPFC. For the compensated system, power circulations of Pc = −20, −10, 0, 10, 20 MW are investigated. Note that a positive Pc denotes that power is circulating from VSC 2 on Line 2-5 to VSC 1 on Line 2-4. With no saturation, the active power flow setpoints are enforced at Pd1 = 0.8Pload1 , and Pd2 = 0.8Pload2 . Whenever a VSC limit is reached, the power flow setpoint is no longer enforced, but replaced by the limit equation. Consider both series VSCs having a rating of 100 MVA. By increasing Pload1 and Pload2 simultaneously, the resulting P V curves for Bus 3 and Bus 6 are shown respectively in Figures 3 and 4, which also include the P V curve of the uncompensated system. Note that the curves are drawn against the total load Pload = Pload1 + Pload2 . The marked points on the P V curves indicate values obtained from converged loadflow solutions. Each dispatch with the circulation power Pc enforced at a specified value generates familiar P V curves, as shown in Figures 3 and 4. These curves clearly demonstrate the impact of power circulation versus no power circulation. The curve with Pc = 0 represents the stand-alone operation of two SSSCs. At Pload = 1000 MW, by increasing Pc from 0 to 10 MW (from VSC 2 to VSC 1), V3 is raised 0.01 pu, and V6 , however, is decreased by 0.005 pu. By increasing power circulation from VSC 2 to VSC 1, reactive power is taken from Line 2-5 and injected into Line 2-4, allowing higher voltage of Bus 4 and 3. Conversely, at Pload = 1000 MW, by circulating Pc from 0 to -10 MW (from VSC 1 to VSC 2), V3 is decreased by 0.01 pu, and V6 is only raised by 0.001 pu. From Figure 4 we can see that the increment on V6 by circulating power from VSC 1 to VSC 2 diminishes quite rapidly as Pload increases. This is because VSC 1 is sited in a weaker transmission path, and is more stressed

A DISPATCH STRATEGY FOR AN INTERLINE POWER FLOW CONTROLLER

and prone to reach MVA rating than VSC 2.

5

specifying a single quantity, namely, the circulation power, readily interpretable P V curves with familiar characteristics can be obtained.

380

1.1

360

No power circulation 340

1.05

Power circulates from VSC 2 to VSC 1 1

300

V3 (pu)

P2−4 (MW)

320

0.95

280

Power circulates from VSC 1 to VSC 2

260

0.9 Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1)

240

220 700

750

800

850

900 P

load

950

1000

1050

1100

0.85

1150

(MW)

0.8 700

No Compensation No IPFC Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1) 750

800

850

Fig. 5. Active Power Flow P2−4 of the 6-Bus System with 100 MVA Rating on the IPFC

900 950 Pload (MW)

1000

1050

1100

1150

Fig. 7. Bus 3 Voltage V3 of the 6-Bus System with 4.5 pu Current Limit on the IPFC 400

1.1 300

No power circulation 1.05

Power circulates from VSC 2 to VSC 1 1

100

V6 (pu)

Q2−4 (MVar)

200

0.95

Power circulates from VSC 1 to VSC 2

0

0.9 −100

−200 700

Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1) 750

800

850

900

950

1000

1050

1100

No Compensation 0.85

1150

Pload (MW)

Fig. 6. Reactive Power Flow Q2−4 of the 6-Bus System with 100 MVA Rating on the IPFC

In the Pload range shown in Figures 3 and 4, VSC 2 does not saturate except for the last 3 solution points when Pc = 20 MW, whereas VSC 1 saturates more readily. The saturation of VSC 1 can be observed in the actual P flow on Line 2-4, as shown in Figure 5. The active power flow P2−4 is maintained at the setpoint 0.8Pload1 until VSC 1 reaches the MVA limit. For Pc = −20 MW, VSC 1 is saturated throughout the Pload range (>700 MW), and as a result, P2−4 is always below the setpoint. The reactive power flow Q2−4 is shown in Figure 6. From Figures 5 and 6 we can see that by enforcing the MVA rating limit, the resulting P and Q flow curves are nonlinear. In fact, it is not obvious how to specify directly the P or Q flow setpoint under the saturation condition. However, by just

0.8 700

No IPFC Pc = −20 MW (VSC 1 to 2) Pc = −10 MW (VSC 1 to 2) Pc = 0 MW Pc = 10 MW (VSC 2 to 1) Pc = 20 MW (VSC 2 to 1) 750

800

850

900 950 Pload (MW)

1000

1050

1100

1150

Fig. 8. Bus 6 Voltage V6 of the 6-Bus System with 4.5 pu Current Limit on the IPFC

Similar study can be conducted for other operating limits. Suppose both series VSCs have a maximum line current magnitude of 4.5 pu. By increasing Pload1 and Pload2 simultaneously, the resulting P V curves for Bus 3 and Bus 6 are respectively shown in Figures 7 and 8. Similar to the study on the MVA rating, by circulating the power from VSC 2 to VSC 1, V3 is increased and V6 is decreased. Circulating power from VSC 1 to VSC 2 results in reversing the variations on V3 and V6 . In the Pload range shown in Figures 7 and 8, both VSCs saturate at the current limit for about the same Pload range (> 930 MW), because the currents on the two transmission paths are of similar level, although one path is weaker than the other.

6

VI.2 The 21-Bus Test System

1.04

No power circulation

1.02 1

Power circulates from VSC 1 to VSC 2

0.98 0.96 0.94 0.92

No Compensation

0.9

2

5

4

1

6

0.86 4000

VSC 2 12

No IPFC Pc = −20 MW (VSC 1 to 2) Pc = 0 MW Pc = 20 MW (VSC 2 to 1) Pc = 40 MW (VSC 2 to 1) Pc = 60 MW (VSC 2 to 1) Pc = 80 MW (VSC 2 to 1)

0.88 11

3

Power circulates from VSC 2 to VSC 1

Nominal Point

V20 (pu)

The sets of P V curves in Figures 3, 4, and 7, 8 are useful in dispatching the IPFC. Voltages at different load centers can be adjusted by circulating power between the VSCs. In the meantime, the voltage stability margin can be monitored to determine whether load reduction action is required. Note that for simplicity we only demonstrate the strategy one operating limit at a time. The strategy, however, can observe multiple limits simultaneously, as illustrated by Table I.

VSC 1

4050

4100

4150

4200 Pload (MW)

4250

4300

4350

4400

13

Fig. 10. Bus 20 Voltage V20 of the 21-Bus System with 100 MVA Rating on the IPFC 10 8

14

7

1.04 15

9

1 20

19

16

18

No power circulation

1.02

0.98 17

21

Power circulates from VSC 2 to VSC 1

Nominal Point Power circulates from VSC 1 to VSC 2

V17 (pu)

0.96 0.94

Load 1

No Compensation

Load 2

0.92

Fig. 9. 21-Bus Test System 0.9

The 21-bus test system in Figure 9 has 5 equivalent generators, 3 equivalent loads, and 2 STATCOMs on Buses 7 and 14. The arrows indicate the active power flow paths. As shown in Figure 9, the loads are concentrated in the southeast part of the system, while the generations are mainly in the northwest area. An IPFC is inserted on two major paths between the generations and the loads. Both VSCs having a rating of 100 MVA. By increasing the loads Pload1 on Bus 20 and Pload2 on Bus 17, we investigate the variations of the voltages V20 and V17 , with or without the IPFC, as shown in Figures 10 and 11. We designate the VSC on Line 4-12 as VSC 1, and the VSC on line 4-11 as VSC 2. For the IPFC dispatches, power circulations of Pc = −20, 0, 20, 40, 60, and 80 MW are investigated. Note that a positive Pc denotes that power is circulating from VSC 2 to VSC 1. With no saturation, the P flow setpoints on VSC 1 and VSC 2 are determined such that the amount of increases in Pd1 and Pd2 are the same amount of increase in Pload1 and Pload2 , respectively, based on a nominal point indicated on the P V curve without the IPFC compensation. Both STATCOMs are in service, but with Q generations fixed at nominal case. Note that the curves are drawn against the sum Pload = Pload1 + Pload2 . As shown in Figures 10 and 11, by circulating power from VSC 2 to VSC 1, V20 and V17 are both increased. For

0.88 0.86 4000

No IPFC Pc = −20 MW (VSC 1 to 2) Pc = 0 MW Pc = 20 MW (VSC 2 to 1) Pc = 40 MW (VSC 2 to 1) Pc = 60 MW (VSC 2 to 1) Pc = 80 MW (VSC 2 to 1) 4050

4100

4150

4200 Pload (MW)

4250

4300

4350

4400

Fig. 11. Bus 17 Voltage V17 of the 21-Bus System with 100 MVA Rating on the IPFC

Pload = 4250 MW, by increasing Pc from 0 to 20 MW (VSC 2 to VSC 1), V20 and V17 are increased by 0.01 pu and 0.006 pu, respectively. This indicates the importance of reactive power support on Line 4-12 to the overall system voltage profile. For Pload in the range of 4290 to 4360 MW, VSC 1 on Line 4-12 of the IPFC begins to saturate, depending on the specific value of Pc . For all the P V curves up to Pc = 40 MW, VSC 2 on Line 4-11 does not reach the 100 MVA limit. The P V curves in Figures 10 and 11 can be used to dispatch the IPFC. For example, if one considers operating V20 at 0.98 pu as acceptable, then when Pload is below 4180 MW, use Pc = 0 MW to keep V20 above 0.98 pu. For Pload beyond 4180 MW, increase Pc until it is no longer possible to maintain V20 at 0.98 pu. In the meantime, the other load bus voltage V17 is maintained at about 0.985 pu. Increas-

A DISPATCH STRATEGY FOR AN INTERLINE POWER FLOW CONTROLLER

ing Pc , however, will demand more Var resources coming from Line 4-11, which are limited in this system. Thus for Pc higher than 60 MW, both voltages V20 and V17 will drop rapidly. These P V curves provide the necessary information for operators and planners to make their decisions. VII. Conclusions A new dispatch strategy for an IPFC operating at rated capacity is proposed in this paper. When an IPFC operates at its rated capacity, it can no longer regulate line active power flow setpoints or the reactive power flow setpoint or both. In such cases, the dispatch strategy switches to a power circulation setpoint control to co-optimize both series VSCs without exceeding one or both rated capacities. The concept can be used to generate P V curves associated with the voltage stability analysis for maximizing power transfer. The modeling and computation are performed using a Newton-Raphson loadflow algorithm. The technique is applied to two test systems to illustrate the effectiveness of this proposed strategy. VIII. Appendix 6-Bus Test System Parameters All network parameters in Table II are given on a base of 100 MVA. TABLE II Transmission Line Data

Line 1-2 2-3 4-3 2-6 5-6

Resistance (pu) 0.00163 0 0 0 0

Reactance (pu) 0.03877 0.09754 0.09554 0.05954 0.05754

Charging (pu) 0.78800 0.39400 0.39400 0.39400 0.39400

The IPFC series VSC transformer leakage reactances are Xt1 = Xt2 = 0.002 pu. Acknowledgements This research is supported in part by NSF under grant ECS-0300025, and in part by EPRI and NYPA. We are grateful to Shalom Zelingher and Ben Shperling of NYPA for their support, Graham Rogers of Cherry Tree Scientific Software for providing the Power System Toolbox, and Bob Waldele and Ken Layman of NYISO for their operation insights.

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[3] C. Schauder, M. Gernhardt, E. Stacey, T. Lemak, L. Gyugyi, T. W. Cease, and A. Edris, “TVA STATCOM Project: Design, Installation, and Commissioning,” CIGRE Meeting, Paris, August, 1996, Paper 14-106. [4] K. K. Sen, “SSSC-static synchronous series compensator: theory, modeling, and application,” IEEE Transactions on Power Delivery, vol. 13, pp. 241-246, 1998. [5] L. Gyugyi, C. D. Schauder, S. L. Williams, T. R. Rietman, D. R. Torgerson, and A. Edris, “The Unified Power Flow Controller: A New Approach to Power Transmission Control,” IEEE Transactions on Power Delivery, vol. 10, pp. 1085-1093, 1995. [6] S. Zelingher, B. Fardanesh, B. Shperling, S. Dave, L. Kovalsky, C. Schauder, and A. Edris, “Convertible Static Compensator Project – Hardware Overview,” Proc. IEEE Winter Meeting, pp. 2511-2517, 2000. [7] B. Fardanesh, B. Shperling, E. Uzunovic, and S. Zelingher, “Multi-Converter FACTS Devices: the Generalized Unified Power Flow Controller (GUPFC),” Proc. Winter Power Meeting, vol. 4, pp. 2511-2517, 2000. [8] C. R. Fuerte-Esquivel and E. Acha, “A Newton-type Algorithm for the Control of Power Flow in Electrical Power Networks,” IEEE Transactions on Power Systems, vol. 12, pp. 1474-1480, 1997. [9] C.R. Fuerte-Esquivel and E. Acha, “Unified Power Flow Controller: a Critical Comparision of Newton-Raphson UPFC Algorithms in Power Flow studies,” IEE Proceedings-Generation, Transmission and Distribution, Vol. 144, No. 5, pp. 437-444, September 1997. [10] C. R. Fuerte-Esquivel, E. Acha, and H. Ambriz-Perez, “A Comprehensive Newton-Raphson UPFC Model for the Quadratic Power Flow Solution of Practical Power Networks,” IEEE Transactions on Power Systems, vol. 15, pp. 102-109, 2000. [11] J. Arrillaga and N.R. Watson, Computer Modelling of Electrical Power Systems, 2nd Ed., John Wiley & Sons, 2001. [12] A. Abur, B. Gou and E. Acha, “State Estimation of Networks Containing Power Flow Control Devices,” 13th PSCC in Trondheim, pp. 427-433, Norway, June 28 - July 2nd, 1999. [13] X-P. Zhang, “Modelling of the Interline Power Flow Controller and the Generalized Unified Power Flow Controller in Newton Power Flow,” IEE Proceedings-Generation, Transmission and Distribution, Vol. 150, No. 3, May 2003. [14] X. Wei, J. H. Chow, B. Fardanesh, and A.-A. Edris, “A Common Modeling Framework of Voltage-Sourced Converters for Loadflow, Sensitivity, and Dispatch Analysis,” the 2003 IEEE General Power Meeting, Toronto, Canada. [15] D. N. Kosterev, “Modeling Synchronous Voltage Source Converters in Transmission System Planning Studies,” IEEE Transactions on Power Delivery, vol. 12, pp. 947-952, 1997. [16] M. Noroozian, L. Anguist, M. Ghandhari, and G. Anderson, “Improving Power System Dynamics by Series-Connected FACTS Devices,” IEEE Transactions on Power Delivery, vol. 12, pp. 1635-1641, 1997. [17] Y. Xiao, Y. H. Song, and Y. Z. Sun, “Power Flow Control Approach to Power Systems with Embedded FACTS Devices,” IEEE Transactions on Power Systems, vol. 17, pp. 943-950, 2002. [18] X. Wei, J. H. Chow, B. Fardanesh, and A.-A. Edris, “A Dispatch Strategy for a Unified Power Flow Controller to Maximize Voltage-Stability Limited Power Transfer,” accepted by IEEE Transactions on Power Systems. [19] G. J. Rogers and J. H. Chow, “Hands-on Teaching of Power System Dynamics,” IEEE Computer Applications in Power, vol. 8, no. 1, pp. 12-16, 1995.

References

Xuan Wei was born in China in 1978. She received her B.S. degree in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China in 1996. She is currently a PhD student in the Electrical, Computer, and Systems Engineering Department at Rensselaer Polytechnic Institute. Her interests include large-scale systems and power system dynamics and control.

[1] C. D. Schauder, M. R. Lund, D. M. Hamai, T. R. Rietman, D. R. Torgerson, and A. Edris, “Operation of the Unified Power Flow Controller (UPFC) under Practical Constraints,” IEEE Transactions on Power Delivery, vol. 13, pp. 630-637, 1998. [2] J. Bian, D. G. Ramey, R. J. Nelson, and A. Edris, “A Study of Equipment Sizes and Constraints for a Unified Power Flow Controller,” IEEE Transactions on Power Delivery, vol. 12, pp. 1385-1391, 1997.

Joe H. Chow (F) is a Professor of Electrical, Computer, and Systems Engineering at Rensselaer Polytechnic Institute. He received his B.S.E.E. and B.Math degrees from the University of Minnesota, Minneapolis, MN, and his MS and PhD degrees from the University of Illinois, Urbana-Champaign, IL. Before joining RPI, he worked in the power system division of General Electric Company, Schenectady, NY. His research interests include modeling and control of power systems.

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Behruz (Bruce) Fardanesh received his B.S. in Electrical Engineering from Sharif University of Technology in Tehran, Iran in 1979. He also received his M.S. and Doctor of Engineering degree both in Electrical Engineering from the University of Missouri-Rolla and Cleveland State University in 1981 and 1985, respectively. Since 1985 he has been teaching at Manhattan College where he holds the rank of Associate Professor of Electrical Engineering. Currently, he is also working as a Senior Research and Technology Development Engineer at the New York Power Authority. His areas of interest are power systems dynamics, control and operation. He is the author or co-author of 20 Journal and over 30 Conference papers. He has worked in the area of power system optimization and optimal operation, non-linear controls and control of robotic manipulators, development of educational software for animated simulation of electric machines as well as application of FACTS controllers in power systems. Abdel-Aty Edris (SM) holds BS degree with honors from Cairo University, MS degree from Ein-Shams University in Egypt, and Ph.D. degree from Chalmers University of Technology in Sweden. He is a Technical Leader of Transmission & Substation Asset Utilization Target of the Science & Technology Division of EPRI in California. Before joining EPRI, Dr. Edris was with ABB in Sweden and the US working on development of reactive power compensation and high voltage DC transmission systems. Dr. Edris is a member of several IEEE and CIGRE Working Groups.