main advantages and limitations of the interline power flow controller

MAIN ADVANTAGES AND LIMITATIONS OF THE INTERLINE POWER FLOW CONTROLLER: A STEADY-STATE ANALYSIS R.L. Vasquez-Arnez USP, São Paulo, Brazil [email protected] Abstract – The IPFC (Interline Power Flow Controller) main advantages and limitations whilst controlling simultaneously the power flow in multiline systems are in this paper presented. In order to observe such advantages and drawbacks, a mathematical model of a two-converter IPFC based on the d-q orthogonal coordinates was developed. Issues like the bus voltage variation in presence of the IPF, the effect of the transmission angle variation upon the controlled region of the series voltages injected and over the compensated system itself, are also presented.

Keywords: FACTS, IPFC, Power flow control, VSC 1

F.A. Moreira UFBA, Bahia, Brazil [email protected] ances is presented. Reference [12], deals with the implementation and simulation of an IPFC laboratory model based on a four-switch single-phase converter. Both [11] and [12] are chiefly orientated to show the benefits attained by the IPFC. Very few references [8], [13] have explored aspects such as the operative limitations related to this FACTS controller. In this paper, a mathematical model based on the d-q orthogonal coordinates will be initially presented. Such a model will be used to analyse the IPFC steady-state response. Thereafter, the main limitations related to its operation within a power system will be presented.

INTRODUCTION

Recently, particular attention was focused on the FACTS (Flexible AC Transmission Systems) devices, especially on controllers aimed to control the power flow in multiline systems. One of these devices is the IPFC (Interline Power Flow Controller) which unlike the rest of the multiconverter controllers, GUPFC (Generalized Unified Power Flow Controller) and GIPFC (Generalized Interline Power Flow Controller) dispenses the shunt VSC (Voltage Source Converter) in charge of locally supporting and compensating the bus voltage variations. Systems without significant voltage variation for example, would benefit from the use of this device. Furthermore, by properly reconfiguring its arrangement (i.e. using some connection switches between the VSCs and the line) it can be converted into a UPFC (Unified Power Flow Controller) and even adapted to the above mentioned controllers. Previous publications on controllers of this kind discuss topics such as its modelling, load flow control and application to some particular systems [1]-[4]. In [5] a method for an optimal dimensioning, sizing and steadystate performance directed to single and multiconverter VSC-based FACTS controllers, applied to a particular real world reduced system, is presented. In [6] and [7] mathematical models for multiterminal VSC-based HVDC schemes and for the GUPFC addressing optimal power flow methods are presented. Nonlinear solutions applied to models of multiline FACTS controllers are presented in [8]. In [9] the PIM (power injection model) model for computing the power flow in a large power system is extended to the IPFC. In [10], where the IPFC concept has been put forward, a comprehensive study on its operation as well as some application considerations are presented. In [11] a control scheme of a 2converter IPFC based on a 3-level NPC (Neutral Point Clamped) VSC aimed at compensating the line imped-

16th PSCC, Glasgow, Scotland, July 14-18, 2008

2

IPFC OPERATION AND ANALYSIS

Figure 1 shows the scheme of a multiconverter IPFC. Basically, the AC side of each VSC is connected to its respective line through a series transformer. The DC side of the VSCs share a common circuit. For ease of analysis, a two-converter IPFC (Figure 2) whose converters VSC-1 and VSC-2 emulate pure sinusoidal voltage sources (VC1 and VC2) will be considered. The reader will soon notice that such a model can easily be extended to a multiconverter IPFC scheme. The injection of VC1 on System 1 (Figure 2) usually results in an exchange of Pse1 and Qse1 between converter VSC-1 and the line. Also, for the sake of analysis, the VC1,2 voltages will be split into its d-q components. Line 3 Line 2 Line 1 Series VSCs

VSC-1 VSC-2 VSC-3

Figure 1: Generic scheme of an IPFC

The VC1q component has predominant effect on the line real power, while the in-phase component (VC1d) has over the line’s reactive power. The reactive power exchange Qse1 is supplied by the converter itself; however, the presence of the active power component (Pse1) imposes a demand to the DC terminals. Converter VSC-

Page 1

The equivalent sending and receiving-end sources in both AC systems are regarded as stiff. The condition for which the switch CB is closed (i.e. V11=V21) also applies to the analysis presented in this section. System 1

V12

V11

VC1

V13

I 14 Z14

Z11 (Pse1+Pse2) = 0

CB

System 2

VC2

V21

Z21

P1 V 14

V22

I 24 V23

Z24

P2

V24

Figure 2: IPFC scheme used in the analysis

It will also be assumed that both AC systems have identical line parameters. Likewise, it is assumed that each converter injects an ideal sinusoidal waveform with only its fundamental frequency [8], [9], [13]. The steady-state power balance of the n number of converters (same number of compensated lines) can be represented by (1): n

∑P i =1

se _ i

=0

(1)

As in our case n=2, we will have,

Pse1 + Pse 2 = 0

(3)

Pse2 = VC2d I 24d + VC2q I 24q

(4)

From Figure 2, the following system equations can be written: V12 d = V14 d − VC1d − X 14 I14 d (5a)

V12 q = V14 q − VC1q + X 14 I14 q

(5b)

V22 d = V24 d − VC 2 d − X 24 I 24 d V22 q = V24 q − VC 2 q + X 24 I 24 q

(6a)

I 24 d = k 2 (V21q − V24 q + VC 2 q )

I 24 q = k 2 (− V21d + V24 d − VC 2 d )

* (9b) S 2 = (P2 + jQ 2 ) = V 24 I 24 Note that System 1 will have two independently controlled variables (i.e. VC1, θC1). Conversely, System 2 will only have one variable (VC2q) to be independently controlled.

3 RESULTS The results shown in Figures 3 and 4 were obtained using the mathematical model developed in Section 2, in which θC1 was varied from 0° through 360°. The area inside the circle corresponds to the ideal region controlled by VSC-1, which will be limited by the magnitude of VC1 (VC1max). The series reactive compensation in System 2 was set to be null (i.e. VC2q=0), thus, only the VC2d component serves as a parameter through which active power is passed from Converter 2 to 1. The way how VSC-2 compensates to its own line, through its available reactive compensation, will be shown in Section 3(c). 0.2

P1, Q1 (System 1)

330°

θC1 =0°

0

120° -0.2

(6b) (7a) (7b) (8a) (8b)

16th PSCC, Glasgow, Scotland, July 14-18, 2008

210°

75°

240°

60°

255°

-0.4

30° -0.6

Pse1 = VC1d I 14d + VC1q I 14q

I 14 q = k1 (− V11d + V14 d − VC1d )

, k2 = 1 ( X 11 + X 14 ) ( X 21 + X 24 ) Equations (2) through (8) allow the main parameters of the elementary IPFC to be calculated (Figure 2). Unlike the GIPFC case addressed in [13], the unknown variable VC2d will be a function of VC1 (specified). Once computed the unknown variables (i.e. the d-q components of V12, V22, I14, I24 and VC2d), the power flow in the receiving-end of Systems 1 and 2, with or without the effect of the series voltage, can be calculated through (9). * (9a) S 1 = (P1 + jQ1 ) = V14 I 14

(2)

So for each line it can be written,

I 14 d = k1 (V11q − V14 q + VC1q )

where k1 = 1

Q (pu)

2 is in charge of fulfilling this demand through the Pse1 + Pse2 = 0 constraint. Unlike VSC-1 (in the primary system) the operation of VSC-2 (secondary system) has its freedom degrees reduced; thus, its series voltage VC2 can compensate only partially to its own line. This is because converter VSC-2 also has the task of regulating the dc-link voltage. So, the Pse2 component of VSC-2 is predefined. This imposes a restriction to this line in that mainly the quadrature component of VC2 can be specified to control its power flow. Under this condition, the primary system will have priority over the secondary system in achieving its set-point requirements.

θ C2=

P2, Q2 (System 2)

300°

0° 150°

-0.8 0.4

0.6

0.8

1

1.2

1.4

1.6

P (pu)

Figure 3: P-Q plane (receiving-end) showing the operative region of Systems 1 & 2 when VC1=0.2 pu & VC2d=ƒ(VC1)

For this particular case, both AC systems were assumed to have similar transmission angles, i.e. δ11_14 = δ21_24 = -30°. Should these angles be different, maintaining the same VC1 = 0.2 pu, the results obtained will be different. Such a case will also be analysed shortly after. Notice how the power flow in System 2 is forced to vary (P2≅0.8pu → 1.2pu, Q2≅-0.6pu → +0.1pu) on account of helping to control P1 & Q1 in System 1. For example, when VC1=0.2 pu∠60°, with which System 1 increases its active power to about P1≅1.4 pu, System 2 (straight line) will need to reduce its active power to

Page 2

P2≅0.94 pu. As seen in these figures, for the full rotation of the series angle (θC1=0→360°), the reactive power Q2 will experience a broader variation.

The rest of the procedure will be analogous to that developed while dealing with only 2 series VSCs (same number of compensated lines). 0.2

System 1

120°

210°

330°

Q (pu)

0

System 3

-0.2

75°

240°

60°

255°

-0.4

-0.6

30°

0.5

0.6

0.7

150°

System 2 0.8

0.9

1

V22

1.05 1 0.95

V12

0.9 0.85

V23 0.8 0

30

60

90

120

150

180

210

240

270

300

330

360

θ c1

Figure 5: Bus voltage variation due to the insertion of VC1

The dashed straight line represents the steady-state behaviour of these voltages when VC1=0 and VC2q=0, that is, as both line parameters are identical, then, V12=V13=V22=V23=0.9879 (pu). One way to avoid trespassing these limits would be reducing the magnitude of VC1. A voltage equal to VC1=0.1∠(0→360°) pu, for example, would keep these bus voltages within the operative limits. The active power in the primary system though will have diminished its control range to ±0.2 pu instead of ±0.4 pu (see Figure 3), around the uncompensated condition (P1=P2=1.00 pu). Back to the condition VC1=0.2∠(0→360°) pu, if we are to limit the bus voltages shown in Figure 5 to, say 0.9pu