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Use of an Interline Power Flow Controller Model for Power Flow Analysis
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Energy Procedia
Energy Procedia (2011)14 000–000 Energy 00 Procedia (2012) 2096 – 2101 www.elsevier.com/locate/procedia
2011 2nd International Conference on Advances in Energy Engineering (ICAEE2011)
Use of an Interline Power Flow Controller Model for Power Flow Analysis Natália M. R. Santosab, O. P. Diasa, V. Fernão Piresab a
Escola Sup. Tecnologia Setúbal / Instituto Politécnico Setúbal, 2910-761 Setúbal, Portugal b Center for Innovation in Electrical and Energy Engineering (CIEEE), Lisbon, Portugal
Abstract The controlled power flow in electric power systems is one of the essential factors affecting the overall development of modern power systems. The Interline Power Flow Controller (IPFC), with its exclusive capability of series compensation, is a powerful device which can provide the power flow control of multiple transmission lines. In this paper, a new IPFC steady-state model is presented. The main characteristics of the model are that it is easily incorporated in power flow software. It provides automatic IPFC parameter adjustment and accounts for IPFC operating limits. Information of its concept and implementation is reported. A case-study is presented with the aim of showing the performance of the proposed IPFC model.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] of 2nd International Conference on Advances in Energy Engineering (ICAEE). Keywords: flexible AC transmission systems (FACTS); interline power flow controller (IPFC); load flow control; power system modeling;
1. Introduction As a consequence of recent environmental legislation, rights-of-way issues, construction cost and deregulation policies, there is an increasing recognition of the necessity to use existing transmission system by improving the power flow distribution. Consequently, a main approach to resolve this situation is imposing a review in the conventional power system concepts and practices to achieve better operating flexibility. In this context, very fast reactive compensators, electronically controlled, and power flow controllers have been developed within the overall framework of the Flexible AC Transmission Systems (FACTS) initiative [1]. Among the last generation FACTS controllers using the self-commutated voltage sourced converter (VSC) [2], the unified power flow controller (UPFC) and the interline power flow controller (IPFC) are the most versatile and powerful devices, improving the transfer capability of existing transmission lines.
1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE). doi:10.1016/j.egypro.2011.12.1213
2
2097
Nat\’e1liaAuthor M. R. Santos al.\ / Energy Procedia 14 000–000 (2012) 2096 – 2101 name / et Energy Procedia 00 (2011)
The UPFC combines the functions of the shunt and series compensation being capable to control the active and reactive power flows in the transmission line [3]. This is an important achievement that can be used in power flow control, load sharing among parallel corridors, voltage regulation, enhancement of transient stability and mitigation of system oscillations. The IPFC with two or more series connected converters working together is conceived for the compensation of multi line transmission system. In this way, the power optimization of the overall system can be realized in the form of appropriate power transfer from overload to under loaded lines. To study the incorporation of the IPFC into the existing AC system, various studies have been proposed on the modelling of the IPFC for power flow control, to explore the behaviour of IPFC in steady state analysis [4-6]. Base on the review above, this paper presents a new IPFC model with the aim of overcoming the problem of incorporating advanced power electronics regulating devices in classical power flow studies. The main characteristics of the proposed steady-state IPFC model are: the easy incorporation in existing load flow software, the inclusion of IPFC operating limits and automatic IPFC parameter calculation, which means that this model takes as input the desired (reference) active and reactive power flowing through the IPFC, and produces as output the correspondent IPFC parameters, which allow the desired power flow to be attained. Such IPFC model is implemented in an existing software package and discussed through numerical examples. 2. IPFC Steady-State Representation The IPFC is a device with the capability of controlling both active and reactive powers between the transmission lines, meaning that voltage phase angle and magnitude are under control. It consists of two or more series connected converters (SSSCs – Static Synchronous Series Compensators) supplied by a common DC voltage link, which enables the IPFC to compensate multiple transmission lines. The basic operation principle of an IPFC can be found in open literature [7]. A simpler schematic representation of the IPFC is shown in Fig. 1(a), which employs two back-to-back dc-to-ac converters. The converters are connected in series with two transmission lines via series coupling transformers and the dc terminals of two inverters are connected through a common DC link. The equivalent circuit of an IPFC used to derive the steady-state model is shown in Fig. 1(b). It is composed by two controllable voltage sources connected in series (VcR) and series coupling transformers impedances (ZcR). Also, an active power constraint equation, linking the two series voltage sources, is required. The controllable series injected voltage sources are defined as: VcR1=VcR1e jθcR1
and
VcR 2=VcR 2e jθ cR 2
(1)
which should be completed by the inequality constraints imposed by the acceptable limits of the angle and magnitude of series injected voltage, respectively: VcR1min ≤ VcR1 ≤ VcR1max
and
0 ≤ θ cR1 ≤ 2π
(2)
VcR 2 min ≤ VcR 2 ≤ VcR 2 max
and
0 ≤ θcR 2 ≤ 2π
(3)
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Nat\’e1lia M. R. Santos et al.\ / Energy Procedia 14 (2012) 2096 – 2101 Author name / Energy Procedia 00 (2011) 000–000
Bus i
ZcR1
+ VcR1 -
ZL1
3
Bus j
Ij
Ii Vj Re{VcR1Ij*+VcR2 Ik *}=0
Vi
ZcR2
+ VcR2 -
ZL2
Bus k
Ik
Vk
Fig. 1. (a) IPFC schematic diagram; (b) IPFC equivalent circuit
The operating constraint of the IPFC, which is related to active power exchange between the two series connected converters via the DC link, is:
{
}
(4)
Re VcR1 I *j + VcR 2 I k* = 0
3. IPFC Steady-State Model Development In this section, a new steady-state model for the IPFC is presented. The general idea is to gather the former equations in a coordinated approach with a dual objective: to allow its inclusion in Newton’s algorithm, in the easiest and most accurate way possible, and to satisfy the specified control requirements. Bearing this idea in mind, the IPFC device is modeled with the help of four fictitious buses as shown in Fig. 2. Vi
I1
jXcR1
a
+ VcR1 -
b
ZL1
I2 i
jXcR2
c
Pa Pb d Qa Qb + VcR2 -
Pc Qc
Pd Qd
Vj
j ZL2
Vk
k
Fig. 2. Equivalent circuit of the new steady-state IPFC model
The starting point of the model development is the replacement of controllable series voltage sources (VcR1 and VcR2), by four virtual buses, denoted as a, b and c, d, respectively (Fig. 2). Buses a, b and c, d, are handled as dummy PQ buses located in lines (L1 and L2), where active and reactive powers are to be controlled. It should be mentioned that series impedance, ZcR1 = jXcR1 and ZcR2 = jXcR2, have been considered. Referring to Fig. 2, the complex voltages at nodes i, a and c are Vi = Vi e jθ i , Va =Va e jθ a and Vc =Vc e jθ c , respectively. Moreover, the controllable series voltage sources removed, VcR1 and VcR2, and
4
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Nat\’e1lia M. R. Santos et al.\ / Energy Procedia 14 (2012) 2096 – 2101 Author name / Energy Procedia 00 (2011) 000–000
currents I1 and I2 across the series reactances are given by the following relations: VcR1 = Va - Vb
and
Vi - Va jX cR1
and
I1 =
VcR 2 = Vc - Vd
(5)
Vi - Vc jX cR2
(6)
I2 =
The model is further developed by including one virtual load at each one of buses a, b, c and d. At the receiving PQ type buses b and d, a “negative” load is injected, whose values, Pb, Qb and Pd, Qd are set equal to the desired reference active and reactive power through the IPFC, Pref1, Qref1 and Pref2, Qref2 respectively, i.e. Pb = - Pref 1
and
Qb = -Qref 1
(7 )
Pd = - Pref 2
and
Qd = -Qref 2
(8)
At the virtual PQ type buses a and c a load is placed at each, with active and reactive power, Pa, Qa and Pc, Qc, respectively. The load values settings are given by the sum of the corresponding reference values with the VcR1 and VcR2 voltage source losses, respectively. Thus, Pa, Qa and Pc, Qc are formulated as follows:
{
}
and
Qa = Qref 1 + Im VcR1 I1*
{
}
and
Qc = Qref 2 + Im VcR 2 I1*
Pa = Pref 1 + Re VcR1 I1*
Pc = Pref 2 + Re VcR 2 I 2*
{
}
{
}
(9)
(10)
In fact, buses a and c are fakes PQ type nodes as Pa, Qa and Pc, Qc are not constant, but instead are iteratively updated using the calculated values of the voltage VcR1 and the current I1, and the voltage VcR2 and the current I2. The active power exchanged between series converters is supplied from the AC power system via the common DC link. Assuming lossless converters operation, the active power supplied to the series converter 2, Pcd, must satisfy the active power demanded by series converter 1, Pab, in accordance with: (11) Pab + Pcd = 0 Therefore, the active power flow is calculated within the iterative process by means of the following equation: Re VcR1 I1* + Re VcR 2 I 2* = 0 (12 )
{
} {
}
As in a standard power flow calculation, at each iterative step Va, Vb, Vc and Vd are calculated. However, further calculations are to be performed within each iteration, namely the evaluation of VcR1 and VcR2, which determines the values of Pa, Qa and Pc, Qc. The series connected voltage sources magnitude and angle (VcR1 and θcR1, VcR2 and θcR2) are to be controlled, in order to ensure the active and reactive powers are equal of the desired reference powers, Pref1, Qref1 and Pref2, Qref2. On the other hand, the constraint described by (12) guarantees that the common DC link voltage, Vdc, is kept constant. Therefore, Vdc is a variable that is indirectly controlled through constraint (12), and is not directly used in
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Nat\’e1lia R. Santos et al.\ / Energy 14 (2012) 2096 – 2101 AuthorM. name / Energy Procedia 00 Procedia (2011) 000–000
the formulation. However, compliance with this constraint implies that the following relationships (13) and (14) should be verified. ⎧⎪ Pa = Pref 1 + Pab (13) ⇒ Pab > Pcd If ⎨ ⎪⎩ Pc = Pref 2 − Pab ⎧⎪ Pa = Pref 1 − Pcd (14) ⎨ ⎪⎩ Pc = Pref 2 + Pcd The IPFC limits constraints are verified at each step during the iterative process. If a limit violation occurs in the voltage magnitude of the series converters, the voltage magnitude of each is fixed at the violated limit and the regulated variable is liberated. This means that voltage VcR1 and VcR2 will no longer be calculated by (5), but instead will remain at a fixed value. No limit violation can either occur, as far as the voltage phase angles of both voltage sources are concerned, because they are allowed to vary between the limits 0-2π. It is important to highlight that the unlimited change in these voltage phase angles guarantee that (11) is satisfied. Furthermore, this will allow that the both reference values Pref and Qref can be still achieved. The above presented details of the calculation algorithms show that this model can easily be incorporated in a standard load flow program. If
Pab < Pcd
⇒
4. Case study and results In order to verify the accuracy and capabilities of the new IPFC steady state model, a test network with five nodes was used. This network is composed by two generators and four loads [8], represented in Fig. 3. Bus 3 is the reference bus with a specified voltage of 1.06 pu and a reference angle of 0º; the voltage magnitude at PV bus 4 is specified in 1.0 pu. The model was implemented using MATLABTM language and incorporated in MATPOWER – A MATLABTM Power Systems Simulation Package. The IPFC device is included in the transmission line connecting nodes 1 and 2 (converter 1) and in the transmission line connecting nodes 1 and 4 (converter 2). The objective is to operate the IPFC in order to set active and reactive powers leaving the IPFC series converter 1 towards node 2 and the series converter 2 to node 4, at reference values Pref 1, Qref1, and Pref 2, Qref2 respectively.
Fig. 3. Configuration of the test network
The results obtained for a case study with Pref1=22.4MW, Qref1=2.6Mvar and Pref2=26.5MW, Qref2=2.5Mvar are presented in Table 1 and Table 2 displaying the complex nodal voltages, active and reactive
5
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Nat\’e1lia M. R. Santos / Energy Procedia 14 (2012) 2096 – 2101 Author nameet/ al.\ Energy Procedia 00 (2011) 000–000
6
power flow, with and without IPFC. For same case study, the calculated IPFC parameters are: VcR1=0.18 pu, θcR1=-121.7º and VcR2=0.17 pu, θcR2=-125.0º. Table 1. Complex nodal voltages with and without IPFC
Bus
Without IPFC V (pu)
θ
(º)
With IPFC V (pu)
θ
(º)
Table 2. Active and reactive power flow with and without IPFC
From Bus
To Bus
1
2
Without IPFC P (MW)
With IPFC
Q (MVar)
P (MW)
Q (MVar)
19.39
2.86
22.40
2.60
1
0.99
-4.64
0.91
-12.75
2
0.98
4-96
0.98
-4.60
3
1.06
0.00
1.06
0.00
3
4
89.33
74.00
88.70
74.18
4
1.00
-2.06
1.00
-2.04
3
1
41.79
16.82
102.55
37.61 -2.50
5
0.97
-5.77
0.97
-5.64
4
1
24.47
-2.52
26.50
4
2
27.71
-1.72
25.60
1.87
4
5
54.66
5.56
53.69
7.30
2
5
6.60
0.52
7.54
-1.26
5. Conclusions This paper has presented a model suitable for including IPFC devices in steady state studies. The proposed model can be used with the traditional power flow algorithms, such as the Newton-Raphson algorithm. Furthermore, it is quite easy to incorporate in existing software allowing for automatic IPFC parameters calculation. Numerical outcomes on test network allow for the verification the effectiveness of the proposed model. This model does not compromise the computational speed since does not require high computing resources. Finally, the values of the IPFC operating parameters that are function of the reference active and reactive power flows through the lines in which IPFC is located, was calculated. References [1] Povh D. Use of HVDC and FACTS. Proc. of the IEEE 2000; 88: 235-245. [2] Hingorani NG, Gyugyi L. Understanding FACTS: concepts and technology of flexible AC transmission systems. IEEEPress Marketing 2000: 2-16. [3] Rosa N, Pires VF, Castro R. A New Model to Incorporate Unified Power Flow Controllers in Power Flow Studies. IEEE PES Transmission and Distribution Conference and Exhibition 2006: 05TD0181. [4] Zhang Y, Zhang Yan, Chen C. A Novel Power Injection Model of IPFC for Power Flow Analysis Inclusive of Practical Constraints. IEEE Transactions on Power Systems 2006; 21:1550-1556. [5] Zhang XP. Modeling of the interline power flow controller and the generalized unified power flow controller in Newton power flow. Proc. Inst. Elect. Eng., Gen., Transm., Distrib. 2003;150:268–274. [6] Babu AVN, Padmanabharaju C, Ramana T. Multi-Line Power Flow using Interline Power Flow Controller (IPFC) in Power Transmission Systems. International Journal of Power Energy Systems Engineering 2010:182-186. [7] Gyugyi L, Sen KK, Schauder CD. The interline power flow controller: a new approach to power flow management in transmission systems. IEEE Trans. on Power Delivery 1999; 14: 1115-1123. [8] Acha E, Agelidis VG, Anaya O. Miller TJE. Power Electronic Control in Electrical Systems 2002: 133-148.
Energy Procedia
Energy Procedia (2011)14 000–000 Energy 00 Procedia (2012) 2096 – 2101 www.elsevier.com/locate/procedia
2011 2nd International Conference on Advances in Energy Engineering (ICAEE2011)
Use of an Interline Power Flow Controller Model for Power Flow Analysis Natália M. R. Santosab, O. P. Diasa, V. Fernão Piresab a
Escola Sup. Tecnologia Setúbal / Instituto Politécnico Setúbal, 2910-761 Setúbal, Portugal b Center for Innovation in Electrical and Energy Engineering (CIEEE), Lisbon, Portugal
Abstract The controlled power flow in electric power systems is one of the essential factors affecting the overall development of modern power systems. The Interline Power Flow Controller (IPFC), with its exclusive capability of series compensation, is a powerful device which can provide the power flow control of multiple transmission lines. In this paper, a new IPFC steady-state model is presented. The main characteristics of the model are that it is easily incorporated in power flow software. It provides automatic IPFC parameter adjustment and accounts for IPFC operating limits. Information of its concept and implementation is reported. A case-study is presented with the aim of showing the performance of the proposed IPFC model.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer] of 2nd International Conference on Advances in Energy Engineering (ICAEE). Keywords: flexible AC transmission systems (FACTS); interline power flow controller (IPFC); load flow control; power system modeling;
1. Introduction As a consequence of recent environmental legislation, rights-of-way issues, construction cost and deregulation policies, there is an increasing recognition of the necessity to use existing transmission system by improving the power flow distribution. Consequently, a main approach to resolve this situation is imposing a review in the conventional power system concepts and practices to achieve better operating flexibility. In this context, very fast reactive compensators, electronically controlled, and power flow controllers have been developed within the overall framework of the Flexible AC Transmission Systems (FACTS) initiative [1]. Among the last generation FACTS controllers using the self-commutated voltage sourced converter (VSC) [2], the unified power flow controller (UPFC) and the interline power flow controller (IPFC) are the most versatile and powerful devices, improving the transfer capability of existing transmission lines.
1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE). doi:10.1016/j.egypro.2011.12.1213
2
2097
Nat\’e1liaAuthor M. R. Santos al.\ / Energy Procedia 14 000–000 (2012) 2096 – 2101 name / et Energy Procedia 00 (2011)
The UPFC combines the functions of the shunt and series compensation being capable to control the active and reactive power flows in the transmission line [3]. This is an important achievement that can be used in power flow control, load sharing among parallel corridors, voltage regulation, enhancement of transient stability and mitigation of system oscillations. The IPFC with two or more series connected converters working together is conceived for the compensation of multi line transmission system. In this way, the power optimization of the overall system can be realized in the form of appropriate power transfer from overload to under loaded lines. To study the incorporation of the IPFC into the existing AC system, various studies have been proposed on the modelling of the IPFC for power flow control, to explore the behaviour of IPFC in steady state analysis [4-6]. Base on the review above, this paper presents a new IPFC model with the aim of overcoming the problem of incorporating advanced power electronics regulating devices in classical power flow studies. The main characteristics of the proposed steady-state IPFC model are: the easy incorporation in existing load flow software, the inclusion of IPFC operating limits and automatic IPFC parameter calculation, which means that this model takes as input the desired (reference) active and reactive power flowing through the IPFC, and produces as output the correspondent IPFC parameters, which allow the desired power flow to be attained. Such IPFC model is implemented in an existing software package and discussed through numerical examples. 2. IPFC Steady-State Representation The IPFC is a device with the capability of controlling both active and reactive powers between the transmission lines, meaning that voltage phase angle and magnitude are under control. It consists of two or more series connected converters (SSSCs – Static Synchronous Series Compensators) supplied by a common DC voltage link, which enables the IPFC to compensate multiple transmission lines. The basic operation principle of an IPFC can be found in open literature [7]. A simpler schematic representation of the IPFC is shown in Fig. 1(a), which employs two back-to-back dc-to-ac converters. The converters are connected in series with two transmission lines via series coupling transformers and the dc terminals of two inverters are connected through a common DC link. The equivalent circuit of an IPFC used to derive the steady-state model is shown in Fig. 1(b). It is composed by two controllable voltage sources connected in series (VcR) and series coupling transformers impedances (ZcR). Also, an active power constraint equation, linking the two series voltage sources, is required. The controllable series injected voltage sources are defined as: VcR1=VcR1e jθcR1
and
VcR 2=VcR 2e jθ cR 2
(1)
which should be completed by the inequality constraints imposed by the acceptable limits of the angle and magnitude of series injected voltage, respectively: VcR1min ≤ VcR1 ≤ VcR1max
and
0 ≤ θ cR1 ≤ 2π
(2)
VcR 2 min ≤ VcR 2 ≤ VcR 2 max
and
0 ≤ θcR 2 ≤ 2π
(3)
2098
Nat\’e1lia M. R. Santos et al.\ / Energy Procedia 14 (2012) 2096 – 2101 Author name / Energy Procedia 00 (2011) 000–000
Bus i
ZcR1
+ VcR1 -
ZL1
3
Bus j
Ij
Ii Vj Re{VcR1Ij*+VcR2 Ik *}=0
Vi
ZcR2
+ VcR2 -
ZL2
Bus k
Ik
Vk
Fig. 1. (a) IPFC schematic diagram; (b) IPFC equivalent circuit
The operating constraint of the IPFC, which is related to active power exchange between the two series connected converters via the DC link, is:
{
}
(4)
Re VcR1 I *j + VcR 2 I k* = 0
3. IPFC Steady-State Model Development In this section, a new steady-state model for the IPFC is presented. The general idea is to gather the former equations in a coordinated approach with a dual objective: to allow its inclusion in Newton’s algorithm, in the easiest and most accurate way possible, and to satisfy the specified control requirements. Bearing this idea in mind, the IPFC device is modeled with the help of four fictitious buses as shown in Fig. 2. Vi
I1
jXcR1
a
+ VcR1 -
b
ZL1
I2 i
jXcR2
c
Pa Pb d Qa Qb + VcR2 -
Pc Qc
Pd Qd
Vj
j ZL2
Vk
k
Fig. 2. Equivalent circuit of the new steady-state IPFC model
The starting point of the model development is the replacement of controllable series voltage sources (VcR1 and VcR2), by four virtual buses, denoted as a, b and c, d, respectively (Fig. 2). Buses a, b and c, d, are handled as dummy PQ buses located in lines (L1 and L2), where active and reactive powers are to be controlled. It should be mentioned that series impedance, ZcR1 = jXcR1 and ZcR2 = jXcR2, have been considered. Referring to Fig. 2, the complex voltages at nodes i, a and c are Vi = Vi e jθ i , Va =Va e jθ a and Vc =Vc e jθ c , respectively. Moreover, the controllable series voltage sources removed, VcR1 and VcR2, and
4
2099
Nat\’e1lia M. R. Santos et al.\ / Energy Procedia 14 (2012) 2096 – 2101 Author name / Energy Procedia 00 (2011) 000–000
currents I1 and I2 across the series reactances are given by the following relations: VcR1 = Va - Vb
and
Vi - Va jX cR1
and
I1 =
VcR 2 = Vc - Vd
(5)
Vi - Vc jX cR2
(6)
I2 =
The model is further developed by including one virtual load at each one of buses a, b, c and d. At the receiving PQ type buses b and d, a “negative” load is injected, whose values, Pb, Qb and Pd, Qd are set equal to the desired reference active and reactive power through the IPFC, Pref1, Qref1 and Pref2, Qref2 respectively, i.e. Pb = - Pref 1
and
Qb = -Qref 1
(7 )
Pd = - Pref 2
and
Qd = -Qref 2
(8)
At the virtual PQ type buses a and c a load is placed at each, with active and reactive power, Pa, Qa and Pc, Qc, respectively. The load values settings are given by the sum of the corresponding reference values with the VcR1 and VcR2 voltage source losses, respectively. Thus, Pa, Qa and Pc, Qc are formulated as follows:
{
}
and
Qa = Qref 1 + Im VcR1 I1*
{
}
and
Qc = Qref 2 + Im VcR 2 I1*
Pa = Pref 1 + Re VcR1 I1*
Pc = Pref 2 + Re VcR 2 I 2*
{
}
{
}
(9)
(10)
In fact, buses a and c are fakes PQ type nodes as Pa, Qa and Pc, Qc are not constant, but instead are iteratively updated using the calculated values of the voltage VcR1 and the current I1, and the voltage VcR2 and the current I2. The active power exchanged between series converters is supplied from the AC power system via the common DC link. Assuming lossless converters operation, the active power supplied to the series converter 2, Pcd, must satisfy the active power demanded by series converter 1, Pab, in accordance with: (11) Pab + Pcd = 0 Therefore, the active power flow is calculated within the iterative process by means of the following equation: Re VcR1 I1* + Re VcR 2 I 2* = 0 (12 )
{
} {
}
As in a standard power flow calculation, at each iterative step Va, Vb, Vc and Vd are calculated. However, further calculations are to be performed within each iteration, namely the evaluation of VcR1 and VcR2, which determines the values of Pa, Qa and Pc, Qc. The series connected voltage sources magnitude and angle (VcR1 and θcR1, VcR2 and θcR2) are to be controlled, in order to ensure the active and reactive powers are equal of the desired reference powers, Pref1, Qref1 and Pref2, Qref2. On the other hand, the constraint described by (12) guarantees that the common DC link voltage, Vdc, is kept constant. Therefore, Vdc is a variable that is indirectly controlled through constraint (12), and is not directly used in
2100
Nat\’e1lia R. Santos et al.\ / Energy 14 (2012) 2096 – 2101 AuthorM. name / Energy Procedia 00 Procedia (2011) 000–000
the formulation. However, compliance with this constraint implies that the following relationships (13) and (14) should be verified. ⎧⎪ Pa = Pref 1 + Pab (13) ⇒ Pab > Pcd If ⎨ ⎪⎩ Pc = Pref 2 − Pab ⎧⎪ Pa = Pref 1 − Pcd (14) ⎨ ⎪⎩ Pc = Pref 2 + Pcd The IPFC limits constraints are verified at each step during the iterative process. If a limit violation occurs in the voltage magnitude of the series converters, the voltage magnitude of each is fixed at the violated limit and the regulated variable is liberated. This means that voltage VcR1 and VcR2 will no longer be calculated by (5), but instead will remain at a fixed value. No limit violation can either occur, as far as the voltage phase angles of both voltage sources are concerned, because they are allowed to vary between the limits 0-2π. It is important to highlight that the unlimited change in these voltage phase angles guarantee that (11) is satisfied. Furthermore, this will allow that the both reference values Pref and Qref can be still achieved. The above presented details of the calculation algorithms show that this model can easily be incorporated in a standard load flow program. If
Pab < Pcd
⇒
4. Case study and results In order to verify the accuracy and capabilities of the new IPFC steady state model, a test network with five nodes was used. This network is composed by two generators and four loads [8], represented in Fig. 3. Bus 3 is the reference bus with a specified voltage of 1.06 pu and a reference angle of 0º; the voltage magnitude at PV bus 4 is specified in 1.0 pu. The model was implemented using MATLABTM language and incorporated in MATPOWER – A MATLABTM Power Systems Simulation Package. The IPFC device is included in the transmission line connecting nodes 1 and 2 (converter 1) and in the transmission line connecting nodes 1 and 4 (converter 2). The objective is to operate the IPFC in order to set active and reactive powers leaving the IPFC series converter 1 towards node 2 and the series converter 2 to node 4, at reference values Pref 1, Qref1, and Pref 2, Qref2 respectively.
Fig. 3. Configuration of the test network
The results obtained for a case study with Pref1=22.4MW, Qref1=2.6Mvar and Pref2=26.5MW, Qref2=2.5Mvar are presented in Table 1 and Table 2 displaying the complex nodal voltages, active and reactive
5
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Nat\’e1lia M. R. Santos / Energy Procedia 14 (2012) 2096 – 2101 Author nameet/ al.\ Energy Procedia 00 (2011) 000–000
6
power flow, with and without IPFC. For same case study, the calculated IPFC parameters are: VcR1=0.18 pu, θcR1=-121.7º and VcR2=0.17 pu, θcR2=-125.0º. Table 1. Complex nodal voltages with and without IPFC
Bus
Without IPFC V (pu)
θ
(º)
With IPFC V (pu)
θ
(º)
Table 2. Active and reactive power flow with and without IPFC
From Bus
To Bus
1
2
Without IPFC P (MW)
With IPFC
Q (MVar)
P (MW)
Q (MVar)
19.39
2.86
22.40
2.60
1
0.99
-4.64
0.91
-12.75
2
0.98
4-96
0.98
-4.60
3
1.06
0.00
1.06
0.00
3
4
89.33
74.00
88.70
74.18
4
1.00
-2.06
1.00
-2.04
3
1
41.79
16.82
102.55
37.61 -2.50
5
0.97
-5.77
0.97
-5.64
4
1
24.47
-2.52
26.50
4
2
27.71
-1.72
25.60
1.87
4
5
54.66
5.56
53.69
7.30
2
5
6.60
0.52
7.54
-1.26
5. Conclusions This paper has presented a model suitable for including IPFC devices in steady state studies. The proposed model can be used with the traditional power flow algorithms, such as the Newton-Raphson algorithm. Furthermore, it is quite easy to incorporate in existing software allowing for automatic IPFC parameters calculation. Numerical outcomes on test network allow for the verification the effectiveness of the proposed model. This model does not compromise the computational speed since does not require high computing resources. Finally, the values of the IPFC operating parameters that are function of the reference active and reactive power flows through the lines in which IPFC is located, was calculated. References [1] Povh D. Use of HVDC and FACTS. Proc. of the IEEE 2000; 88: 235-245. [2] Hingorani NG, Gyugyi L. Understanding FACTS: concepts and technology of flexible AC transmission systems. IEEEPress Marketing 2000: 2-16. [3] Rosa N, Pires VF, Castro R. A New Model to Incorporate Unified Power Flow Controllers in Power Flow Studies. IEEE PES Transmission and Distribution Conference and Exhibition 2006: 05TD0181. [4] Zhang Y, Zhang Yan, Chen C. A Novel Power Injection Model of IPFC for Power Flow Analysis Inclusive of Practical Constraints. IEEE Transactions on Power Systems 2006; 21:1550-1556. [5] Zhang XP. Modeling of the interline power flow controller and the generalized unified power flow controller in Newton power flow. Proc. Inst. Elect. Eng., Gen., Transm., Distrib. 2003;150:268–274. [6] Babu AVN, Padmanabharaju C, Ramana T. Multi-Line Power Flow using Interline Power Flow Controller (IPFC) in Power Transmission Systems. International Journal of Power Energy Systems Engineering 2010:182-186. [7] Gyugyi L, Sen KK, Schauder CD. The interline power flow controller: a new approach to power flow management in transmission systems. IEEE Trans. on Power Delivery 1999; 14: 1115-1123. [8] Acha E, Agelidis VG, Anaya O. Miller TJE. Power Electronic Control in Electrical Systems 2002: 133-148.