Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy
Load Flow Management in the Interconnected Power Systems Using UPFC Devices C. Bulac Member IEEE, M. Eremia Senior Member IEEE, R. Balaurescu, and V. Ştefănescu
Abstract - The deregulation of electricity supply industry has introduced new opportunity for competition to reduce the cost and cut the price. It is a tremendous challenge for utilities to maintain an economical and reliable supply in such an environment. The PFAC program developed by authors to analyze the power flow in power systems with FACTS devices, has been tested on the 220kV-400kV network of the Romanian Power Grid. We have taken into consideration several possible scenarios, leading to two types of congestions: the first type is related to nodal power release, and the second to the supply of a deficit area. Simulations prove the fact that in both cases we can regulate power flow so that to reduce and eliminate congestions if we use the UPFC device. Keywords: Congestions management, UPFC device.
II. UPFC STEADY - STATE MODEL The Unified Power Flow Controller is the most versatile and complex power electronic equipment that has emerged for the control and optimization of power flow and voltage in electric power transmission systems. It consists of two back-to-back, self-commutated, voltage source converters, sharing a shunt capacitor on the DC side [1]. One converter is coupled to the AC system via a shunt transformer and the other is coupled to the AC system via a series transformer (Figure 1). Uk
Ui
Pref+jQref
k
i
Transmission Line
j
I. INTRODUCTION
A
s the energy market is becoming increasingly free, and there are more and more open access power systems, load flow and congestions management is becoming of more importance as well. Under these circumstances, the paper proposes the implementation of UPFC (Unified Power Flow Controller), which is the most efficient FACTS device in this kind of applications. The first part presents the steady-state model of the UPFC device and implementation in the PFAC (Power Flow Analysis and Control) software, developed in Visual C++, using the OOP technology and the NewtonRaphson method. In the second part, this program has been used on the 220kV - 400kV network of the Romanian Power Grid (SEN). Thus, starting from a base case (a steady-state power flow), we have examined 5 other operating modes that could appear in the current operation. Besides, for each new case, we have considered a few incidents that should lead to congestions related to nodal power release and, respectively, power supply for a deficient part of the system. The results obtained by using the UPFC device, which function as real “electronically controlled locks”, prove the fact that we can redistribute power flow in order to eliminate congestions, thus keeping SEN in function in normal parameters and to increasing reliability and flexibility.
C. Bulac is with the Department of Power Engineering POLITEHNICA University of Bucharest, Romania (e-mail:
[email protected]). M. Eremia is with the Department of Power Engineering POLITEHNICA University of Bucharest, Romania (e-mail:
[email protected]). R. Balaurescu and V. Ştefănescu are with the TRANSELECTRICA Company, Romania
0-7803-7967-5/03/$17.00 ©2003 IEEE
C
UPFC Controller Fig. 1. Block diagram of a UPFC device
The series converter is controlled to inject a synchronous voltage in series with the transmission line. In the process of doing this, the series converter will exchange real and reactive power with the line. The series inverter electronically provides the reactive power and the real power is transmitted to the DC terminals. The shunt inverter is operated in such a way as to demand this DC terminal power (positive or negative) from the line, thereby regulating the voltage of the DC bus. The net real power absorbed from the line by the UPFC is thus equal to the losses of the two converters and their transformers. Assuming a free loss converter operation, the UPFC neither absorbs nor injects active power with respect to the AC system. Hence, the active power supplied to the shunt converter PD, must satisfy the active power demanded by the series converter, PS [3][4][6]. The equivalent circuit consists of two ideal voltage sources US and UD representing the fundamental Fourier series component of the switched voltage waveforms at the AC converter terminals (Figure 2). The source impedances included in the model represent the positive sequence leakage inductances and resistances of the coupling UPFC transformers. Although the UPFC has many possible operating modes, we will consider that the shunt converter will be operated in automatic voltage control – AVC mode and the series converter will be in automatic power flow control –
APFC mode [5]. In these modes the shunt converter reactive current is automatically regulated to maintain the transmission line voltage at the point of connection (bus k) to a reference value, while the series injected voltage is determined automatically and continuously by a vector control system to ensure that the desired active and reactive powers are maintained despite system changes. k Ik
ZS
Iki
S
US
i
j
ZL
Ii
• active power supplied by the shunt inverter
(
)
*
PD = Re U D I D =
U DU k [G D cos (θ D − θ k ) + BD sin (θ D − θ k )] − U D2 G D
(5)
• active power supplied by the series inverter
(
*
)
PS = Re U S I S =
U S U k [G S cos (θ S − θ k ) + B S sin (θ S − θ k )] −
(6)
U S U i [G S cos (θ S − θ i ) + B S sin (θ S − θ i )] − U G S 2 S
ID ZD Uk
PD+PS=0
D
UD
Ui
YL 2
III. IMPLEMENTING OF UPFC MODEL IN NEWTON RAPHSON
YL 2
ALGORITHM
Transmission ligne Fig. 2. Steady-state model of UPFC
The general transfer admittance matrix for the UPFC is obtained by applying Kirchhoff current and voltage laws to the electric circuit k- i shown in Figure 2 and is given by: U k I k Y kk Y ki Y kS Y kD U i (1) = I Y 0 U S i ik Y ii Y iS U D where: Y kk = y S + y D , Y ki = Y ik = Y kS = − y S
Y kD = − y D , Y ii = Y iS = y S
For power flow analysis UPFC device is modeled by means of two loads as shown in Figure 3. In this model, a fictitious bus i (the sending end of controller) is introduced to force Pijref + jQijref to flow in the transmission line. This auxiliary nod is handled as a PQ bus, whilst the bus k (the receiving end of controller) is handled according to the control type of device. Thus, if the FACTS controller is an UPFC that operate in AVC mode, the bus k is converted to a PU bus. Otherwise the type of bus is not changed.
Power System j
i
k
Transmission line
(2)
FACTS
y S = G S + jBS = 1 Z S and y D = G D + jB D = 1 Z D Hence, the active and reactive power equations are: •
Pk ,UPFC
at bus k: = GkkU k2 +
Power System
[ U U [G U U [G
]
U kU i Gki cos(θ k − θ i ) + Bki sin(θ k − θ i ) + k
S
kS
k
D
kD
]
]
cos(θ k − θ D ) + BkD sin (θ k − θ D )
Qk ,UPFC = − BkkU +
]
U kU i Gki sin(θ k − θ i ) − Bki cos(θ k − θ i ) +
]
(3)
S
k
D
]
k D sin (θ k − θ D ) − Bk D cos(θ k − θ D )
• at bus i: Pi ,UPFC = GiiU i2 +
[ [G
] )]
U iU k Gik cos(θ i − θ k ) + Bik sin(θ i − θ k ) + U iU S
iS
cos(θ i − θ S ) + BiS sin(θ i − θ S
Qi ,UPFC = − BiiU + 2 i
[ [G
] )]
U iU k Gik sin(θ i − θ k ) − Bik cos(θ i − θ k ) + U iU S
iS
Pijref+jQijref
j
sin(θ i − θ S ) − BiS cos(θ i − θ S
Pk,FACTS Pi,FACTS= - Pijref Qk,FACTS Qi,FACTS= - Qijref Fig. 3. UPFC power flow model
k S sin (θ k − θ S ) − BkS cos(θ k − θ S ) +
k
i
cos(θ k − θ S ) + BkS sin(θ k − θ S ) +
2 k
[ U U [G U U [G
k
(4)
Furthermore, each UPFC device introduces four auxiliary unknowns (the angle and magnitude of series and derivation voltage), which once they have been determined, make possible to find the other electrical measurements and to program parameters of the control and command system, respectively. In these conditions, the mathematical model for determining the steady-state of an electric power system in which there are UPFC devices meant to control power flow is obtained starting from the standard model of the steady-state (equations of nodal powers balance) as follows: (i) The equations of nodal power balance at i and k buses, between which we have connected the converter, are changed as fallow:
f Pk ( [X Bus ] , [X FACTS ] ) = Pkref − Pk ,FACTS − Pk = 0
f Qk ( [X Bus ] , [X FACTS ] ) = Qkref − Qk ,FACTS − Qk = 0 f Pi ( [X Bus ] , [X FACTS ] ) = Pi ref − Pi ,FACTS − Pi = 0
[X ] = [[X Bus ][X FACTS ]]T . We can determine the nodal state variables [X Bus ] , and the UPFC devices state variables [X FACTS ] either simultaneously or alternatively. In
(7)
f Qi ( [X Bus ] , [X FACTS ] ) = Qiref − Qi ,FACTS − Qi = 0 where
[X Bus ] = [θ , U ]
is the steady-state variables vector
(amplitude and modulus of nodal voltages), [X FACTS ] is the vector of state variables that have been added by the UPFC devices (the modulus and the amplitude of derivation and series voltages), and Pk , FACTS , Qk ,FACTS , Pi , FACTS and Qi , FACTS are the powers at these terminals that can be determined by applying (3) and (4). (ii) For each UPFC device we introduce the following supplementary equations: • Equations corresponding to control strategy Pi ,UPFC = − Pijref
Qi ,UPFC = −Qijref
(8)
U k = U kref completed by the inequality constraints imposed by the acceptable limits of the angle and magnitude of series and derivation voltage, respectively: U Smin ≤ U S ≤ U Smax and U Dmin ≤ U D ≤ U Dmax (9) 0 ≤ θ S ≤ 2π and 0 ≤ θ D ≤ 2π where Pi ,UPFC and Qi ,UPFC are nodal powers at i bus of the device, which can be determined with equation (4). • Active powers balance equation at inverters’ level (10) PD = PS where PD and PS are given by equations (5) and (6). Therefore, we can determine the steady-state operation of power systems containing UPFC devices by solving the nonlinear equations system: f ([X Bus ] , [X FACTS ]) = 0 (11) g ([X Bus ] , [X FACTS ]) = 0 which included the equations of the nodal powers balance modified according with equation (7), and the strategy of control equations, with respect to unknowns
simultaneous determination method the Newton-Raphson algorithm is applied to equations system (11) [6]. The alternative method uses the principle of decoupled state variables [X FACTS ] from the buses variables [X Bus ] , and it consists in two steps [3]. In the first step, knowing the components of the vector [X Bus ] , we can determine the
components of the vector [X FACTS ] . Therefore, we use the Newton method in order to solve the system of non-linear equations g ([X Bus ] , [X FACTS ]) = 0 . In the second step, we consider the values of [X FACTS ] as known, and we determine the angle and magnitude of voltages using the NewtonRaphson algorithm in order to solve the system of equations f ([X Bus ] , [X FACTS ]) = 0 . Thus, each FACTS device is represented by the terminal powers that have been determined using the [X FACTS ] values in the first step. The alternative method has been implemented in the program PFAC (Power Flow Analysis and Control) that has been developed in Visual C++ using the OOP (Orientated Object Programming) technology. IV. CASES STUDIES In order to verify the possibility of using the UPFC devices in load flow and congestions management, we used the 220kV 400kV network of the Romanian Power Grid. In this respect, starting from an operating mode R0, defined as base case, we considered 5 other operating modes that may appear in the current operation. Furthermore, for each new case we envisaged several incidents that may lead to congestions concerning energy release from a power plant (cases R1, R2, and R3) and energy supply of a deficitary area (cases R4 and R5), respectively. These operating modes, as well as congestions that may appear, have been determined by means of the PFAC program, and they are described in Table I in short.
TABLE I ANALYZED OPERATING MODES AND CONTINGENCIES Case R0 R1
Changes from R0 case Normal operating scheme with power flow in acceptable limits. Production increases by approx. 210 MW in bus 24.
R2
400kV transmission line 14-15 is tripped.
R3
Importing approx. 140MW from the neighbour system (bus 423), following the withdrawal of a local power generator. 400kV transmission line 14-15 is tripped. Deficit of 390MW in critical area
R4
Incident
Tripp of one circuit from 220kV power line 24-57
Tripp of 400kV power line 5-6. R5
Deficit of 390MW in critical area, and 400kV transmission line 6-8 is tripped.
Load flow/Congestion Overloading of the operating transmission line 24-57 by 0.8% Overloading of the operating transmission line 24-57 by 5% Overloading of the operating transmission line 24-57 by 3.5% Overloading of the operating transmission line 24-57 by 14.2%
circuit
of
circuit
of
circuit
of
circuit
of
Overloading of the 220kV transmission line 9477 by 7.16% Overloading of the 220kV transmission line 9477 by 17.3%, and of the 220kV transmission line 77-43 by 2.08%
423
423 R0
355.5+j67
(47.21%)
178.2-j52.11 (58.9%)
9
423
672.1+j19.3 (19.11%)
9
135.8+j171.2
(41.6%)
(12.36%)
606.4+j1.9 41.7+j135.1
(13.65%)
9
15
(52.72%)
206.7-j30.7
) 2% 1. 4 (
428-j13 142.7+j63.6
(36.7%)
(16.2%)
181.3+j40.1
371.9+j21.1
15
42 3. 2j2 3. 0
) 7% 2. 3 (
(91.7%)
366+j23.6
5. 4
15
33 4. 9j3
(43.25%)
172.5-j9.7
15
57 (103.5%)
(105.%)
332.9+j63.4
(62.3%)
180.4+j8.7
(62.3%)
57 326+j46.7
57
57 180.4+j8.7
(Table II) imposed on the one hand by the necessity to eliminate the congestion, and on the other hand, by the necessity to prevent other congestions. We find out that the least favourable situation is in R1 state, when the limitation of the power flow on the still operating line may lead to overloading of the autotransformer 14-24.
(114.2%)
In order to control congestions that may appear in operating modes R1, R2, and R3 following the tripping of a circuit from the transmission line 24-57 (Fig. 4), it is necessary to add a FACTS device on this line, which should redistribute power flow. Thus, the device controls the power flow on the operating line so that it stays the same as the standard values
(65.32%)
9
423
R1
R2
R3
Fig.4. Power flow (MW-MVAr) in the neighbourhood of buse 24.
250+j60
423
732.34+j32
9
423
(16.17%)
(63.16%)
90.9+j160.2
9
(12.2%)
650.1+j9.6 8.64+j138.3
(14.92%)
136.8+j101
434-j12.8 (42.17%)
(71.46%)
(71.5%)
) 1% .2 2 (4
15 283.7+-j16.8
15 283.7-j17.3
43 4j2 3. 66
(97.8%)
388.8-j10.5
15
(76.11%)
57 (76.11%)
250+j60
57 (96.43%)
310+j60
57
(71.21%)
9
423
R1
R2
R3
Fig. 5. Power flow (MW-MVAr) in the neighbourhood of buse 24 the presence of an UPFC TABLE II Controller
UPFC
Regime R1 R2 R3
Scheduled line power P[MW] Q[MVAr] 310 60 250 60 250 60
Load [%] Line 24-57 AT 14-24 96.40 97.30 76.11 71.50 76.50 71.50
In order to control congestions that may appear in operating modes R4 and R5 following the tripping of the 400kV transmission line 5-6, it is necessary to add a FACTS device on the 220kV transmission line 94-77 in order to restrict the power flow toward the deficit area. The results obtained when using the UPFC device, which also regulate nodal voltage in 94 to a value of 1 p.u., show the fact that power flow limitation on line 94-77 leads to an increase of power flow on 220kV
US [p.u] 0.2488 0.1514 0.1825
Steady state of FACTS controller UD [p.u] θS [deg] -108.69 0.9295 -188.70 1.0760 142.3744 1.0942
θD [deg] 5.16 2.48 2.08
transmission lines going through 42, 50, 81, 88, 75, and 119 buses. Thus we have a redistribution of power flow, which leads to congestion eliminations. Figure 6 shows power flow for operating mode R5 on the transmission lines that supply the deficit area when there is, and when there is not an UPFC device to regulate power flow on transmission line 94-77 at (250+j60) MVA.
119
21-j11 (7.7.3%)
Critical Zone 102
57+j2.4 (18.3%)
96.+j10 (38.7%) 110-j21 (38.7%)
6 307-j21 (102.1%)
119
81
5
43
77
88
75
8
150-j34 (48.1%)
77
159-j29 (51.4%)
196+j23 (60.4%)
202-j4.8 (70.1%)
81
5
43
50
42
78-j38 (27.6%)
Critical Zone 102
88
75
206-j42 (73.1%)
6
50
8
263-j37 (84.2%)
42
250+j60 (74.6%)
371+j74.6 (117.3%)
10 94
10
FACTS 94
Fig.6. Power flow (MW-MVAr) on 220kV lines for operating mode R5 V. CONCLUSIONS
VI. REFERENCES
In this paper we have analyzed the possibility of using flexible UPFC device in controlling power flow and congestions that may appear in power systems when certain equipments are not available. In this respect, we have developed the steady-state models of the device that have been implemented in the PFAC program. This program, based on the Newton-Raphson method, is meant to analyze power flow in power systems and it has been tested on the 220kV-400kV network of the Romanian Power Grid (RPG). We have taken into consideration several possible scenarios, leading to two types of congestions. The first type of congestion is related to nodal power release, and the second to the supply of a deficit area. Simulations prove the fact that in both cases we can redistribute power flow so that to reduce and eliminate congestions if we use the UPFC device. Similarly, the FACTS devices can be installed on interconnection lines in order to redistribute power flows thorough the RPG interconnection interface to a second synchronous area, and in the future with UCTE, in order to avoid congestions in the internal network, in the interconnection interface or in the neighbor networks. Bearing in mind the achievements of the UPFC device, and also his high price, a lot of research is needed before deciding whether to install such devices. It requires economical research as well as a complete analysis of the FACTS effects on the steady state and on the dynamic behavior of the power system. We may conclude that using the UPFC devices, if we leave aside the high costs or the technical details, is a viable alternative to load flow and congestions management in power systems, as well as for increasing their reliability and their flexibility.
[1] Hingorani N.G., Gyugyi L. – Understanding FACTS : Concepts and technology of flexible AC transmission systems. IEEE Press Inc., New York 2000. [2] Song Y. H. and Johns A. – Flexible ac transmission systems - FACTS. IEE Press, London, 1999. [3] Nabavi-Niaki A., Iravani M.R. – Steady State and Dynamic Models of UPFC for Power System Studies. IEEE Trans. PWRS Vol. 11, No.4, November 1996. [4] Cañizares C.A. – Power Flow and Transient Stability Models of FACTS Controllers for Voltage and Angle Stability Studies. Proceedings of the 2000 IEEE-PES Winter Meeting, Singapore, January 2000. [5] Schauder C.D., Gyugyi L., Lund M.R., Hamai D.M., Rietman T.R., Torgerson D.R. and Edris A. – Operation of the Unified Power Flow Controller (UPFC) under Practical Constraints ”. IEEE Trans. on Power Delivery, Vol. 13, No.2, April 1998. [6] Fuerte-Esquivel C.R., Acha E., Ambriez-Perez – A Comprehensive Newton-Raphson UPFC Model for the Quadratic Power Flow Solution of Practical Power Networks. IEEE Trans. PWRS Vol. 15, No.1, February 2000. [7] Eremia M., Trecat J., Germond A. – Réseaux Electiques Aspects actuels. Editura Tehnică, Bucureşti 2000.
