14th PSCC, Sevilla, 24-28 June 2002
Session 24, Paper 2, Page 1
OPTIMAL DESIGN OF ACTIVE SHIELDING FOR POWER LINES Pedro Cruz Romero Universidad de Sevilla Sevilla, Spain
[email protected]
Carlos Izquierdo Mitchell
Manuel Burgos Pay´an
Universidad de Sevilla Sevilla, Spain
[email protected]
Universidad de Sevilla Sevilla, Spain
[email protected]
Abstract - This paper analyzes the design of cost-effective active-loop magnetic field shielding of power lines. In this way a mathematical model is developed, and minimization problem formulated, being the objective function the shield cost. The shield efficiency is compared with other shielding alternative, series-compensated passive shield. Several selected mitigation locations are considered: locally, at a specific point, or at a stretch delimited by two points. Both location modalities can be unidirectional (one line-transversal direction) or bidirectional (two line-transversal directions). The method is applied to several typical Extra High Voltage (EHV) power line cases (horizontal flat,vertical, delta and double-circuit vertical), and mitigation and cost results are provided.
shield. The shield is located at the passive shield position that minimizes the field far from the line (about 100 m). In this paper, a novel, cost-effective active shield design is introduced, based on the optimization problem formulation whose objective function is the installation cost of shield. The inputs of the problem are the following:
Position of phase conductors
Highest phase current carried by power line
Number of shield conductors Length of the shield.
The design parameters are the following:
type of power source: connected to the grid, or isolated.
Keywords - magnetic field mitigation, active and passive loop, right-of-way, series compensation, resultant magnetic field, super-bundle configuration.
Position of shield conductors. Electric resistance of shield conductor ( ). Lower values reduces the power needed, but increases the supporting poles cost.
1 INTRODUCTION HE possibility of mitigating magnetic fields generated from power lines has been extensively studied during last decade. In particular, passive and active shielding methods, introduced by Olsson et al [1], are based on the counteracting effect of a current that flows in shield conductors. If the current is just induced in shield conductors the shield is named passive. Partial cancellation of shield inductance by means of series capacitors improves the shielding effectiveness, as the current amplitude increases, and phase changes in the right direction. If an external power source is provided (active shielding), it is possible to tune the amplitude and phase of shield currents in order to increase the field reduction. Jonsson et al [2] analyzed the three-conductor passive and active shield application to an inverted delta 400 kV line, locating the shield conductors at the ground wire positions and underground. Injected current to active shield is iteratively calculated starting from an arbitrary value of amplitude and phase. Pettersson [3] proposed an approximate formulation of the field created by a three-phase line and a shield loop, based on dipole decomposition. This formulation is valid at medium distances from the line (about 50 m). For a flat configuration he obtains the loop location that maximizes the reduction far from the line: coplanar with line conductors. Pettersson again [4] proposed locating efficient active shield in the same way than passive shield. Lately Cruz [5] determined analitically the impressed current to the shield that minimizes the residual field at a particular distance to the line, and applies it to the two-conductor, three-conductor, and four-conductor
Shield injected current vector ( ).
Several constraints related to highest allowed magnetic field and minima clearances are introduced:
Allowed field limit type. Highest resultant field at a specific transversal distance (traditionally the rightof-way (ROW) edge) or the mean highest resultant field between two transversal distances to the line. Both field limit criteria can be applied to one direction from the line or two.
Highest allowed resultant field ( )
Minimum clearance shield conductor-power conductor Minimum clearance shield-ground
The optimization problem has been solved with the help of GAMS (General Algebraic Modeling System) package (non-linear constrained problem solver) [6]. 2 PROCEDURE DESCRIPTION Due to the fact that the conductor resistance is a discrete variable, the problem is solved for several conductors. On the other hand, the lowest value for the magnetic field with no cost-effective (mitigation-effective) active shield has to be lower than . On the contrary, the problem has no solution. Likewise, it would
14th PSCC, Sevilla, 24-28 June 2002 be interesting to determine if is higher than the lowest value of the magnetic field with no cost-effective series-compensated passive shield . In that case active shielding could not be needed, due to the higher cost of active solution. Eventually, if is higher than the lowest value of the magnetic field with mitigation-effective non-compensated passive shield , this type of shield would be enough. These considerations are included in the procedure layout shown in fig. 1. For the selected allowed field limit type the diagram sequence is repeated with every tentative shield conductor resistance, and final decision taken from comparison of cost-resistance table. In this paper it will be assumed that , so the objective is obtaining the active shield that verifies the limit with the minimum cost . To obtain it is needed to develop a model for series-compensated shield.
Session 24, Paper 2, Page 2
1. The ground effect is neglected. This is true for distances involved in the analysis (tens of meters). 2. Phase and shield conductors are straight and infinitely long, located at a height equal to the lowest span point of the lowest conductor. 3. Reciprocal effect of ground wire and shield current is neglected. By means of Biot-Savart Law it is possible to obtain the magnetic field complex vector generated by the line:
Re[ ] Im[ ] Re[ ] Im[ ]
(1)
where and are the spatial directions, normal to the line direction. Likewise, if the shield currents are known, the field is determined. 3.2 Shield induced EMF and current Let be three-phase line currents given by the RMS
vector , and a -loop passive shield (fig. 2). It is well known that the loop RMS current vector can be expressed as [4]
"!$#&%('*),+-%/. being0132 2 2 2 2:9 ; ; 465 758 "=?=?= 132 the per-unit -loop self-impedance, where 2 5 2 A@CBEFHD G I J3K < 2 58 @
(2)
(3)
(4) (5)
with
Figure 1: Procedure flowchart for the active and passive shield design.
3 MODEL DESCRIPTION 3.1 Calculation assumptions Several conventional assumptions are included to cal culate the magnetic field created by the line ( ) and shield ( ), as well as the induced/injected current in passive/active shield:
vacuum magnetic permeability @BED: :line frequency J313K2 ; : mean geometrical radius of shield conductors 2 : -loop width
: i-loop series capacitance value. 013On 2ML the other hand;; 99 ;; 99 ; @BED 4 )QPSRT 4 TPSRU) W =?=?= 0132ML < N 2 FG I8O 4 )QPSRU) O 4 13T2*PS1QR; LT PS9 R ;" O R N @ O BEN D FVG I J3K 4 )QPSRU) O
(6)
are respectively the per-unit mutual impedances between two independent loops (four-conductor shield), and between two common-conductor loops (three conductors short-circuited at both ends) respectively. All shield con; ductors are supposed to be ; equal. 9 Finally
5
13XY2ML
Z @ BEN D F G I8O V O
4 ; T/PSR 9 4 )QPSR
"=?=?= R "=?=?=
(7)
14th PSCC, Sevilla, 24-28 June 2002
Session 24, Paper 2, Page 3
The power source includes the solar cells, battery, regulator and inverter. A control system needs to be added to regulate the phase and amplitude (from 0 to 220 V) of the output ac voltage , according to the power line load. The total cost of the power source is given by
with
Figure 2: Phase conductors and mitigation loops.
(12)
3.5 Reactive compensation
For the 1-loop shield (2) yields
0 13X6L L 5 )
where
a constant.
(8)
(9)
is the EMF induced in the loop. 3.3 Injected current in an active loop In flow diagram of fig. 1 it is needed to determine the active shield for lowest field. The problem is twofold: 1. Determination of shield conductor geometrical positions 2. Determination of shield injected currents
9
Most of the power required by the loop is reactive. This fact makes convenient to insert reactive compensation by means of a capacitor. It may be series or parallel connected. With the series arrangement (fig. 3), for shield lengths of few hundreds of meters the capacitance that results is quite high, tens of milifarads. Taking into account that the reactive power can be of tens of kVAr’s, the compensation modules become huge and costly. For loop lengths of thousands of meters the capacitance reduces about ten times, but reactive power required increases also about ten times (hundreds of kVAr’s). This high reactive power makes practically non-viable the isoX lated active shield with those lengths. In our case we will N m. For this length assume that the shield length value parallel reactive compensation (fig. 4) could be a feasible alternative, where capacitance is in the millifarad range and reactive power some tens of kVAr’s.
For simple shields it is easy to obtain the injected current that minimizes the field at a point 46 D P D , if the shield coordinates are known. For example, for the simple loop [5] the injected current components are given by9 9
! D Re 46 Re
! D Im 46 Im
D ! D Re 46 D T 9 D T D 9 (10) ! D D Im 46 D T D T D 9 where D U4 P D 9 (11) D U4 P D The height of the point D is considered constant and "< m. the value conventionally taken is D
Figure 3: Electric diagram for series-compensated active shield.
0
0
3.4 Power source Cost of power source is dependent on type of source. One rough classification could be connected to the grid or isolated. The isolated option could be attractive in those scenarios where there is no conventional low voltage supply near the power line, or it is not convenient to take the power from an existing one. In this paper it is assumed that the power is provided by a photovoltaic system. The peak power and type of shield (one-phase, three-phase) affect the cost of the source. We assume here for the sake of simplicity that the shield is one-phase (a simple loop), although better mitigation results are obtained with threeconductor shields [1, 2] or even multi-phase shields [7].
Figure 4: Electric diagram for parallel-compensated active shield .
To reduce the capacitance value it is needed to include a transformer. In this way the capacitor required is a conventional one. Cost of capacitor and transformer are the following:
E
" !C # $%
&
#
(13) (14)
14th PSCC, Sevilla, 24-28 June 2002
Session 24, Paper 2, Page 4
$% # : highest output voltage(220 V) # : reactive power required by transformer and loop (kVAr) : nominal power of transformer (kVA) & ":! voltage ratio of transformer P P P : constants.
where
Nominal power and voltage ratio are obtained by
"!
%
&
# $ % % # # 5 # # #
T
(16)
"! # % # # #
3.6 Cost of shield arrangement
Shield loop can be arranged in two ways: taking advantage of the power line towers, and by new poles. The cost of hanging up loop conductors from existing line towers is quite higher than from independent poles. In some loop locations it is inevitable to string one or both loop conductors from line towers. This happens when loop conductor is inside segment formed by extreme line conductors, and loop conductor height is at least higher than one line conductor height. In fig. 5 shaded areas represent zones where this; happens 9 ; for 9 flat ; 9 and ; delta lines. To take into account in the formulation the of cost a bi; K ) 4 K T 4 ( isincrease the loop conductor nary function K 4 "< P N ) is2 defined, X where1 X 9 index, ;9 ! ! X 9 ! K ) 4 X N 2 ! 1 4 X 9 (18) ;9 6 4 ! ! X 46 9 ! K T 4 N (19) 2 2:9 X 46 !
& &
with X 46 X
P
9 L9 9 9 and the loop -conductor position coordinates
max(abs 46 ) 9 =?=?= abs 46 L/9 =?=?= abs 46 9 9 (20) L/9 46 ) =?=?= abs 46 =?=?= abs 46 L min(abs (21) where 46 P is the R -phase conductor coordi forposition nates ( for single circuit; double circuit).
H< It is easy to see that K 4
;
if -conductor is hanged
)
) 1K T K
T
1
2
(23) (24)
where K is the conductor sag for a span of 200 m (heights are defined at the lowest point of loop conductor spans). The cost of loop arrangement lays:
where
&
P P
2 T 4
