Sensitivity Analysis in Medium Voltage Distribution Systems

Sensitivity Analysis in Medium Voltage Distribution Systems

Sensitivity Analysis in Medium Voltage Distribution Systems

Saad Ouali #1, Abdeljabbar Cherkaoui 2

1,2 Laboratory of Innovative Technologies (LTI), National School of Applied Sciences, Abdelmalek Essaadi University

Tangier Morocco

Abstract This paper presents a sensitivity analysis of radial distribution systems, with a focus on medium voltage distribution systems in Morocco, The proposed analysis can offer an analytical tool able to quantify how the network conductors characteristics and how the variation in active and reactive power loads and distributed generation connected to a medium voltage distribution systems may affect the voltage plan of the network. Obviously, any change in a system input impact the system performance. However, some inputs may have more impacts whereas others inputs may have less or more influence impacts. Voltage plan of radial systems is a function of their conductors characteristics and connected active/reactive power. The main aim of this paper is to compute a sensitivity coefficient to quantify the impact of active and reactive power on the voltage plan, this type of sensitivity information is useful for estimating the expected voltage changes, and may also be used for choosing the optimal placement of distributed generation, reactive compensation and voltage control actuator. The proposed analysis had been applied to a radial distribution of 16 bus, this application had lead to know how a distributed generation can affect the voltage plan, and how changing its connected point, may lead to increase or decrease its impacts on the network performances. Also a comparison with several conductors characteristics with real underground cable and overhead lines information is presented in this paper, such a comparison had proved that network reinforcement can also be a choice for voltage control and had also lead to know the most impacted in underground and overhead networks by distributed generations integration and the migration from a passive to an active mode.

Keywords Sensitivity Analysis, Radial distribution system, Backward/forward sweep, Medium voltage system.

1. INTRODUCTION

   Medium vltage distributin systems in Mrcc are radial with large number f ndes, branches, and cmplex tplgy cnfiguratins that can be changed fr maintenance activities, emergency peratins r netwrk cnfiguratins.

   The Mrccan medium vltage distributin system is made f 3 phases, with neutral grunded in the HV/MV substatin. Tw nminal magnitudes vltages are used 20KV and 22KV.

   Three frms f medium vltage distributin system can be distinguished: 100% verhead lines, 100% undergrund cables r a cmbinatin f bth.

   The undergrund netwrks are made f 3 single-phase cables. The verhead netwrks are made f three bares

   cnductrs, the mst used tplgy is the radial cnfiguratin

   The penetratin f distributed generatrs in Medium Vltage (MV) distributin netwrk will challenge the future grid peratin. Mre intelligent methds shuld be used fr a better utilizatin f the distributin netwrk, in rder t maintain, r even t imprve, the pwer-supply reliability and quality. Vltage rise is nrmally the main limiting factr t prevent the increase f distributed generatin in distributin netwrks [1].

   The develpment f a vltage management strategy is a challenging task due t the nn-linear relatinship between the netwrk lad and the grid vltage. In the present paper we present a simple analytical tl t quantify vltage sensitivity due t the injectin f active and reactive pwer at ne r mre ndes f MV distributin netwrks.

   Sensitivity analysis in electric systems is an imprtant tl t quantify the impact f variatins in parameters n the system perfrmance. Vltage regulatin, lss reductin, netwrk expansin planning, ptimal placement f reactive surces, and many ther applicatins regarding bth planning and peratin f pwer systems in which it is necessary, r even simply useful, t predict the changes f vltage magnitude caused by variatins in lads and generatins.

   The main aim f this paper is t develp an analytical tl t quantify nde vltage variatins due t injectins f active and reactive pwers at ne r mre ndes f radial distributin netwrks. And t mitigate hw nde distances frm the rigin, sectin and type f cnductr, verhead line r undergrund cable influence the netwrk sensitivity.

   In what fllws, we present the impact f distributed generatin n netwrk vltage in sectin II. Next in Sectin III we prvide the theretical fundatin f the methd used t btain mathematical expressins that link vltages sensitivity t nde active and reactive pwers variatin, in sectin IV we present a case study f the prpsed methd with the use f the IEEE 15-bus system infrmatin, in sectin V we discuss the results btained frm the case study, and the cmparisns with the Mrccan Medium Vltage system, sectin VI cncludes this paper.

2. IMPACTS OF DISTRIBUTED GENERATION ON THE

   NETWORK VOLTAGE

   Considering the radial system shown in Fig1.

   Fig 1: One line diagram to illustrate the voltage variation in a distribution system with DG.

   In the case of any distributed generation (DG) connected to the node 2, the relationship between the voltage of node 1 and 2 it:

   # Start

   # Cnstructin f the Ybus Matrix

   # Make an estimate f the vltage plan

   # Substitute the ld values int pwer equatins fr the next iteratin

   # btain the new value

   # cmpare the new value with ld value

   # If (New value ld value) < specified tlerance; then end therwise g t step 4.

   Fig 2: Pseud-cde prcedure fr analyzing lad flw in a pwer system

   Several wrks had been presented in the scientific literature; the methds used can be divided int tw principal categries: Methds based n the ameliratin and adaptatin f transmissin methds such as fast-decupled, and thers are based n pwer summatin methd [3].

   In what follow we adopt the power summation approach, so, lets consider [F] a column vectors, dimension (n x 1),

   = 12 12 + 12 12

   1 2

   2

   (1)

   whose elements are, the injections powers of network nodes.

   In the case of the presence of a distributed generation (DG)

   connect a t the node 2,

   [] = [ ] [ ] = [ ] + [] (4)

   = ( 12 ) 12 +/ ( 12 ) 12

   1 2

   2

   (2)

   Where PDG and QDG are active and reactive power of the DG. Equation (2) indicates that if the active power generated bu the DG is larger than the feeder load, power may flow

   from the DG to the substation and causes a voltage rise.

   Equation (2) indicates too that, if the DG absorbs reactive power, the DG can either increase or decrease the voltage drop.

   Where [P] and [Q] are the column vectors, dimension (n x 1)

   , whose elements are, respectively, the node active and reactive powers.

   The complex conjugate of [S] is given by:

   [] = [] [] = [ ] [ ] (5)

   The current injections of network nodes are:

   [ ][ ]

3. PROPOSED SENSITIVITY ANALYSIS METHOD

   [] =
   []

   (6)

   The mst used analysis methds in electrical system:

   Gauss-Siedel methd, Newtn-Raphsn methd and Fast Decupled methd.

   The first step is the cnstructin f the Y-bus admittance matrix using the transmissin line and transfrmer input dat. The Gauss-Seidel analysis methd uses an iterative methd based n Gauss equatin, the Newtn-Raphsn is based n the expanding in Taylrs series abut the initial estimate the active and reactive pwer frmulatin, the terms are limited t the first apprximatin f the equatins. The Fast Decupled Pwer analysis Methd is ne f the imprved methds, which is based n a simplificatin f the

   Newtn-Raphsn methd, the cnvergence is gemetric.

   A cmmn prcedure f the three methds, adpted fr analysing electrical system in a pwer netwrk is discussed in the pseud-cde shwn in Fig.4 [8].

   But medium vltage distributin systems in Mrcc are characterized by a high R/X ratins and a strngly radial structure, which leads t ill-cnditined matrices and pr cnvergence characteristics f thse lad flw methds.

   The prblems have been revealed in a number f papers, where the classic transmissin methds were nt apprpriate t slve practical prblems presented when analysing distributin systems.

   Current injectins and relatinship between the bus current injectins and branch current can be btained by applying Kirchhffs current law (KCL) t the distributin netwrk. The branch currents can then be frmulated as functins f equivalent current injectins.

   A sample distributin system drawn belw is taken n fig- 2 t illustrate the methdlgy chsen t develp a vltage sensitivity analysis method:

   Fig 3: Single line diagram of a radial distribution network

   By applying Kirchhoffs current law, the branch currents I1, I2, I3, I4, I5, I6 and I7 can be expressed by equivalent current injections as:

   1 = 2 + 3 + 4 + 5 + 6 + 7 (6.1)

   2 = 3 (6.2)

   3 = 5 + 6 (6.3)

   4 = 5 (6.4)

   5 = 6 (6.5)

   5 = 6 (6.6)

   6 = 7 (6.7)

   Therefore, the relationship between the bus current

   injections and branch currents can be expressed as:

   matrix represents the relationship between bus current injections and branch currents. The corresponding variations at branch currents, generated by the variations at bus current injection can be calculated directly by the BIBC matrix. Combining equation (7) and (10.2), the relationship between bus current injections and bus voltages can be expressed as:

   [] = [][][] = [][] (11)

   Where DLF is a multiplication matrix of BCBV and BIBC

   matrices

   Lets consider two matrices [R] and [X] as :

   1 1 1 1

   1 1 1

   2	0	1	0	0	0	0 3
   3 =	0	0	1	1	1	0 4
   4	0	0	0	1	0	0 5
   5	0	0	0	0	1	0 6
   [6]	[0	0	0	0	0	1] [7]

   2

   Or [] = [] × [] (7)

   [R ] = real([DLF]) and [X ] = im([DLF]) (12)

   The element (i,j) of the matrix [R] is the sum of the

   resistance of the branches in which both Pi+1 and Pj+1 flow. For instance, in order to obtain the element (3,2) of [R], the branches in which both P4 and P3 flow are J1.

   [][]

   The constant BIBC matrix is an upper triangular matrix and contains values of 0 and +1 only.

   [] = [1] ([ ] + []) (
   [] ) (13)

   The relationship between branch currents and bus voltages can be obtained as follows:

   2 = 1 112 (8.1)

   3 = 2 223 (8.2)

   4 = 2 324 (8.3)

   5 = 4 445 (8.4)

   6 = 4 546 (8.5)

   7 = 2 627 (8.6)

   Where Vi is the voltage of bus i, and Zij is the line

   impedance between node i and node j. Substituting (8.1) and

   Simplified linear expressions can be derived from (13)

   under the following hypotheses (commonly accepted in distribution networks analysis) [4]:

   • The phase difference between node voltages is negligible and, as a consequence, if phasor V1 is chosen on the real axis, only the real part of voltage [V]= real[V] is considered.

   • Constant current models are considered for loads (node powers are referred to system nominal voltage instead of actual node voltage).

     Equations (13) can be written as:

     into (8.6), the equation (8.6) can be written as:

     7 = 1 112 223 626 (9)

     [] = [1] ([ ] + []) (

     For a node i:

     1

     [][]

     ) (14)

     = 0

     ( + ) (15)

     From (9), it can be seen that the bus voltage can be

     expressed as a function of branch currents, line parameters and the substation voltage. Similar procedures can be performed on other nodes; therefore the relationship between

     From equation (15), the voltage of node i depend on the

     active and reactive power injections or consumed of all node networks.

     As the node 1 is the slack bus, its voltage is always

     branch currents and bus voltages can be expressed as:

     constant. The sensitivity ( )

     of voltage at node i with

     1

     1

     2

     3

     12	0	0	0	0	0
     12	23	0	0	0	0
     12	0	34	0	0	0
     12	0	34	45	0	0
     12	0	34	0	56	0
     [12	0	0	0	0	6

     1

     2

     respect to the active power and reactive power at node j, can

     be written as:

     1

     1 4 =

     3

     ( )

     =

     =

     1

     1 [1]

     5

     6 [7]

     4

     5

     7 ] [6]

     {

     ( )

     =

     = 1

     (16)

     (10.1)

     The total differential of function Vi is:

     Or : [] = [] × []

     =

     +

     (17.1)

     (10.2)

     = ( )

     + ()

     (17.2)

     The BCBV matrix represents the relationship between branch current and bus voltages. The corresponding

     Considering all network nodes:

     1

     variations at bus voltage, generated by the variations at

     1

     1

     1

     branch currents can be calculated directly by the BCBV

     1

     [ ] = [

     1

     1 1 ]

     (18)

     matrix.

     The BIBC and BCBV matrices are developed based on the topological structure of distribution systems. The BIBC

     1

     1

     1

     [ ]

     Lets consider [S], as the sensitivity matrix (nx2n), whose elements are the sensitivity of network nodes to active and reactive power variation.

     The matrix [F], can be written as:

     [] = [| ] (19)

     the a network with 35mm² conductors section, and in the fig 8, the same comparison is done but with the 95mm² conductors. Fig 7 and Fig 8 shows that the undergrounded cables are more sensitive to active power varation. And the overhead lines are more sensitive to reactive power variation

     For the same distance from the substation, for example

     1

     1

     1 1

     10Km as a distance from the substation, and in a 20KV

     network, the voltage sensitivity at a node located in 10Km,

     [] = [ ] =
     []

     with respect to the variations of its active and reactive power

     1

     (20)

     is given in table VI.

     TABLE I

     1

     1

     1 1

     VOLTAGE SENSITIVITY OF A NODE LOCATED AT 10KM FROM THE

     SUBSTATION

     [ ] = [ ] =

     	Cable section	Sp	Sq	Sp/Sq
     Underground cable	35 mm²	-0.337	-0.1	3.37
     	95 mm²	-0.124	-0.09	1.38
     Overhead line	35 mm²	-0.259	-0.194	1.33
     	95 mm²	-0.096	-0.178	0.54

     []

     1

     {

     Those expressions allow quantifying voltage variations at

     each network node due to active and reactive power variations at any other node of a radial distribution network.

     Reactance and resistance of cables are given as a value per kilometer:

     Table IV shows that the undergrounded cables are more

     =

     and =

     (21)

     sensitive to active power variation. And the overhead lines are more sensitive to reactive power variation. We can also

     Equation () can be expressed as:

     observe that the voltage sensitivity is more important for the

     ( )

     =

     = 1

     1

     (22)

     35mm² cables than the 95mm² cables. So its to highlight that for the underground networks, the nodes voltages are more influenced by the active power variations, than the reactive

     {( ) =

     =

     power variations. And for the overhead line, the nodes

     Where Lij are:

   • for i=j the sum of the branch lengths forming the path from the origin (node 0) to node i

   • for ij the sum of the branch lengths forming the path from the origin to the common node of the paths formed by the origin and nodes i and j.

   A graphical representation is useful to mitigate how section and type of conductor (overhead line or underground cable line) influence the network sensitivity. And to get immediate perception of sensitivity variation with node distance from the origin.

4. NETWORK CHARACTERISTICS AND THE IMPACT ON THE NETWORK VOLTAGE PLAN

   By considering the electrical proprieties of conductors used in [2]:

   Underground cable with section 35mm²:

   r= 0.675Ohm/km and x= 0.2 Ohm/km Underground cable with section 95mm²:

   r= 0.249 Ohm/km and x= 0.18Ohm/km Overhead cable with section 35mm²:

   r= 0.519Ohm/km and x= 0.388Ohm/km Overhead cable with section 95mm²:

   r= 0.193Ohm/km and x= 0.357Ohm/km

   Fig 6, gives a representation of the sensitivity of voltage plan with two conductors sections. Such a graphical representation is useful to get how conductors sections impact the voltage plan of the network, and its clear that is more is section is smaller, more the influence of active and reactive on the voltage plan is more important.

   Fig 7, gives a comparison between overhead and underground network, and their impact on the voltage plan of

   voltages are more influenced by the reactive power

   variations, than the active power variations. And the voltage sensitivity is greater for the smaller sections.

5. VOLTAGE SENSITIVITY AND MV DISTRIBUTION

   SYSTEM IN MOROCCO

   The Moroccan MV distribution networks are radial. So, to connect a new DG into a Moroccan Medium voltage distribution system, first, its to distinguish the form of the network: 100% overhead lines, 100% underground cables or a combination of both.

   For the overhead lines: its to highlight that overhead network in Morocco had an arborescent structure, with derivations stemming from a main-line, and grouping into a cluster, as shown in fig 5.

   In such network structure, the main-line is made from conductors with bigger sections than the derivations conductors. In the case of having different possibilities to chose a connection point of a new DG, the best emplacement to connect the new DG, is the point presenting the shortest distance from the substation, and the point located in the part of the network with the biggest conductor section.

   For controlling the network voltage, the most influencing regulator is a system able to adjust its consumption and injection of reactive power.

   For the underground networks: The most used topology is the open loop (ring configuration) in which, each MV/LV

   substation is connected to the two others substations, as shown on Fig.4.

   Fig 4: Single line diagram of the open-loop topology

   A new DG must be connected as closer as possible to the substation, and the must influencing regulators are the systems, able to act at their consumption or injection of active powers.

   Fig 5: MV Overhead distribution system

   For a network composed of overhead and underground conductor, a new DG must be connected as closer as possible to the substation, and for choosing the optimal placement of voltage regulator, its preferable to process to the

   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Km

   Sp Underground cable 35mm² Sq Underground cable 35mm² Fp Underground cable 95mm² Fq Underground cable 95mm²

   0

   -0.1

   -0.2

   Sensitivity values

   -0.3

   -0.4

   -0.5

   -0.6

   -0.7

   -0.8

   Fig 6: Graphical representation ofthe influence of conductor sections on voltage sensitivity.

   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

   Sp Underground cable 35mm² Sq Underground cable 35mm² Sp Overhead lines 35mm² Sq Overhead lines 35mm²

   0

   -0.1

   -0.2

   Sensitivity values

   -0.3

   -0.4

   -0.5

   -0.6

   -0.7

   -0.8

   Fig 7: Graphical representation of the comparison of the comportment of underground and overhead 35mm² network.

   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Km

   Fp Overhead Cable 95mm² Fq Overhead Cable 95mm² Fp Underground cable 95mm² Fq Underground cable 95mm²

   0

   -0.05

   -0.1

   Sensitivity values

   -0.15

   -0.2

   -0.25

   -0.3

   -0.35

   -0.4

   -0.45

   Fig 8: Graphical representation of the comparison of the comportment of underground and overhead 95mm² network.

   computation of voltage sensitivity using the presenting method in this paper.

6. CONCLUSIONS

A analytical methd t quantify the vltage sensitivity t the variatin f active and reactive pwer variatin is presented in this paper, The prpsed methd is develped based n the explitatin f the radial structure f medium vltage distributin system, and the backward/frward sweep cncept, by frming tw matrices: bus injectin t bus current (BIBC) and branch current t bus vltage (BCBV).

As shwn in this paper, the vltage f any nde f the netwrk depends n the active and reactive pwer f all

netwrk ndes. The prpsed methd is able t quantify this influence in a case f the variatin f active r reactive pwer f any nde f the netwrk, n the vltage f any ther part f the netwrk.

The results btained by the prpsed methd may be interesting fr tw applicatins:

• Chsing the cnnectin pint f a new DG, in the case f the presence f several feeders, in the vicinity f the DG site.

• Chsing the best way t cntrl the vltage f a certain nde f the netwrk, by acting at the mst influencing factr: active r reactive pwer and at which pint.

REFERENCES

[1] G. Mokhtari, A. Ghosh, G. Nourbakhsh, and G. Ledwich, Smart robust resources control in LV network to deal with voltage rise issue, IEEE Trans. on Sustain. Energy, vol. 4, no. 4, pp. 10431050, Oct 2013.

[2] S.Conti, S.Raiti, G.Vagliasindi, Voltage sensitivity analysis in radial MV distribution networks using constant current model, Industriel Electronics (ISIE), IEEE international Symposium, Nov. 2010

[3] S. OUALI, A. Cherkaoui: Load flow analysis for moroccan medium voltage distribution system, Conférence Internationale en Automatique & Traitement de Signal (ATS-2018), Proceedings of Engineering and Technology PET, Vol.36 pp.10-16

[4] G.W Stagg and A.H. El-Abiad, Computer Methods in Power System Analysis, McGraw Hill, 1968.