The Optimized Implementation of the District Metered Areas ...

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dx.doi.org/10.22093/wwj.2019.140550.2718 12 Original Paper Journal of Water and Wastewater Vol. 31, No. 1, 2020 Jouranl of Water and Wastewater, Vol. 31, No.1, pp: 12-24 The Optimized Implementation of the District Metered Areas in the Water Distribution Networks Using Graph Theory M. R. Shekofteh 1 , M. R. Jalili Ghazizadeh 2 MSc Student, Dept of Water Resources Engineering, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran Assist Prof, Dept of Water and Wastewater Engineering, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran (Corresponding Author) m_jalili@sbuacir (Received July 17, 2018 Accepted Feb. 4, 2019) To cite this article: Shekofteh, M. R., Jalili Ghazizadeh, M. R., 2020, “The optimized implementation of the district metered areas in the water distribution networks using graph theory” Journal of Water and Wastewater, 31(1), 12-24. Doi: 10.22093/wwj.2019.140550.2718. (In Persian) Abstract For better utilization of water distribution networks (WDNs), it is recommended that the existing networks be converted into Distinct Metered Areas (DMAs). Due to the complexity of the old networks, the conversion of these networks into DMA is a costly and sensitive issue. In this paper, a model has been developed to optimize implementation of the old networks into DMA by using the graph theory and water distribution system modeling software (EPANET), while the minimum required standard pressure is met and the number of linked pipes between the proposed areas is minimum. The minimum number of linked pipes will minimize the cost of the needed flowmeters. The developed model has been successfully applied for Poulakis WDN with 30 nodes and 50 pipes in different statuses and for the actual Bushehr WDN with about 3740 nodes and 3980 pipes. The output result shows that the developed model, in a satisfactory way, converts water distribution networks into DMAs with respect to the hydraulic constrainsts. Keywords: District Metered Area (DMA), Graph Theory, Leakage Management, Water Distribution Network (WDN).

Transcript of The Optimized Implementation of the District Metered Areas ...

Page 1: The Optimized Implementation of the District Metered Areas ...

dx.doi.org/10.22093/wwj.2019.140550.2718 12Original Paper

����� � �� �� Journal of Water and Wastewater ����� ���� ����� ����� Vol. 31, No. 1, 2020

Jouranl of Water and Wastewater, Vol. 31, No.1, pp: 12-24

The Optimized Implementation of the District Metered

Areas in the Water Distribution Networks Using Graph Theory

M. R. Shekofteh1, M. R. Jalili Ghazizadeh2

1.MScStudent,Dept.ofWaterResourcesEngineering,FacultyofCivil, WaterandEnvironmentalEngineering,ShahidBeheshtiUniversity,Tehran,Iran2.Assist.Prof.,Dept.ofWaterandWastewaterEngineering,FacultyofCivil,

WaterandEnvironmentalEngineering,ShahidBeheshtiUniversity,Tehran,Iran(CorrespondingAuthor) [email protected]

(Received July 17, 2018 Accepted Feb. 4, 2019)

To cite this article: Shekofteh, M. R., Jalili Ghazizadeh, M. R., 2020, “The optimized implementation of the district metered areas

in the water distribution networks using graph theory” Journal of Water and Wastewater, 31(1), 12-24. Doi: 10.22093/wwj.2019.140550.2718. (In Persian)

Abstract For better utilization of water distribution networks (WDNs), it is recommended that the

existing networks be converted into Distinct Metered Areas (DMAs). Due to the complexity of the old networks, the conversion of these networks into DMA is a costly and sensitive issue. In this paper, a model has been developed to optimize implementation of the old networks into DMA by using the graph theory and water distribution system modeling software (EPANET), while the minimum required standard pressure is met and the number of linked pipes between the proposed areas is minimum. The minimum number of linked pipes will minimize the cost of the needed flowmeters. The developed model has been successfully applied for Poulakis WDN with 30 nodes and 50 pipes in different statuses and for the actual Bushehr WDN with about 3740 nodes and 3980 pipes. The output result shows that the developed model, in a satisfactory way, converts water distribution networks into DMAs with respect to the hydraulic constrainsts.

Keywords: District Metered Area (DMA), Graph Theory, Leakage Management, Water Distribution Network (WDN).

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dx.doi.org/10.22093/wwj.2019.140550.2718 13مقاله پژوهشي

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Fig. 1. Example of edges score for a (a) branched graph, (b) looped graph CZ�&g$�� �&����)a(�� H�� �� ( �) �(��.�b�� (&Y�#0F H���(��.�

����& 6��,a��U )��B@ ����-�3��I� �F���� S������7 &K$Edge Betweenness &�GN8_��@ (� H�� ����@ �� 6����� ,

C,��� =��"$� �!� =2� (m�2�.���- �& =��@�� 6$4� ��@&�J� 6����-�>����� 6O�����7 (3��I� �F����)&K$��I$��J� �, q����}

.2� =��"$� 6&���7&��- K$&=�@�� 6$4� �@&�J� 6��- ��6�&Y) >��� =��r#- �@ (�� (�r(�- q��� ��I$�J� ��- ()*� ��� q���

�& ��� =��"$�� H��� Y����.(Newman and Girvan, 2004,

Csardi and Nepusz, 2006) .���7 ��&K$GN �� (- 2$-& Y&����&$� Y�{��D$ �

=������� T�� .��- )B@��>���� ��0� ���4 S�&����� ����$��- ���2@ (- �$B&H`F ()*� |��2��� ����7 ��0� 2�,� .&K$U����7 =��"$� �- �����B&(- q�� �, ��I$J� K$ ���Z �& �

!� �, ���g$� (*��X��S� �&��()*� �����,� ���g&6$4�&- (� �7���$B&$� 6�()*� C� H`F , ��� � ����� ���g$� �2I� (*��X�� �&��<�- ����=2��.�����\ ���g�,� ��� SF�� ��)@.S)� ��kga�&(�� H�� Y(��.� � .!�� =2�� =�� C��B�

_#4 (� ������&J� Y�- ���� , >��� =�� 6&=�� �($��� ���, ��J� SZ�F (1�.I� �2��-����&)�B@ � !��� Y���� S.2����

1 Girvan–Newman algorithm (GN) 2 Community 3 Breadth-First Search (BFS)

=�� ��$� ���&��- ���� !�� ������ =2 $� (� ��� �� � �&������ ���� (- SD$� &�� Y$� .���� �&���� ��&�2�^@ ��- j����$� ����

��r��& (� !� �&C� (1�.I��&�� �� (- .2��- ����]� ���' �& ��) >��� =�� (- SD$� !�� !.�rS)� �� (kga=��� ���\ ��� �

&(1�.I��, !� .� (-�7� 6�$� S� �&6&��v�� .���&���� 6=�� ���.@ ��- �� ��I� >��� ��� ��� �� , ���&���.@ !$����� �

�� >.� S)�� �,� �21 .2���kga$� ������ � �& Y�&�������� C�B� � H�� .2��

$� ����#0F H�� �� �� ��� � �&��=��� (0�Z�4 , C , ��- ��� ���!� j���$� S)� .kgb&�� C�B� � (��.� ��#0F H�� Y.2���

S)�� �)�B� �21kgb$� , =��� C , ��� ��&��3���< �2�1 , ���.�@�@ =����,2� �- j���$� =�� �� jk�� C�B� � .2�� �,2�k�

=�� (0Z�4 , C , (*��X� =�X� S)�� H��� ���- ��kgbC��B� ��� ^@ SF�� ���\�04 .2����=�� ��- (0Z�4 , C , 6H��� ����

S)� ��o�� =2��B� (- C� SF�� , ��� ���Z&�!�0X@)�S�U (- A�- �&�� ���Z 6��:(��

kg7, C ,�=�� (r�- �-�-kC� (0Z�4 ,(dr)��V� �� �"�Z �- �-�-�� ($4�� (0Z�4 .����^@ ���- ��$����U ��� =��� C , 6$� , ��� �� �

&��H�� ���.!� og=�� ��i�J.� ��&��r�- �-�- �� ,1== ri ww(0Z�4 ,�

�- �-�-1+= ri dd.!�� 2�� ug=�� ��-j�J.� ��&=��� �2�� �� �� ����i&S�F�� ��) &�� �Q$� �:���

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����� � �� �� Journal of Water and Wastewater ����� ���� ����� ����� Vol. 31, No. 1, 2020

�=�� ��- ��� ��j(0Z�4 ��� C� (0�Z�4 �!�� =2�B� 6���^@ � �- �-�-1+= ij dd�- �-�- C� C , ,ij ww =�� .���

�=�� ��- ��j(0Z�4 , 2���- =2�� l&�^@ �1+= ij dd�2���- = 2� (- C� C , =����iw�� �&34 :2-�&ijj www +=.

�=�� ��- ��j(0�Z�4 , 2���- =2�� 6���^@ �1+< ij dd�2���-

�.� ����i@ C� C , .2�� vg(0F�� ��)@u�� �@&� (� ��C , , (0Z�4 C,2- ���� �2��*�.

=�� ���.@ ��- (0Z�4 , C , (*��X� TU $� (*��X� ��- ���� ���& SF�� ��&�� �' ���� kg=�� C��� �QB� )��- ���l.H�� �� (

Fig. 2. The steps for calculating weight and distance for the vertices of a graph CZ�,g�- (0Z�4 , C , (*��X� SF���=�� ���&YH��

set weight and distance for vertex r:

wr = 1, dr = 0START

Set weight and distance for all vertices i adjacent to r:

wi = wr = 1

di = dr + 1

set weight and distance for vertices j adjacent to one of

those vertices i

All nodes analyzed?

vertex j has already been

selected?

END

dj = di + 1

wj = wi

is it "dj = di + 1"?wj = wj wj = wj + wi

Yes

No

No

Yes

Yes No

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18

����� � �� �� Journal of Water and Wastewater ����� ���� ����� ����� Vol. 31, No. 1, 2020

og(-&)��- =�� (- SD$� ��l�J.� , (&) C� ��i$� �(���-�- � �

�-l

i

ww�� =�� {�D$ .���

ug$� (������ �&�� ���&����&��@�,� (� �&=��� ��@ (0�Z�4 6���� /,���� �2����� � >����� 0X@) �����������U S�&A���- (��- 6����I�

�� ���$� (*��X� ��- .(� �&=��� (- SD$� ��i,j(0�Z�4)j(�-r

-�(0Z�4 �$Bi(-r$� /�.I� (!�� �&����&=�� (� �j����� �� (- !*J� , ��$B�&�U ���`� ���&6�- ���� ��< �@k>.�������

�� �SZ�F �� T�� ,j

i

ww�� �c .���

vg(0F��u=�� (- (� ���� �@r��)@ �2��-��.��� $� (�� �� �� ,� � �& S)�� �� �"��- , 3���< ��kgb(���.� ���- ��� (*��X� $� (*��X� ��- .���� �&S)�� �� 3���< ��kgb%�*'

�- �=2� ($"� SF��&���*1 SZ�F 2( )j

i

wwA1 ×+-(=��,� !���

�� .���&�I�iw=��� C ,v,jwC , =���y�,2�� %-����k

!� SZ�F .j

i

ww��- �-�-

31�2�#� .!��A/��.I� ��- ��-�-

$�� �&�� ���&�&6&3��< ��!� =�� (�y.!� ��$B� C� ���� =2��B� (� �����.� ���� �& ��- �7� �&, 6&����, ()*�� �� ���a

�-��- ��2�&�2#� 6A�� �"Z �- �-�- ��� �� .��� �&$� !�� ��&��

�- �-�- 3��<31�� $� (*��X� ��- .��� �� � �& S)�� �� �"��- ��

kgb�iw=�� C ,o,jw=�� C ,v�,2� %-���k.!�

SZ�Fj

i

ww�- �-�-k�2�#� .!��A$� /��.I� ��- ��-�- �� �

&�� ���&�&6&=�� (� !� �"�- ��v��$B� ���� ��!�.

��"1&g�2#� �- (0Z�4 , C ,�=�� ���S)� H��kgbTable 1. The weights and distance for vertices of the

graph in Fig. 1-b Nodes

No.Adjacent

toAlready assigned dj=di+1 Distance Weight

r - - - 0 11 r - - 1+0 12 r - - 1+0 1 3 1 No - 1+1=2 13 2 Yes Yes 2 1+1=24 2 No - 1+1=2 15 3 No - 2+1=3 2 5 4 Yes Yes 3 2+1=36 4 No - 2 1

��� =2���B� (� �����.� ,� ����� �& ��J.� �� 3���< , 3*�� ��&�� &�&6&=�� , 2��� ��< �"�- ��v�-���- .!� ��$B� ���� ��&6

�2��#�A$� /���.I� ���- ���-�-��� ,� ���& 3����< , 3*��� ��&����^

34

31

1 =+��� �� (��� !�����& !$���� ���& ���- ���-�- �"���- ��37

-(!����2&� =��� ����.@ ��- A�- SF�� ��)@ �- . , >���� ����-($� S� /�.I� C��,� !������� � ��� ���.@ (�- �, ���� , 2���

�� ��I� ����\ �@ �,� ��� T�� .����-��-&�2@ (- �� 6&|�&������@A�- �-&$� 6���� H`F ���2��� �� �&!2��\ (�- ()*��&(�^��� 6J#@�K�2�-�2*@ �=2&�� S �� .���& �I�&)�B@ >���� 6��=2�� S

�V� ���� �3I� �F�� C�.�!�.

,/,/�5�� (-�)# C>AQD +�%6 +��8*Q>[ 2��

=��"$� ���� ?,� �0� ���\�04 ��,aU 6& �� S)� ��uC��B� =�� TU �2� ��, ��� �� .!� =2� ��& �@ ()*�� (B#� !4� �& >

�� , �&����7 =��"$�� ��- ��-���� 3I� �F�� �2^@ !4�&K$U�(7�7 �2^@ C��� S<2F ���*� �- �����B - ����F�� �� 6�()*�� �(

J#@ 3I� �F�� (- ���� K �@ .2��&(�- _�#4 ()*� �(0F�� 6C���1&0X@ ����� =��� H�� Y��!�� (�$4�� ���< S,�� �����< ���2��7,�2�< C���� (4�c �- (�� �� .!� =2B� (0�J� ��, �) �� ���2��7,�2�(7�7 �2^@ ���� , �) ��� - _-���- ()*� ��F�� 6�(�� ��@�� .���

���7 %*' 3I� �F��&K$GN (�7�7 S<2F �- ��- _�-� �����6U �F����� ����B - .��� (- (��@ �&�A�.^� ()� ()*�� ������ ����

(- �$�� ���Z ?�$�J� C��� �,��� (�- ,&(�$4� s��"@ ��$.� �2���� - (� 2$4�F�� ,� 6�_#4 (&�- ���< _-� (7�7 Y��������.� , ��

�[*< (� (7�7 �2^@ (- �2� ��� - _-� ����F�� �� 6����-� (�- �( |����� �!� .(-S�7� 6�.� < C���� (4�c �- ��� 2��7,�2��(0��J� (�- �)

�� �^� (7�7 ��� U ����- �����B�C��� �$.� .��� �$.� � �F�� 6(7�7 (- ��&��^� 6!� �, (- (��� (0�(�7�7 +�*@� �� �� ���� ���

(7�7 �2^@ ���� ��- .��� >�< ()*� � �- �'��*@� �������� 6F����(&(- ��2�^@ ���� �@��*1 ��-� |��� U b��' �����=2�� �����B

���7 _��@ �F��&K$GN ��� �- �34EPANET =�� +��*@� 2��(��- ,*��� �()*��� �� ����B4 S<2��F E��"F , ����$�� ����V���(� ��������7,�2�����I� �) 2��� )Eck, 2016(. ����&H`��F ����- ����� 6

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Fig. 3. The steps for definition of DMAs CZ�.g0� SF����^@&lF���3I�

(7�7 �_-� ��� +�*@� & ��) �& (�7�7 6, =2�� >��< ()*�� ��- ���� ���� ��B4 S<2F �� _���@ ()*�� �EPANET ���$�� 2�� ��� .

�1� C��n.� ���`� (7�7 H`F TU ��B4 S<2F&�����- ���� !(7�7 H`F � ���&�� �@ ��&��)@ _-� (7�7 6�� T�U ��� .���

+�*@� C��� >�<& �)&(7�7 6()*�� �� � A ���B4 S<2�F �����1�& (- ���B� !&��.� (�� !� ��^� 6 C��@ �& ()*�� � (�7�7 6

�� (- ()*� +�#� ��^- ��B4 , ��� H`F& ���*1 C�&(�7�7 6�-��- .��� ��$J-& +�*@� �2I� 6&=2�� S�Z, ()*�� ��- (7�7 6,� H`F C�)�&(7�7 �� ����- _-� �������� .&%-���� SF�� 6

S)�u�� �@&(�� _-� (7�7 6.!4�&

./+��)� F��\� ��- ����� (�-�����7 ��&U K$� �� �������B �& (�^7��� ,� ��Q- 6

(^7��� .2� ����- ����� �A�U ()*� �,�7��� ���� ,T�(^�,�

�@ ()*�&����- ��� � >.��-

./&/]>G^)[ A?�)Poulakis et al., 2003(

()*� �A�U H,�^��(�� T���ut�=���yt, (�7�7 �& C3�Q� Y!� S)� ��v!� =2� =�� C�B�.��' (7�7 ��� �#4 ,���.1

(- j�@�@ kttt ,ottt �$�.!� �A�U ()*��!7�F �� T b�� (- l0$Q� ���&0X@ ���� ���S

��<!4�� l7gJ#@�F�� (� (- ()*� K�3I� (

� ���� ��B4 S<2F !7�F ,� �� (0�J����- ��-�- ()*�� �kv,oy(�$4�� ��V� �� � C�$� �$� ��- �'��*@� (�7�7 !�B� .2�� r���

���7&K$GN S)� %-���y- ����< 3I� �F�� 6!4�� (���@ �- .�� (-&� _�7,�2��$� , �)&��B4 !7�F �� �2� |kv�� ��$� C��@

S)� %-���yga!�[1 (7�7 �� ���- , ���� >��< � =2�� ��`��

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20

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�1�&�-� ��� (7�7 ,� ���, ���B4 S<2F !- |���3�I� �F�� 6�4��!� ���B4 !�7�F �� ��� .oyS)�� %-���� ��$�ygb_�#4 ��� �- (�7�7 (� , ��� H`F � ()*� (7�7 |�U C�@�3�I� �F��� 6

@ ��-f��� ���� ���B4 6� �!�(- .(�7�7 +�*@� �� �@��*1 (4��c !7�F �� =2�b�< �=�� ��^- ��B4 ��� > ��$.� (- ��oy��$�

�� .2��

g ��&� ���� ��B4 S<2F �Q- 6���- ��-�- , !�-�e ()*� �� �kv (�$4�� ��V� �� �$� F�� ,� (�- ()*�� �, !�7�F �� .2�� �� �� , (

F�� ���\ (- �,� !7�F�2�*@ 3I� (&S)�� .2�� S�ga�� � ()*�� �F�� ,� !7�F��� C�B� 3I� (�2�.U _-� (7�7 |�U �%�*' �����B

�7���&K$GN -�� ,� 6�F��!�[1 (7�7 ���\ �( ()*� =2� ��`�

Fig. 4. Poulakis water distribution network CZ�Sg �@ ()*�&>�A�U ��T

Fig. 5. Establish 3 DMAs in poulakis WDN with minimum pressure head equals: (a) 14m, (b) 25 m CZ�_g2*@&S�A�U ()*��TF�� (� (-�() :��B4 S<2F �- 3I�a(kv) ��$�b(oy�$�

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Fig. 6. Establish poulakis WDN with minimum pressure head 14 m into: (a) 2 DMAs, (b) 4 DMAs CZ�`g2*@&S�A�U ()*��T!-�e ��B4 S<2F �-kv) :(- �$�aF�� ,� (�() � 3I�bF�� ���\ (�(3I�

�� � _#4 , ��� >�< C�@&�- _�-� (7�7 Y��4��� 3�I� �F��� 6!� S)� .�gbF�� ���\ !7�F �� � ()*� ����� C�B� 3I� (2���

(�&- _-� (7�7 =� ��F�� ���\ 6�����7 %*' =2� �QB� (&K$GN �� ��< ���$� .��&� |�7,�2�C�B� �2� �) �� ()*�� (7�7 �� (��� � �-� ��� �- (7�7 |�U , ��� >�< C�@ - |����F��� 63�I��� ��< ��.��(-� ���*1&�� ��&(7�7 |�U �) �- _�-���F��� 6)B@�S)�� �� =2� S�gb �� ����� H`�F �& (�- (���@ ��- ���]� 6&=�� ��B4 �+�#� /�"@� C��- C�J)uk�@�,� (�&C3Q� �@ (0Z�4 6

�$.� (- ���� �kv���� � C�$� �$���.2-�&

./,/%8�)6 %8� �� A?�

����- ���3��� ���� �� �����- C�$�� �&C� .!�� �$.�J< �@ ()*� (B#�& � >&S)� �� ��� 6z .!� =2� =�� C�B� �& 6

�,2F ��� ()*�uzvt , =��u~xt (7�7 !�� _���$� H��D� .- ��- �, C�� ���=�� �$B ��ux/t7���e �- �$ �� (,���B4 S<2�F

�- �-�- ()*� �� �I�kv$�2� ($4�� �V� �� �!� =.!7�F ��I� TU F�� l0$Q� ����(��� �� ��2�-& !&()*� 6

�- ���7 r��&K$GN (- �ktF���S)� %*' 3I� (x�J#@�.2�� K�,2�o=�� �2^@ �F�� �� �� ()*� ������ C�B� � 3I� (.2�� 7� (-�U S�n� ��2&()*� 6�(�7�7 �2^@ /�.I� �- _�-� �����6

����7 _���@ 3I� �F��&K$GN �uu�2�1 !�� (4��c T�U .

< C2�� ��� ���2 ��7,�2���$� ��2�� (�- �)&C��B� ���,� |�� (����� +�*@� C�@kvS)�� %-��� � ()*� _-� (7�7~���� >��< �

C,2-&����*1 (�- .���� �$.� �I� S<2F ()*� +�#� ��B4 ()��&2*@ ��- ��& �@ ()*� S&� � >(- ����- ��ktF���3I� (�(�-

S<2Fk~- �'�*@� (7�7�� �F�� 6� �!�.2*@ TU&(�- 3�I� �F��� (- ()*� S ��2�^@ 6$�J- !�01

(7�7 �� !1�� ,���� ()*� +�#� ��^- ��B4 ���&���^- �� C�(7�7 34 ��&�&�!4(- .2�*@ TU ��]� C��1& S�&(�- ()*�� 6kt F���(- �3I���$B&�2�#� (- ()*� ��B4 6kk2�Z�� ,����� -��$B&(�7�7 �� !1�� 6�2�#� (�- ()*�� ����ot2�Z�� 3�4&�

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Fig. 7. Simulated model of Bushehr WDN CZ�ag*� �2� , C[U�( �������- � ()*�

Fig. 8. Recommended DMAs for Bushehr WDN CZ�bgF���3I��U�����B �- =2������- ��� � ()*�

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Fig. 9. The status of the closed pipes and the pipes with suggested flowmeter for Bushehr WDN

CZ�cg^c,�!(7�7 ���(7�7 , ($J- ������U |����B4�����B��2� _��@

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DMAs NO. 1 2 3 4 5 6 7 8 9 10 No. of nodes in

each DMA 498 428 565 367 363 287 299 328 269 337

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