possibilities of losses reduction in medium voltage...

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POSSIBILITIES OF LOSSES REDUCTION IN MEDIUM VOLTAGE DISTRIBUTION NETWORKS BY OPTIMAL NETWORK CONFIGURATION

Aleksander Kot / AGH University of Science and Technology in Kraków Jerzy Kulczycki / AGH University of Science and Technology in Kraków

Waldemar Szpyra / AGH University of Science and Technology in Kraków

1. COMPLEXITY OF NETWORK AND CONSUMER STRUCTUREElectrical power distribution networks play a very important role in electrical power system – they distrib-

ute energy and supply it to end users. Due to their function, they are characterized by extreme complexity, and they cover, practically speaking, the area of the whole country. These networks include 110 kV networks, enabling delivery of energy from UHV/110 kV stations and its initial distribution, and MV networks and LV networks, which are mainly responsible for distribution of energy to a great number of consumers. Table 1 presents, based on [1], the length of distribution network, by individual voltage levels. Apart from the figures given, LV connectionsof the total length of ca 145 000 km, not included in LV network here, should also be taken into consideration.

Tab. 1. Length of electrical power lines according to the data for 2007 [1]

Voltage level Length [km]

110 kV network 32 600

Medium voltage network 299 700

Low voltage network 417 000

Table 2 shows the number of electrical energy consumers in Poland by individual voltage levels and the volume of energy supplied to these consumers. The big disproportion of the number of small and big consumers, with their total number of over 16 million, is worth noting.

Tab. 2. Number of consumers and volume of energy by supply voltage level according to the data for 2007 [1]

Voltage levelNumber of consumers Energy

[number] [%] [GWh] [%]consumers at HV 287 0,0 27 064 23consumers at MV 28 988 0.2 39 881 34consumers at LV 16 005 000 99, 8 50 705 43TOTAL 16 034 275 100,0 117 650 100

Fig. 1 and 2 show, respectively: share of consumers at individual voltage levels in total number of energy consumers and distribution of the supplied energy among consumers connected at various voltages.

Possibilities of Losses Reduction in Medium Voltage Distribution Networks by Optimal Network Configuration

Abstract

The article presents an analysis of the possibilities of reducing power and energy losses in MV distribution networks by the use of the most popular non-investment method, that is optimal network configuration, also calledoptimization of partition points.

The article begins with a characteristic of distribu-tion networks, structure of electrical energy consumers and a classification of losses in distribution networks. Loss-es in real, wide-area MV voltage networks were analyzed.

The problem of partition points optimization in a network was presented. The methods of partition points optimiza-tion and some Polish tools for making such calculations were reviewed. The results of performance of the tools on an example of a real wide-area network were compared. The article ends with some remarks on practical aspects of calculating partition points in big networks, with spe-cial emphasis on various constraints in location of partition points.

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The drawings indicate that the proportions of the energy consumed by individual groups of consumers are totally different than their quantitative distribution, that is a very small number of huge and big consumers of 110 kV voltage and MV consumes considerable volume of energy compared to the energy consumed by a great number of low voltage consumers.

2. LOSSES ALLOCATION IN DISTRIBUTION SYSTEMEnergy flow through electrical power grids is always accompanied by losses. They are connected with

current flow through its individual elements. Table 3 presents distribution of the total of technical losses in dis-tribution network by their individual types and elements of the network based on [2.] The data provides some information on areas of losses allocation in the distribution system.

Tab. 3. Average technical losses in elements of distribution networks in [%] of their share in total technical losses [2]

No Type of lossesShare in total losses

[%] 1. Load losses in 110 kV network 362. Load losses in MV network 223. Load losses in LV network 164. No-load losses in MV/LV transformers 95. Load losses in MV/LV transformers 56. No-load losses in transformers 110/LV 4

Total 1÷6 927. LV meters 2.88. Load losses in 110/MV transformers 1.69. LV wiring system 1.310. Leakage conductance losses in MV network 0.911. Leakage conductance losses in 110 kV network 0.612. In 110 kV capacitors 0.513. No-load losses in MV/MV transformers 0.314. In MV capacitors 0.115. IN LV capacitors <0.116. Load losses in MV/MV transformers <0.1

17. Leakage conductance losses in LV network <0.1

Total 7÷17 8TOTAL 1÷17 100.0

The first 6 items of the table cover 92% of technical losses of energy, whereas the remaining 11 items re-fer to 8% of the losses. The first three items show load losses in 110 kV, MV and LV networks. Such an order canbe explained by the volume of energy flowing through networks of individual voltage levels. Transformation tolower voltage level refers to smaller and smaller volume of energy, due to the existing demand of consumers of the given voltage level (Tab. 2 and Fig. 2).

Fig. 1. Share of consumers at individual voltage levels in total number of electric energy consumers

Fig. 2. Energy supplied to end consumers at individual voltage levels

Consumers at HV Consumers at MV Consumers at LV Consumers at HV Consumers at MV Consumers at LV

Aleksander Kot; Jerzy Kulczycki / AGH University of Science and Technology in Kraków Waldemar L. Szpyra / AGH University of Science and Technology in Kraków

0.0% 0.2%

99.8%

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3. POWER LOSSES IN MV WIDE-AREA NETWORKSSome results of the analyses made on big MV distribution networks are presented below. The networks

of eight electrical power regions, located in southern part of Poland, were investigated. Table 4 presents pa-rameters of the networks, their peak load and load power losses in MV lines. The losses were calculated by the use of software for calculation of power flow, by the use of detailed network models and estimation of loads ofindividual MV/LV transformer stations.

Regions A – D have networks working at 20 kV, which is less popular in Poland. Power losses at peak load in the analyzed networks are at the level of below 1%. More detailed analysis of the networks of the regions A – D is presented in the further part of the article, devoted to practical aspects of optimization of partition points in wide-area networks.

Tab. 4. List of parameters of MV wide-area networks and power losses occurring at peak load

Region’s nameNominal voltage of the network

Number of MFPNumber of

MV/LV stationsTotal length of MV network

Load at peak Power losses Relative losses

[kV] [pieces] [pieces] [km] [MW] [kW] [%]

Region A 20 6 889 969 64.69 578.6 0.89

Region B 20 7 542 520 55. 41 239.8 0. 43

Region C 20 7 991 1048 60.19 349. 4 0.58

Region D 20 7 1157 1277 61.04 497.7 0.82

Region E 15 5 582 511 44.98 948.3 2.11

Region F 15 7 1124 1079 72.79 1182.6 1.62

Region G 15 5 885 862 62.37 1046 1.68

Region H 15 6 1028 938 45.34 902 1.99

Regions E – H operate at the most typical in Poland nominal voltage of MV, that is 15 kV. Their power losses level, presented in Table 5, is from ca 1.6% do 2.1%. The quoted loss ratio does not provide information on the losses in individual circuits of the network.

The analysis whose results are presented in Fig. 3–5 was made to illustrate losses distribution and their dif-ferences in individual circuits. The networks of the regions E – H include 202 circuits of very different parameters, that is: total length, wire cross section, number of stations fed and peak load. They include short cable lines of ur-ban networks, feeding a few MV/LV transformer stations, as well as wide-area circuits of rural network of the length of a few tens of kilometres, feeding a very big number of stations. The following diagrams present:

• Fig. 3 – relative power losses in the lines, depending on their peak load• Fig. 4 – relative power losses in the lines, depending on their total length• Fig. 5 – relative power losses in the lines, depending on the number of MV/LV stations fed.

The presented diagrams provide information on losses distribution and their considerable differences in individual circuits of the network.

Fig. 3. Relative power losses in 202 MV circuits (Regions E – H) as a function of their peak load

Fig. 4. Relative power losses in 202 MV circuits (Regions E – H) as a function of their total length

Rela

tive

loss

es [

%]

Loads [kW]

Rela

tive

loss

es [

%]

Total length [km]


46

4. OPTIMIZATION OF PARTITION POINTS – A PRESENTATION OF THE PROBLEMOptimization of partition points is one of the basic activities of non-investment character, leading to re-

ducing losses in a distribution network. MV distribution networks are built as closed structures, but they operate in open configuration. Points of division which unambiguously determine to which circuits individual MV/LV sta-tions belong are called partition points.

The task of optimization of partition points consists in selecting network division points in such a way as to obtain a system characterized by the least total load losses. Solving such a problem for a real network, e.g. for one distribution region, comes down to solving the problem of minimization of a function of many variables, most often with constraints. It usually requires application of relevant tools and algorithms due to the size of the problem (number of variables) and the structure of the system (considerable number of mutual circuit con-nections).

As mentioned above,in rural wide-area MV network, consisting of from a few tens to a few hundreds of nodes (stations), finding optimal – in terms of minimum power losses – partition points is not easy.

Fig. 6 presents an example of power losses in a double-feed distribution line, depending on the partition point. Power losses are the smallest for the partition near the point of the lowest voltage.

Fig. 5. Relative power losses in 202 MV circuits MV (Regions E – H) as a function of the number of MV/LV stations fed

Number of stations [pieces]

Rela

tive

loss

es [

%]

Fig. 6. Power losses in a double-feed distribution line, depending on the partition point of the line

Obtaining the effect in the form of reducing losses by changing partition points requires specified techni-cal and organizational activities, which involves relevant costs.

If a change of the line partition requires purchase and installing of new switches, the costs can be calcu-lated the following:

Pow

er lo

sses

[kW

]

Number of partition points


9.8

8.0

5.7

4.03.3 2.8 2.7 2.9

3.7

4.75. 4

6.7

9.3

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(1)

where: Kro – total cost of purchase and installing of switches; Ko – investment cost of one switch; Kmi – cost of installing a single i-th switch; no – number of installed switches.

The cost of installing a single switch takes into consideration the costs of labour and the costs of transport:

(2)

where: kg – cost of one work hour of an employee; tBR – employee work time devoted to installing a single switch; lBR – number of employees; kkm – cost of one kilometre of transport; lkm – length of transport route.

If changes of partition points are made in a network equipped with switches in each point in which it is possible to partition the line, then the costs come down to the costs connected with switchings in the network:

(3)

where: Krp – total cost of switchings; np – number of switchings made.

Switchings will result in reduction of power losses by ∆∆P and of energy by ∆∆E. Profit Zp, resulting from reduction of power and energy losses, is calculated from the following:

(4)

where: ∆Pst, ∆Est – energy and power losses in the analyzed network before switchings; ∆Pno, ∆Eno – energy and power losses in the analyzed network after switchings; ∆∆P – reduction of power losses; τ – utilization pe-riod of maximum power losses; SS – fixed component of network charge (cost of power); k∆E – unit cost of energy in the network (price of energy + variable component of network charge).

Effectiveness of the activities taken up can be assessed by calculating simple payback period (SPP) of the layouts made:

(5)

where: K – cost of purchase and installing of (Kro) or switchings (Krp).

Example 1The problem of partition points is considered in a model MV loop of electrical power network, feeding 120

transformer stations in 10 network loops of the following parameters of a single loop (line):• the sum of power of transformer stations installed in one line Stc = 5 800 kVA• maximum current flowing to loop: Imax = 120 A• energy introduced into network E = 28 059 kWh• length of a single line lt = 2 600 m• cross section of cable core: s = 120 mm2 AL.The calculations were made for the following additional data:• unit cost of energy losses (together with the variable component of network charge) k∆E = 0,20 PLN/kWh• unit cost of power losses (fixed component of network charge) k∆P = 80 PLN/kW/year

Kmi = kg tBR lBR + kkm lkm


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• number of employees lBR = 2 persons• cost of one work hour of one employee kg = 37 PLN/h • employee work time tBR = 4 h• length of transport route lkm = 10 km• unit cost of transport kkm = 3,0 PLN/km• number of switchings np = 8• utilization period of maximum power losses τ = 2 100 [h/a].It was additionally assumed that the transformer stations’ load is proportional to nominal power of the

transformers and that the loop network has switches that enable making partitions in each section.

In a loop network partition points can be located in various sections of the line It was assumed for the calculations that all loops are identical, but the partition points are located in different places. Table 5 presents the results of calculations of power losses in individual loops for a certain system of partition points, whose specification is given in second line. Minimal losses that can be reached in the analyzed set of loops due tochange of location of all partition points to optimal location are also given.

Tab. 5. Power losses in loops

Loop number 1 2 3 4 5 6 7 8 9 10

Partition point number (according to Fig. 6) 8 3 5 9 7 4 2 7 8 1

Power losses in loops (according to Fig. 6) [kW] 2.9 5.7 3.3 3.7 2.7 4.0 8.0 2.7 2.9 9.8

Total losses total in loops – existing state [kW] 45.7

Minimal losses in loops (according to Fig. 6) [kW] 27.0

Reduction of power losses ∆∆P [kW] 18.7

If there are no technical constraints, then change of eight partition points in the analyzed network can result in losses reduction by ∆∆P = 18.7 kW.

Simple payback period (SPP) (Formula 5) of costs of partition points dislocation in the network were calculated for the data adopted:

• cost of switching in the network:

Krp = np × (kg ×tR × lRB + kkm× lkm) = 8 × (37 × 2 × 4 + 10 × 3) = 2 608 PLN

• profit resulting from reduction of power and energy losses:

Zp = ∆∆P × (SS + k∆E × τ) = 18.7 × (80 + 0.2 × 2 100) = 9 350 PLN

• simple payback period:

SPP = Krp/Zp = 2 608/9 350 = 0.28 years (3 months and 11 days).

Average value of losses reduction per one switch-over is obtained by dividing the volume of losses reduc-tion by the number of switchings needed to achieve it: δ∆P = ∆∆P/np. Fig. 7 presents dependence of simple payback period of costs on power losses reduction due to making one switch-over in the network, calculated for various values of utilization period of maximum power losses.

Payback of layouts connected with change of partition points in the analyzed example depends on the utilization period of maximum power losses and unit power losses reduction per one partition point δ∆P.

It follows from Fig. 7 that for the networks technically prepared for making partition points in any trans-former station and for the value of losses reduction per one partition point δ∆P ≥ 1 kW/partition point, the costs connected with change network partition are returned after ca 1 year.


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Fig. 7. Simple payback period of switching costs in the network, depending on average value of losses reduction ΔΔP, per one partition point for various utilization periods of maximum power losses

For loop networks or spindle type of networks and for the networks that can be reduced to such struc-tures, calculations of power and energy losses can be made by the use of a spreadsheet – it is not necessary to use specialized software. A spreadsheet enables calculation of losses for the existing work configuration andselection of configuration of partition points matching minimum losses.

5. REVIEW OF METHODS AND TOOLS FOR OPTIMIZATION OF PARTITION POINTSMany methods for reduction of energy and power losses by proper selection of partition points have been

developed. Heuristic methods, which enable analyzing networks of a big number of nodes have been applied in practice. SIEĆ, DRZEWO and STROP software can be examples of such solutions.

The formula 3I2R is used in the methods of SIEĆ, DRZEWO, STROP software to calculate power losses. Each of the methods makes use, in various forms, of the following data:

• the analyzed network data• information on network connections system• number of network sections• length of individual sections of overhead and cable lines• cross sections of cables and overhead wires

• network nodes data• number of nodes• loads of peak active and reactive power of each of the nodes• utilization period of maximum power losses or load curve (step curve) to calculate energy losses

• catalogue data (enabling selection of network elements parameters)• catalogues of overhead lines• catalogues of cable lines• catalogues of transformers.

SIEĆ softwareThe problem of optimal division of MV distribution network in SIEĆ software is solved in two stages [3], [4]:

Stage IInitial solution is obtained in the first stage. In the nodes there is only active power for peak load, and

the network branches are mapped only with resistances. The same voltages in feed points are assumed. At this

Sim

ple

payb

ack

perio

d [y

ears]

Profit on power losses per one partition point [kW]


50

stage, partition points are determined based on the results obtained from multiple (iterative) calculations of active power flows according to simplified Newton’s method. Total power losses are the minimized objectivefunction.

Stage IIAdjustment of network partition obtained in stage I is made. In this calculation model, branches are mapped

with longitudinal and transverse conductivities. Distribution of node loads (active and reactive load) is mapped by the use of step curve. Radial configuration in the first step is the starting point in second stage. Multiple iterativecalculations of power flows in the network enable gradual modification of the initial configuration, till optimal con-figuration is obtained. The sum of energy losses is the minimized objective function in the second stage.

SIEĆ software system consists of BAZA software and ROZA and REGA subsystems. BAZA software is used to create sets of data. ROZA subsystem is used to process primary data, to calculate power flows and shortcircuit power and to determine optimal partition points in the network, taking into consideration optimal assign-ment of lines to buses in two-system stations. Using the sets of node and branch data for individual MFP, REGA subsystem determines parameters of voltage regulators of transformers in MFP and location of tap changers of MV/MV and MV/LV transformers. Diagrams of radial network, together with calculations results (of flows, shortcircuits and optimization of voltage levels) can also be developed by the use of REGA subsystem.

SIEĆ software enables making calculations for a network of practically any number of nodes and branches. The sets of node and branch data can contain any number of elements (e.g. network modelling by 10 000 nodes requires ca 4 MB of RAM).

Further information on SIEĆ software can be found in literature [3], [4].

STROP softwareSTROP software [5] optimizes configuration of partition points according to adjusted Rosenbrock algo-

rithm [6]. Optimal location of partition points in the network is specified with the view of minimum losses ofactive power. Branches are reduced to concentrated loads, connected in proper nodes of the mains and are not subject to the process of optimization of partition points.

Rosenbrock’s method [6] belongs to the group of non-gradient methods of simple search. In this method, ob-jective function is examined (minimum of power losses) only in one or two points in the direction of the search (meet-ing the technical requirements). The way of selecting the points is determined at the beginning of each iteration.

The essence of modifications of Rosenbrock method in STROP software comes down to controlling thelength and the sense of the step (understood as a vector) and to imposing on the objective function a penalty for a solution outside the search direction. Each iteration in Rosenbrock method consists in making trial steps in all possible search directions. If reduction of the value of objective functions is obtained (power losses reduction) as a result of making a trial step, then the step length in increased. Otherwise, the step length is shortened and its sense is changed.

In terms of calculations related to MV network according to [5], STROP software does the following: • calculation of power losses in the analyzed network• location of the capacitor unit of the given power in the line, with regard to minimum power losses• optimization of power of capacitor unit and its location in the line, with regard to minimum power losses• analysis of feed voltages in feed points of MV network• calculation of voltage levels and drops and determining regulation zones of MV, LV transformers in

normal work conditions• short circuit calculations in normal work conditions of the network• calculations of voltage levels and drops in reserve state • short circuit calculations in reserve state of the network• optimization of partition points in the network (minimum active power losses)• determining feed variants in the case of a failure in the line (if there is technical capacity for such feed).In STROP software, the maximum size of the network, understood as a single set for calculations, can

include: 90 main feed points – MFP (power supply units), 1 000 lines, 5 000 nodes, 5 000 line (in the mains of the network, not more than 3 500 line sections).

Further information on STROP software can be found in [5].


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r < exp(–δΔP / T )

DRZEWO softwareThe method of Simulated Annealing – SA [7], [8], [9] was used for optimization of partition points in

DRZEWO software. Power losses in the network were adopted as the economic criterion of selecting the optimal variant.

Let us assume that the initial solution (e.g. operation configuration applied by the services of the givenregion) of ∆P1 power losses (Fig. 8) is known. The solution can be enhanced if e.g. gradient algorithm is used:

• in each iteration, there is a randomly selected solution (network configuration) in the environment ofthe current solution

• only the solutions of the losses lesser than in the previous solution are accepted.The possibility of getting stuck in the local optimum is the disadvantage of such an algorithm. For the

example from Fig. 8, starting from the point (of the network configuration) of ∆P1 losses, using the gradient method, calculations will end in the local optimum (network configuration of the losses of ∆Pmin²).

Fig. 8. Set of possible network configurations of various power losses

In the algorithm of “stimulated annealing” it is possible to accept solutions of higher losses than the ones obtained so far. Proceeding according to SA algorithm comes down to the following rules:

• change of ∆∆P losses as a difference of the current solution and last accepted one is calculated in each iteration step

• if losses are reduced (∆∆P < 0), then the solution is accepted• increase of losses (∆∆P > 0) does not result in direct rejection of the calculated network configura-

tion; it can be accepted if the following condition is satisfied:

(6)

where: T – denotes a parameter simulating the temperature expressed in loss units; r – random number of uniform distribution from the interval (0;1).

A calculation algorithm constructed in such a way enables accepting a solution of ∆P3 losses (Fig. 8), de-spite ∆P3 > ∆P1. It is possible to obtain a solution of ∆Pmin4 of power losses, which for the presented set of solu-tions is a global minimum. If parameter T, which in real physical systems represents temperature, is decreas-ing, starting from the adopted maximum value and according to a specified rule, then the described process isanalogous to do annealing (cooling, tempering) of metals in crystallization process [8].

In DRZEWO software, switching off the line feeding a randomly selected network node is the element changing the network configuration, the result being – a fragment of an isolated network. Then the disconnectednode is fed from all live nodes. Objective function is calculated for each new configuration (with changed loca-tions of partition points). If the new configuration has smaller losses, it is accepted, otherwise a solution accord-ing to the modified rule is adopted for further considerations (6).

DRZEWO software is designed for optimization of development of MV distribution network of a tree struc-ture. Calculation of optimal partition points in the network is an extra option. The software enables calculations for distribution networks of tree structure of practically any number of nodes and branches.

A commercial version of the software has not been developed.

Power losses∆P

configurations


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6. COMPARATIVE CALCULATIONS OF OPTIMIZATION OF PARTITION POINTS IN REAL NETWORK BY THE USE OF VARIOUS TOOLS

Example 2A real network of one of electrical power supply regions was chosen for optimization of partition points in

MV distribution network. It is a network located in mixed rural and urban area, in which most circuits have an option of double-feed.

Number of receiving nodes in the network is 970, and the number distribution nodes – 648. The network consists of 1 793 sections, of which 73% are overhead sections, and 27% - cable sections.

Power and energy losses in the network configuration before and after optimization of partition points aswells as and profit due to power and energy losses reduction were calculated. The calculations were made forthe following data:

• operating voltage of the network Ur = 15,75 [kV]• utilization period of maximum power losses τ = 3 106 [h/a]• unit costs of power losses Ss = 36.36 [PLN/kW/a]• unit costs of energy losses k∆E = 0.25 [PLN/kWh/a].The calculation results are presented in Table 6.Effectiveness of change of partition points in the network was calculated based on the results obtained.

The costs of installing switches (adopted cost of a switch ko = 4 000 PLN, other data for the calculations, as in example 1) and simple payback period costs were calculated form (1)÷(5). The calculations are given in Tab. 7.

Tab. 6. Comparison of results of calculations of annual energy and power losses for the network of the region

Software name

Power losses [kW] Energy losses [MWh]

Profit [thousand PLN]before

optimizationafter

optimizationdifference

before optimization

after optimization

difference

DRZEWO 571.1 504.1 67.0 1773.8 1565.7 208.1 54. 44

SIEĆ 612.1 515.6 96.5 1901.2 1601. 4 299.8 78.64

STROP 582.1 461.1 121.0 1808.0 1432.2 375.8 98.14

Tab. 7. Simple payback period costs of installing disconnecting switches in the network

Software

Number of partition points in the net-work as it is now

[pieces]

Number of proposed changes of network parti-

tion points location [pieces]

Number of new switches[pieces]

Investment cost of switches

[thousand PLN]

Simple payback period of costs

[years]

DRZEWO 99 62 62 248 4.7

SIEĆ 99 77 77 308 4.1

STROP 99 71 71 284 3.0

The literature provides descriptions of other methods of optimization of partition points: cycles and penal-ties [10] and based on evolution algorithms [11]. Paper [11] presents a comparison of results of the calcula-tions made by the use of cycles and penalties method and an evolution algorithm for examples of electric power networks consisting of a small number of nodes and lines.

Based on the analyses made, one can formulate the following general conclusions:1. Calculation of optimal partition points with regard to minimum energy and power losses in big net-

works of multi-meshed structure requires application of specialist software.2. Each of the software - DRZEWO, SIEĆ, STROP can be used for optimization of partition points with

regard to minimum power losses in big MV distribution networks.


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3. The results of calculations of power losses generated by the software differ. The differences are due to:• application of different methods of looking for optimal partition points in the network• way of calculating loads in individual transformer stations.

4. In the networks of regular structure (spindle, loop) and the networks that can be reduced to such structures, optimization of partition points with regard to minimum power losses can be made by the use of a spreadsheet.

7. PRACTICAL ASPECTS OF OPTIMIZATION CALCULATIONS IN WIDE-AREA NETWORKSThe results of the calculations and the experience gained during optimization of partition points in me-

dium voltage networks in a few distribution regions are presented below.STROP software, developed in Częstochowa University of Technology, was used to calculate optimization

of partition points [5]. The software enables, inter alia, making calculations of power flow in electrical powerdistribution networks, optimization of partition points location, and voltage calculations.

Developing a proper model of the considered electrical power network is the basis for losses analysis and their optimization. It was achieved in a few stages mentioned below:

• development of a precise model of the network structure – the model consists of all the existing sections of medium voltage lines, with specification of the ways of their mutual connection and the parameters ofa substitute diagram (resistance, reactance, susceptance); the model has also the information on all parti-tion points of the network in the existing configuration

• estimation of loads on MV/LV transformer stations – determining the active and reactive load demanded by individual transformer stations at peak load, based on available measurement information coming mainly from MV lines in MFP and the information on the load levels in the stations

• equipping the structure model with node loads – assigning the loads of individual transformer stations to proper nodes in network model.Such a model of an object is a starting point for making calculations of the configuration of the network in

the existing configuration, and then for optimization of location of partition points.The calculations were made for four medium voltage distribution networks. Each of the networks covered

the area of one distribution region.Table 8 presents the data characterizing individual networks.

Tab. 8. Parameters characterizing the analyzed distribution networks

Region’s nameNominal voltage of the

networkNumber of MFP

Number of MV/LV sta-

tions

Total length of MV network

Average cross section of the

network

Number of partition points

[kV] [pieces] [pieces] [km] [mm2] [pieces]

Region A 20 6 889 969 80 101

Region B 20 7 542 520 93 58

Region C 20 7 991 1 048 72 135

Region D 20 7 1 157 1 277 69 107

The table presents parameters characteristic for the network, that is: nominal voltage, number of feed 110kV/MV stations, number of MV/LV stations, total length of MV network, average network cross section and the number of partition points.

The calculations of load flows and power losses in the existing configuration were made based on the net-work models and mapping of loads of all MV/LV stations. The results of those calculations are presented in Table 9, with values of power losses in kW and value of relative losses with reference to demand power.

Analyzing the volume of power losses appearing in the medium voltage networks of the considered elec-trical power regions, one can say that already in the existing configuration they are at a very low level. It meansthat relative losses ratio referred to demanded power, is between 0. 43% and 0.89%. Such a low value of losses results from a number of factors, which include:


54

• high value of nominal voltage of distribution networks• high cross section of the network, whose measure is the mean value of the line cross section given of in

Table 9 • favourable structure of the network, namely small number of circuits of big lengths• low load in comparison to transmission capacity.

Then the optimization calculations connected with change of the configuration of the network, the socalled global optimization, were made. Global optimization means determining configuration of the network ofminimal power losses, which is subject to any constraints connected with location of partition points. It means that each partition point can freely change its location, and its target location can be in any selected section of the network. But one must note, however, that such a solution of the network configuration is possible onlytheoretically. In practice, there are many factors constraining both the possibility of moving some partition points and constraining the potential new locations. These issues are discussed in more detail in the item on constraints of location of partition points.

Calculations of global optimization enable specifying potential, maximum possibilities of reducing losses that can be achieved by network reconfiguration. It means that the calculations set upper effectiveness limitsof such activities.

The results of the calculations of power losses in the optimally configured networks (without any con-straints) for individual distribution regions are presented in Table 9. The values of losses in kW and percentage level of losses after global optimization in comparison with losses in the existing configuration.

Table 9. Results of calculations of power losses in the existing configuration and after global optimization

Region’s namePeak load with active power

Power losses in exiting configuration

Power losses after global optimiza-tion

Level of losses with refer-ence to existing configura-

tion[MW] [kW] [%]* [kW] [%]**

Region A 64.69 578.6 0.89 310 54

Region B 55. 41 239.8 0. 43 199.9 83

Region C 60.19 349. 4 0.58 282.5 81

Region D 61.04 497.7 0.82 380. 4 76

* the ratio was calculated with reference to peak load active power** the ratio was calculated, referring losses in optimized configuration without constraints to power losses in the existing configuration

The percentage ratio given in the last column of Table 9 is the lowest for region A - 54%. It means that in this region reconfiguration can bring, potentially, the biggest effect. In the other areas (the ratio from 76% to83%), the existing configurations of the network are much closer to global optimum.

But the real possibilities of losses reduction due to reconfigurations will result from the detailed analysisof the exiting constraints of division point locations.

An analysis of the configurations in real conditions in which wide-area distribution networks operate andof the conditions determining the work configurations of networks indicates that in practice there are many fac-tors that make the locating of partition points of the network in any place impossible.

Constraints of partition point locations can be divided into two basic groups:• determining – constraints due to the necessity of having partition points in strictly defined locations of the

network – some partition points of the network have pre-defined locations and cannot be moved• limiting – constraints connected with lack of possibilities of locating divisions in any section of the network

– they limit the possibilities of changes of location for the partition points for which the location can be changed.The existence of determining constraints is caused by the factors of legal or technical character, which

include:• binding electrical energy supply and sales contracts with the consumers that have their own transformer

stations, paying for two power supplies• saving proper configuration of feeding substations• proper operation of automatic transfer switch in MV and LV network • different ways of operation of star points of 110kV/LV transformers


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• borders of operation of the areas of the network and points of settlement measurement of electrical en-ergy

• other issues connected with e.g. separating systems to provide for proper cooperation of sources with MV distribution network.The existence of limiting constraints is due to the factors of technical and operational character, which

include:• lack of switches in some sections of the network • rated current of existing switches• difficult access to a given point of the network• no access to stations at each time of the day and night• other issues, e.g. organizational, connected with ownership structure of elements of distribution net-

work.The presence of determining constraints means that some locations of partition points cannot be changed.

It results in decrease of the number of variables in the task of optimization of the given distribution network.And the presence of limiting constraints means that not all the indications for moving partition points,

obtained as a result of optimization procedure, can be fully implemented. In such cases, they are implemented in the section that is the closest to the optimal section, where it is possible to make the division.

Both leaving a certain group of partition points outside optimization procedure and imprecise moving of some movable partition points results in increased power losses in the configuration with constraints, comparedto globally optimized configuration.

Many optimization calculations for the networks of individual regions - A to D were made taking into con-sideration the above mentioned constraints concerning location of partition points. Such calculations enable:

• indicating implementable changes in network configurations• possible identification of optimal location of some partition points• identification of the needs of installing new switches.

The selected results of the calculations are presented in Table 10. It contains information on the number of the existing constraints, the number of optimally located partition points, the values of power losses in op-timized configurations, taking into consideration all the constraints and changes of power losses compared topower losses in the existing configurations.

Tab. 10. Results of calculations of power losses after optimization of network configurations, taking into consideration the constraints

Region’s name

Total number of constraints

Number of optimally located partition points

Power losses in optimized configuration with constraints

Losses reduction compared to the existing configurations

[%]*) [%]*) [kW] [%]

Region A 59 29 543.1 6.1

Region B 71 21 237.9 0.8

Region C 53 36 341.7 2.2

Region D 51 32 466.8 6.2

*) relative values calculated in relation to the total number of partition points in the given distribution region

By analyzing the results presented in Table 10, one can formulate the following remarks: • in practical calculations of configuration optimization of distribution networks one should be aware of the

existence of a considerable number of constraints of location of partition points; in the case of the objects discussed, the constraints referred to from 50% to even 70% of the total number of partition points

• a considerable number of optimally located partition points (from 21% to 36%) among the variables whose location can be changed is also significant; it can mean that the services are well aware of the loads andthat they do take care of maintaining proper configuration of the network

• reconfiguration resulted in reduction of losses from 0.8% to 6.2%; the effect, translated into savings onannual reduction of energy losses, is estimated at ca 18 000 PLN to 21 000 PLN for the regions D and A

• the existing configurations of the distribution network is, to a great extent, determined by the factors oflegal and technical character.


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The effectiveness of losses reduction obtained due to optimization of partition points obviously depends on individual features and properties of the distribution network under analysis. Better effects can be expected in the networks of lower nominal voltages (e.g. 6 kV), long circuits and considerable load.

The results of the research of Edward Siwy from Silesian University of technology [12] on configurationoptimization of MV distribution networks indicate that effectiveness of such operations can be high. Table 11 presents effects of optimization of partition points in 3 distribution networks.

Additionally, using the results of calculations of power losses for a dif ferent number of constraints in the locations of the partition points of the analyzed regions A, B, C and D, a diagram illustrating the depend-ence between power losses and the number of existing constraints was developed. The diagram is presented in Fig. 9. The number of constraints was expressed in [%] in relation to the total number of partition points. Power losses were expressed in relative units in relation to the losses occurring in the configuration withoutconstraints.

Tab. 11. Possibilities of reducing energy losses after optimization of partition points in MV urban networks in selected areas (according to [12])

Number of MV/LV stations [pieces]

Length of MV lines [km]

Reduction of losses [%]

Estimated savings [thousand PLN/year]

600500 16 130

780550 4 80

430430 11 50

Rela

tive

incr

ease

of l

osse

s [-

]

Number of constraints [%]

Fig. 9. Dependence of power losses as a function of the number of constraints of partition points locations of the network

The diagram shows that in each case the increase of the number of forced locations of partition points results increase in power losses in the network. The dependence is different for each network area.

Change of power losses per one partition point, resulting from keeping its location or impossibility of its free movement can be, as the drawing indicates, very different. Each time, determining those values requires calculations with the use of the network model.

It can be interesting to find out about the circumstances causing a significant increase of losses due tomaintaining a small number of partition points in their original locations.

An MV generation unit of considerable power, connected to the distribution network, cooperates with the region A network.

Due to continuous changes in voltage conditions in the network caused by changes of the operational status of the unit, a separate feeder must be maintained connecting the generator with the power substation (MFP).


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Another case encountered in practice is that of a network of significant power losses, whose configura-tion is forced by a non-uniform ownership structure of the network. In this case, power losses reduction would require feeding of some of the consumers via a substation, which is not owned by the distributor. The costs of potential transit would not be covered by the profit resulting from losses reduction.

The considerations presented above referred to cases of forced location of partition points whose change would significantly reduce losses. In the other situations, the change of power losses per one partition point withconstraints was much smaller.

The issues presented above referred to constraints of determining character. The constraints from the other group (the so called limiting constraints), concerning the impossibility of free location of movable parti-tion points is also worth mentioning. In the situation in which the indication of the optimization procedure re-ferred to the section in which, for various reasons, the division could not be made, a division in the closest point was proposed, with calculation of the differences of losses resulting that change. The differences were usually small or simply insignificant. In particular, in no case a change of losses that would justify install a new switch inthe network was observed.

Optimization of configuration of distribution network is one of the most often mentioned ways of no-in-vestment reduction of power losses. A solution of such a problem for a big real network requires application of adequate calculation tools and developing the network model.

Proper estimation of loads of individual transformer MV/LV stations is one of the significant problems. It isdue to the lack of measuring devices in distribution network. The load data of individual lines, results of periodi-cal measurements in MV/LV stations and the expertise of operation staff of the distributor were helpful.

Four distribution regions of typical size, of typical scope of network and average power demand were analyzed. The small power losses in the existing configurations can be explained by the high value of nominalvoltage, considerably big average cross section and a compact structure of the network.

Calculations of the configuration optimization made without taking into consideration constraints enableinitial identification of maximum effects of a network reconfiguration. But before detailed analysis of the con-straints of individual partition points occurring in a given configuration is made it is not possible to assess thescope of losses reduction that can occur due to practical implementation of the change of configuration of thenetwork.

Constraints of location of partition points can be of twofold character: determining or limiting. In the firstcase they come down to the necessity of maintaining partition points in strictly defined locations of the net-work, and in the other one – they do not allow totally free location of the partition points whose location can be changed. Those constraints are due to formal-legal or technical-operational reasons.

The presence of limitations on the location of partition points which are among the constraints of optimi-zation negatively affects the level of the achieved optimal solution. A configuration with constraints always hasbigger power losses than a configuration without constraints.

The presented examples indicate a considerable number of limitations in the practical tasks of reconfigu-ration of wide-area distribution networks – the constraints apply to more than 50% of existing partition points.

Also noteworthy is the considerable number of partition points located optimally in the initial configura-tion (from 21% to 36%).

The analysis and possible changes of configuration of the network gave an effect in the form of losses re-duction up to ca 6% at peak load. The effect can be seen in savings on lower energy losses, which annually reach the amount of 18–21 thousand PLN. So significant savings on energy losses can be made even in a network ofsmall losses before reconfiguration and a considerable number of constraints. As Table 11 shows, such savingscan be of much higher value in other distribution networks.

The potential for losses reduction per one partition point with constraints varies considerably and requires individual calculations with the use of the network model. The reasons for maintaining unfavourable locations of partition points of big losses reduction potential can be complex and vital for the network.


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8. CONCLUSIONSOptimization of partition points is one of the basic ways of non-investment reduction of losses and a sub-

ject of numerous publications, in Poland as well as abroad, devoted to losses reduction in distribution systems.The essence of optimization consists in finding such configurations of MV network, determined by the

given location of partition points of the network, so as to obtain a configuration characterized by the smallestpower losses.

For simple network structures, such as a loop or a spindle, optimization calculations can be made inde-pendently for each variable (each partition point), e.g. by the use of a spreadsheet. More complex configurations(more connections, more meshed) require adequate calculation techniques and specialist software.

Each of the software, that is SIEĆ, STROP and DRZEWO, can be adapted to optimization of partition points with regard to minimum power losses in big MV networks. The differences between the solutions obtained for the same network by the use of different tools are due to application of different algorithms of looking for an optimal solution and the way of calculation of loads of individual MV/LV transformer stations.

Practical implementation of optimization of configuration of the network must take into considerationvarious constraints connected with the impossibility of changing the location of some partition points and in-complete set of possible allocations determined by the existence of switches only in selected sections and access reasons (e.g. access to some partition points).

For the locations of partition points forced by legal issues (consumer pays for two supplies), real costs of maintaining the division in the given point of the network should be calculated and transferred in the fixedcomponent of power charge paid by the consumer.

The effectiveness of reconfiguration operations that can be achieved in a real network surely depends onindividual features and properties of the distribution network analyzed. Better results can be expected in the networks of lower nominal voltages (e.g. 6 kV), long circuits and significant load.

The development of the energy market and the increased operational effectiveness of energy companies will probably stimulate distributors’ interest in non-investment reduction of losses in distribution networks.

The modern IT power industry dedicated systems for network assets management and advanced meas-urement-settlement systems will be of significant assistance in analyzing optimal configurations of distributionnetwork. Such IT and measurement systems will enable implementation of network configuration optimizationwith regard to minimum energy losses in a given time period, which is now hard or impossible to implement.


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LITERATURE

1. Folder: Electrical Energy Statistics 1997–2007, Ministry of Economy of the Republic of Poland www.mg.gov.pl.2. Kulczycki J. (ed.), Ograniczenie strat energii elektrycznej w elektroenergetycznych sieciach rozdzielczych, PTPiREE,

Poznań 2002.3. Harasimowicz L., Optymalizacja pracy sieci rozdzielczych średnich napięć, Materiały konferencji naukowo-technic-

znej – Straty Energii Elektrycznej w Spółkach Dystrybucyjnych, Poznań 17–18.05.1999, pp. 289–295.4. Harasimowicz L., Suboptymalny podział dużych sieci rozdzielczych dla potrzeb eksploatacji, rozprawa doktorska,

Instytut Energoelektroniki Politechniki Wrocławskiej, Wrocław 1992.5. Czepiel S., Obliczenia optymalizacyjne i inżynierskie dla sieci średniego napięcia. Instrukcja obsługi programu STROP,

Instytut Elektroenergetyki Politechniki Częstochowskiej, Częstochowa 1999.6. Kręglewski T., Rogowski T., Ruszczyński A., Szymanowski J., Metody optymalizacji w języku FORTRAN, PWN, Warszawa

1984.7. Brożek J., Kot A., Kulczycki J., Szpyra W., Bezinwestycyjne metody zmniejszania strat energii w sieciach rozdzielczych

w pracach badawczych zakładu elektroenergetyki AGH, Materiały konferencji naukowo-technicznej – Straty Energii Elektry-cznej w Spółkach Dystrybucyjnych, Poznań 17–18.05. 1999, pp. 264–277.

8. Chiang H.D., Jean-Jumean R.M., Optimal Network Reconfiguration in Distribution Systems, IEEE Transactions onPower Delivery, vol. 5, No 4, November 1990.

9. Mazur P., Ograniczanie strat mocy i energii w sieciach zamkniętych SN. Praca dyplomowa Wydz. EAIiE AGH, 2001.10. Kujszczyk Sz., Nowoczesne metody obliczeń elektroenergetycznych sieci rozdzielczych, WNT, Warszawa 1984.11. Helt P., Parol M., Piotrowski P., Metody sztucznej inteligencji w elektroenergetyce, Oficyna Wydawnicza Politechniki

Warszawskiej, Warszawa 2000.12. Siwy E., Żmuda K., Intensyfikacja wykorzystania sieci w spółce dystrybucyjnej, Przegląd Elektrotechniczny No

3/2009, pp. 243–246.


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