Optimal Voltage Control in Medium Voltage Power ...actaenergetica.org/uploads/oryginal/pdf_import/06f...Voltage control options, resulting from application of means mentioned above,

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OPTIMAL VOLTAGE CONTROL IN MEDIUM VOLTAGE POWER DISTRIBUTION NETWORKS

Waldemar Szpyra / AGH University of Science and Technology in CracowAleksander Kot / AGH University of Science and Technology in Cracow

1. VOLTAGE DEVIATIONS LIMITATIONS

Limitations for voltage deviations in power distribution networks are given in the Ordinance of the Minis-ter of Economy dated May 4, 2007 on specific conditions of electric power systems. (Journal of Laws no 93 dated 29 May 2007, item 623) [17], called in short “system regulation”. The Ordinance imposes a duty on power line operators to observe specified quality parameters of supplied power. It stipulates that in a network operating without disturbance, every week 95% out of a set of 10 minute average values of effective input voltage should remain within the following deviation range:

• for consumers classified as group I and II connected to a grid:of nominal voltage:Un = 400 kV: +5% /–10%Un Un = 220 i Un = 110 kV: ±10%Un• for consumers classified as group III ÷ V (supplied with network of nominal voltage below 110 kV)

– every week 95% out of a set of 10 minute average values of effective input voltage should be in the deviation range ±10% rated voltage.

For consumers of group I and II – power quality parameters may, in their entirety or in part, be substi-tuted by other parameters specified in the power sales contract or in a contract for rendering power transmissionand distribution services.

Failure to observe quality standards of supplied power to consumers from group III, IV and V specified inthe system regulations [17], entitles consumers to bonuses and discounts. The discount values are determined according to §37 of the Ordinance of the Minister of Economy dated 2 July 2007 on specific principles governingthe calculation tariffs and financial settlements in electric power trading (Journal of laws dated 18 July 2007, no 128, item 895) [16]. Both Ordinances were issued on the grounds of delegation stipulated in the Act on Energy Law [21].

The Acts referred to above do not define the term “grids operating without disturbance”. “Instructions of Transmission System Operation and Maintenance” [4], on the other hand, define disturbance as: “Unplanned automatic or manual shut-down(s) or impossibility to keeping of the expected operating parameters of the com-ponents of network assets. The disturbance can take place with or without the damage to the network assets”.

A conclusion may be drawn from the definition that energy quality parameters need not be met in systemsother than typical/normal systems. Thus, the regulations related to voltage in distribution networks in force today are more liberalised as compared to those binding before the system regulation of May 2007 became effective (regulations on operations of power engineering systems issued before 2007 did not stipulate any restrictions as to “networks operating without disturbance”.

Optimal Voltage Control in Medium Voltage Power Engineering Networks

AbstractPower flow in elements of the network causes

voltage drops in these elements. Therefore, in order to ensure the proper voltage of electric power delivered to consumers it is necessary to regulate voltage in power en-gineering grids. The article presents voltage requirements in power engineering grids, the impact of regulation on losses in distribution lines and various criteria for optimis-ing voltage regulation. Depending on the adopted criteria, indications for tapping switch settings in transformers and input voltage may differ for various lines or even be quite the opposite.

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2. DEVIATION AND VOLTAGE DROP BALANCE The deliberations refer to a MV network supplied by a HV/MV transformer installed in a power distribution

substation (DS). A single transformer feeds 6 ÷ 10 medium voltage lines. Each line feeds several to few dozen medium voltage/low voltage (MV/LV) transformer stations, which supply low voltage circuits. An example of the supply system from distribution substation to the consumer connected in point k of the low voltage network with marked deviations and voltage drops is given in Fig. 1.

Fig. 1. Deviations and voltage drops in the system from distribution substation to the consumer connected in point k to the low voltage system. Key: R – point of network split; TS - MV/LV transformer station; other designations in text

In the case given in Fig. 1 the voltage deviations δU in point k of the low voltage system may be deter-mined from the deviations and voltage drop datasheet expressed in the following equation:

(1)

where: δUnn – is the voltage drop in the low voltage system from the TS to point k; ΔUT – drop in voltage in the MV/LV transformer; δUzT – voltage deviation resulting from the position of the tap changer to medium/low voltage transformer ratio control; ΔUSN – voltage drop in medium voltage network; δUz – deviation voltage in network supply point; Unn – rated voltage of low voltage lines; δUϑ – voltage deviation resulting from the dif-ference between the relations of the transformer rated voltage and the network rated voltage:

(2)

where: ϑnT – rated MV/LV transformation ratio; ϑnS – the relation of medium network and low network rated voltages; UnG – rated voltage of the MV winding of MV/LV transformer, UnD – rated voltage of the LV wind-ing of MV/LV transformer, USN – rated voltage of MV networks, Unn – rated voltage of LV networks,.

Voltage deviation in any point of medium and low voltage system must comply with the range given in the system regulation, i.e.

(3)

In a normally operating system the maximum voltage deviations occurs in the end of the low voltage line supplied by the most loaded TS distanced from the grid feeding medium voltsage network (usually close to the point of network split). Minimum voltage deviations occur in the case of minimum network load at the beginning the low voltage system, fed by the TS located near DS.

To assess the voltage in distribution networks it is necessary to know all the elements of the deviation and voltage drop datasheet (1). Usually a model, reflecting precisely the network parameters from the grid feeding

LV line

LV line

Aleksander Kot / AGH University of Science and Technology in CracowWaldemar L. Szpyra / AGH University of Scie nce and Technology in Cracow

Customer load Customer load

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MV network to low voltage busbars in TS, is built to analyze a distribution network. Precise models of low volt-age networks are not developed. This results from the big number and diversification of low voltage circuits inthe system.

In practice calculations are made of the power current flow and voltage drop in the MHV network to as-sess the network operating conditions. Therefore, it is justified to specify the voltage drop limits, i.e. valuesthat allow for the present voltage adjustment system to maintain the deviation level for the consumer within the admissible range. Specifying the admissible voltage drop in the MHV network is possible provided values of certain datasheet components are adopted (1). The most often made assumptions involve:

• use of the full admissible voltage range on MV bus bars is possible in the network feeding point, which means that deviation of input voltage δUz may read +10%Un (control practice used by power distribut-ers often restricts the supply voltage deviation in the MHV network in GPZ to δUz = +5%Un – primarily because bigger customers belonging to group III have their own MHV/LV transformer stations)

• voltage deviation resulting from the difference between the relations of the transformer rated voltage and the network rated voltage (δUϑ) shall be compensated by relevant setting of tap changer (δUzT)

• a voltage drop in the MV/LV transformer (ΔUT) is calculated using the average known transformer load in the circuit and its rated parameters

• low voltage networks are designed according to guidelines given in [22] and thus we can assume that voltage drops occurring in these systems (ΔUnn) do not exceed the values given in the last column of Table 1.

Table 1. Admissible voltage drops in medium and low voltage lines according to guidelines given in [22]

SpecificationMV network Low voltage

networknormal disturbed

Towns supplied by 110 kV/MHV lines located within town borders

2% 4% 4.5%

Towns supplied by MFP located within town borders 8% 10% (3÷4.5)%

Towns supplied by distanced MFP 8% 13% (7.5÷10)%

Industrial consumers Supplied from regional grid

8% 13% (3÷4.5)%

Voltage drop in a MV/LV transformer may be calculated according to the following formulae:

(4)

where: SN – transformer rated power [kVA]; S – transformer load [kVA]; cosφ – transformer load coef-ficient (ratio of active to complex transformer demand); ur – active component of transformer’s short-circuit voltage [%]; ux – reactive component of transformer’s short-circuit voltage [%];

(5)

(6)


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where: Pk – load loss of transformer (cooper losses) [kW]; uk – transformer short circuit voltage [%].Table 2 presents the voltage drop value for typical MV/LV transformers used in distribution systems in the

load function S/SN, and load coefficient of cosφ = 0.9.

Table 2. 15.75/0.4 kV transformer voltage drop under varied load

Sn Pk uk Transformer load factor S/Sn

0.3 0.4 0.5 0.6 0.7 0.8 0.9

kVA kW [%] Voltage drop in transformer ΔUT [%]

63 1.20 4.5 1.19 1.59 1.99 2.39 2.79 3.19 3.59

75 1.85 4.5 1.24 1.65 2.06 2.48 2.89 3.31 3.72

100 1.75 4.5 1.19 1.59 1.98 2.38 2.78 3.18 3.58

160 2.25 4.5 1.05 1.41 1.76 2.11 2.47 2.82 3.18

200 3.90 4.5 0.94 1.26 1.57 1.89 2.20 2.52 2.84

250 3.00 4.5 0.99 1.33 1.66 1.99 2.33 2.66 3.00

400 4.25 4.5 0.91 1.21 1.51 1.82 2.12 2.43 2.74

630 6.10 6 1.09 1.46 1.83 2.20 2.58 2.95 3.32

The average peak transformer load in distribution networks reaches 40÷50% of rated power, which means that the average voltage drop in transformers should not exceed 2%.

Assuming that: δUz = +10%; δUϑ = –5%; δUzT = +5%; ΔUT = –2%; ΔUnn = 10% and admissible voltage deviation for consumers supplied from low voltage networks, amounting to δUdop = 10%, the voltage drop and deviations (1) show that the maximum voltage drop in MV lines should not exceed:

This means that full range voltage regulations in DS allow for assuring the required low voltage level at the consumer’s end (voltage drop in MV network amounting to circa 7.5%).

3. VOLTAGE REGULATION MEANSVoltage deviation in low voltage networks can be controlled:1. without investment outlays – using transformer’s regulation capacity, i.e.:

a. change of input voltage to the MV network – regulating voltage on MV busbars in DS – by chang-ing the HV/MV transformation ratio operating under load, by ±10% in 8 steps or ±16% in 12 steps

b. change of MV/LV transformer ratio control while the transformer is switch-off),– the extent of change depends on the transformer’s year of built and reaches: δUzT = {-5%, 0%, +5%} or δUzT

= {–2,5%, 0%, +2,5%, +5%, +7,5%}.2. investment related – applying additional technical means to reduce the drop in network voltage, i.e.:

c. installing condenser batteries to compensate reactive powerd. installing condenser’s in series to compensate line reactance e. installing controlling auto transformers in series (buck transformers)f. connecting new circuits to DS taking over delivery to some of the TSg. shortening low voltage circuits by adding new TS.

Voltage control options, resulting from application of means mentioned above, are limited because:a. higher input voltage to the medium voltage network is limited by the maximum voltage upward devia-

tions limited by inequality (3), and sometimes by contract conditions with consumers

Aleksander Kot / AGH University of Science and Technology in CracowWaldemar L. Szpyra / AGH University of Science and Technology in Cracow

= 10 – 5 + 5 – 2.5 – 10+10 = 7.5 [%]

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b. MV/LV transformation ratio is connected with consumer trip off and results in generating costs of the rigging team and is in practice rarely applied (once or twice a year or even less often). Additionally, the increase of rated voltage in low voltage networks in 2003 resulted in growing maladjustment of trans-former ratio control and relation of rated voltage in medium and low voltage networks – the value of δUϑ was modified from +0,25% to –5% and as effect up to 5% of the medium/ low voltage transformerregulation range is used for compensating the effects of increased voltage in the low voltage network

c. application of additional technical means to reduce voltage drop requires considerable investment out-lays, which in practice rarely give the opportunity for return on investment. Every decision related to investments aimed at improving voltage in the network should be preceded by a detailed technical and economic analysis of various solutions to the problem.

4. IMPACT OF VOLTAGE REGULATION ON NETWORK LOSSESThe impact of changes in voltage on the network demand is described by the static voltage characteristics

of network demand [1, 2, 9]. In the case of minor voltage deviations (±5% Un), changes in network demand are described by coefficients of voltage static characteristics of the network active demand α and reactive demand β. These coefficients show the percentage shift of active and reactive network demand by one percent voltagechange.

According to [2] the active and reactive network demand on real voltage Ur may be calculated using ap-proximated relationships:

(7)

(8)

where: Pr, Qr – are active and reactive network demand at real voltage Ur respectively; Pn, Qn – active and reactive network demand at nominal voltage respectively; α, β – factor of voltage static characteristics of active and reactive demand respectively; Un – nominal voltage; δU – deviation of supplying voltage:

(9)

The value of angle factor of voltage static characteristics of active power drawn from the network is given in Table 3 with the value of coefficient of voltage static characteristics of reactive power given in Table 4.

Table 3. The value of factor of voltage static characteristics of active demand α for selected types of power distribution systems

Types of power distribution systems Source:

Value of factor of voltage static characteristics of active demand α within hours of::

Morning peak load Evening peak load Night load

Grid suppluing big towns with small industrial consumers

[2] 0.90÷1.20 1.50÷1.70 1.50÷1.60

Grid suppluing small towns with small industrial consumers

[2] 0.60÷0.70 1. 40÷1.60 1. 40÷1.60

Rural networks [2] 0.50÷0.68 1.50÷1.60 1.50÷1.60

20 kV network of Distribution Company X [1] 1.20 1. 46 –

15 kV network of Distribution Company Y [9] 1.15 2.25 0.95


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Table 4. The value of angle factor of voltage static characteristics of reactive power β for selected consumers, with voltage deviation in the range ±5%Un

Types of power distribution systems Source:

Value of factor of voltage static characteristics of reactive demand β within hours of:

Morning peak load Evening peak load Night load

Grid suppluing big towns with small industrial consumers

[2] 3.00 2.60 3.10

Grid suppluing small towns with small industrial consumers

[2] 3.00 2.60 3.10

Rural networks cosφ ≥ 0.85 0.80 ≤ cosφ < 0.85 0.70 ≤ cosφ < 0.80 cosφ < 0.70

[2]

2.302.502.803.10

2.60 3.10

20 kV network of Distribution Company X [1] 2.85 4.14 –

15 kV network of Distribution Company Y [9] 5.95 2.60 2.30

The impact of supplying voltage changes as well as transformation ratio control on network demand, power and energy losses can be traced on the example of a simple medium voltage circuit comprising of a medium volt-age line, MV/LV transformer and low voltage demand. The circuit and equivalent diagram are presented in Fig. 2.

Voltage on consumer terminals may be changed by changing the supplying voltage Uz and/or position of the transformer tap changer resulting voltage deviation δUzT. Various combinations of input voltage changes and transformer ratio control are possible. Two cases involving extreme changes are given below:

a. changes of input voltage Uz with simultaneous changes position of the transformer tap changer by δUzT, so that the voltage on the consumer terminals Uo remains unchanged

b. changes of input voltage Uz with no adjustment of transformation ratio control so resulting in voltage change on the consumer terminals Uo


Fig. 2. Medium voltage circuit and its equivalent diagram

4.1. Adjusting input voltage with simultaneous changes of transformer ratio controlSimultaneous changes in input voltage feeding the network and change of transformer ratio control so

that voltage in consumer terminals remains unchanged Uo = const – power (and energy) supplied by the net-work for delivery remains the same. However, the following changes take place:

• current in the supply line – inversely proportional to voltage change • power loss of transformer idling – proportional to the square of voltage change value. Changing current causes change a load loss in the circuit – proportional to the square of that change.

Loss of energy in the circuit is also subject to change. In this case the direction of loss change depends on: the direction of changed voltage, circuit load and volume of transmitted energy.

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Example 1. For the transmission system as in Fig. 2 energy loss was calculated in three variants differing in terms of line input voltage Uz and the location of the transformer tapping switch.

Variant „Un”: Uz = Un = 15.0 kV, tapping switch position δUzT = 0%Variant „1.05Un”: Uz = 1.05Un = 15.75 kV, tapping switch position δUzT = – 5%”Variant „0.95Un”: Uz = 0.95Un = 14.25 kV, tapping switch position δUzT = +5%.In the case of such line input voltage and transformer tapping switch positions the output voltage in con-

sumer terminals remains the same for every variant. For each variant calculations were performed using follow-ing data: line elementary impedance R0 = 1.227 Ω/km, elementary reactance X0 = 0.398 Ω/km, line length l = 1 km; three values of utilization periods of maximum losses: τ = {1 670; 2 580; 3 560} h/a. (which corresponds to the following utilization periods of peak load: Ts = {3 000; 4 000; 5 000} h/a; transformer load changes range from 25 to 625 kW with power factor cosφ = 0.94; transformer parameters: rated power Sn = 630 kVA, rated transformer ratio ϑn = 15,0/0, 4 kV, load loss Pk = 6.1 kW, no load loss P0 = 0.97 kW, short circuit voltage uk = 6%, idle current i0 = 1%.

Calculation results are given in Fig. 3 in graph form showing the relative changes in energy loss in the transmission system in terms of transformer load. The chosen point of reference was the energy loss in the system (corresponding to the given load) calculated at zero voltage deviation (Variant „Un”).


Fig. 3. A relative change of energy loss as a function of transformer demand factor in the case of simultaneous changes supplying voltage and transformation ratio control

The graphs show that when the transformer is underloaded an increase in input voltage concurrent with the same relative increase of transformer ratio cause energy loss in the system. The loss increases with the de-crease in transformer load and the shortening of time intervals of peak power consumption. For example in re-sult of growing input voltage and transformation ratio by 5% and transformer load of So = 30% Sn and time values for peak power consumption Ts = 3 000 h/a, energy loss grows by less than 8.5% and in time value Ts = 5 000 h/a circa 6.5%. Relative loss changes diminish with growing transformer load (when the transformer load exceeds a specific value the direction of change switches to the opposite sign, i.e. losses decrease with growing voltage).

On the basis of graphs in Fig. 3 we can state that in the case of adjustments involving simultaneous changes of input voltage and transformer ratio, a change in energy loss direction in the system depends above all from the system load and time intervals of peak power consumption. In the case of small load and short time intervals of peak power input voltage should be decreased and simultaneously the transformer ratio reduced in order to reduce losses. In contrast, with big loads and long time intervals of peak power consumption, input voltage and transformer ratio should be increased. On the other hand, the comparison of calculation results for two line lengths indicates that losses decrease with falling transformer loads – resulting from the impact of big-ger voltage drop on transformer idle loss.

Transformer demand factor, [%Sn]

Rela

tive

chan

ge o

f ene

rgy

loss

, [%]

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Fig. 4 shows the range of load power factor cosφ depending on the value of factor of voltage static char-acteristics of the active power α, when load loss of power in the circuit fall with the growing voltage. The curves represent three values of factor of voltage static characteristics of reactive power β. The curves are constructed so that the intersection point of the straight line, representing load power factor value cosφ, with the straight line representing the value of factor of voltage static characteristics of the active power α, lies above the curve representing the value of factor of voltage static characteristics of the reactive power β, then load power loss in the circuit diminishes with the growing voltage.


Fig. 4. Range of power factor cosφ in terms of factor of voltage static characteristics of active power α, when load loss of active power de-creases with the growing voltage

Table 3 indicates that the factor of voltage static characteristics of the active power α is less than one in principle only during the morning peak load when the value of load power factor is low (power factor values cosφ in MV networks are given in Table 5). In practice this means that situations of network load loss decrease while supplied voltage grows occur very rarely.

Table 5. Power factor cos� in medium voltage network in various seasons, days and hours [15]

Kind of network Season (daytime)Power factor cosφ

Before noon In the evening At night

Network supplying big town

Winter (workday) 0.86 0.89 0.77

Summer (workday) 0.74÷0.80 0.74÷0.80 0.63

Network supplying rural areas

Winter (workday) 0.50÷0.70 0.98 0.98

Summer (workday) 0.52÷0.67 0.78÷0.98 0.90÷0.98

Summer (Sunday) 0.88 0.98 0.78÷0.93

Generally, input voltage growth accompanies growth of load losses in the circuit. Only in the cases of high power factors cosφ, in that time of the day when the factor of voltage static characteristics of the active power α < 1, the load losses may decrease with the growing input voltage. When the factor α ≥ 1, load losses always grows together with growing supplying voltage (because of the factor α is always bigger than 1).

As the factor of voltage static characteristics of the active power is always bigger than zero, growing sup-plying voltage will always be accompanied by the growth of active power consumption. In most cases (except for consumers requiring a fixed amount of energy for their technological process) the amount of energy used bythe consumers also grows.

Pow

er fa

ctor

cos

φ

Factor of voltage static characteristics of active power α 0.50 0.55 0.60 0.65 0.70. 0.75 0.80 0.85 0.90 0.95 1.00

1.00

0.95

0.90

0.85

0.80

6.02.62.3

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4.2. Adjusting input voltage with no change of the transformer ratio controlWhereas the change of input voltage is not accompanied by a change of the transformation ratio, volt-

age changes in consumer terminals. The relative changes by δU in the supplying voltage supplying the circuit will cause almost the same relative voltage changes on the transformer terminals and consumer terminals. As a result of above voltage change the next changes will take place:

• of the consumed active and reactive power supplied by the network – in compliance with the voltage static characteristics of the consumed power

• of energy consumed from the network• power loss of transformer idling. Changes in the delivered power consumed result in changes of the current in the circuit, and thus the load

loss. The direction changes of total power loss in the circuit depend on the power factor, ratio of transformer load and time of the day.

Example 2. Similarly as in example 1, calculations were made for the transmission system of power changes and energy consumed from the network, power and energy losses in the system with rated transfor-mation ratio for three values of supplying voltage (the same as in example 1). Other parameters used in the calculations were the same as in example 1.

Fig. 5 shows relative changes in energy loss against energy loss at rated voltage.


Fig. 5. A relative change of energy loss as a function of transformer demand factor in the case of changes supplying voltage and fixed trans-formation ratio

Fig. 5 indicates that an increase of input voltage by 5% causes growing power and energy loss of over 10%, whereas a 5% voltage drop leads to a nearly 10% reduction of power and energy loss.

4.3. ConclusionsThe deliberations presented above indicate that:1. Voltage regulation in distribution networks have an impact on both power and energy loss in the network

and power and energy consumption from that system, and thus on company costs and revenues.2. In extreme cases voltage regulation, reducing power and energy loss, may result in decreasing the

amount of energy used by consumers and thus reduce revenues for transmission charges. We should emphasise that the example selected well depicts the nature of changes in progress. In real

network circuits supplying a bigger number of stations, operating under varied loads and time of peak consump-tion, the situation is not as clear. In order to determine the input voltage level and MHV/LV transformer ratio set-ting that is the most appropriate, in terms of loss, MHV/LV transformer ratio requires optimising calculations.

Rela

tive

chan

ge o

f ene

rgy

loss

, [%]

Transformer demand factor, [%Sn]

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5. OPTIMAL VOLTAGE CONTROLThe key objective of voltage regulation is assuring voltage deviation in every point of the medium and low

voltage networks within the admissible range. In the process of achieving this objective we can also optimise the voltage level in the network.

The solution for optimising voltage regulation comes down to finding voltage values for MV busbars in DS feeding the network and all MV/LV transformation ratio setting values, where the target function of a speci-fied quality control criterion reaches the optimum and is concurrently compliant with limitations resulting from admissible voltage deviations and technical capacity to effect the control (e.g. transformation ratio control range). The number of targeted voltage values for MHV busbars depends on the number of time zones per day The setting of MV/LV transformer tapping switches is the same for all time zones in the analysed period. Cal-culations are performed for the period of a year or separately for particular seasons, e.g. autumn/ winter and spring/summer.

The solution for optimum voltage control for networks feeding n TS in time T, comprising r time intervals, is the vector determining all MV/LV transformer tapping switches settings in the analysed network, containing information on the relevant level of input voltage in DS where the target function of adopted optimum criterion reaches an extreme value.

(10)

where: δUzTi – voltage deviation connected with the position of the MV/LV transformer tapping switch in i station; δUzp – oltage deviation in MV busbars in DS connected with the position of the medium to low voltage 110 kV/MV transformer tapping switch in time interval p.

If we assumed optimisation for a period of one year broken down to hours, the number of input voltage levels in DS to be identified would be huge and amount to r = 8 760. Thus, the vector (10) would be very long and the problem difficult to solve. Therefore, the need for decomposition.

Decomposition of the problem involves a breakdown of the hourly sets to a small number of subsets called zones, where a fixed input voltage level in DS is assumed. This corresponds to agreeing on network load intervals for which input voltage to DS remains constant. Usually several (4–6) such zones are agreed. In this situation the solution vector takes the following form

(11)

where s – the number of time zones, s << r.

5.1. Optimum voltage regulation criteriaIt is possible to formulate varied criteria for optimum voltage regulation:(1) minimising costs of economic losses for consumers resulting from voltage deviation from nominal value [14]:

min KOdb (12)

(2) minimising costs of power and energy loss in the network of the distribution company [18, 19]:

min KS = min (KΔP + KΔE) (13)

(3) minimising costs of the distribution company, i.e. costs of power and energy loss in the network and costs of discounts and allowances granted to consumers for failure to control voltage deviation in the admissible range [18, 19]:

min KD = min (KS + KB) (14)


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(4) minimising relative energy losses in the network [18, 19]:

(15)

(5) maximising profits of the distribution company for the sale of power [18, 19]:

max ZD = max (DS – KZ) (16)

(6) minimising joint costs (total), i.e. costs of power and energy loss in the distribution company’s net-work and economic losses incurred by consumers (minimising total costs in criteria (1) and (2) [18, 19]:

min KC = min (KS + KOdb) (17)

(7) minimising voltage deviation at the consumers [5, 6 and 7]

min ∑δU2 (18)

where: KΔP – power loss costs; KΔE – energy loss costs; ΔE – energy losses in the network, E –energy fed to the network; Ds – revenues generated by the sale of energy; KB – cost of discounts and allowances granted to consumers for exceeding admissible limits; Kz – purchase costs of energy from 110 kV network, KOdb – costs incurred by consumers in result of voltage deviation from rated value; ΣδU2 – the sum of voltage deviation square at the consumers in the analysed time intervals.

While we optimising using criteria (1)÷(5) and (7) we accept voltage deviation that does not exceed permissible values expressed by inequality (3), whereas using criterion (6) voltage deviation beyond the admis-sible range is acceptable. Nevertheless, each criterion must comply with restrictions resulting from technical conditions like e.g. limited range of transformer tapping switches or permissible voltage in terms of insulation strength.

The mathematical model (in the form of target function and constraints conditions) of optimising voltage regulation under criterion (1) was presented in a PhD thesis [14].

Mathematical models for optimising under criteria (2) ÷ (6) are presented in detail in the papers [18, 19]. The target function accounts for the impact of changes in voltage on network demand (in accordance with the voltage static characteristics of consumed power). To solve the problem of optimising voltage regulation in the distribution network a specially constructed neural network was applied.

A detailed description of an optimising method under criterion (7) can be found in the papers [5, 6 and 7]. In this case special computer software based on evolutionary algorithms [3, 10] was developed to solve the problem of optimum voltage control in the distribution network.

5.2. Input data for calculationsIn order to calculate the optimum voltage on medium busbars in DS feeding the network and to choose

the setting for MV/LV transformation ratio control according to the optimising criteria given above, the following data on the optimised network is required:

1. network connection scheme and parameters of particular MV lines (length of sections, cable diameter or unit line resistance and reactance)

2. rated parameters of MV/LV transformers installed at the transformer stations, i.e. rated demand, rated voltage of primary and secondary windings, rated load loss (cooper loss), short circuit voltage, possible tapping switch positions and related transformation ratios

3. demands of particular transformer stations (or information required to determine that demands)4. possible tapping switch positions and and related transformation ratios of 110 kV transformer feeding

the network


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5. annual demand profile of 110 kV transformer feeding the network.In In the case of criteria (2) to (6), taking into account the impact of voltage regulation on network de-

mand, additional data is required:6. value of coefficients of voltage characteristics of active demand α and reactive demand β7. rated no-load loss (iron loss) of active power in iron (idle loss), no-load current idle current of MV/LV

transformers8. information referring to economic losses incurred by consumers in result of voltage deviation.

6. EXAMPLES OF CALCULATIONS FOR REAL NETWORKS

6.1. Optimisation accounting the influence of voltage changes on network demandCalculations were performed for a real 15 kV network fed by 110/15 kV distribution substation applying

the criteria (2)÷(6), referred to in the paragraph above. The network is located in the south of Poland.

Example 3. The 15 kV network, fed by a 110/15 kV distribution substation (DS X) comprises 7 circuits total length circa 168 km. These circuits supply 136 15/0. 4 kV transformer stations of total rated demand of transformers of 13 MVA. A topographic diagram of the network is given in Fig. 6 and characteristic data of par-ticular circuits is presented in Table 6.

Table 6. Basic parameters of MV network circuits supplied by DS X [18]

Circuit noNumber of MV/LV trans-former stations supplied

[pcs]

Total rated demand of MV/LV transformers

[kVA]

Length of MV line

[km]

Average cable cross-section of MV circuits lines

[mm2]

1 18 1 472 19.2 34. 4

2 18 1 699 28.8 33.7

3 24 2 604 41.1 41.0

4 22 1 760 24.2 31.9

5 30 2 038 29.1 30.2

6 5 389 7.2 44.2

7 19 1 456 18. 4 37.9

Total 136 11 218 167.9 35.6

The following optimising calculations were performed for this network:• voltage on MV busbars in DS for three time zones• setting tapping switches in all MV/LV transformers supplied by the network• value of target function according to criteria (2), (3), (4) and (5).

Calculations were performed for the autumn/winter season broken down to three day time zones, i.e. morning peak – sr, evening peak – sw and other hours of the day (off peak zone) – sp. The circuit load was as-sumed as for the winter peak network load. Value of factor of static voltage characteristics of active and reactive demand was assumed according to [2]. The assumed initial conditions for the calculations were the same, for all three time zones voltage on MV bus bars in DS equal to Usr = Usw = Usp = 15.3 kV and the tap switch position of all 15/04 kV transformers in position δUzT =0. These conditions satisfied all the constraints (voltage rangedwithin permissible values), and the target function was calculated for criterion (5) on minimizing total loss and amounted to PLN 248.7 thousand. Cost calculations assumed: power unit costs at 67.56 PLN/kW a and energy unit costs in morning peak hours at 115.23 PLN/MWh. evening peak hours at 188.31 PLN/MWh, and off peak hours at 57.61 PLN/MWh.


101

Fig. 6. A topographic diagram of the 15 kV network fed by DS X [19]

The basic calculation results are presented in Table 7. The Table shows the optimum voltage (for each of the four criteria) that should be maintained in particular periods of the day on MV busbars in DS and target func-tion value prior to and following optimisation. It should be noted that the calculations were only performed for the autumn/winter season from October 1 to March 30.

Table 7. Results obtained applying various optimising criteria [19]

Criterion

Optimum voltage on MV busbars in DS

Tapping switch setting1)

Target function valueUnit

Usr[kV]

Usw[kV]

Usp[kV]

δUzt[%] initial optimum

(2) minimum costs of power And energy losses

14.54 14.67 14.58+2.5

or +5.057.2 54.0 Thous. PLN

(4) – minimum relative loss 15.75 15.75 15.75 0.0 3. 483 3. 475 %

(5) – maximum profit 15.28 15.25 15.75 0.0 1 354.0 1 413.6 Thous. PLN

(6) – minimum total costs 14.37 14.51 14.52+2.5

or +5.0250.3 207.2 Thous. PLN

1) A voltage increase in percentage share is given resulting from setting tapping switches . „+2.5” or „+5” means that transformer tapping switches should be set so that voltage grows by 2.5% or 5%, and „0,0” means that tapping switched in all transformers should be in neutral position (the program calculated the optimum tapping switch settings for particular stations).


– 15/04 kV transformer station No – X401

– DS X

Key

102

On the grounds of results given in Table 7 we can draw the following conclusions:1. The improvement of voltage regulation quality indicator is possible by applying the optimising crite-

rion.2. Depending on the used optimising criteria we obtain indications for voltage levels on MV busbars in DS

and settings for transformer tapping switches.3. Various criteria may be selected depending from the point of view:

• in terms of company interests, distribution companies should control voltage according to cri-teria (2), (4), (5) or (6)

• in terms of social costs voltage should be controlled according to criteria (1) or (7).4. Optimisation according to criteria (6) allows the admissible voltage deviation to exceed the rated value,

which could be beneficial for distribution companies when system regulation requirements stipulatemandatory investments in the network. This also derives from the rules for calculating discounts for exceeding admissible voltage deviations.

5. Optimisation under criterion (1) has no practical application as it is difficult to assess economic costsrelated to voltage deviation.

6. With the restructuring of the energy sector and breaking up into energy trading companies criterion (5) loses significance for network companies. Criteria (1) and (5) may be substituted by criterion (7).

6.2. Optimum voltage regulation according to the criterion of minimising voltage deviation at the consumer’s

Below is a very brief example of optimising voltage regulation according to the criterion of minimising voltage deviation at the consumer’s in a real network, cooperating with off grid generated sources.

A program dedicated for the purpose was used to perform the optimisation calculations. A real model has been developed of a 110 /15kV distribution substation located on the area of one of the distribution companies in the southern part of Poland. It feeds 156 medium/low voltage transformer stations supplied by 4 circuits (circuit length: 3÷95, km, number of stations 6÷83). To the biggest circuit connected a water power plant of attainable power reaching 1050 kVA. Network is supplied by 110/15 kV transformer of rated demand 16 MVA and voltage control range of of +/– 16% with distribution capacity of 1.78%, and resultant +/– 9 positions of the tapping switch. A registered annual load history was used with an imposed random power generation history of the power plant.

Optimum parameters of the evolution algorithm was attained applying a population of 200 individuals in 9000 generations, probability of crossing 0.9, probability of mutation 0.01. The calculation time for one algo-rithm processing lasted circa 4 hours. (processor AMD Athlon 2000XP). A typical optimising process for three program cycles is presented in Fig. 7.


Fig. 7. Optimising process for 3 calculation cycles

Adap

ting

Generation number

Cycle 1

Cycle 2

Cycle 3

103

Optimising calculations were made for the presented facility using a program assessing load history with randomly imposed generation for two seasons – winter and summer.

Particular studies provided solutions for adapting to: winter season 689 181. 4 summer season 707 320. 4 The solution comprises a set of optimum settings for tapping switches of all MV/LV transformers and op-

timum supply voltage on medium voltage busbars in DS for all time zones. Due to the length of the vector, full solutions are not given but only adapting values.

The selection of optimum setting for tapping switches of all MV/LV transformers in the distribution net-work of a given facility allows us to proceed to the next stage. This stage involves continuous voltage regulation in DS for every time interval, taking into account the network load and generation power at source.


Fig. 8. Optimum voltage in DS in terms of network load and generated power – winter season

Fig. 9. Optimum voltage in DS in terms of network load and generated power – summer season

Figures 8 and 9 present the optimum input voltage to the network in DS (tapping switch number) in terms of network load and power generation coefficient for the winter and summer season respectively.

The solution to the problem of voltage regulation in the distribution network, including off grid sources is possible by applying techniques based on evolutionary algorithms. The appropriate choice of parameters in

110/15 kV Transformer

tapping switch no

Load factor w

Generation coefficient g

110/15 kV Transformer

tapping switch no

Load factor w

Generation coefficient g

104

the calculation process allows for solutions of adequate precision and repetitiveness in case of diversified initialpopulation.

The introduction of heuristic elements to the calculations (knowledge of problem properties) allows for acceleration of optimum solution results.

The calculation tool can be applied both for distribution networks including sources as well as reactive networks.

Off grid generation in the MV network has an impact on the voltage regulation system (MV/LV transformer tapping switch settings and DS voltage). The presence of randomly operating power sources deteriorates volt-age regulation conditions.

Optimal choice of tapping switches sets, with the participation of power generation, of MV/LV transformers, which regulate DS voltage, allow for minimising the number of tapping switch connection in the 110kV/MV transformer.

The influence of changes in power generation in off grid sources on the 110/MV transformer voltage regu-lation depends on the distribution network structure, load, location of off grid generating units and the power generated and supplied to the network. Sources of lesser power feeding the 15 kV distribution station located nearby have a negligible impact but the influence becomes apparent with growing distance of the busbars con-nection point and generated power. In terms of DS voltage control, the number of stations in the circuit/circuits with generation to the total number of stations supplied by a given 110 kV/MV transformer is significant. It is determined by the form of the applied target function.

The characteristics of optimum voltage regulation in DS, in terms of network load and power generation in off grid sources, may give grounds to a decision to equip a given facility with a follow up voltage regulation system of the 110/MV transformer based on continuous estimation of voltage conditions of the input distribution network taking into account the present network load and the generated power of cooperating generating units.

In order to implement input voltage regulation in a network with changeable load in DS (for MV network with no generation) the application of current compensation is suggested for the 110 kV/MV transformer volt-age regulation.

Identification of proper compensation parameters is possible basing on results of the program referredto above and the voltage model of the analysed network. Compensation parameters R and X and the voltage U after the compensation impedance is selected to obtain the optimum voltage changes on MV busbars in DS in the entire range of the annual 110 kV transformer load feeding the network.

7. SUMMARYSumming up the deliberations referring to control and optimisation of voltage in the distribution network,

we can note the following observations.Voltage regulation in the distribution network influence power and energy consumption and losses in the

network. The nature of this influence was analysed in part 4 of the article on relatively simple examples. In realcircuits supplying a bigger number of stations, the identification of the most appropriate, in terms losses, inputvoltage to the network and tapping switches settings for the MV/LV transformers requires optimising calcula-tions.

These requirements on voltage deviation in the network are included in “system regulations” [17]. The permissible voltage deviation range for a network operating without disturbance is specified so the presentregulations in force regarding voltage conditions in distribution networks are more liberal than those mandatory prior to the regulation.

Voltage drop and deviation balance indicates that the use of the full voltage regulation range in DS can ensure the required voltage delivered to LV customer from a MV network in the case of a voltage drop of up to 7.5% in the MV network.

The primary means of voltage regulation in distribution networks is exploitation of 110 kV/MV and MV/LV transformation ratio control. Application of additional technical means to reduce voltage drop requires consid-erable investment outlays, which in practice rarely give the opportunity for return on investment.

We can formulate various optimising criteria for voltage regulation which have been described in more detail in item 5.1. An analysis of a real network indicates that depending on the adopted optimising criteria we obtain indications for voltage levels on MHV bus bars in DS and setting transformer tapping switches.

Aleksander Kot / Akademia Górniczo-Hutnicza w KrakowieWaldemar L. Szpyra / Akademia Górniczo-Hutnicza w Krakowie

105

The selection of the appropriate criterion for optimum regulation is discussed in the conclusions following item 6.1. With the restructuring of the energy sector and introduction of market instruments, minimising volt-age deviation at the consumer’ seems to be gaining on significance.

Effective solutions for optimum voltage regulation in real distribution networks involve techniques classi-fied as artificial intelligence methods, i.e. artificial neuron networks and evolutionary algorithms.

Computer software developed for optimising voltage regulation using the techniques described above are not products for commercial operations.

LITERATURE

1. Biniek M., Kinsner K., Łabuzek M., Pomiarowe wyznaczanie napięciowych efektów regulacyjnych mocy czynnych i biernych w systemie elektroenergetycznym, Zeszyty Naukowe Wyższej Szkoły Inżynierskiej w Opolu, Seria Elektryka z. 42, Opole 1995, pp. 53–60.

2. Bogucki A., Lawera E., Przygrodzki A, Szewc B., Podatność częstotliwościowa i napięciowa systemu elektroenergety-cznego i jego elementów, Politechnika Śląska, Skrypty uczelniane No 1116, Gliwice 1983.

3. Goldberg D., Algorytmy genetyczne i ich zastosowania, Wydawnictwa Naukowo-Techniczne, Warszawa 1998.4. Instrukcja ruchu i eksploatacji sieci przesyłowej. [Instruction of Transmission System Operation and Maintenance]

Warunki korzystania, prowadzenia ruchu i planowania rozwoju sieci, version 1.2, consolidated text valid as of 5 November 2007 PSE – Operator S.A.

5. Kot A., Ewolucyjna optymalizacja regulacji napięcia w rozległej sieci rozdzielczej zawierającej lokalne źródło mocy, Przegląd Elektrotechniczny No 9/2006, pp. 124–126.

6. Kot A., Optimal voltage control in the medium voltage networks containing dispersed generation, Archiwum Ener-getyki, tom XXXVII (2007), No 1–2, pp. 261–276.

7. Kot A., Optymalna regulacja napięcia w sieciach średniego napięcia zawierających źródła generacji rozproszonej, praca doktorska [doctorate disertation] AGH, Kraków 2005.

8. Kot A., Program komputerowy do optymalizacji regulacji napięcia w rozległych sieciach rozdzielczych, Energetyka, Zeszyt tematyczny No XIII, pp. 96–100.

9. Lipart K., Charakterystyki statyczne mocy, praca dyplomowa[diploma thesis] AGH, Faculty EAiE, Kraków 1996.10. Michalewicz Z., Algorytmy genetyczne + struktury danych = programy ewolucyjne, WNT, Warsaw 2003.11. Standard PN-88/E-02000, Napięcia znamionowe.12. Standard PN-EN 50160: Parametry napięcia zasilającego w publicznych sieciach rozdzielczych [Voltage Character-

istics in Public Distribution Systems], Polski Komitet Normalizacyjny, December 2002.13. Standard PN-IEC60038:1999, Napięcia znormalizowane [Standard Voltages].14. Piotrowski P., Optymalizacja regulacji napięć w elektroenergetycznych sieciach rozdzielczych w oparciu o teorię

sieci neuronowych, rozprawa doktorska, Politechnika Warszawska Wydział Elektryczny, Warsaw 1994.15. Popczyk J., Żmuda K., Sieci elektroenergetyczne. Ocena stanu i optymalizacja według podejścia probabilistycznego,

Skrypty Uczelniane Pol. Śl., Gliwice 1991.16. Ordinance of Minister of Economy of 2 July 2007 on detailed rules of calculation of tariffs and power supply/de-

mand settlements (Journal of Laws of 18 July 2007, No 128, pos. 895).17. Ordinance of Minister of Economy of 4 May 2007 on detailed conditions of functioning of electrical power system

(Journal of Laws No 93 of 29 May 2007, pos. 623).18. Szpyra W., Optymalna regulacja napięcia w rozległej sieci rozdzielczej średniego napięcia, Archiwum Energetyki,

tom XXIX (2000), nr 1–2, pp. 27–47.19. Szpyra W., Optymalna regulacja napięcia w rozległej sieci rozdzielczej średniego napięcia, praca doktorska [doctor-

ate dissertation], Akademia Górniczo-Hutnicza, Kraków 1998.20. Szpyra W., Optymalna regulacja napięcia sieci rozdzielczej średniego napięcia w warunkach rynkowych, in: Wilkosz

K. (ed.), Problemy systemów elektroenergetycznych, Polska Akademia Nauk, Komitet Elektrotechniki. Seria wydawnicza Sekcji Systemów Elektroenergetycznych Komitetu Elektrotechniki PAN, Oficyna Wyd. Pol. Wrocławskiej, Wrocław 2002,Chapter 16, pp. 409–433.

21. The Act of 10 April 1997 – The Energy Law, consolidated text: Journal of Laws of 2003, No 153, item 1505, with later amendments.

22. Guidelines for programming development of distribution networks, Instytut Energetyki, Zakład Sieci Rozdzielczych, Warszawa – Katowice 1986.


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