Assessment of maximum distributed generation penetration levels in low voltage networks using a probabilistic approach

Electrical Power and Energy Systems 64 (2015) 505–515

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Assessment of maximum distributed generation penetration levels in low voltage networks using a probabilistic approach Marko Kolenc ⇑, Igor Papicˇ, Boštjan Blazˇicˇ University of Ljubljana, Faculty of Electrical Engineering, Trzˇaška 25, 1000 Ljubljana, Slovenia

a r t i c l e

i n f o

Article history: Received 2 September 2013 Received in revised form 16 July 2014 Accepted 26 July 2014

Keywords: Monte Carlo methods Distributed generation Distribution planning Data sampling

a b s t r a c t The main objective of network planning is to determine the technically and economically optimal solution that will ensure continuity of supply and adequate power quality as well as allow further integration of distributed generation (DG), despite its substantial impact on the network performance. The maximum DG penetration level also has to be planned or at least assessed, and is heavily dependent on the DG location and size and on the voltage control method. The paper presents a probabilistic approach to network planning, which has many advantages compared to the traditional approaches using estimated peak values and empirically defined simultaneity factors. The method enables the evaluation of the future voltage conditions and therefore the comparison of different network development scenarios, taking into account the stochastic natures of future DG location and loads consumption. By analyzing different solutions, it is possible to minimize the necessary investments in the network. The planning method is presented on an actual low-voltage (LV) distribution network, but it can be used also in medium-voltage (MV) network planning as well. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction Background Network utilities should always provide sufficient network capacity to meet electricity peak demand [1]; therefore network planning is based on projections of consumption. The analysis usually consists of studying a feeder at a time, using estimated peak values for loads and empirically defined simultaneity factors, as not all the loads operate at their nominal power all the time. Since the only available data is the number of consumers and their requested peak power, the planning is based on some empirically defined rules [2]. Often, little attention is dedicated to the LV networks. The main and usually the only planning criteria in the LV distribution networks is the required voltage-drop compliance with standards. The software tools used for LV network planning are relatively straightforward. Such an approach results in low utilization factors many times [2]. Nevertheless, this type of an empirical approach has served distribution companies well for many years.

⇑ Corresponding author. Tel.: +386 1 4768 901; fax: +386 1 4768 289. E-mail addresses: [email protected] (M. Kolenc), [email protected] (I. Papicˇ), [email protected] (B. Blazˇicˇ). http://dx.doi.org/10.1016/j.ijepes.2014.07.063 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

For better utilization of the current infrastructure and for increasing DG penetration limits at the lowest possible costs, planning could be upgraded to the next level. Due to the stochastic nature of the LV networks, statistical approach seems adequate [3,4]. The initial idea of statistical approach of network planning is that planning with the assumption of the worst possible condition in the network is too pessimistic. Requested capacity is only a single number, providing no insight in the probabilities of occurrences [1]. To form the basis of planning decisions, different from the worst case scenario analysis, an approach which provides information on the probabilities of attributes such as voltage limits or power losses should be used [5]. The paper describes LV network planning based on the statistical Monte Carlo approach, taking into account the stochastic nature of future DG location and stochastic consumption. With random patterns and repetition of experiments, the probabilities of future voltage levels can be calculated and thus the maximum DG penetration limits can be assessed. Problem formulation In recent years, a huge amount of DG is connecting to the network and their growth is still increasing rapidly. Because of this, the network operator’s task is more difficult when planning the LV networks, as he must not only predict the consumption, but also

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the generation from DG. Even if he uses the most advanced methods to determine the amount of newly installed DG, their location usually cannot be determined. To solve this problem, the statistical Monte Carlo method should be used. Since the similar topic is discussed also in [7,8], it has to be noted that the presented method takes into account new options which have not been discussed yet, for example sampling with unequal probabilities, which is presented in Section ‘Solutions for increasing network hosting capacity’. Secondly, when dealing with the necessary number of the Monte Carlo experiments, a confidence interval was set, and this allowed varying the number of experiments depending on the desired accuracy. This problem is not addressed in [7,8], and the number of experiments was fixed to 100. Furthermore, the problem of certain potentially influential variables (e.g. DG size) on the hosting capacity is presented in the paper and discussed. On the basis of the results, obtained by this method, the optimal technical and economical solution for network development can be selected. The advantages of the proposed method are presented on an actual LV distribution network case. However, the method can be used also for MV network planning. The structure of the paper is as follows: the methodology of the proposed network planning approach is presented in Section ‘Methodology’, possible solutions for increasing network hosting capacity are discussed in Section ‘Solutions for increasing network hosting capacity’, the proposed method is validated by a case study in Section ‘Case study’ and, finally, conclusions are given in Section ‘Conclusion’. During the review of this paper some interesting researches which confirm the suitability of this approach have also been published and are cited in the last Section ‘Appendix’. Methodology Statistical Monte Carlo method The Monte Carlo method is used in all branches of science to study systems in which analytical solution cannot be or is hard to be obtained [9]. A specificity of the method is the usage of random section techniques, which provides the approximate solution. When investigating the loading capability of a distribution network, the statistical Monte Carlo method was used in [6]. In [10], it was used when investigating DG systems performance. In [11], the authors presented a method for the selection of the optimal size of a photovoltaic (PV) system, based on the hourly solar radiation. In [1], the Monte Carlo simulation method is applied in dealing with probabilities of occurrences of peak loads and in [12], Monte Carlo is used for evaluating the power system reliability indices. As said already in the introduction, the formulated problem is solved by Monte Carlo method. For example, the operator can predict that in a few years from now in some LV network around 1 MW of PV is to be installed. Two questions arise: how many PV present a total installed capacity of 1 MW and where will they be located. The first question can be fairly easy to answer; an average DG unit has to be considered and the power divided. The location, however, remains unknown in most cases. To solve this problem, the statistical Monte Carlo method with a large number of repetitions can be used. The idea is that the expected number of PV is situated randomly into the network and then the load-flow conducted. This procedure is repeated many times (N times) and in the end, statistical data is obtained, expressing in what percentage of the experiments the voltage levels (or any other criteria) were unsuitable, which can be, in simple form, written as:

PN ¼

M N

ð1Þ

where PN is the non-compliance probability expressed in percentage, M is the number of times when voltage constraints are violated and N is the number of the load-flow calculations (experiments). The larger the number N, more accurately the probability can be defined. If this procedure is conducted for different amounts of installed DG capacity, a curve which provides the probability density function or cumulative density function of relevant variables [6] with respect to installed capacity of DG can be obtained. Sampling without replacement with unequal probabilities One of the important pieces of input data used in the proposed method is based on the analysis of the facilities in the network facing the load growth in the medium and long-term. The likelihood of installing a PV on the facility is given as a weight when randomly selecting the sites. There is a term for this selection process in mathematics which is called ‘‘balanced sampling without replacement with unequal probabilities from a finite population’’. The concept of sampling with unequal probabilities is of recent origin [13]. The use of unequal probabilities in sampling was first suggested in [14] (1943). Some years later the use of symmetric sampling with unequal probabilities was presented [15]. Since then many papers were published dealing with this topic, and many of them are summarized in [13]. This is a wellknown problem in mathematics and appears in all branches of science, especially when solving mathematical problems [16–19]. The usage of this method is proposed in this paper as it avoids the possibility of samples i.e. buildings being selected more than once and takes into account that the probabilities of installing a PV on the facility can vary based on their type, age, connection power, etc. It is important that the network operator makes analysis of the available data and determines whether there are any correlations to be taken into account in the further analysis of their networks. Sampling with unequal probabilities can be expressed analytically. For three numbers, i.e. objects A, B and C, when selecting two of them, the probabilities of occurrence Pa, Pb and Pc can be derived from likelihood three, expressed as:

2

Pa

3

2

1

6 7 6 wb 4 Pb 5 ¼ 4 Ewa wc Pc Ewa

wa Ewb

1 wc Ewb

wa Ewc wb Ewc

32

wa

3

76 7 54 wb 5 1 wc

ð2Þ

where wa, wb and wc are weights for each object and E is the sum of the weights. Eq. (2) can be generalized for any number of variables. The satisfactory number of Monte Carlo load-flow experiments As the results of repeating the experiments N times, the vector v of length N is obtained. It contains only two different numbers:  1 – indicating that in the selected simulation the voltages are inadequate and  0 – indicating that in the selected simulation the voltages are within the limits. This can be written as:

v ð1 . . . NÞ 2 f0; 1g

ð3Þ

where v presents the results vector with a Bernoulli distribution. The voltage limits are defined by SIST EN 50160 standard used by Slovenian utilities [20], which states that under normal operating conditions excluding the periods with interruptions, supply voltage variations should not exceed ±10% of the nominal voltage. In the limit case when the number N goes to the infinity, the probability P1, using (1), can be written as

M. Kolenc et al. / Electrical Power and Energy Systems 64 (2015) 505–515

PN

i¼1

lim

v ðiÞ

N

N!1

¼ x1 ) P1

ð4Þ

where x1 is the arithmetic mean of the vector v, which in the case of an infinite number of load-flows, results in the probability P1. Since an infinite number of samples (load-flow simulations) cannot be taken, approximation with a finite number of N samples has to be given, which can be written as:

x1...N ¼

N 1X v ðiÞ N i¼1

ð5Þ

 x1...N can be also written as P1. . .N. Probability can be predicted more accurately, the greater the number N is. The satisfactory number of load-flow experiments can be determined by the confidence interval. Usually 95% is used. This is the interval for which we can be 95% certain (there is a 95% probability) that the true unknown parameter P1 lies in [21,22]. Analytical formula for the 95% confidence interval of the arithmetic mean is the following:

x1...N 

1:96  r1...N 1:96  r1...N pffiffiffiffi pffiffiffiffi 6 P1 6 x1...N þ N N

where

r1...N is the standard deviation of the sample, defined by:

r1...N

ð6Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 XN 2 ¼ ðv ðiÞ  x1...N Þ i¼1 N1

ð7Þ

In many papers, such as [23–26] a very large number of Monte Carlo simulations is used to obtain a sufficient accuracy, up to 10,000. In our case, a high number of load flows is acceptable only when simulating the voltage conditions for a specific amount of DG in the network. To obtain the probability curves which convey the probability as a function of installed amount of DG in the network, which changes in small steps, the computational time increases greatly. By applying the confidence interval, the desired accuracy can be determined and the necessary simulations reduced greatly. An example of calculating the Monte Carlo probability using confidence interval (6) as a function of the number of simulations N, is presented at the end of the Results section. To simplify the syntax, the probability P1. . .N will be hereinafter simply marked as P. Consumption and generation modelling A characteristic of LV networks is also a very stochastic consumption (beside generation). Consumption no longer has its

0.5

P / kW

0.4 0.3 0.2 0.1 0

0

5

10

15

20

25

Time / one day Fig. 1. Example of a load diagram from of a single Slovenian household (4 measurements per hour).

507

typical form as it is known from MV networks (see Fig. 1) [27] and thus no typical individual consumption exists [1,28]. Also, the form of PV generation diagram varies very quickly as it depends mostly only on the weather which is difficult to predict. Therefore, to consider a stochastic nature of loads when running the simulations, not only DG locations and generation profile were varied but also the loads. A number of random loads were selected from the existing database of measured loads (households) and at each step, when randomly determining the DG locations, also the load profiles were randomly distributed between the households. The existing database of the customer loads consists of real measurements (more than 3000 households) from the smart meters, which were provided by one of the Slovenian distribution utilities. Of course, it should be noted that the connection power of a household has to be taken into account and the load profiles have to be correspondingly scaled.

Load-flow based algorithm Fig. 2 provides a flowchart of the proposed load-flow based algorithm with the following steps: (1) Model a distribution network in a load-flow program. (2) Determine the expected DG penetration using established planning methods. (3) Given the average size of DG in the network and DG penetration, determine their expected number. (4) Determine the probability weights for each building separately, depending on characteristics like age, type (household, commercial building), and connection power. (5) As different events are observed, set their occurence counter to zero. Determine the number of Monte Carlo experiments N and set the initial number to zero. (6) Carry out the sampling with unequal probabilities and allocate DG randomly into the network. (7) Randomly delete some DG based on their expected number in operating condition. (8) Import the load profiles. They can vary in type, days of the week and season. (9) For each type of load, multiple load/generation diagrams exist due to their stochastic nature. Attribute the selected diagrams randomly to the loads. (10) Scale the load profiles properly according to the connection power. (11) Modify the original network according to the aforementioned steps. (12) Now all the necessary data is gathered and thus the loadflow for every day in the week or season and desired observation period can be calculated. (13) The obtained data from every load-flow calculation can be compared and analyzed according to several criteria. The data is saved for later analysis. (14) The procedure returns to step (6) and is repeated N-times, until the maximal predefined number of Monte Carlo repetitions is reached (MAX count). Following this process, a vector v, as defined by (3), is obtained for different observed criteria (count2, count3,. . .) and then the statistical probability can be expressed, using (5). The algorithm is based on the fact that the expected DG installed power is known. If the whole algorithm (except step 1) is repeated for different amounts of DG installed power, curves which provide the information on the probabilities of voltage constraint violations (or any other observed criteria such as thermal constraint violations) with respect to installed capacity of DG can be obtained.

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Model the original distribuon system

Determine the installed DG capacity [kW]

Determine the number of DG based on the average size of one unit

Determine the probability weights for every building Set the counters for different events on the inial value (count = 0, count2 = 0, count3 = 0, count4 = 0) Set the maximal number of random experiments (MAX count) Sampling without replacement with unequal probabilies and randomly allocate DG into the network Randomly delete some DG based on their expected number in operang condion

Import arbitrary number of load and generator diagrams (depending on the season, day of the week)

Random placement of load and generator diagrams to the selected facilies (due to stohasc consumpon/generaon)

Scaling the load diagrams according to the connecon power

Modify the original distribuon system Mulple load-flow calculaon (for each day of the week and season ) count = count + 1 Any other criteria can be counted

Are the voltage limits exceeded ?

Are the elements overloaded?

Are the voltage limits exceeded and the elements overloaded?

count2 = count2 + 1

count3 = count3 + 1

count4 = count4 + 1

count ≥ MAX count

No

Yes END (The stascal data of compliance with the selected criteria (standards) are obtained)

Fig. 2. The algorithm flow chart.

M. Kolenc et al. / Electrical Power and Energy Systems 64 (2015) 505–515

Solutions for increasing network hosting capacity By applying the presented method into the planning process, possible solutions to minimize the future network problems can be evaluated, such as:  Network reinforcement: The network can be reinforced by the installation of additional or bigger transformers or by a replacement of older cables with the thicker ones. By doing so, the serial impedance can be reduced, resulting in the reduced voltage rise. Analysis can be done for transformers of different sizes and cables, replaced only on some parts of the analyzed network.  Use of static Q(U) characteristic: Nowadays, many countries like Slovenia [29] have set up rules for DG to use static characteristic Q(U) for the contribution with the local voltage control [27]. On the basis of local voltage measurement and current active power output of DG, their necessary reactive power is determined. That kind of control allows reducing the voltage at connection point by consuming reactive power and increasing the voltage by injecting it. By implementing this control action into operation of DG, a higher level of DG integration can be achieved, without major intervention into the power grid infrastructure. Example of static Q(U) characteristic prescribed in [29] is presented in Fig. 3. Characteristic in Case (a) is prescribed for DG at LV level (up to 16 A of current per phase) and in Case (b) for DG with up to 250 kW installed capacity.  Installation of the MV/LV OLTC transformer: The classical MV/LV distribution transformers have a fixed step size, which can be changed only manually whenever the transformer is de-energized. OLTC technologies can nowadays also be used at MV/LV voltage transformation. This is a promising technology, as it greatly increases the flexibility of the network [30], but it is unfortunately also very expensive. The implementation of MV/ LV OLTC must thus have a strong economic ground, based on the studies and economic evaluation of an individual network.  Coordinated control: With the implementation of communication technologies, the centralized MV/LV OLTC control can be upgraded with multiple voltages measurement points from the so-called critical nodes and provide the OLTC with a suitable voltage set point [30]. Additionally, this voltage control can be upgraded to a coordinated voltage control. In this way, the reactive power set points can be sent to DG in situations which cannot be solved by the OLTC transformer. The effectiveness of different coordinated voltage controls can also be analyzed with the proposed planning method.

509

 Demand-side management, etc. The implementation of individual actions is strongly linked with the voltage quality, complexity and the expected development of the analyzed network, share of DG in the network and the required financial budget. Case study Defining the input parameters and boundary conditions Before simulating the network, some necessary input data, described in Section ‘Methodology’, have to be defined. For an average size of PV for the simulations, the installed power of 10 kW is presumed. Around 5–6 kW is the average size of PV identified by European Smart Grid project MetaPV [31]. Year-to-year efficiency of newly installed PV is better and their average rated power is higher than ten years ago. It is expected that the average PV installations in the future (at least in Slovenian rural area) is expected to be higher than 6 kW. Ref. [32] gives insight in the PV situation in Slovenia where it can be seen that around 10 kW for PV for one average residential house is fairly common. However, the analysis of the impact that the average size of solar plants has on the voltage profile is also presented in the results section. Simulations are carried out by using unequal sampling. It is assumed that the houses connected to the feeder 4 (see Fig. 5) are older buildings. These objects are given a weight ‘‘0.2’’ and others obtain the weight ‘‘1’’. However, sampling with only equal probabilities is also presented. This way, it can be observed what the impact of the weights on the probability curves, i.e. accuracy of the model on the obtained results is. With the arrival of new technologies, a better insight into the network will be enabled and weights more precisely defined. The load data measurements are quarter-hourly averaged and subdivided to the same type consumer groups. Because of the stochastic nature of the loads, it is rational to have a large number of load profile diagrams at our disposal. Only PV’s are taken into account in the paper, but the analysis can be easily generalized to other types, such as wind or small hydro power plants. The seasonal diagrams, which vary mostly upon the weather, are used for PV diagrams. When planning the LV networks, it has to be noted that the voltage at the primary side of the distribution transformer is not constant. The MV voltage when planning the LV network is dependent upon the daily fluctuations of consumption and generation, the

Fig. 3. Example of static Q(U) characteristic for DG.

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location along the MV feeder, the installed level of DG, and upon the type of different possible voltage control. Each OLTC transformer has an associated automatic-voltage-control relay which can monitor the voltage of the transformer secondary or uses line-drop compensation (compounding) to adjust the tap position [33]. This highlights the fact that the LV network planning strongly depends upon the MV network situation and thus it also has to be analyzed. However, to represent the dynamic voltage at the primary side of the transformer, HV/MV OLTC control is assumed to be upgraded to use multiple measurement points in real time in the critical areas around the network. Taking into account the voltage drop on an MV/LV transformer, ±2.5% and ±5% adjustable step and LV feeders feeding loads, the MV voltage limits are set to ±5%. Similar OLTC control when analyzing MV network performance is used in [27]. Since the simulation of a whole day is time-consuming, simulation is performed only for three most interesting operation conditions. Similar approach was taken in [3], where the authors also simulated one-year situation when dealing with numerical tools for Monte Carlo studies in distribution networks. They divided one day into periods in which the statistical parameters of the loads and DG are constant; these periods are:  peak hours,  day-off peak and  night,

rated power, located in the transformer station. Maximum operating power measured through the transformer is 120 kV A; at such loading the minimal voltage in the network may drop to around 0.92 p.u. which happens usually in the January. The network supplies 84 customers in the rural area. Typical shape of consumption of 84 consumers is presented in Fig. 4. The cables are of type X00-A, X00/0-A; the main lines have cross section 150 and 70, and more distant lines consist of 35 and 16 cables (mm2). Total length of fall the cables is 5580 m. The length of the cables divided by the different R/X ratio is:    

936 m of 150 mm2 cable: R/X = 1.25, 2012 m of 70 mm2 cable: R/X = 5, 995 m of 35 mm2 cable: R/X = 0.98, 1636 m of 16 mm2 cable: R/X = 21.

The single-line diagram of the analyzed network is shown in Fig. 5. The majority of network consist of overhead lines, and only the dashed lines indicate the underground cable. The loads and DG were modeled as R–X impedances, of which the loads are also voltage dependent (in the voltage range 90– 110% of the nominal value) and were modeled as composite loads consisting of 60% constant impedance and 40% constant power [34]. For loads, a power factor cos u  0.95 was presumed. The network was modeled in Matpower 4.1 [35]. Simulation results

for each of the four seasons. By doing so, the duration of overvoltage cannot be defined anymore; only the data in case of a violation is detected and counted, as noted by (3). We can go further by reducing the number of simulations to obtain quicker computational time. In the end, only summer Wednesday can be left in which case similar results would be obtained as this tends to be the worst case scenario (see the Results section). However, by doing this interesting indicators are lost which can be used for more than just network planning, for example displaying the results by days and seasons, etc. Nevertheless, according to the needs, the method can be easily manipulated and changed.

Simulation results for different, previously described technical solutions for increasing DG share in the network are analyzed in this section. The results present the probability (P) of voltage

Simulated network description To illustrate some practical implications of the proposed voltage-control algorithm, the operation is demonstrated on an actual LV Slovenian distribution network model which is located relatively near an HV/LV OLTC transformer substation. The network operates radially and is fed by 20/0.4 kV transformer of 160 kV A

150

P / kW

100

50

0

0

5

10

15

20

25

Time / one day Fig. 4. Typical load diagram of 84 consumers.

Fig. 5. LV distribution system under study.

511

100

100

80

80

Probability / %

Probability / %

M. Kolenc et al. / Electrical Power and Energy Systems 64 (2015) 505–515

60 40

Probability P using peak values Probability P using me varying load profiles

20

60 40 PV operate using cosφ = 1 PV operate using Q(U)

20

5 % probability 0

0

100

200

300 400 500 Installed power/ kW

600

700

800

Fig. 6. Comparison of probability curves in the case of classical network planning and in the case of planning using time-varying load profiles. DG operate with cos u = 1 and current 160 kV A MV/LV distribution transformer is used for all the cases.

violations in the network as a function of installed PV capacity in the network. Firstly, the comparison between a conservative planning method, considering worst case scenarios (maximal consumption and no generation, minimal consumption and maximal generation), and the method, taking into account varying load profiles, is given. The blue1 line in Fig. 6 presents the conservative planning approach and the red line using time-varying load profiles. It can be observed that conservative planning, assuming only worst case scenarios, can result in an oversized network. The red probability curve (PV inverters operate with cos u = 1) will be taken as a reference when comparing different network planning solutions. At a 5% acceptable risk, the hosting capacity amounts to 170 kW. In the previous example, photovoltaics operated with a constant power factor cos u = 1. By using the static Q(U) characteristic, as discussed in Section ‘Solutions for increasing network hosting capacity’, the hosting capacity increases. In Fig. 7, voltage situation comparing both cases is presented. The red line presents the reference probability curve when photovoltaics operated with a constant power factor of 1 and the green line presents using static Q(U) characteristic. It can be seen that the maximum allowable installed power of DG has increased. At a 5% acceptable risk, the value is around 205 kW, which is a 35 kW (21%) improvement. Although the allowable installed power of all DG is higher than the transformer nominal power, which is 160 kV A, the transformer is not overloaded. Around noon, when the generation is highest, the consumption is also relatively high and not all generated power is flowing through the transformer into the MV network. The average power flowing through the transformer into the MV grid at 5% probability at noon is around 90–115 kV A (depends mostly on the solar irradiation). Fig. 8 presents the situation in case of the installation of a bigger transformer, with a rated power of 250 kV A, which is the next commercially available transformer size. The red line presents the probability curve with the current 160 kV A transformer and when all photovoltaics operate with cos u = 1. The blue line presents the situation when the current transformer was replaced with a 250 kV A transformer. If a bigger transformer is installed into the network, the voltage drop due to the loads decreases. Therefore, the static tap position has to be lowered. The hosting capacity increases for about 80 kW (47%) and amounts to 250 kW. Furthermore, the blue curve presents probability in the

1 For interpretation of color in Figs. 6–10 and 14, the reader is referred to the web version of this article.

5 % probability 0

0

100

200

300 400 500 Installed power / kW

600

700

800

Fig. 7. Comparison of probability curves in the case of cos u = 1 operation and static Q(U) operation. Current 160 kV A MV/LV distribution transformer is used for all the cases.

case of 250 kV A transformer and PV Q(U) operation. The voltage situation is even better in this case; there is also no concern of overloading the transformer as the average power flowing through the transformer is 105–140 kV A, which means that the transformer is 50% loaded during the peak hours. It has also to be noted that the installation of a bigger transformer has its own limits. The analysis was made also for a 400 kV A transformer. It turns out that the probability curves are no better than for the 250 kV A transformer as the transformer voltage drop is already very small in the latter case. Next, the existing 160 kV A transformer was replaced with the MV/LV OLTC transformer and centralized control, where the tap position is controlled based on multiple voltage measurements in the network. The OLTC has the possibility of 9 steps in the range of 0.75% [36]. The new voltage situation is presented in Fig. 9. The red line presents the reference probability curve using the existing 160 kV A transformer and DG constant power factor operation. The blue line presents the probability curve in the case of a new MV/LV OLTC transformer. Additionally, the green line presents the probability curve for the combination of the MV/LV OLTC transformer and the use of static Q(U) characteristics of DG. The hosting capacity increases for 190 kW (112%) and amounts to 360 kW. The average power flowing through the transformer at 5% probability is around 165–200 kV A, which means that at noon the transformer will be overloaded for a short time. The border which defines hosting capacity is, in this case, determined by the nominal power of the distribution transformer. However, if the 160 kV A transformer is replaced by 250 kV A MV/LV OLTC, the hosting capacity is 400 kW (135% improvement) and maximal power flowing through transformer at 5% probability at noon is around 180–225 kV A. Let us now consider the influence of sampling with unequal vs. equal probabilities. As described in Section ‘Defining the input parameters and boundary conditions’, the houses connected to the feeder 4 are assumed to be older buildings and are given the weight ‘‘0.2’’ and others obtain the weight ‘‘1’’. In the following example, all the buildings have the same weight ‘‘1’’. In this way, we can observe the impact of the weights on the probability curves, i.e. the accuracy of the model on the obtained results. The blue line in Fig. 10 presents the results when sampling with unequal probabilities and the green line, curve when sampling with equal probabilities. For both cases, the installation of 160 kV A MV/LV OLTC transformer was considered. The benefits of having an MV/LV OLTC transformer increases greatly when the distribution sources are more homogenous. As a consequence of this homogenous penetration, feeders exhibit similar properties and voltage rise occurs in almost all feeders.

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100

Probability / %

80

60

Current 160 kVA transformer & PV operate using cosφ = 1

40

Bigger, 250 kVA transformer & PV operate using cosφ = 1

20

Bigger, 250 kVA transformer & PV operate using Q(U) 5 % probability

0

0

100

200

300

400 500 600 Installed power / kW

700

800

900

1000

Fig. 8. Comparison of probability curves in the case of installation of a bigger distribution MV/LV transformer.

100

Probability / %

80

60

Current 160 kVA transformer & PV operate using cosφ = 1

40

Use of 160 kVA OLTC transformer & PV operate using cosφ = 1

20

Use of 160 kVA OLTC transformer & PV operate using Q(U)

5 % probability 0

0

100

200

300

400 500 600 Installed power / kW

700

800

900

1000

Fig. 9. Comparison of probability curves in the case of installation of 160 MV/LV OLTC transformer.

100

Probability / %

80

60

Current 160 kVA transformer & PV operate using cosφ = 1 & Sampling with unequal probabilies

40

Use of 160 kVA OLTC transformer & PV operate using cosφ = 1 & Sampling with unequal probabilies Use of 160 kVA OLTC transformer & PV operate using Q(U) & Sampling with equal probabilies

20

5 % probability 0

0

100

200

300

400 500 600 Installed power / kW

700

800

900

1000

Fig. 10. Comparison of probability curves in the case of sampling with unequal and sampling with equal probabilities.

However, if sampling with unequal probabilities is taken into account, the feeder 4 exhibits different properties as the others, the voltage rise does not occur in such an extent and when shifting the tap-changer, the lower limit for this feeder is reached sooner, which means that OLTC cannot minimize the voltage rise anymore. In this case, different actions have to be taken into account, if possible for example reinforcement of certain lines in the feeder 4 or the implementation of reactive power control. It can be observed that the precise input data and a precise method can have a great impact on the planning results, especially when considering implementing an MV/LV OLTC transformer. By implementing

new technologies into the LV distribution networks, the newly acquired available data have to be analyzed and determined whether there exist any useful correlations to be taken into account in the further analysis and thus planning improved. Table 1 summarizes the simulation results showing the DG capacity (penetration level) when there is a 5% probability that the voltage limits are exceeded at least once a year (assuming that this is an acceptable risk when planning the network and defines the maximal amount of DG that can be connected to the network). Firstly, it can be seen that only the improvement of the planning methods with the use of actual load profiles, can help increase

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M. Kolenc et al. / Electrical Power and Energy Systems 64 (2015) 505–515 Table 1 Comparison of different investments based on acceptable risk.

a

Action/operation mode

Max. amount of installed DG capacity at the 5% acceptable risk (kW)

Capacity increase (%)

Classic (conservative) network planning (DG ? max., PLOAD = 0); DG operate with cos u = 1 New probabilistic network planning; DG operate with cos u = 1 New probabilistic network planning; DG operate using Q(U) Installation of bigger transformer (250 kV A); DG operate with cos u = 1 Installation of 160 kV A MV/LV OLTC transformer; DG operate with cos u = 1 Installation of 250 kV A MV/LV OLTC transformer; DG operate with cos u = 1 Installation of 160 kV A MV/LV OLTC transformer; sampling with equal probabilities; DG operate with cos u = 1

115

/

170 205 250 360a 400 438a

Base case 21 47 112a 135 158a

Only voltage limit violations criteria is considered.

100

Monday

100

Probability / %

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60

5 kW average PV units 40

7 kW average PV units

20

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40

Friday Saturday

20

Sunday

5 % probability 0

100

200

300

400

500

15 kW average PV units 5 % probability 100

200

300 400 500 Installed power / kW

600

700

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Fig. 11. Probability curves for different average size of PV. Average size of photovoltaics has to be carefully considered as it has a great influence on the results.

the utilization of the system. Secondly, in some cases it may seem that the acceptable installed power is relatively high and the transformers or cables could be overloaded. We must bear in mind that the actual generation is never the same as the installed power. Nevertheless, as presented by the flowchart in Fig. 2, the overloading of the elements should or can be taken into account as well. In all previous cases, the average size of one PV unit was 10 kW; if the installed capacity increases, the number of photovoltaics increases. Assuming different average size of photovoltaics, the probability curves change is presented in Fig. 11. It can be observed that if the DG units are smaller and more spread, the voltage violations occur at higher values of installed PV capacity. If the units are larger and their number is smaller, the voltage violations occur at smaller values of installed photovoltaics. However, one big PV unit at the end of the feeder could result in higher violated voltage rise compared to the larger number of smaller PV units distributed through the same feeder. The choice of determining an average size of PV unit, therefore, has to be, due to the significant impact on the results, precisely defined. In this study, a relatively large average PV unit has been chosen, whereas at the lower values the results are better. The presented method is very flexible and it can be used to represent a variety of information. Fig. 12 presents voltage conditions for summer, midseason and winter peak for different days during the week and Fig. 13 presents the voltage conditions for Wednesdays for different times of year and different hours (peak, night and day-off peak). Different correlations can be identified using such an accurate representation of the results, for example, it can be seen that in the presented case there were less voltage constraint violations during the weekends, which is logical since the consumption of residential customers is higher on those days. It can also be observed that the voltage violations first begin to

Probability / %

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600 700 800 Installed power / kW

80 60 40 20

5 % probability

0

0

100

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500

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0

80 60

0

10 kW average PV units

Peak summer day

Tuesday Wednesday

80 60 40 20 0

5 % probability 0

100

200

300

400

Fig. 12. Probability curves splitted by season and by day of the week.

appear during the summer peak hours. Therefore, the question arises if there really is a need to make the voltage calculations for weekends and for winter days. To obtain the accurate results for the particular type of network with a high share of photovoltaics and minimal average consumption during the summer, analyzing only summer working days during the peak hours would be sufficient. The red line in Fig. 14 presents an example of probability dependence on the number of experiments N by using (5). It can be seen that after a series of experiments the bulk of samples settles around one point. The red curve presents the arithmetic mean of the samples which presents the probability P. Using (6), the 95% confidence of the arithmetic mean is determined, presented as the two blue lines above and below the arithmetic mean curve. The green line presents the width of the confidence interval. It can be observed that in the presented case, for a confidence interval of

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Winter peak

Wednesday

Winter dayoff peak

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80

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60 0

Midseason night

40 0

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20

Summer night 5 % probability

0

0

100

200

300 400 500 Installed power / kW

600

700

800

Fig. 13. Probability curves for Wednesdays for different times of year and different hours (midday peak, night and day-off peak).

100 Probability P 95 % confidence interval

Probability / %

80

Width of the 95 % confidence interval 60

40

20

0

technical and economical optimal solutions and allows further integration of DG, despite its substantial impact on the network performance. With random patterns and repetition of experiments using the Monte Carlo approach, the voltage situation in the future can be assessed. Curves which convey the violation probability of voltage constraints (i.e. deviations from the standards) as a function of expected DG capacity, can be obtained. The results show that the accuracy of planning relies heavily on the assumptions relating the predicted customer load profiles and the network model. The proposed method is simple in structure and easy to manipulate. The results can be obtained using different amounts of input data which allows planning with different desired accuracy; if more data is available the network can be planned more precisely. This method can, therefore, also be used to improve the network planning by considering the data which until now were not taken into account. Our future work will be focused on the development of planning software with optimization of operation speed and compliance with SIST EN 50160 standard, paying attention to the selection of accurate input data. In this paper, only LV network planning is presented; by analyzing also the MV network, the proposed approach presents a viable alternative for today’s established distribution planning methods. Appendix A

0

1000

2000

3000

4000

5000

6000

Number of experiments Fig. 14. Dependence of the probability P upon the number of experiments N.

less than ±5%, the necessary number of experiments is N = 309, for ±2.5% N = 1260 and for ±1% N = 7555. Nevertheless, the desired satisfactory accuracy has to be determined by the network planner. The best solution for increasing hosting capability is a compromise between the amount of increased hosting capacity and the necessary investment. Because of this it is difficult to define the best solution and the decision depends upon the engineering judgement. However, in the presented case-study it can be seen that only by locally changing the power factor of photovoltaics, a significant increase in allowable PV penetration can be achieved with little intervention into the grid. Thus, if there is any existing ICT already in the network, such as a communication infrastructure, it could be considered for establishing a coordinated voltage control. If this is not possible, investments into the network infrastructure are needed. According to the analyzed solutions, installation of an MV/LV OLTC transformer with multiple voltage measurement points is technically the most effective, however, also costly. If the replacement of the current 160 kV A transformer with a bigger 250 kV A transformer is considered, the hosting capacity increases for about 80 kW (47%), which seems reasonable compromise. Also, if deciding for this option of network reinforcement, the estimated investment costs can be reduced by taking into account that the replaced transformer can be reused in a weaker network. Conclusion Numerous electric utilities are still using the methods for LV network planning which are based on estimated peak values for loads and empirically defined simultaneity factors, which usually results in the low utilization of the system. Such approach also ignores the increasing number of DG, which is the main reason to upgrade the ‘classic’ network planning. The presented solution is based on a statistical planning method, which allows determining

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