Assessing the Voltages and Currents in a large DutchRegional Power Distribution Grid

Werner van Westering∗§, Jacco Heres§, Tobias Dekker§, Matthijs Danes§ and Hans Hellendoorn∗∗Delft Center of Systems & Control, Delft University of Technology,

Delft, Mekelweg 2 2628CD, The Netherlands§Alliander N.V., Duiven, Dijkgraaf 4, 6921 RL, The Netherlands

Abstract—Modeling low voltage networks poses a challenge toDistribution System Operators (DSOs) because the low voltagenetworks generally consists of millions of cables. This paper pro-vides a method to model congestion problems and applies this tosuch a large low voltage network. By modifying the load model ofa customer, a linear load flow model was created. Using a customsparse solver model, all instantaneous currents and voltages werecalculated for the network of Liander DSO, containing over 20million cables and 3 million power customers. The model tookonly 30 seconds to simulate the entire network. The results showsthat the network of Liander DSO can accommodate quite a largenumber of solar power installations with relative ease. Also, step-change transformers are shown to have quite some potential tosolve voltage issues that can arise due to solar power.

Keywords—Distribution grid, Energy transition, Power quality,Voltage problems, Load flow approximations,

I. INTRODUCTION

The energy landscape is expected to change significantly inthe Netherlands over the next decades, as the share of renew-able energy is increasing. This poses a significant challenge forDistribution System Operators (DSOs), which are responsiblefor maintaining a reliable and affordable electricity distributiongrid. Especially the rise of solar power is challenging, as theseinstallations can cause local voltage problems which can bevery expensive to solve.

While large scale medium voltage networks have beenstudied to some extend [1][2], large scale low voltage networkshave not had much attention. One of the major uncertaintiesin low voltage networks is the actual number of problemsthe solar power installations will cause. This paper providesa method to model congestion problems in very large lowvoltage networks, which makes it possible to anticipate theseproblems.

Subject of this study is the Liander DSO low voltage elec-tricity grid. This network operates at 230V (single phase) andconnected to higher voltage levels by distribution transformers.Liander DSO is the largest distribution grid operator in theNetherlands with over three million electricity customers.

II. MODEL ASSUMPTIONS AND PRINCIPLES

Conventional load flow models have been around for along time [3]. However, most load flow solvers are only fitto solve networks up to medium size. Solving the load flowequations for networks with over 1,000 buses is already quitea computational challenge. The Liander network has over

3.1 million buses, making conventional solutions, such as thewidely used Newton Raphson method[3], unsuitable.

The model proposed in this paper is a regular load flowmodel based on Ohms law, but with one major differencein assumption. In conventional load flow modeling, the endusers are modeled as requiring a ’constant power load’, thusdecoupling their energy use from the power grid entirely,as any difference in voltage will not influence the powerconsumption of the end user.

However, it can be argued that modeling the end users as a’contstant impedance’ load model is at least just as accuratelyas a ’constant power’ load model. In reality, customers willhave a mix of devices which require a constant power load,such as home computers and TVs, and devices which are inreality a constant impedance load, such as boilers and heaters.

Modeling all end users as a constant impedance load has adistinct advantage. The load flow equations can be made linearand without iterations. Because of the linear properties of thismodified power flow problem, it can be solved for very largenetworks in a very short time span.

III. RESULTS

All end user voltages in the Liander service area werecalculated. Using an custom sparse linear solver and a singlecore of an Intel Xeon 2.1370 GHz CPU, the network equationsLiander network containing over 3 million buses and 20million cables was solved within 30 seconds.

The Dutch voltage regulations require the end user voltageto be 230V +/- 10%. Figure 1 shows the number of voltageproblems in the Liander service area if all customers use 1.1kW. The number of 1.1 kW was chosen because this is thecurrently used ’design power’ in Liander asset management.However, the 1.1 kW power load is not entirely realistic,since the coincidence-formula’s such as Velander [4] were notapplied. The transformers were set at 230V. It can be notedthat since the model is linear, from which can be concludedthat the map of problems due to a feed-in of 1.1 kW will lookexactly the same.

Table I shows the percentage of voltage problems atcustomers in the whole Liander service area. All customersare given a certain peak PV power. The ’Voltage’ correspondsto the single phase voltage at the secondary side of thetransformer.

At a feed-in power 10W, transformer tap setting #1 alreadyresults in 100% power problems. This is to be expected,

Fig. 1. Voltage problems in the low voltage networks in the Liander servicearea if all customers were given a 1.1 kW peak solar panel installation.

since the voltage at the transformer is already 253V, which isprecisely the maximum allowed voltage. Also, the percentagesat 5.5 kW are particularly interesting, since this is the currentlylargest single phase allowed peak PV power for a single userby Dutch law.

It can be observed that many problems can potentially besolved by changing the tap setting of the transformer. However,the current calculations do not take potential problems dueto regular load into account. It may very well be that bymitigating a feed-in voltage problem by changing the tapsetting a load voltage problem is created. This is subject tofurther study.

TABLE I. PERCENTAGE OF VOLTAGE PROBLEMS AT LIANDER’SAPPROXIMATELY THREE MILLION CUSTOMERS GIVEN A CERTAIN PEAK PV

POWER AND TRANSFORMER TAP SETTING.

Tap setting 1 2 3 4 5Voltage 253V 248V 242V 236V 231V

PV Power 10W 100% 0% 0% 0% 0%500W 100% 4% 1% 0% 0%1000W 100% 16% 4% 2% 1%2000W 100% 37% 33% 6% 4%4000W 100% 60% 33% 20% 13%5500W 100% 70% 44% 29% 22%8000W 100% 78% 57% 42% 33%

IV. CONCLUSION

A model has been constructed which is capable of calcu-lating all voltages in the Liander service area in a very shorttime span. The model is fast enough to be used in a timeseries approach, opening a array of new applications. First ofall, it will be used to determine the number of expected voltageproblems due to the energy transition.

Secondly, the model will be used to assess the usefulnessof one of the proposed solution to voltage problems, namelydynamic step-change transformers which can change theirtap settings multiple times a day. The model will be usedfor determining in which cases step-change transformers arenecessary to solve the voltage problems due to new energytechniques and in which cases a single transformer tap changeis sufficient.

Furthermore, the proposed low voltage model is currentlya part of the Liander project ’Buurtbatterij’, which translatesto ’Neighbourhood Battery’. The model is used to detect andpredict congestion problems, both voltage and current wise.The controller of the neighbourhood battery then anticipateson possible congestion problems by ensuring that it is eitherfull or empty.

The developed model deviates around a percent of regularload flow models in typical low voltage networks. A fullvalidation using low voltage measurement data is part of the’Buurtbatterij’ project.

With this versatile and fast low voltage network model,Liander DSO can monitor the most important aspects ofits low voltage network, namely voltage and currents. Thiswill help accommodating new energy technologies in the lowvoltage networks, thereby accelerating the transition to a moresustainable energy society.

REFERENCES

[1] W. van Westering et al., Assessing and mitigating the impact of the energydemand in 2030 on the dutch regional power distribution grid, 2016IEEE 13th International Conference on Networking, Sensing, and Control(ICNSC),2016

[2] Else Veldman, Madeleine Gibescu, Han (J.G.) Slootweg, Wil L. Kling,Scenario-based modelling of future residential electricity demands andassessing their impact on distribution grids, Energy Policy, Volume 56,May 2013, Pages 233-247, ISSN 0301-4215

[3] B. Stott, Review of load-flow calculation methods, Proceedings of theIEEE, vol. 62, no. 7, pp. 916-929, July 1974.

[4] E. Lakervi, E.J. Holmes, Electrical distribution network design, 2ndEdition, IEEE Power Engineering Series 21, 2003