UPTEC ES13 002
Examensarbete 15 hp
Juni 2012
Hosting capacity for photovoltaics
in Swedish distribution grids
Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student
Abstract
Hosting capacity for photovoltaics in Swedish
distribution grids
Tobias Walla
For planning issues, it is useful to know the upper limit for photovoltaics (PV) in the electrical grid with current design and operation (defined as hosting capacity) and how this limit can be increased. Future costs for grid reinforcement can be avoided if measures are taken to implement smart grid technology in the distribution grid.
The aim of this project is to identify challenges in Swedish electricity distribution grids with a high penetration of local generation of electricity from PV. The aim is also to help Swedish Distribution System Operators (DSOs) to better understand hosting capacity issues, and to see which room for PV
integration there is before there is need for actions to maintain power quality.
Three distribution grids are modelled and simulated in Matlab: Rural area, Residential area and City (Stockholm Royal Seaport). Since the project is a cooperation between Uppsala University and Fortum, three different representative grids from Fortum’s grid software ”Power Grid” have been used as input to a flexible simulation program developed at Uppsala University. The simulation includes Newton-Raphson power-flow computing but has also been improved with a model of the temperature dependency of the resistance.
The results show that there is room for a lot of PV systems in the Swedish grids. When using voltage rise above 1.1 p.u. voltage as limitation, the hosting capacity 60% PV electricity generation as a fraction of the yearly load were determined for the rural grid and the suburban grid. For the city grid, which is very robust, the hosting capacity 325% was determined. When using overload as limitation, the hosting
capacities 70%, 20% and 25%, were determined for the same grids.
Executive Summary
This thesis examines the hosting capacity (maximum amount of added distributed gen-eration with current grid and opgen-eration) for PV in three representative Swedish distri-bution grids. It is shown to be between 20% and 325% in all grids, depending on as-sumptions. This means that all houses can produce 20% of electricity self-consumption without causing problems to the power quality, which is a significant amount. The re-sults also show that overvoltage problems only occur in a limited number of hours of the year, and can therefore be dealt with in quite easy ways.
Popul¨
arvetenskaplig sammanfattning
I detta examensarbete vid civilingenj¨orsprogrammet i energisystem vid Uppsala Uni-versitet och SLU unders¨oks hur mycket solceller som kan installeras i distibutionsn¨aten innan det blir vissa specifika elkvalitetsproblem. Studien genomf¨ors med hj¨alp av dator-simulering i mjukvaran Matlab.
Men varf¨or unders¨oka storskalig solenergiutbyggnad i Sverige, som ju ¨and˚a ligger p˚a en v¨aldigt nordlig breddgrad? Jo, framf¨orallt av tv˚a olika sk¨al:
1. Delar av Sverige har samma solelpotential som norra Frankrike eller Tyskland. Detta beror framf¨or allt p˚a att instr˚alningen mot optimalt vinklade ytor inte ¨ar l¨agre, men ocks˚a p˚a att vi har ett kallare klimat och d¨arf¨or mer h¨ogpresterande solceller.
2. Solcellspriserna har rasat de senaste ˚aren, vilket g¨or att ˚aterbetalningstider under 10 ˚ar b¨orjar bli m¨ojliga.
Examensarbetet tar avstamp i erfarenheterna kring solceller fr˚an andra europeiska l¨ander (fr¨amst Tyskland), d¨ar kostsamma n¨atf¨orst¨arkningar och ¨okad risk f¨or blackouts (dvs. omfattande str¨omavbrott) har varit baksidan av en annars v¨aldigt lyckad solcellsexpan-sion. Begreppet ”hosting capacity” (acceptansgr¨ans) beskriver hur mycket solel som f˚ar plats i distributionsn¨atet innan oacceptabla avvikelser inom vissa givna elkvalitetsindika-torer uppst˚ar.
Genom att simulera tre olika svenska eln¨at hos Fortum, med data s˚a n¨ara verkligheten som m¨ojligt, har acceptansgr¨ansen best¨amts med avseende p˚a l˚angsamma sp¨ annings-variationer samt ¨overbelastning i kablar och s¨akringar. Simuleringen bygger vidare p˚a ett ber¨akningsprogram i Matlab som Joakim Wid´en (forskare vid Uppsala Universitet) utvecklat i sin doktorsavhandling. I examensarbetet har dessutom en modell f¨or kabel-resistansens temperaturberoende samt testrutiner f¨or maxkapaciteter implementerats i programmet.
n¨ar milj¨okrav i nya stadsdelar best¨ams. Exempelvis har de senaste etapperna i Norra Djurg˚ardsstaden krav p˚a 30% egenproduktion av fastighetsel, n˚agot som man i simu-leringarna ser ligger l˚angt under maxgr¨ansen f¨or vad n¨atet klarar av.
Preface
Contents
1 Introduction 7 1.1 Background . . . 7 1.2 Aim . . . 8 1.3 Research questions . . . 8 1.4 Expected contributions . . . 91.5 Scope and delimitations . . . 10
1.6 Structure . . . 10
2 Theory 10 2.1 Hosting capacity . . . 10
2.2 Standards and terminology . . . 10
2.3 Power flow calculation . . . 12
2.4 Cable temperature . . . 12
3 Methods and data 13 3.1 Literature survey . . . 14
3.2 Simulation in Matlab . . . 15
3.3 Case grids . . . 17
3.4 Peak condition simulation . . . 25
3.5 Monte Carlo simulation . . . 25
4 Results and analysis 29 4.1 Summary of literature review . . . 29
4.2 Peak condition . . . 30
4.3 Monte Carlo simulation . . . 40
4.4 Comparison with other grids . . . 42
4.5 Validation of results . . . 42
5 Discussion 44 5.1 General discussion regarding the results . . . 44
5.2 How to increase hosting capacity? . . . 45
5.3 Sources of error . . . 45
5.4 Lessons from project . . . 46
5.5 Further work . . . 46
5.6 Rules of thumb for Fortum . . . 47
Abbreviations
• DG - Distributed generation
• DSO - Distribution System Operator • HPPV - High penetration photovoltaics
• kWp - Kilowatt peak. Nominal power from photovoltaic device under standard
test conditions (STC). This measure is often used to compare di↵erent PV panels. • NZEB - Net zero energy buildings
• PV - Photovoltaics
1
Introduction
1.1 Background
During the last two decades the installed photovoltaic (PV) capacity in the world has in-creased almost exponentially. Global PV installation during 2011 rose by approximately 26 GWp and reached 66 GWp according to analysts [1, 2]. Germany has historically
been the dominating actor, but they were last year passed by Italy as the biggest PV investment market [3]. These kinds of massive increases of PV systems have led to new challenges for the electrical distribution grid. To avoid problems such as damaged com-ponents, it is important to study the implications for the power system from extensive PV deployment. This should be done even if the problems have not yet occurred in Sweden, since development can be very rapid, as seen in a couple of European countries. When economical and legal obstacles are removed, the possibility to have a solar energy expansion boom is quite large in Sweden since the global PV production and sales mar-kets are already highly developed. And since research and knowledge about this type of system questions possibly takes a long time to build up, it is important to start studying these issues well in advance.
Even if a big part of the globally installed PV power comes from large-scale solar power plants it is more likely that Sweden will focus on smaller setups, due to our geographic location. These systems are often connected to the power system by the distribution grid. With extensive PV system deployment in the distribution grid, overvoltage and overload in components will be the major limiting factors of how much solar electricity can be injected [4]. The maximum limit to distributed generation possible in an existing grid with current operation is often called hosting capacity [5]. By controlling the balance between active and reactive power in a PV inverter, the net voltage can be lowered, thereby making it possible to increase the hosting capacity and simultaneously be able to skip expensive reinforcements of the grid [2]. There is a need to review the grid codes for middle and low voltage grids to improve the system supporting functions, also called ancillary services, of PV inverters.
Even if solar electricity is a very small contributor in the Swedish energy mix, there are a number of reasons why it is good to learn from other countries’ experiences. First, it is a fact that the solar energy penetration level can rise significantly in a short time, if the right conditions occur. Germany, Italy and Spain have all had PV booms, driven by economical reasons. When the life cycle cost is paid back by sales income and subsidies in a reasonable length of time, there is nowadays no real hindrance for PV growth. In the three named countries there have been big subsidies to solar electricity; mainly as feed in tari↵s [2].
taken to implement smart grid technology in the distribution grid. Experience from Germany shows that much planning can be done in advance of extensive PV deployment in order to save money and permit a higher amount of renewable energy generation in the distribution grids [4].
Stockholm Royal Seaport (Norra Djurg˚ardsstaden) will in some years reach a for Sweden unusually high penetration level of PV-DG (distributed photovoltaic generation). This is mainly because of new requirements on local energy supply on landlords from the Municipality of Stockholm[6]. This is why it is important for Fortum to know the hosting capacity for this type of grid, in order to communicate the right message to the politicians and avoid future power quality problems. There is also a general lack of knowledge at Swedish distribution system operators (DSO’s) on how much solar electricity that can be injected into the grid before power quality deviates from allowed regions.
1.2 Aim
The main aim is to quantify hosting capacity for PV in Swedish distributions grids. Another aim is to help Swedish DSO’s to better understand hosting capacity issues, and give rules of thumbs for planning and knowing the ”safe operation space” for PV injection.
1.3 Research questions
The project’s goal is to answer the following research questions:
1. What can be learnt from other countries concerning hosting capacity for photovoltaics in distribution grids?
2. How much solar electricity can be installed in some representative Swedish distribution grids before reaching the hosting capacity?
3. How could the hosting capacity be increased in order to handle more solar electricity?
These questions are described in more detail below, in terms of methodology and moti-vation for inclusion in the project.
1.3.1 What can be learnt from other countries concerning hosting capacity for photovoltaics in distribution grids?
economic and technologic viewpoints? Empirical results from some key components, such as PV inverters, smart substations, reactive power control and energy storage systems are of big interest.
1.3.2 How much solar electricity can be installed in some representative Swedish distribution grids before reaching the hosting capacity? Answering this question involves many di↵erent simulation tasks that are performed in the calculation software Matlab.
Firstly a single time step simulation will be conducted, with the so-called peak conditions (maximum PV generation and minimum load) as input data. Thereafter a Monte Carlo simulation will be done (see section 3.5) , which will be based on distribution profiles from simulated PV generation characteristic and measured household electricity usage patterns. In this way the impact on the grid from the PV systems will be easier to fully grasp. This objective is mainly focused on the voltage rise impact from PV systems, but some overload issues are also examined.
Three distribution grids are modelled: City (Stockholm Royal Seaport), Residential area and Rural area. The first two are low-voltage grids and the last one is a middle-voltage grid. As much real data as possible are used to model the grids, but where that is not possible some estimation or data from other locations are used.
1.3.3 How could the hosting capacity be increased in order to handle more solar electricity?
The answer to this question is based on answers to the first two questions. Results from simulations are combined with experience from real full-scale projects, and is then condensed to guidelines and observations that can be used by DSO’s, politicians and other interested parties. This is done as a concluding discussion.
1.4 Expected contributions
The main contribution to the scientific area is mainly to implement some scientific meth-ods on real grids with real load and cable data. The report will be transformed into a conference paper that will be included as an oral presentation in the 27th European Photovoltaic Solar Energy Conference in Frankfurt 24-28 of September 2012.
1.5 Scope and delimitations
The project is mainly a simulation study of physical limitations in the electrical grid. Therefore some areas must be omitted, such as economy, urban development, environ-mental and policy issues. Since this project belongs to an interdisciplinary field these areas are probably as important as the technical issues for PV deployment. One example is that the awareness of the climate crisis makes politicians change taxes in order to make it easier for PV deployment, which makes the public able to buy PV systems.
Other delimitations is that this thesis has avoided to examine the roof areas in the case grids (which has been done in an earlier master’s thesis [7]), and also avoided to calculate the likelihood for high penetration PV grids in Sweden.
1.6 Structure
The necessary theory is described in Section 2. This is followed by the methodology in Section 3. The results, together with analysis, are presented in Section 4. Discussion and conclusions can be found in Section 5 and 6.
2
Theory
2.1 Hosting capacity
The design of distribution grids and the included components (substations, secondary substations, cables etc.) often limit the maximum amount of solar electricity that can be permitted. The upper limit is called hosting capacity. If this limit is passed it may cause overloading of the components, which can lead to power failure or shorten the lifetime of facilities. A formal definition of hosting capacity is:
”The hosting capacity is defined as the maximum distributed generation (DG) penetra-tion for which the distribupenetra-tion network still operates according to design criteria and network planning practices based on the European standard EN50160.” [8]
The hosting capacity is illustrated in Figure 1. As performance index it is suitable to use a power quality indicator, such as voltage rise, overloading or harmonics.
2.2 Standards and terminology
Figure 1: Hosting capacity illustration.
As described in the earlier section, a performance index must be used in order to calculate the hosting capacity. Limits for the performance index should be based on reasonable assumptions and reliable sources. In this report, overvoltage is used as a performance index. The upper limit for voltage was determined to 10% above nominal voltage. Nominal voltage is the same as normal voltage in a grid, that all equipment is adjusted to. For low voltage (LV) grids the nominal line-to-line-voltage is 400 V. For middle voltage (MV) grids, the nominal voltage is in the range 10 to 50 kV. The electrical transmission system operates with high voltage (HV), due to lower losses, and is usually at 100-400 kV [9].
The voltage in the grid is usually not exactly the nominal voltage. Then it is good to use p.u. (per unit) instead of Volts. For example, a node with line-to-line voltage 440 V in a grid with nominal voltage 400 V is 1.1 p.u. (because it is 10% above nominal voltage) [9].
The following citation was a guideline in choosing the limit: ”The European voltage norm EN50160 states that the 10 minute average RMS voltage at the point of common coupling (PCC) must lay within the±10% Unom limits for 95% of the time, with Unom = 230 VRMS”[10]. After discussing with my supervisors and experts at Fortum, 10% was chosen as upper limit. Both because it suited well with the standards, but also because it is widely spread in Fortum as the allowed region.
A substation is the system that includes a transformer, and is situated between HV and MV grid, or between two di↵erent voltage levels on the MV grid. A secondary substation is situated between the MV and the LV grid [9].
2.3 Power flow calculation
Newton-Raphson’s method for solving nonlinear equation systems is often used to solve power flow problems [11]. All branches in the grid build up an admittance matrix and all nodes build up a voltage matrix. In order to fill these matrices with the correct numbers, a calculation based on Kirchho↵’s law is performed for each position. Jacobians, which are for equation systems what the slope is for a single function, are used to search and find the answer by guessing and repeating until mismatch is within tolerance level. By every iteration the mismatch decreases.
2.4 Cable temperature
The cable calculation in this project is based on IEC 287-2-1 [12] and IEC 287-2-2 [13], A diagram on cable temperature dependency on loading rate and surrounding temperature can be found in Figure 2 [14]. From that diagram a second order function was chosen with Matlab fitting tool, based on ground temperature 15 C, which is a good estimation of the yearly mean value:
T = 73.5L2+ 1.6387L + 14.9860, (1)
where T is temperature and L is load rate.
The temperature in the cable can be used together with a resistance increasing factor in order to calculate the resistance in the cable:
f = 1 + 0.00398(T 20 C), (2)
where f is the resistance rise factor.
Figure 2: Cable temperature dependency on loading rate and ground temperature [14].
3
Methods and data
This section outline the methods used in the project for information gathering, data processing, calculation and simulation. Important parameters and data used in each of these steps are also listed. The main part of the project is Matlab simulation. In order to get useful results it was important to plan what kind of diagrams that are most easy for readers to understand. PV penetration level is for example possible to represent in many ways, but only the two most pedagogic ways were chosen (same system on each roof or a certain degree of self-sufficiency). Also the choice of which grids to simulate is largely based on the supposed reader.
Figure 3: Method overview.
3.1 Literature survey
In order to get a quick overview on the subject a pre-study was made. The pre-study included a literature survey on particularly important reports written on the subject. As the project continued more information were needed, especially in order to answer research question 1 (What can be learnt from earlier experience). Another literature survey was then conducted. The second literature survey is based on sources in Table 1 and search terms in Table 2.
Source Description
Google Scholar Makes it possible to search reports and papers in a large number of scientific databases at the same time IEEE Explore Scientific database in the electricity area
Conference Proceedings Papers from solar energy conference 2011 from 26th EU-PVSEC
Table 1: Literature survey sources.
Search terms
hosting capacity photovoltaics hosting capacity PV
hosting capacity photovoltaics experience germany integration photovoltaics distribution grid
power injection by distributed generation high penetration photovoltaics
Table 2: Literature survey search words. Date of search: 15th of april 2012.
3.2 Simulation in Matlab
The main part of the project is the simulation part. In order to answer research question 2, a calculation software was needed. Matlab was most suitable for this task, and it was possible to use and extend an existing Matlab script used in research at Uppsala Uni-versity [15]. Other benefits over specialized power flow programs are listed below:
• Flexibility.
• Easy to implement new grids.
• Possibility to make Monte Carlo simulation in the way this project aims. • Full control over the code.
The program is based on the Newton-Raphson method (described in chapter 2.3). A detailed overview of the program is shown in Figure 4. On the left hand side of the overview the input and output variables are listed in four di↵erent boxes (one for each software used). On the right hand side the test mode selection is described, with three di↵erent modes. In the middle of the overview the program structure is described, with all iteration possibilities marked as purple arrows. The dark yellow boxes are indicating calculation steps. The diamond boxes indicate a junction with two di↵erent possible roads to go. The program part with the power flow calculation contains both voltage calculation in all nodes and current calculation in all branches.
The main parts of the program are:
• Calculation of voltage in each node (Newton-Raphson method). This part is mainly based on Grainger & Stevenson [11] and Wid´en [15].
• Calculation of current in cables. • Calculation of temperature in cables.
• Test routine for capacity limits in cables and fuses
MA T LA B S C R IP T : P O W ER F LO W Star t Gr id d es ig n Nod e ch ar ac te ri st ic s Se le ct t es t m o d e In pu t da ta s to ra ge line_i n c. tx t li n e_i m p .t x t ca p aci ty .t x t fu se .t x t lo ad _a ct iv e. tx t lo ad _r ea ct iv e. tx t ge n er at io n .t x t ye ar ly. tx t Se le ct or 1. S in g le t es t ru n On e ru n Sp ec if y PV g en er at io n 2. P V a rr ay s b as ed o n y ea rl y co n su m p ti o n Ge n er at io n c o rr es p o n d s to a p ro p o rt io n o f ye ar ly el ec tr ic it y co n su m p ti o n 0% -100% St ep : 1 0 % 3. P V a rr ay s b as ed o n k W p p er h o u se 0-15 k W p p er h o u se St ep : 1 k W p Ru n p o w er f lo w c al cu la ti o n (N ew to n -R ap h so n ) Te st f or t ol er an ce OK ? Te st if t em pe ra tu re is s ta bi liz ed Ca lc ul at e ca bl e te m pe ra tu re OK ? Te st if la st t im e st ep is r ea ch ed OK ? Te st if a ll si m ul at io ns a re d on e ac co rd in g to t es t m od e Ru n ag ai n Us e pr ev io us t em pe ra tu re as n ew in pu t Ad d 1 ti m e st ep OK ? In cr ea se P V a rr ay s iz e by 1 s te p Pr oc es s an d co lle ct d at a En d Ou tp ut d at a st or ag e No d e vo lt ag e m ag n it u d e No d e vo lt ag e p h as e an g le Ov er h ea te d c ab le s Ov er lo ad ed f u se s Ex ce l p re se nt at io n Da ta t ab le s fo r be tt er o ve rv ie w Gr ap h s sh o w in g ho st ing c ap ac it y Pr o p o rt io n o f ye ar ly co n su m p ti o n Qu an ti ty o f in st alle d k W p Ra w d at a pr oc es si ng Ex ce l Da ta s o u rc e 1 Da ta s o u rc e 2 Ma tl ab Da ta s o u rc e 1 Da ta s o u rc e 2 Ye s Ye s Ye s No No No No Ye s
3.3 Case grids
Three case grids where chosen. The requirements are listed below:
• Case grids should be representative for di↵erent kinds of Fortum grids. • All required input data for simulation should be available for the case grid. After having a meeting with a reference group at Fortum these grids where selected:
• Case grid 1 - City grid in Stockholm Royal Seaport • Case grid 2 - Suburban grid outside Stockholm • Case grid 3 - Rural grid in V¨armland
3.3.1 Description City grid
The city grid used in this thesis is not yet built. It is a part of an area in the zoning plan over Stockholm Royal Seaport that can be seen in Figure 5.
Number of houses 8
Number of apartments 400
Office area 1000 m2
Supermarket area 1300 m2
Mean el. consumption 3462 kWh/apartment
Number of nodes 11
Number of branches 10 Table 3: City Grid
Number of houses 176
Distribution substations 1
Mean el. consumption 19073 kWh
Number of nodes 215
Number of branches 214
Table 4: Suburban Grid.
Figure 5: Stockholm Royal Seaport [16].
Figure 7: Grid structure of suburban grid. The square in the middle represents the distribution substation. The smaller boxes are cable cabinets, and the size of these boxes corresponds to the number of connected customer.
Rural grid
Number of houses 312
Distribution substations 44
Mean el. consumption 13487 kWh
Number of nodes 73
3.3.2 Network structure
In order to convert the network structure for the case grids into a simple form, a Microsoft Excel document was created. The input file for the excel document was created in Power Grid, Fortum’s grid management program. The file contains all the required information, but has a complex structure not so easy to understand.
The output files contain the network structure in terms of nodes and branches, where ”nodes” are points of load or generation connections and junctions, and ”branches” are conduction segments between two nodes.
The following steps are performed in the Excel document:
• All nodes get numbers based on their ID number. Numbered from 1 to [number of nodes].
• Cables that are spliced are joined together into single branches.
• Double or triple cables laid parallel are joined together into single branches. • Test for loops. A possibility to remove loops by canceling or changing some
branches.
• Test for errors. Possibility to remove branches that are not supposed to be in the grid.
• Branches are numbered.
• Source and target node of each branch is collected. • Network structure is exported to a text file.
• The distance between node 1 (transformer) and each node is calculated and presented in a table.
Most of these steps are automatized by a Visual Basic macro, made by joining together several di↵erent routines which are recorded by the macro recorder in Microsoft Excel. The programming is mainly done in Excel cells, mainly using IF statements and lookup-table functions such as VLOOKUP(), in order to collect and process data from many di↵erent tables, (see Figure 9).
3.3.3 Cables
Figure 9: Part of Excel document for collecting network structure data for Matlab script. The sheet contains a number of steps and each step contains either a mathematical function or a logical expression.
in cables and fuses where collected and imported into Matlab, in order to give warning when components where overloaded. Table 6 lists some of the cables used. The following steps are done in Excel in order to obtain cable information.
• Cable dimensions are used to obtain resistance and reactance per meter. • Length is used to calculate total impedance for each branch.
• When cables are spliced, the one with highest resistance is chosen to be used for the whole distance.
• When two identical and parallel cables are subsisted with one cable, a replacement impedance is calculated.
• Maximum current for fuses are collected for each branch. • Impedances and maximum capacities are exported to text files 3.3.4 Load
Dimension Description R X Material Name max current (⌦/km) (⌦/km) (A) 16 mm2 + 16 mm2 3x16/16 1.15 0.082 Cu FKKJ 115 185 mm2 + 57 mm2 3x185/57 0.164 0.074 Al AKKJ 345 240 mm2 + 240 mm2 4x240 0.125 0.078 Al SE-N1XV 400 240 mm2 + 72 mm2 3x240/72 0.125 0.073 Al AKKJ 400 50 mm2 + 25 mm2 3x50/25 0.387 0.078 Cu FKKJ 215 95 mm2 + 95 mm2 4x95 0.32 0.078 Cu SE-N1XV 310
Table 6: Some cables and data from cable handbooks [14, 9].
for load data are listed. In order to only simulate real load points (and not dead ends) the grid has been examined in the program Power Grid.
Case grid
Source for load data 1 2 3
Power Grid program x x
Meter data x
Fortum ”pilot” project with meters x in apartments in Stockholm
Swedish Energy Agency x x
measurements data [18]
Office and supermarket x
measurements [19]
Table 7: Sources for load data.
3.3.5 PV electricity generation
Tilt 30 degrees
Array loss 10%
Inverter efficiency 97%
Inverter power factor 1 Albedo (ground-reflectance) 0.2
Location Stockholm
Table 8: PV electricity generation parameters for the model used.
3.4 Peak condition simulation
The first part of the simulation consists of a single point in time that is simulated for all grids. The chosen time point is one specific hour at ”peak condition”, which describes the moment of the year when the reverse flow of power is highest. This means that the di↵erence between electricity generation and load at this hour shows the maximum stress on the grid from PV. More details of assumptions made in peak condition simulation can be found in Table 9. The overall PV efficiency used is what can be expected from PV systems at maximum, as percentage of the nominal power during laboratory conditions. The smoothening e↵ect from adding the generation from many PV systems is included. That means that all PV systems in an area is not assumed to reach peak generation at the same time, as roof tilting and local shadowing may change the conditions. Yet, the local weather is often very similar for a distribution grid, which gives similar performance all across the grid. The efficiency 90% can be considered as a quite high estimation. But since it is a peak condition simulation, it is better to estimate in the upper edge than opposite.
Chosen hour Between 12 PM and 13 PM
Chosen date 30th of June
Peak condition overall PV panel efficiency 90%
Load power factor 0.95
Table 9: Assumptions for peak condition simulation.
3.5 Monte Carlo simulation
The second part of the simulation consists of Monte Carlo simulation for all grids. Simu-lation details can be found in Table 10. The datasets are divided into 3 seasons (winter, summer and autumn/spring) and 3 parts of the day (night, day and evening). Then, 1000 hours of the year are chosen by random, and values of the corresponding season and hour are picked as input data in the main Matlab program. In this way you get the possibility to see the probability for di↵erent voltage levels. For instance, if the maximum voltage in the modelled grid is over 1.1 p.u. in 10 of the simulated parame-ter settings, then the conclusion is that there is a probability of 1% to get overvoltage problems during one year.
Number of hours picked at random 1000
Definition of winter November-February
Definition of summer June-August
Definition of autumn/spring the remaining months
Definition of night 22 PM - 6 AM
Definition of day 6 AM - 14 PM
Definition of evening 14 PM - 22 PM
Table 10: Assumptions for Monte Carlo simulation.
higher loads and lower electricity generation, and for summers the opposite condition occurs. A randomly picked hour in both of the datasets will sometimes lead to a summer load and a winter generation, and therefore give the wrong results. That is why the dataset must be divided into 9 parts (shown in Figure 13 and Figure 14), which will remove the dependency problems.
0 5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Hour of day kW / apartment 0 2 4 6 8 10 0.35 0.4 0.45 0.5 Month of year kW / apartment
0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Hour of day W / Wpeak 0 2 4 6 8 10 0 0.05 0.1 0.15 0.2 Month of year W / Wpeak
All year Winter Autumn/Spring Day Night Summer Evening
Figure 13: Load distributions in the form of duration graphs. These profiles show loads in apartments, and are used as input data in the city grid. Units are kW/apartment (y-axis) and probability (x-axis).
Figure 14: PV generation distribution in the form of duration graphs. These profiles show PV electricity generation in Stockholm at 30 degrees tilt angle. Units are W/Wp
4
Results and analysis
The results chapter is divided into four parts. The first part sums up the most important findings from the literature survey. The second part consists of simulation results from peak condition, which happens when the reverse power flow is at its maximum level. The third part shows results from Monte Carlo simulations in order to analyse the probability for overvoltage events, and the fourth part shows validation results.
4.1 Summary of literature review
The complete literature review can be found in Appendix I. In this section the most important findings will be presented, in order to answer research question 1. The findings are listed below.
• In general no detrimental e↵ects on the power quality was found in four examined built grids with high penetration PV in Europe. (See literature post 17 in Appendix I)
• Overvoltage caused by high penetration PV could be relived by reactive power control in most cases, according to simulations of a real MW grid. (Post 9) • In LV grids, special attention needs to be paid to voltage variation and power flow
in cables, according to simulations. (Post 5)
• In Germany the peak load can be reduced by 5% on a working day in October if 30% of the houses are equipped with 7 kWp PV systems.(Post 10)
• For new areas, any capacity limits would be avoided by setting tap changers to between 0.98 and 1 p.u. (Post 17)
• For majority of end customers in Sweden, the voltage dip frequency may be reduced with distributed PV. (Post 12)
• As a rule of thumb, use 70% of transformer rating as maximum amount of installed PV capacity. (Post 17)
From the literature study, the conclusion is that the best ways to increase hosting ca-pacity should be reactive power control, which has shown good results in Germany, and to adjust tap changers after season. In this way the cost for grid reinforcements will be decreased. The literature also pinpoints overvoltage and overcurrent to be the most important parameters in hosting capacity studies.
4.2 Peak condition
4.2.1 Voltage profiles
This section shows diagrams where voltage acquired from the simulation is plotted for each node in the network. This gives a good profile of how the grid is a↵ected by ex-tensive PV deployment. Profiles have been created for four di↵erent parameter inputs; 5 kWp PV system at each roof and PV systems corresponding to 30, 50 and 100% of
yearly electricity usage at each individual end-user. The reason why both of these units of measurement are needed is that they show di↵erent conditions. The percentage unit is highly dependent on the electricity usage for the customers. An area with low yearly consumption gives a higher degree of self-sufficiency than an area with high yearly con-sumption, with the same PV system sizes. Both units of measurement give possibilities for easy and pedagogical presentation of data.
Fixed system sizes at each house
Figure 15 shows the suburban grid (case grid 2) with 5 kWp PV panels at each rooftop.
Detailed explanation of the grids and assumptions can be found in chapter 3 on page 13. Each point in the diagram is a house, and the x-axis shows how far away each house is from the secondary substation. On the y-axis the voltage at each node are shown.
Figure 15: Voltage profile in suburban grid with 5 kWp at every house and peak
condi-tions.
limit for the hosting capacity in the grid. If the ”limiting node” is within acceptable voltage regions, then the whole grid is considered as acceptable. The results show that 5 kWp PV systems on each house will not violate the overvoltage limit at 1.1 p.u. The
reason why the voltage increases with distance from the distribution substation, is that the transformer has fixed voltage (stable grid) and each generation point lead to voltage rise. As more and more generation units are aggregated when moving away from the transformer, the voltage rises.
Figure 15 also shows that voltage is distributed along some clear lines in the diagram. These lines are following the radial structure of the grid. The slope of the line shows how fast the voltage is rising along with the cable. If there are a lot of houses close together then the voltage increases faster. The dimension of the cable is also an important factor, the better conductivity the slower the voltage increase. Therefore one can say that from an overvoltage point of view it is important to identify the weakest radial in the low voltage grid, and focus should be on improving those cables if network reinforcements are necessary.
Figure 16: Voltage profile in rural grid with 5 kWp at every house and peak conditions.
Figure 16 shows the rural grid (case grid 3) with 5 kWp PV panels at each rooftop.
The rural grid is a medium voltage feeder with a couple of houses at each secondary substation. Each point in the diagram is here a secondary substation, and the x-axis shows how far away each secondary substation is from the feeder substation. On the y-axis the voltage at each node is shown.
medium voltage grid in Figure 16. Above all it shows significant di↵erences from the voltage profile in the suburban low voltage grid. That is mainly because it is a completely di↵erent type of grid structure. Only one of the substation’s feeders is modelled, and therefore only one line is visible in the diagram. The fastest increase is happening in the middle of the feeder, and this is due to limited transmission capacity. The maximum voltage in the grid is about 1.06 p.u. at 18 000 meters from the substation. Therefore there are no problems to put 5 kWp PV systems on all houses in this grid either.
In the same way the voltage have been plotted for case grid 1, the city grid (see Figure 17). Since the distance is shorter than in the other grids, the correlation between distance and voltage is not clear at all. The voltage rise is more dependent on each cable dimension and each building’s net generation, as most of the buildings in this grid are directly connected to the transformer.
Figure 17: Voltage profile in city grid with 50 kWp at every house and peak conditions.
System size proportional to part of the annual electricity consumption
Yet, it is a little surprising that we can reach halfway to net-zero building without coming close to the limit. The maximum voltages in these cases are about 1.09 at the highest (suburban grid). These diagrams show that the studied Swedish distribution grids are very robust and can handle a lot of distributed generation. Especially the city grid seems very robust, as the distances are short, the cables are generously dimensioned and the demand coincides more favorably with the PV electricity generation.
The overall pattern is very similar between the three simulations. Even if the PV systems here are di↵erent on each house (matching exactly part of the annual consumption of the building) the only thing that happens when penetration level increases is that the voltage profile is prolonged with almost the same appearance. The conclusion from this is that it is more important to know the grid structure than to know all PV system sizes in detail, in order to make predictions on overvoltage problems. If you only know a rough total PV electricity generation, it might as well be spread out on the houses without losing any significant accuracy.
Figure 19: Voltage profiles at 50% penetration level and peak conditions.
4.2.2 Hosting capacity: overvoltage
In Figure 21, the hosting capacity is shown as a red dashed line at 1.1 p.u. voltage. The curve shows how voltage (y-axis) increases at the node with the highest voltage in the grid, when the degree of self-sufficiency is increased (x-axis).
Figure 21: Voltage rise as a function of the degree of self-sufficiency at peak conditions.
The conclusion from Figure 21 is that the hosting capacity can be determined to the PV penetration corresponding to 60% of annual electricity usage in the suburban and rural grids. For the city grid, the limit is high above 100%. This means that it is very hard to reach the upper limit for PV systems in a strong city grid, and these can be considered to be very stable against overvoltage problems induced by PV systems. Another conclusion is that the increase is almost proportional to the PV electricity penetration, meaning that results from a real grid with a decent amount of PV systems easily can be scaled in order to examine e↵ects with higher PV penetration.
Figure 22 uses the number of installed kilowatt-peaks as a measure of PV penetration. In this way the hosting capacity can be determined by the size of PV panel on each rooftop. In the city grid, PV system sizes between 0 and 150 kWp per roof have been
investigated. In the other two grids, systems between 0 and 15 kWp per roof have been
chosen. A 5 kWp system corresponds to PV arrays with module efficiency 15% and
array area of 33 m2. From this follows that 15 kW
Figure 22: Voltage rise as a function of PV system sizes at peak conditions. Note that x-axes are di↵erently scaled.
corresponds to 1000 m2.
Figure 23: Voltage rise as a function of the degree of operational electricity self-sufficiency at peak conditions.
4.2.3 Hosting capacity: overloading
In the Matlab script it was quite easy to implement a test routine for overloading of cables and fuses. As a result of that, these data were collected and presented after each test run. The data possible to obtain was: (1) Number of cables that reached upper design limit for temperature, and (2) Number of fuses that reached the upper current limit. These data are presented with the percentage of problem cables on the y-axis. The total number of cables in each grid is 10 for the city grid, 214 for the suburban grid and 72 for the rural grid. Note that data on fuses was hard to obtain from the rural grid, and is therefore omitted.
Hosting capacity is considered reached as soon as fraction of cables >0%, as each fault is a violation on the grid stability and can damage components. This is a simplification of reality, as cables are designed to cope with higher current than the maximum current for shorter periods of time without any faults.
In Figure 24 the fractions of problem lines are presented in the same way as Figure 21. In the city and suburban grid the hosting capacity is determined to be just beneath 30%. In both cases fuses will break before cables are overloaded, which is clearly visible in the diagrams. In the rural grid no data on fuses were available, and therefore cables set the limit for the hosting capacity. In this case the hosting capacity is determined to be about 70% for the rural grid.
depending on local conditions. One spot with limited capacity has the function of a bottleneck for the whole grid, which has been observed in the simulation of the case grids. In the rural grid the hosting capacity is higher than when voltage rise is used as performance index. This can be the result of not including the grid below the substations in the model.
Figure 24: Overload problems as a function of the degree of self-sufficiency at peak conditions.
In Figure 25 the fractions of problem lines are presented in the same way as Figure 22. In the city grid the hosting capacity is determined to be about 43 kWp. In the suburban
grid the hosting capacity is determined to be just beneath 6 kWp. As before, the fuses
will break before cables are overloaded, which is also here clearly visible in the diagrams. In the rural grid the hosting capacity is determined to be just beneath 10 kWp. The
results can be interpreted in the same way as the results from Figure 24.
4.2.4 Hosting capacity summary for peak conditions
Figure 25: Overload problems as a function of PV system sizes at peak condition.
4.3 Monte Carlo simulation
In order to fully understand the problems with overvoltage in the grids a Monte Carlo simulation was conducted. The results from a Monte Carlo simulation give some indi-cation on how likely the problems described earlier in this chapter are.
Figure 27: Cumulative distribution for voltage based on results from Monte Carlo sim-ulation in case grid 1 (city grid). Degree of electricity self-sufficiency is 0% (blue), 30% (green), 50% (red) and 100% (turquoise).
In Figure 27 the cumulative distribution function is plotted for the voltage in the city grid. As an example, the curve for 100% PV electricity self-sufficiency has the value 0.88 at the voltage 1.03 p.u.. This means that the voltage is below 1.03 p.u. 88% of the time, and from that follows that the voltage is over 1.03 p.u. 12% of the time.
The conclusion of Figure 27 is that the voltage rise from distributed PV generation is well within acceptable limits for all investigated simulation setups. It is also interesting to see that the voltage is not dropping below 1.02 p.u. in any setup, and that it is very stable in the lower regions. This is probably due to low degree of electrical heating in the city grid.
Figure 28: Cumulative distribution for voltage based on results from Monte Carlo sim-ulation in case grid 2 (suburban grid). Degree of electricity self-sufficiency is 0% (blue), 30% (green), 50% (red) and 100% (turquoise).
drop can be seen for about 20% of the time. This is due to more electricity dependent heating systems during wintertime. It is interesting to see that the voltage rise at 30% of electricity self-sufficiency is corresponding to the voltage drop in the same simulation (same magnitude and probability). That means that a grid that is built with the load as the main design criteria should carry these amounts of PV electricity if tap changer is disregarded.
Figure 29: Cumulative distribution for voltage based on results from Monte Carlo sim-ulation in case grid 3 (rural grid). Degree of electricity self-sufficiency is 0% (blue), 30% (green), 50% (red) and 100% (turquoise).
4.4 Comparison with other grids
In order to compare the results from the case grid, a fourth grid has been briefly studied. This grid is like case grid 1 situated in Stockholm Royal Seaport, but is considerably larger, with more houses and longer cables. Therefore the results, which can be seen in Figure 30, show that this area has smaller hosting capacity than case grid 1 (city grid).
The reason for comparing case grid 1 with another city grid (case grid 1b) is that it is interesting to see if the other grid di↵ers a lot in results. Case grid 1 was very strong, due to short distances and relatively few customers. The comparison grid’s results indicate that the hosting capacity is somewhere between case grid 1 and case grid 2 (suburban grid). This means that this city grid also is stronger than both the suburban and the rural grid in this study, even if not as strong as case grid 1.
4.5 Validation of results
Figure 30: Another city grid (1b) was simulated in order to compare the results between the di↵erent grids.
not included[22].
In a suburban grid in that study (grid B) with 107 customers a voltage over 1.01 p.u. was obtained in 552 hours of the year for 3 kWp systems. In this case the transformer was fixed at 1.0 p.u.. In this project the transformer is fixed at 1.02 in the simulation. In the simulation of 5 kWp systems in a suburban grid a voltage over 1.03 is obtained in about 300 hours. This means that voltage rise is not as large as in Wid´en’s study. The result can possibly be explained by a larger self-consumption of the grid, due to higher resistance since temperature increases a↵ects the cable impedances.
5
Discussion
The discussion section is divided into five di↵erent subsections. The first three are a continuation on the results section, but with a broader approach on the topic. The fourth is discussing sources of error. The two last sum up the project from the DSO’s point of view and look further into the future.
5.1 General discussion regarding the results
The most obvious observation from the graphs is that the hosting capacity is much higher in the city grid than on the other grids. This means that big PV projects in the city are easier to cope with than on the countryside. Time will tell where PV systems will get most popular in Sweden. One possibility is that farmers will be one big customer category, as they have high energy consumption, large roof areas and usually are in favour of long term investments.
It is important to make clear that the results in this thesis are based on simulation and are validated but not verified by measurements in the grids. Therefore the results should be interpreted as what they are. Yet, the simulation in this project should be more correct then other simple power flow calculations, since cable temperature is included. The power flow calculations used in the project is accepted according to the conventions. As measurements in Swedish high penetration PV grids are not possible (because there are none) the thesis tries to give an estimation as good as possibly achievable.
Roof top areas, positions and angles are not discussed in the results. Roofs are a very e↵ective limitation on how much rooftop PV systems that can be built, and some of the PV penetration levels discussed are probably impossible. As a 15 kWp system with 15%
efficiency occupies 100 m2 roof space and most roof’s in a suburban area is lesser than that, it can be interesting to have the spacing in thought when analysing the results. The area issue is left out in this project, since it doesn’t fit in the scope and time plan, and since this topic has been investigated thoroughly one year ago by another master’s thesis [7].
There are di↵erences in roof areas between the three case grids. In the city, the houses are bigger and can therefore contain larger PV systems. Meanwhile the buildings are built higher, as the building plots are more expansive. This leads to a low people/roof-ratio, which reduces the possibilities for high penetration PV. In the countryside the roof areas are larger, and there is also accessibility to barns and other farm buildings that can be suitable for PV arrays.
said, it is interesting to see that more and more skilled observers bring solar energy forward as an good alternative for conventional energy sources, even economically, in a near future.
The three case grids in this project are representative in the current circumstances. The comparison grid however shows that results can di↵er with other grid designs. In this case the cable distances were longer than in case grid 1, and therefore the hosting capacity decreased.
5.2 How to increase hosting capacity?
There are mainly five types of measures that can o↵set voltage increases and capac-ity problems in distribution grids [2]. Two of them are associated with ordinary grid management, and three are often considered as part of smart grid technology. The last proposal is the most ”futuristic” and can be combined with introduction of electrical vehicles.
• Voltage regulation by tap changer in distribution transformers. • Grid reinforcements.
• Limiting injection of solar power. • Reactive power control.
• Local energy storage.
5.3 Sources of error
The following list shows possible sources of errors in this project. They are all hard to quantify, but according to earlier assumptions and theory they should not have that large impact.
• Approximation of cables. When details for the cable type not have been found, a similar cable dimension has been used.
• Assumptions and simplifications in the Matlab model, such as dielectric losses. But since reactive losses is responsible for a vast majority of cable losses, and they are modelled as good as possible, the results should be relevant.
• Voltage is fixed at the transformer. This can lead to an overestimation of hosting capacity in areas where PV penetration is large not only in one single distribution grid but also in a bigger area.
• Since the examined grids sometimes are very old and have gone through a number reparations and reinforcements, there is a risk with wrong data.
• Number of time-steps in Monte Carlo simulation is only 1000. It could have been higher, but that e↵ects the simulation time. Since the cumulative distribution curves looks quite smooth the number of time steps is probably enough.
• Power factor uncertainties. It is hard to now the power factors for the households, as there are no measurements available. And it also changes with the season, as di↵erent types of load have di↵erent power factors.
• Cables in rural grid instead of hanging lines. In order to scale it properly, a probable dimension where used. The reason why using cables instead of lines is that the temperature dependency model used cables in ground for calculation base. • Dimensioning of cables in city grid is made entirely based on a plan for the area. • Office and supermarket load data are based on reports on how this types of locals
is usually used.
5.4 Lessons from project
There are some lessons to learn from this project:
• Time management: Much more time then expected is used for data collection and processing. A good formula taken from the reality for calculating the time required in projects is: time = ⇡· timeplan.
• Use only one program instead of two di↵erent (Excel and Matlab). The connection possibilities between the programs are not so good, and Excel works slow with a lot of data. Maybe a more programming friendly tool should be used, such as Python calculation libraries like NumPy.
• As validation is very important, more time could be used for that. More types of validations are also suitable, such as checking simulations with actual monitored grid voltages.
5.5 Further work
Further work can be to test more grids with the same approach in order to see what di↵ers between di↵erent grid parameters, and how you easily can determine what type of grid you are dealing with. Also to examine hosting capacity increase strategies more in detail.
5.6 Rules of thumb for Fortum
• The process for connecting single electricity sources for the grid is working as it is. The ”MikroAMP” (a handbook on connecting micro-production) is a good guideline.
• At the moment no special guidelines for customers should be developed because of the results in this project, because the hosting capacity was very high in all examined grids. It is better to first wait for new grid codes and implement them together with organizations such as ”Svensk Energi”.
• Voltage deviations because of PV systems in ordinary grids are still years ahead. • New city areas with especially high PV penetration should be dimensioned with
this in mind. Think double compared to regular dimensioning with 30% PV elec-tricity self-sufficiency. Regular dimensioning is when designing a grid with maxi-mum winter load as dimensioning factor for cables, fuses and substations.
• The simplest way to increase the hosting capacity in problem grids is to introduce seasonal adjustments of tap changers in the substations or distribution substation.
6
Conclusions
• From other countries, conclusions can be drawn that overvoltage is the main con-cern regarding hosting capacity.
• In Swedish grids it should be possible to install a lot of distributed generation including PV systems. They are suitable as they have strong cables that are dimensioned for high loads.
• City grids have better possibilities for PV electricity generation then rural grids, since the grids are stronger, and the load is coinciding more with PV electricity generation.
Acknowledgements
There are lots of people that have helped me during the project, and I am very thankful for all your help. Without all the inputs from you, this project would not have been possible.
I first would like to thank Fortum Distribution AB for giving me an opportunity to investigate a really interesting topic. And without the people from BEESG (Built En-vironment Energy Systems Group) at Uppsala University, this project would not have been possible at all, so thank you very much for helping me.
I would especially like to thank my supervisors Joar Johansson, that have been really helpful and supportive all the way, and Joakim Wid´en that have not just given me all kind of support in the project, but also helped me with conference application, sponsorship and a folk music concert.
Many thanks to Lars Selberg, Catarina Naucler, Christer Bergerland, Johan Tezelson, Daniel Terranova and all other people at Fortum for giving me help in di↵erent stages of the project. Also great thanks to my opponent David Lingfors for giving me good advices on how to make my report better.
I also want to thank Johan Paradis for helping me in the start-up phase of the project with very good advices on topic choice and people to collaborate with.
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