Decarbonizing the electricity grid: The impact on urban energy systems, distribution grids and district heating potential

Applied Energy 191 (2017) 125–140

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Decarbonizing the electricity grid: The impact on urban energy systems, distribution grids and district heating potential Boran Morvaj a,b,⇑, Ralph Evins b,c, Jan Carmeliet a,d a

Chair of Building Physics, ETH Zürich, Swiss Federal Institute of Technology, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland Empa, Urban Energy Systems Laboratory, Überlandstrasse 129, 8600 Dübendorf, Switzerland c Department of Civil Engineering, University of Victoria, 3800 Finnerty Road, Victoria, BC, Canada d Empa, Laboratory of Multiscale Studies in Building Physics, Überlandstrasse 129, 8600 Dübendorf, Switzerland b

h i g h l i g h t s
Model that integrates DES, linearized AC power flow and district heating design.
Simultaneous district heating layout design and pipe sizing.
Development and integration of a distribution grid upgrade model.
Impact on DES of different levels of renewable energy share in the electric grid.
Renewable share of the grid has significant impact on the solutions.

a r t i c l e

i n f o

Article history: Received 8 October 2016 Received in revised form 11 January 2017 Accepted 24 January 2017

Keywords: Distributed energy systems AC power flow Electric grid upgrade Multi-objective optimization District heating potential

a b s t r a c t Many energy policies set a goal of decreasing the carbon emissions of the energy sector by up to 100%, including the electricity grid. This is a long term and gradual process. Energy systems in cities will likely be the starting point for greenhouse gas emissions mitigation since they account for 80% of global carbon emissions. This paper analyses the impact on urban districts of decarbonizing the electric grid supply. A multi-objective optimization model has been developed that combines the optimal design and operation of distributed energy systems, the design of district heating (DH), electricity grid constraints based on linearized alternating current (AC) power flow and grid upgrade options. A number of scenarios were defined corresponding to different levels of renewable energy share in the electricity grid. For each scenario, we analyse the changes to the design and operation of the urban energy system, the impact on the district heating potential, and the impact on the operation of the distribution grid as well as the grid upgrade potential. The results showed that the renewable share of the grid has a large impact on the optimal solutions obtained. When the renewable share is below 55%, a lot of photovoltaic (PV) electricity has to be used to offset the carbon emissions from the grid. Conversely, when the renewable share is above 70%, the use of PV decreases and heating systems become electrified by producing heat with heat pumps (HP). District heating is used regardless of the renewable share in the grid, but as carbon emissions limits are tightened the potential of DH decreases. Only when the renewable share in the electricity grid is 100% it is possible to have a carbon-neutral district. In the carbon optimal solutions of each scenario there is no need for DH, but the grid has to be upgraded to enable electrification of the heating system. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction EU energy policy sets reduction of the country’s greenhouse gas emissions as a key challenge for the overall energy sector, with ⇑ Corresponding author at: Urban Energy Systems Laboratory, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland. E-mail address: [email protected] (B. Morvaj). http://dx.doi.org/10.1016/j.apenergy.2017.01.058 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

goals of a 20–30% reduction of the carbon emissions from the 1990 level by the year 2020 and further 80% reduction by 2050. Additionally, some countries such as Denmark [1] have set a goal of 100% renewable energy generation by 2050. There has been lot of research into the transition to 100% renewable energy systems and the design of such systems. The best path to achieving 100% renewable electricity supply has been analysed specifically for many countries such as Denmark [1], Portugal [2], Macedonia [3], Croatia [4], China [5], and New Zealand

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Nomenclature Abbreviation AC alternating current CHP combined heat and power DES distributed energy systems DH district heating HER heat to electricity ratio LB lower bound NPV net present value PV photovoltaics SOC state of charge UB upper bound Parameters Bn;m line susceptance [p.u.] C tech investment cost of technology tech [€/kW] CF grid carbon factor for grid electricity [kg CO2/kWh] CF gas carbon factor for natural gas [kg CO2/kWh] C elec cost of grid electricity import [€/kWh] imp C elec cost of grid electricity export [€/kWh] exp C pipe cost of heat network pipes [€/kW] COP coefficient of performance of HP Di;j distance between building i and j [m] G price of gas [€/kWh] Gn;m line conductance [p.u.] Hload heat demand [kWh] i;t Heatlossi;j heat loss between building i and j [%] HER heat to electricity ratio for CHP [-] ir discount rate [%] Lload electricity demand [kWh] i;t amount of self-discharge [%] nself nch efficiency of charging [%] ndis efficiency of discharging [%] nPV efficiency of PV [%] solar irradiation [kWh/m2] Psolar t Rnm line resistance [p.u.] U0 nominal voltage level [p.u.] line reactance [p.u.] X nm Variables binary variable which defines if heat pipeline between dpipe i;j building i and j is installed don binary variable which defines the state of technology i;t;tech tech

[6]. The design of an energy system which is based on 100% renewable energy on a generic country level has been analysed in [7]. Large shares of renewables which are inherently intermittent require some type of storage to buffer possible quick changes in power output. Steinke et al. [8] estimated the required backup power in 100% renewable scenarios in Europe. Similarly, the decarbonization of the electricity sector and value of energy storage in the U.S. state of Texas has been addressed in [9]. In most of the mentioned publications, electrification of the heating sector was assumed. However, one of the questions that arises in decarbonized energy systems is the role of district heating which is mostly based on fossil-fuels. Connoly et al. [10] evaluated the potential of district heating in the EU for 2030 and 2050. They indicated that with district heating, the EU energy system will be able to achieve the same reductions in primary energy supply and carbon dioxide emissions as the other alternatives proposed. Similarly Lund et al. [11] analysed the role of district heating in a 100%

DU nm;t D#nm;t APV;i C inv C op Carbem DHin j;i;t DHout i;j;t ESOC i;t Inm;t Inom Pðn; tÞ Pi;t;gen Pi;t;load Ptech i;t Pboiler i;t PCHP i;t PHP i;t PPV i;t Ptech max;i Ptech con ði; tÞ Ptech gas;i;t

voltage magnitude difference voltage angle difference area of PV installed [m2] investment cost [€] operational cost [€] carbon emissions [kg CO2] heat energy received through heating network [kWh] heat energy exported to heating network [kWh] state of charge of heat storage [kWh] branch current [A] maximal branch current [A] active power at bus n [kW] active power of the generator [kW] Active power of the load [kW] output of technology tech in building i [kWh] heat energy from boiler [kWh] total electricity produced by CHP at building i [kWh] electricity produced by HP at building i [kWh] electricity produced by PV at building i [kWh] installed capacity of technology tech in building i [kW] amount of consumed active power [kW] amount of gas used by technology tech in building i [kWh] Ptech gen ði; tÞ amount of generated active power [kW] Pgrid amount of electricity imported from grid [kWh] imp;i;t Q ðn; tÞ reactive power at bus n [kVAr] Q i;t;gen reactive power of the generator [kVAr] Q i;t;load reactive power of the load [kVAr] Q tech con ði; tÞ amount of consumed reactive power [kVAr] Q tech gen ði; tÞ amount of generated reactive power [kVAr] Q ch charging energy of storage [kWh] i;t Q dis extracted energy from storage [kWh] i;t maximal heat transferred between building i and j [kW] Q max;i;j ygrid binary variable which defines if the grid is upgraded Indices i,j n,m ota otr t tech

buildings bus technologies that produce/consume active power technologies that produce/consume reactive power timestep [h] available technologies

renewable energy system for Denmark. Therefore, it is important to consider the electrified and district heating as well as storage together in order to find the best solutions. The aforementioned publications use top-down approach and provide results for a country or continental level. The results usually give the optimal energy mix of different energy sources, socioeconomic costs and carbon emissions for different levels of renewable energy resources integration. Energy systems in the cities will be likely the starting point for greenhouse gas emissions mitigation since they account for two-thirds of global primary energy consumption and 80% of global carbon emissions [12]. However, the results from the aforementioned works provide no spatial information about where to place technologies, heating network layouts or the level of (de)centralization required. It is possible to use bottom-up approaches to determine the optimal design and operation of urban energy systems for different levels of renewables in order to assess DH network potential and layout as well as grid

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constraints and grid upgrade requirements. Applying these in a general way can provide detailed, rigorous solutions to problems usually addressed in a top-down manner. The optimal design and operation of distributed energy systems for the current share of renewables in the electrical grid has already been extensively analysed by use of optimization models for single- and multi-objective optimization for economic and environmental objectives [13–16]. Furthermore, many publications looked at the optimal design and operation of distributed energy systems (DES) and district heating [17–21]. In the aforementioned publications the electrical grid was assumed to have unlimited capacity for integration of local energy sources. This can lead to solutions that are not possible to integrate in the electrical grid because they may cause over- and under- voltages, have currents exceeding the ampacity of the lines, and potentially cause blackouts. The design of DES with electric grid constraints but without district heating was considered in [22–26]. Electric grid constraints were expressed as an energy balance for each line. However, an energy balance for power flows does not give information about voltage levels and assumes unidirectional flow. Large shares of local energy sources in distribution grids can cause bidirectional flows and an AC power flow study is needed to ensure stable operation of the grid. Design of distributed generation with AC power flow was considered in [27–29]. But in these publications district heating was not considered, and the power flow study was performed after and cannot influence the design or operation. AC power flow has to be linearized in order to efficiently integrate in optimization problems. Linearized AC power flows give information about voltages, currents and both active and reactive power flows at each line for each timestep, and can directly influence design and operation of DES [30]. In conclusion, in the existing literature a top-down approach is often used to study the design of energy systems with 100% renewable electricity supply on a country or continental scale. Results of such studies give the optimal energy mix of different energy sources and are useful for developing roadmaps and energy policies for the cost effective transition to decarbonized energy systems. However, it gives no information about how distributed energy systems in urban areas should be designed and operated with different levels of renewable energy share. The issue of whether such systems can cope with the additional loads and flows imposed is not addressed; high-level analyses assume that local systems can be upgraded if needed, although grid costs represent an increasingly large proportion of the total cost of energy. On the other hand, there are many studies that look at the optimal design and operation of distributed energy systems but only for the current share of renewables in the electrical grid. They do not provide information how urban energy systems will change in the process of decarbonizing the electrical grid. Furthermore, no model considers optimal design and operation combined with linearized AC power flow, district heating network layout optimization and grid upgrade possibilities. It is important to include all these aspects in a single model while so that synergies between the different energy streams and networks can be utilized respecting the operational limits of electrical and heat networks. In this paper the impact on urban energy systems of different levels of renewable energy share in the electric grid supply is analysed on a district level. We examine how urban districts should be optimally designed in the (near) future when the goals of energy roadmaps are achieved. A novel integrated optimization model is developed in order to evaluate the optimal design and operation of DES, district heating potential and distribution grid upgrade potential. The main contributions of this work compared to the existing literature are: (i) a new optimization model that integrates linearized AC power flow and district heating design, (ii) simultaneous district heating layout design and pipe sizing, (iii) develop-

127

ment and integration of a distribution grid upgrade model, (iv) the application of the model to a residential district with low voltage distribution grid in order to investigate the following questions: how should the urban energy systems be designed for different levels of renewable energy share in the electric grid supply?; what is the potential of district heating?; is there a trade-off between installing district heating and upgrading the electrical distribution grid so that heating can be electrified?; what is the impact on the operation of the distribution grid? Section 2 outlines the developed modelling framework. The components of the framework are defined and models explained. A case study is presented in tion 3 in order to investigate the questions above. Results regarding the system design, district operation, district heating potential and distribution grid upgrade potential under different renewable shares in the electricity supply are given in Section 4. Finally, conclusions regarding the impact of decarbonizing the electricity supply on urban energy system design are given in Section 5.

2. Modelling framework 2.1. Overview The optimization framework developed can simultaneously determine the optimal design and operation of a distributed energy system, district heating network layout and the electrical distribution grid upgrades needed while ensuring that the solutions are within the distribution grid limits using linearized AC power flow. The framework is based on the coupling of an energy hub modelling approach for building systems design, building energy simulations for obtaining heat and electrical demand profiles, an electrical grid model for power flow calculation, constraints and grid upgrades, and mathematical formulation for district heating network design. An overview of the model is shown in Fig. 1. The original formulation of the energy hub [31] has been extended in order to consider more buildings and include gas boiler, combined heat and power (CHP), photovoltaic panels (PV), heat pump (HP) and water heat storage as possible technologies, each of which can be installed in any building. Also included in the design optimization is the district heating layout: buildings can be connected to form a number of decentralised district heating (sub-)networks by installing connections between them [32]. The operational optimization considers heat exchange via the network as an energy input and output to each building (if connected). The model builds upon the previous work presented in [30,33]. The framework is used for simultaneously minimising two objectives – cost (investment plus operational) and carbon emissions for a given electricity renewable share. Generally a MILP formulation is primarily used for single objective optimization. The augmented e-constraint method [34] is used in order to perform multi-objective optimization. First, two single objective optimization for cost and carbon emissions is performed to find the end points of pareto front. Secondly, the optimizations problem is formulated to minimize the primary objective function while all other secondary objective functions are translated into additional inequality constraints for which the limit (e) is varied to obtain a trade-off front of solutions. In this paper total cost was used as the primary objective and carbon emissions as the secondary objective. 2.2. Objective functions The objective functions are the minimization of total cost and carbon emissions. The total cost consists of investment and operational cost. The investment cost C inv (€) is defined as:

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Fig. 1. Overview of the framework.

!  X tech tech X pipe þ ygrid  C grid C inv ¼ C  Pmax;i þ Q max;i;j  C pipe  Di;j  di;j i

j

ð1Þ where C tech is the cost of available technologies (€/kW), P tech max;i is the installed capacity of technology tech in building i in kW, Q max;i;j is the maximum heat energy transferred between building i and j used for pipe sizing in kW, C pipe is the cost of laying pipes (€/m), Di;j is the distance between buildings i and j in m, dpipe is a binary variable i;j determining if a pipe is laid between buildings i and j, ygrid is a binary variable determining if the grid has to be upgraded and C grid the cost of upgrading the grid, which consists of the cost of reconductoring (80 €/m) and the cost of upgrading the transformer (21,000€ for 630 kVA) [35]. The operational cost C op (€) is defined as:

C op ¼

XX i

 elec grid tech grid C elec imp  P imp;i;t þ G  P gas;i;t  C exp  P exp;i;t  NPV

ð2Þ

t

where C elec imp is the cost of importing electricity from the grid (€/kWh), Pgrid imp;i;t is the amount of electricity imported from the grid for each building i at timestep t in kWh, G is the price of natural gas (€/ kWh), Ptech gas;i;t is the output of technologies that use natural gas as an input in kWh, C elec exp is the price gained by of exporting electricity

to the grid (€/kWh) and Pgrid exp;i;t is the amount of electricity exported to the grid in kWh. The lifespan of equipment was assumed to be 20 years on average [36], so the operating costs are calculated over a period of 20 years. Net present value (NPV) was used for discounting the future value of transactions to the current value: years

NPV ¼

ð1 þ irÞ 1 year ir  ð1 þ irÞ

ð3Þ

where ir is the discount rate of 4%. The secondary objective is the minimization of the carbon emissions Carbem , calculated as follows:

Carbem ¼

 XX tech CF grid  Pgrid imp;i;t þ CF gas  P gas;i;t  years i

ð4Þ

t

where CF grid and CF gas are the carbon factors (kg CO2/kWh) for electricity and natural gas. CF grid is varied in order to reflect different levels of renewable share in the electricity supply (see Section 3.1). Carbon emissions are calculated for a period of 20 years. Only operating emissions are taken into account and not life cycle emissions. Also, it is assumed that no carbon benefit is given for the electricity exported to the grid. 2.3. Building level Each building is represented by an energy hub to allow conversion and storage at the local level [31]. The energy hub is

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a framework that can easily define the conversions and storage of different types of energy vectors needed to satisfy various energy demands. The original formulation has been extended to include heat storage, district heating and linearized AC power flow. The results specify which technologies should be used at what capacities, what is the optimal operation and how buildings should exchange heat energy through heat network. It is assumed that a suitable control approach can be used for the real system that can match the optimized operation schedule, which is reasonable at hourly resolution. 2.3.1. Energy demand constraints The electricity demand of each building

Lload i;t ,

electricity

imported from the grid Pgrid imp;i;t , electricity exported to the grid CHP P grid or generated by PV PPV i;t , exp;i;t , electricity generated by CHP P i;t

and electricity used by heat pump (HP) P HP i;t have to be in balance for each building and timestep: grid HP grid CHP PV Lload i;t þ P exp;i;t þ P i;t ¼ P imp;i;t þ P i;t þ P i;t

8i; t

ð5Þ

Similarly, the heat demand of each building Hload can be met by i;t energy from the heat network, CHP, gas boiler, heat storage or HP:

Hload i;t ¼

Xh

i out CHP boiler Heatlossi;j  DHin j;i;t  DHi;j;t þ P i;t  HER þ P i;t

The state of charge of the storage at the last timestep of each day has to be equal to the state of charge at the first timestep of that day, since initializing the stored energy at a set value can influence the results. This way the initial and final state of charge is left to be optimized.

In this paper an approximation of AC power flow is used as presented in [38] in order to obtain active and reactive power flows, voltage and current magnitudes to ensure stable operation of the distribution grid. The linearized AC power flow equations on arc (n,m) are expressed as:

Pððn; mÞ; tÞ ¼ U 0  Gnm  DU nm;t  U 20  Bnm  D#nm;t Qððn; mÞ; tÞ ¼ U 0  Bnm  DU nm;t  U 20  Gnm  D#nm;t X

where

Pðn; tÞ ¼

X X Pi;t;load  P i;t;gen i

X

Q ðn; tÞ ¼

8i; t

ð6Þ

is the amount received through the heating network,

DHout i;j;t is the amount of heat sent to the heating network, Heatlossi;j is the fractional heat loss of exchanging heat through the network between two buildings, HER is the heat to electricity ratio of the CHP, COP is the coefficient of performance of the HP, and Q dis i;t and

8t 8t

8n; t

X

X X Q i;t;load  Q i;t;gen

8n; t

ota

X tech þ Pcon ði; tÞ 8n; i; t and ota ota

2 technologies that produce=consume activ e power ð17Þ

8i; tech

ð7Þ

X

Q ðn; tÞ ¼ QLload i;t 

otr

2 technologies that produce=consume reactiv e power

ð8Þ

The minimum part load of CHP and HP is set to 40% because of technical limitations [37]:

8i; t; tech 2 CHP; HP

ð9Þ

  tech on 8i; t; tech 2 CHP; HP 0:4  Ptech max;i 6 P i;t þ M  1  di;t;tech

ð10Þ

where don i;t;CHP is a binary variable which denotes if the technology is running or not, M is an appropriately large number (the ‘‘Big-M” method of formulating binary constraints for linear programming). The formulation ensures that if CHP or HP is installed, it has to operate between 40% and 100% of the installed capacity otherwise it has to be turned off. Heat storage is characterized by the state of charge variable ESOC stor governed by a continuity equation: ch dis SOC ESOC i;tþ1 ¼ Ei;t  nself þ Q i;t  nch  ndis  Q i;t

X tech Q con ði; tÞ 8n; i; t and otr þ

Psolar : t

8i; t

8i; t

X tech Q gen ði; tÞ otr

Furthermore, photovoltaic output is determined by the area of

on Ptech i;t 6 M  di;t;tech

ð16Þ

X tech Pgen ði; tÞ

lower bound LBtech and upper bound UBtech :

solar PPV i;t ¼ APV;i  nPV  P t

ð15Þ

i

Pðn; tÞ ¼ Lload i;t 

2.3.2. Conversion technology constraints Installed capacities of all technologies must be between their

panels APV;i , efficiency of panels nPV and solar irradiation

ð14Þ

where P is active power, Q is reactive power, Gnm is line conductance, Bnm is line susceptance, DU nm;t voltage magnitude difference and D#nm;t voltage angle difference. The linearized AC power flow equations are integrated in the energy hub model where Eqs. (15) and (16) are expressed as:

Q ch i;t are the amounts extracted from and saved to the heat storage.

tech LBtech P Ptech max;i P UB

ð13Þ

i

i

dis ch þ PHP i;t  COP þ Q i;t  Q i;t

ð12Þ

2.4. Integrating distribution grid constraints and grid upgrade options

j

DHin j;i;t

8i; t 2 day

SOC ESOC i;firstt ¼ Ei;lastt

ð11Þ

where nself is the amount of self-discharge per timestep (%), nch is the efficiency of charging and ndis is efficiency of discharging the heat storage.

ð18Þ where gen denotes generation and con consumption. Using values obtained for voltage magnitude and angles from Eqs. (13), (14), (17) and (18) the branch current can be calculated as:

Inm;t ¼

Rnm  ðU n  U m Þ þ X nm  ðU n  #n  U m  #m Þ þi

R2nm þ X 2nm X nm  ðU n  U m Þ þ Rnm  ðU n  #n  U m  #m Þ

¼ ReðInm;t Þ þ ImðInm;t Þ

R2nm þ X 2nm ð19Þ

However, Eq. (19) is non-linear and a series of approximations and linearization techniques have to be applied in order to linearize the expression and implement it in the MILP model. For more details, the reader is referred to [30]. Grid upgrade is defined as installing a new transformer with higher nominal capacity and installing new lines with higher ampacity. New lines will have different R and X values which will impact power flow and voltage variations.

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In order to implement the grid upgrade option first the following has to be predefined:
Line resistance Rnm and reactance X nm of the existing grid for each line segment
Line resistance Rnm;upg and reactance X nm;upg of the upgraded grid for each line segment
A binary decision variable ygrid denoting if the grid is upgraded (1) or not (0)

named Izr;nm;ref and Izr;nm;upg . Secondly, it can be concluded that the lower bound of the current is 0 and the upper bound is the maximum allowed current Inom . Finally, the linearized real part of the current for the reference grid can be defined by the following set of constraints:

0 6 Izr;nm;ref 6 Inom  ygrid

ð30Þ

Ir;nm;ref  Inom  ð1  ygrid Þ 6 Izr;nm;ref 6 Ir;nm;ref

ð31Þ

And for the upgraded grid current: Real part of current (Eq. (19)) can be rewritten to include grid upgrade option as:

Ir;nm ¼

ð32Þ

ðRnm  ð1  ygrid Þ þ Rnm;upg  ygrid Þ  ðU n  U m Þ þ ðX nm  ð1  ygrid Þ þ X nm;upg  ygrid Þ  ð#n  #m Þ  2 Rnm  ð1  ygrid Þ þ Rnm;upg  ygrid þ ðX nm  ð1  ygrid Þ þ X nm;upg  ygrid Þ2

Similarly, the imaginary part of current (Eq. (19)) can be rewritten to include the grid upgrade option as:

Ii;nm ¼

0 6 Izr;nm;upg 6 Inom  ygrid

ð20Þ

Ir;nm;upg  Inom  ð1  ygrid Þ 6 Izr;nm;upg 6 Ir;nm;upg

ðRnm  ð1  ygrid Þ þ Rnm;upg  ygrid Þ  ð#n  #m Þ  ðX nm  ð1  ygrid Þ þ X nm;upg  ygrid Þ  ðU n  U m Þ

Rnm;ref ðU n  U m Þ þ X nm;ref ð#n  #m Þ

Ir;nm;ref ¼

R2nm;ref þ X 2nm;ref

Ir;nm;upg ¼

Rnm;upg ðU n  U m Þ þ X nm;upg ð#n  #m Þ R2nm;upg þ X 2nm;upg

ð22Þ

ð23Þ

And similarly for the imaginary part of current for the reference grid Ii;nm;ref and upgraded grid Ii;nm;upg :

Ii;nm;ref ¼

Ii;nm;upg ¼

ð21Þ

ðRnm  ð1  ygrid Þ þ Rnm;upg  ygrid Þ2 þ ðX nm  ð1  ygrid Þ þ X nm;upg  ygrid Þ2

It can be seen that these terms are nonlinear, so they have to be linearized. This can be done first by defining separate variables for the real part of current for the reference grid Ir;nm;ref and the upgraded grid Ir;nm;upg :

Rnm;ref ð#n  #m Þ  X nm;ref ðU n  U m Þ R2nm;ref

þ

X 2nm;ref

Rnm;upg ð#n  #m Þ  X nm;upg ðU n  U m Þ R2nm;upg þ X 2nm;upg

ð24Þ

Similarly applying it to imaginary parts gives:

0 6 Izi;nm;ref 6 Inom  ygrid

ð34Þ

Ii;nm;ref  Inom  ð1  ygrid Þ 6 Izi;nm;ref 6 Ii;nm;ref

ð35Þ

And for the upgraded grid current:

0 6 Izi;nm;upg 6 Inom  ygrid

ð36Þ

Ii;nm;upg  Inom  ð1  ygrid Þ 6 Izi;nm;upg 6 Ii;nm;upg  0  ð1  ygrid Þ

ð37Þ

Then the linearized real part of the current Ir;nm;LIN can be expressed as:

Ir;nm;LIN ¼ Ir;nm;ref  Izr;nm;ref þ Izr;nm;upg

Then the real and imaginary parts of the current can be expressed as:

Ir;nm ¼ Ir;nm;ref  ð1  ygrid Þ þ Ir;nm;upg  ygrid

ð26Þ

Ii;nm ¼ Ii;nm;ref  ð1  ygrid Þ þ Ii;nm;upg  ygrid

ð27Þ

The terms are still non-linear due to the multiplication of the continuous and binary variable. The following linearization formulation for continuous variable x between lower bound (LB) and upper bound (UB), and binary variable y is used:

LB  y 6 z 6 UB  y

ð28Þ

LBð1  yÞ 6 x  z 6 UBð1  yÞ

ð29Þ

where z is a new variable introduced to replace the product x  y. To linearize Eq. (26), first two new variables have to be introduced for the non-linear terms Ir;nm;ref  ygrid and Ir;nm;upg  ygrid ,

ð38Þ

And the linearized imaginary part of the current Ii;nm;LIN as:

Ii;nm;LIN ¼ Ii;nm;ref  Izi;nm;ref þ Izi;nm;upg ð25Þ

ð33Þ

ð39Þ

Afterwards, Ir;nm;LIN and Ii;nm;LIN have to be squared using the piecewise linear formulation as described in [30]. Similarly, the aforementioned linearization is also applied to voltage magnitudes (Eqs. (40) and (41)) and angles (Eqs. (42) and (43)):

U LB  ygrid 6 DUznm;t 6 U UB  ygrid

ð40Þ

DU nm;t þ U LB  ð1  ygrid Þ 6 DUznm;t 6 DUznm;t þ U UB  ð1  ygrid Þ

ð41Þ

#LB  ygrid 6 D#znm;t 6 #UB  ygrid

ð42Þ

D#nm;t þ #LB  ð1  ygrid Þ 6 D#znm;t 6 D#znm;t þ #UB  ð1  ygrid Þ

ð43Þ

where U LB and U UB are lower and upper bound for voltage magnitudes, DUznm;t is the new variable introduced for linearizing voltage magnitude terms, #LB and #UB are lower and upper bound for voltage angles, and D#znm;t is the new variable introduced for linearizing

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voltage angle terms. The linearization introduces no error since it is based in reformulating the problem in a linear way with additional constraints [39]. Afterwards, the cost objective function has to be expanded to include the term describing the cost of upgrading the grid multiplied by binary variable ygrid . The advantage of this linearization method is that only one additional binary has to be introduced and all other new variables are continuous. This retains the linear nature of the formulation and does not cause extra computational effort associated with adding many binary variables. Furthermore, it allows the grid upgrade option to be determined by the optimization, where it directly influences the objective function and other decision variables. The formulation is easy to extend to include a binary for each line segment, which would enable to partially upgrade the distribution grid. However, upgrading only parts of the distribution grid is not very likely. The transformer is sized according to the highest possible current in the grid that it is supplying. If only one line segment is upgraded, the transformer still has to be upgraded for the worst case scenario, along with grid the protection gear. As the transformer is usually the most expensive part of the distribution grid, it is reasonable to assume that the transformer along with all line segments will be upgraded so that the overall capacity of the distribution grid increases. 2.5. Integrating district heating

X out DHi;j;t j

boiler 6 PCHP þ i;t þ P i;t

X in DHj;i;t  Heatlossi;j

8i; t

ð44Þ

j

Heat energy can be exchanged between buildings only if the buildings are connected to the heating network: pipe DHout i;j;t 6 M  di;j

Fig. 2. Needed pipe diameter for maximum heat capacity transferred.

eter needed for the maximum heat capacity transferred. To model the fact that the investment cost of the pipe increases as more heat is transferred through the pipe, the investment cost C pipe is expressed per meter of distance and per kW of capacity of pipe. The constraints still allow solutions with a centralised CHP supplying the whole DH network and solutions with (sub)networks with a number of decentralized sources. 3. Case study

The district heating network is assumed to be a decentralised network where each building is a prosumer – heat can be produced or consumed. This approach has been analysed and found technically feasible in [40]. It is one of the concepts of the smart thermal grid, also called 4th generation district heating [32]. The district heating network is formed by a number of buildings (nodes) that are directly connected with a pipe connection. The heating network can consist of a single network or a number of subnetworks. A building connected to the heating network can (partially) use or store heat energy, export heat to the network or reroute the heat energy through the network if no energy is added or removed. This is ensured by Eqs. (6), (44) and (45): boiler PCHP 6 i;t þ P i;t

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8i; j where j – i

ð45Þ

The framework was applied to a case study which is based on the IEEE European Low Voltage Test Feeder case [42]. The feeder is a widely-used benchmark for low voltage feeders in Europe which is representing a number of common low-voltage configurations. It consists of 55 residential buildings and a radial network with 4 branches. 3.1. Electrical grid In order to reduce computational complexity, the buildings that are connected to the same grid connection point were aggregated. The case study consists of 37 residential buildings connected by a three phase low voltage (0.4 kV) radial distribution grid. The layout of the case study can be seen in Fig. 3. Numbers denote building number (used later in the results section), and the letters correspond to which phase the buildings are connected to. The orange squares denote buses. The light orange square is the location of the transformer and is assumed to be the slack bus. The grid is assumed to be balanced and the mutual impedances are taken as 0. The line parameters are shown in Table 1 for the reference grid and the upgraded grid.

where dpipe is a binary variable which defines if buildings i and j are i;j connected. Additionally, each heating network link can only be one directional to maintain constant supply and return temperatures (maintained over the whole time horizon): pipe dpipe 6 1 8i; j where j – i i;j þ dj;i

ð46Þ

The maximum heat energy transferred between two buildings, used for pipe sizing, has to be bigger than heat transferred at any point in time and is only calculated if the connection is present:

Q max;i;j P DHout i;j;t Q max;i;j 6 M  dpipe i;j

8i; j; t where j – i

ð47Þ

8i; j where j – i

ð48Þ

Using Q max;i;j , pipe diameter can be determined for each pipe segment using the function plotted in Fig. 2. The function was interpolated based on the data from [41] and shows the pipe diam-

3.2. Buildings and systems The construction and geometry parameters of the buildings are given in Table 2. The buildings were modelled in EnergyPlus [43]. Weather data for Zürich, Switzerland was used for the simulation, which was run with an hourly timestep for the whole year. Afterwards, average 24 h profiles for each month were calculated for heat and electricity demand in order to decrease the complexity of the problem (making in total 288 timesteps). Building demands were scaled to meet the electricity profiles from the IEEE feeder definition. Electricity and heat demand (consisting of heating and DHW demands) are shown in Figs. 4 and 5; the demand profiles of the whole district consisting of individual profiles from all buildings. This gives an overview of the individual contribution of each building to the total district demand. Building numbers correspond to the numbers in the case study layout (Fig. 3). The black line shows the total demand of the district.

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Fig. 3. Case study layout. Numbers denote building number, and the letters correspond to which phase the buildings are connected to.

Table 1 Line parameters for the low voltage distribution grid. Grid

Cable type

Resistance Rph (p.u./km)

Reactance Xph (p.u./km)

Ampacity (A)

Reference Upgraded

70 AL 300 AL

0.8431 0.1890

0.1342 0.1300

160 465

Sbase

100 kVA

Vbase

Table 2 Construction parameters of the residential buildings. Parameter

Value

Window area Wall construction Roof construction Floor construction Window glass

27 m2/floor 1.7 W/m2 K 2.75 W/m2 K 2.85 W/m2 K 3.5 W/m2 K

Heat consumption Total consumption

115 kWh/m2/y 160 kWh/m2/y

The assumed efficiencies, capacity bounds and costs for each technology are shown in Table 3. The assumed electricity grid price is 0.2 €/kWh [44] and the natural gas price is 0.08 €/kWh [44]. The price for selling electricity back to the grid was assumed to be 0.08 €/kWh. The prices are taken to be constant throughout the optimization period and potential variations are outside the scope of this paper due to being almost impossible to predict it. It was assumed that there is no carbon ‘credit’ given for exported electricity. 3.3. District heating District heating network can be formed by any number of connected buildings. It was assumed that building (prosumers) can be

0.23 kV

connected to any other building by a district heating pipe through which the heat energy can be exchanged. Should the district heating network follow certain rules (e.g. the layout of the roads), additional constraints can be easily introduced in the model. Two new metrics are introduced in order to quantify the district heating potential. The first measures the size of the network, i.e. how many buildings are connected by the network. The second measures how much DH is utilized, i.e. how much heat energy is exchanged through the connections. They are adapted from the graph theory indices gamma and theta used commonly in the transport systems analysis [47]. District heating size (DHsize ) is based on the gamma index which is the ratio between the number of observed links and the number of possible links. The values range between 0 (no network at all) and 2.8 which is completely connected network (each vertex is connected to all other vertices) that is highly unlikely in reality. A value of 1 corresponds to the case where all buildings are connected to a sources by a tree network. DHsize is defined as:

DHsize ¼

e

v

¼

number of pipes number of buildings

ð49Þ

where e is the number of links and v is the number of vertices. In this analysis the number of links corresponds to the number of installed pipes, and the number of vertices corresponds to the number of buildings.

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Fig. 4. Electricity demand for all residential buildings.

Fig. 5. Heat demand for all residential buildings.

Table 3 Assumed efficiencies, capacity bounds and costs for each technology. Technology

Efficiency

Capacity bounds

Linear cost

CHP [14] Gas boiler [45] PV [46] Thermal storage [11] HP [14]

gel: 30%. HER: 2

0–50 kW 0–50 kW 0–30 kWp 0–40 kWh 0–50 kW

500 €/kW 50 €/kW 2500 €/kWp 70 €/kWh 600 €/kW

80% 15% 99% per timestep COP: 3

It shows the level of decentralization for meeting heat demands. Value 1 means that buildings have no individual heating systems, and 0 means that whole heat demand is supplied by the local building heating system. Using the defined metrics, it is possible to consistently quantify DH potential both in size and usage, and compare it objectively between different results. 3.4. Scenarios and analysis process

DH utilization (DHutilization ) is based on the theta index that measures the average usage per link. The measure can also be applied to the whole network. The higher the value, the more is network used. The factor is normalized so that 0 means no heat energy is exchanged and 1 which means that whole heat demand is supplied by district heating from a single source. DHutilization is defined as: Q

v DHutilization ¼ Q max v max

ð50Þ

where Q is the total heat energy exchanged through the network, v is the number of connected buildings, Q max is the total heat demand of all buildings and v max is the number of connections needed to connect all buildings from a central source using a tree structure.

The current level of renewables in the electric grid in the EU is 25% [48]. 6 scenarios have been defined with different renewable energy shares (25%, 40%, 55%, 70%, 85%, 100%) in the electricity supply (see Fig. 6). As the renewable share gets larger, the carbon factor of the electricity supply gets smaller. The first scenario evaluates the current state (25%) as a reference point. The carbon factor of the grid electricity at the current state is 0.5 kg CO2/kWh [49]. For other scenarios the carbon factor is incrementaly decreased to 0 kg CO2/kWh which corresponds to 100% renewable share. This provides an insight into how the energy systems in cities should be designed as the integration of renewables increase. The carbon factor of natural gas is 0.202 kg CO2/kWh [50] and constant for all scenarios. Furthermore, only operating emissions are taken into account and not life cycle emissions.

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Fig. 6. The scenarios and analysis process for determining the design of the system, grid operation, grid upgrade potential and district heating potential.

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Fig. 6 shows the analysis process conducted. Each scenario is implemented in the optimization framework. The inputs to the model described in the previous section are technology information, electrical grid layout and upgrade possibilities, heating network parameters and demand profiles. For each scenario a multiobjective (cost versus emissions) optimization is performed and a Pareto front is obtained. The results for each scenario give grid upgrade status, district heating potential and network layout, optimal buildings system design, and optimal operation for all buildings and the electrical grid. The MILP model consists of 2,012,176 variables (out which 21,542 are integers), and 2,259,806 constraints. Because of the long run time needed to solve the individual problem on a personal computer (more than 15 days), solving was performed in parallel on the Empa Hypatia cluster with 960 computing cores and 128 Gb of RAM, where the average solving time was 7 days. 4. Results 4.1. Impact on the cost and carbon emissions The Pareto front obtained for each scenario is shown in Fig. 7, giving annulized carbon emissions and annulized total cost (consisting of investment and operational cost). The single-objective case (minimising cost with no carbon constraint) is the lowerright point for each scenario, with the highest emissions but lowest cost. The other points for each scenario correspond to each subsequent e constraint limit on carbon emissions until the minimum emissions are achieved(upper-left). Even though the renewable share increases, there is still a trade-off between cost optimal and carbon optimal solutions. As the renewable share increases the minimum achievable carbon emissions decrease, and the range of possible carbon reductions gets larger. The minimum achievable carbon emissions for scenario 25% is 230 tCO2/y. For other scenarios minimal emissions are subsequently 220, 160, 125, 60 and 0 tCO2/y. Only in the 100% scenario it is possible to have a carbon-neutral district. This is because there is no carbon benefit given for the exported electricity to the grid. If the carbon benefit would be given, the district could be carbon neutral even with a lower renewable share in grid electricity but would probably cause PV to be used significantly more, and could be more difficult to maintain the stability of the distribution grid. Also, the distribution grid would export much more electricity to the higher electricity network to which it is connected which

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may affect the stability of other networks. One way that this can be avoided is by introducing a maximum limit on how much an urban district can export electricity at any given point. However, the limit should not be imposed arbitrarily but based on the detailed analysis of the greater grid. Table 4 shows the maximum reduction in carbon emissions and the related total cost for all scenarios. The possible emissions reduction increases as the renewable share increases. The reason is that the heating system gradually changes from gas based to electricity based as the electricity supply becomes less carbonintensive. Similarly, the cost increase is smaller because less PV (which is still relatively expensive) is needed to offset the emissions associated with using electricity from the grid. 4.2. Impact on system operation Fig. 8 shows the aggregated electricity and heat sources for each scenario. Each column gives the Pareto front points as shown in Fig. 7. It shows the range from cost optimal to carbon optimal solutions and their respective minimal achievable carbon emissions. The lowest point is the carbon neutral case where the carbon emissions are zero (only achievable in the 100% scenario). The grey area shows non-achievable carbon emissions for each scenario. Based on the optimal operation results at the building level, the total district consumption or generation for each technology is calculated and plotted relative to the total electricity or heat demand. The darker the color, the more the technology is used. The technologies are split into electricity-based and heat-based. HP and CHP feature both energy streams and are calculated separately for electricity and heat part. For heat, all technologies represent heat sources whereas for electricity, PV and CHP represent generators and HP an additional electric demand. This gives detailed overview of the energy mix of the district for each scenario. Looking at PV, it can be seen that it is used in the (near) carbonoptimal solutions for the scenarios with 25%, 40% and 55% renewable share. The electricity generated represents more than 180% of the electricity demand which means that at least 80% is exported to the grid. In order to decrease carbon emissions, PV electricity has to be used as much as possible. However, the irradiation during the winter time is smaller than during the summer. A lot of PV capacity is needed to meet the electricity demand during the day in the winter time which means that during the summer PV is oversized and a lot of electricity is exported to the grid. In the 70% scenario, the carbon factors of gas and electricity from the grid

Fig. 7. Pareto fronts for all scenarios.

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Table 4 Maximum change in emissions and total costs for all scenarios.

Maximum reduction in emissions Increase in cost

25%

40%

55%

70%

85%

100%

32% +50%

35% +42%

49% +49%

58% +37%

76% +36%

100% +36%

Fig. 8. Aggregated supply for the district based on the optimal operation of each building, given relative to the total electricity and heat demands. Each data point corresponds to a point on the Pareto front for that scenario.

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are similar (around 0.2 kg CO2/kWh). This is why there is a noticeable change in how much PV electricity is produced in the carbon optimal solutions between the 55% and 70% scenarios. PV is not so much needed to offset the grid carbon factor so HP and CHP are more used. Heat pumps are mostly used in the carbon optimal solutions for scenarios with 55% and more renewables share as part of the move towards electrified heating. However, in the (near) cost optimal solutions of all scenarios, HP is used very little because economically is better to use CHP as it produces both heat and electricity. Additionally, HP can represent 65% of the total electric demand which is a significant additional load compared to the base load for which the grid was designed. This highlights why it is important to include grid constraints in the analysis, to see if optimal solutions can be integrated in the distribution grid and reliable grid operation ensured. CHP, contrary to HP, is used predominantly in the (near) cost optimal solutions for all scenarios. In the 25% and 40% scenarios the utilization of CHP decreases only slightly for the (near) carbon optimal solutions. However, in other scenarios the use of CHP drops as the carbon emissions decrease, and it is not used at all in the carbon-optimal solutions. The heat produced gives up to 72% of the total heat demand. The gas boiler supplies only up to 3% of the heat demand; the lower the carbon emissions, the less it is used. It is used primarily for meeting peaks or demand lower than minimum load of HP and/or CHP. 4.3. Impact on building system design Fig. 9 shows the installed capacities of each technology for different carbon limits for each scenario. Each line corresponds to the capacities installed in each building (therefore solutions consist of 37 lines). It can be seen that the heat storage (HS) is installed at the maximum capacity in all scenarios for all carbon limits. HS is used to store excess heat from CHP and HP and use it for periods when the heat demand is lower than the minimum part load of CHP and/ or HP. Looking at scenarios 25% and 40%, the following trends can be seen as the carbon limit decreases: HP capacity gradually increases, boiler capacity decreases, CHP capacity mostly remains the same and CHP is always present, PV capacity increases significantly. Similar trends are valid for the remaining scenarios except that CHP is not installed at all in the carbon optimal solutions. In scenarios 25%, 40% and 55%, more PV is installed compared to the other scenarios. Also, the spread of capacities in individual buildings is higher which means that in the cost optimal solutions PV is almost not used at all and in the carbon optimal solutions the installed capacities increase significantly. As result, the installed HP capacities are higher as well, because excess PV electricity should be used as much as possible for heating. In scenarios 70%, 85% and 100%, PV is not installed so much because the grid electricity is not so carbon intensive and HP capacities are lower because less excess electricity is generated. The spread of the PV capacities is proportional to the amount of PV electricity generated as shown in Fig. 8, so in scenarios 70%, 85% and 100% the generated PV electricity remains mostly constant. 4.4. Impact on the district heating and grid upgrade potential District heating and grid upgrade options are shown in Fig. 10 for each point in the Pareto front for each scenario. The size of the circle corresponds to the factor DH size and the colour of the circles corresponds to the factor DH utilization as previously described in Section 3.3. The black dashed squares show that the grid was upgraded. The grey area shows carbon emissions reductions which are not achievable. The figure provides insight into when district heating and grid upgrades should be considered. Grid upgrade is needed when currents or voltages exceed their stable

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operational limits and a new transformer as well as cables with larger diameter and ampacity are needed for integrating more local generation from PV and CHP or additional consumption from HP. The size of the DH network and its utilization gradually decrease from the cost optimal solutions to no district heating in the carbon optimal solutions. In certain solutions the DH size is higher than 1 which means there are more connections than a tree structure and rings are formed between some buildings. This happens because the DH network is unidirectional and heat can be supplied by multiple buildings (prosumers), which makes ring structures overall economically more beneficial for the district than having a single heat source with a tree structure DH network. In scenarios 25% and 40%, district heating potential is decreasing because more PV is installed so there is less need for electricity from CHP. However, CHP is still important for meeting the heat demand, but it is only used for meeting the building’s own demand, and not for providing heat to other buildings in the district. As there are more renewables in the electrical grid (scenarios 55%, 70%, 85%, 100%), there is no need for DH for the carbon optimal solutions because more PV and HP are integrated and the heating system is becoming electricity based. The maximum DH utilization is 0.2 which means that the system is fairly decentralized and the heat is not supplied by a single building for the whole district. The cost of CHP is expressed with a linear cost (€/kW) in order to reduce model complexity and computational time, and the economy of scale cannot be fully taken into account. However, as the carbon emissions limit decreases, the cost has smaller impact on the results and adding capacity-dependent cost would not change the overall trends. In the carbon optimal solutions, no matter the efficiency of CHP and DH pipe heat losses, HP-PV coupling on the building level will always be preferred since PV operating emissions are zero. Regarding the grid upgrade option, it can be seen that the grid is upgraded only in the carbon optimal solutions when the use of PV and HP cause operational limits of the grid to be exceeded. Being carbon neutral is only possible by upgrading the grid, which was not designed for so much distributed generation and additional demand from heat pumps. However, the emissions of a district cannot reach zero emissions in lower renewable penetration scenarios because of the time mismatch between PV production during the day and heating by HP during the night. Battery storage (in addition with heat storage) is needed to account for the temporal mismatches but the price of batteries is still relatively high and the lifetime expectancy is small compared to heat storage so it is not very likely that individual users will have additionally battery storage. 4.5. Impact on the distribution grid Aggregated phase-to-neutral voltages (expressed per unit) are shown in Fig. 11 as a box plot. The aggregated result is based on the voltage data of all timesteps for all carbon limits and buses within each scenario. The box plot is calculated from 741,312 data points for each scenario. Scenarios 25% and 40% are notably different compared to the other scenarios; the interquartile range (IQR) as well as lower and upper quartiles of scenarios are much smaller. The reason is that in these scenarios there is a coupling of PV to HP (PV electricity used for heating by HP) and CHP to HP (excess electricity of CHP is used by HP to meet the heat demand). As a result of this building level coupling, the buildings have minimal impact on the grid. The values above 1.0 p.u. are associated with over dimensioned PV during the summer time when there is a lot of excess electricity that is exported to the grid. The values below 1.0. p.u. are originating when the HP is run by electricity imported from the grid. The outliers above 1 p.u. start to decrease after scenarios 55% when the electricity is less carbon intensive than the natural

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Fig. 9. Capacities of installed technologies in each building for different carbon limits (denoted by color) for all scenarios (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

gas. Subsequently less PV is needed to offset the carbon intensity during the winter period and therefore less excess electricity is exported to the grid during the summer period. In scenarios 55%, 70%, 85% and 100%, the heating system is predominantly based on grid electricity. As a result, HP is used more in the winter period which decreases further voltage magnitude. This is why the IQR is bigger and the median is lower. Additionally, CHP is used less so the HP uses more electricity from the grid which then has a bigger impact on grid stability. As a consequence the distance between the upper and lower quartiles of the voltage variation increases. Furthermore, when the heating system is electricity based only, the distribution grid has to be upgraded so that the voltage and current limits are not exceeded. The upgraded grid has larger diameter cables which have smaller resistance. This decreases the losses and the same amount of distributed resources

cause smaller overall currents and voltage drops. What influences the minimum voltage magnitude in a scenario is the case just before upgrading the grid. In scenario 85%, in the case before the grid has to be upgraded (100 kg CO2/y), has more HP installed compared to the case before upgrading the grid in scenario 100% (65 kg CO2/y). This causes bigger voltage drops and the outliers are lower in scenario 85% than in 100% (as seen in Fig. 11). The reason is that CHP is economically more feasible than HP. However, it is uses natural gas which is more carbon intensive than electricity from the grid in these scenarios. In scenario 85% more HP has to be used and less CHP can be used, in order to offset the carbon intensity of the grid. In scenario 100% the grid is carbon neutral so more CHP can be used. As a result, the case in scenario 85% has bigger impact on the grid with lower voltage magnitudes than the case in scenario 100%.

B. Morvaj et al. / Applied Energy 191 (2017) 125–140

Fig. 10. DH potential and grid upgrade for all solutions for each scenario. Each data point corresponds to a point in the Pareto front for that scenario. Colour indicates how much DH is used; size of the circles indicates the size of DH; hash indicates if the grid has to be upgraded to integrate distributed energy resources. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 12. Aggregated branch currents for all scenarios. The violing plots have rotated kernel density plot on each side and show the probability density of the data at different values. The red line marks the maximum current in the reference grid. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

large amount of PV which is not used locally by the buildings but exported to the grid. Scenario 55% has the largest maximal current because, in addition to PV, it has lot of HP integrated in the carbon optimal solutions which increases the electricity demand. As the carbon intensity of the electricity grid decreases in scenarios 70%, 85% and 100% (and has a smaller carbon factor than natural gas), there is less need for PV electricity, and the peaks in current mostly originate from the use of HP as the heating system gets more electrified. 5. Conclusions

Fig. 11. Aggregated phase-to-neutral voltages for all scenarios.

Fig. 12 shows aggregated branch currents for all timesteps for all branches and phases within each scenario. The currents are plotted using violin plots, which are similar to a box plot but instead of boxes they have rotated kernel density plot on each side and show the probability density of the data at different values. The red line marks the maximum current in the reference grid (see Table 1). If the current exceeds this limit, the distribution grid has to be upgraded. The violin plot is calculated from 741,312 data points for each scenario. It can be seen that most of the current values are below 100 A which is good for stable operation of the distribution grid. However, when designing the grid it is important to take into account the extreme points (which may occur rarely) to ensure that the grid is also stable during these periods. Otherwise, there is a chance that the distribution grid will become overloaded and have to be disconnected, which causes customers discomfort, and may lead to propagation of the disturbance to the rest of the grid and cause further blackouts. Maximum current values are much higher in scenarios 25%, 40% and 55%. This comes from the fact that in those scenarios there is a

An integrated optimization framework is presented that incorporates the optimal design and operation of distributed energy systems combined with electrical grid constraints, distribution grid upgrades and the design of district heating networks. It consists of building energy simulations for obtaining demand profiles, an energy hub model for the design and operation of building systems, a district heating model for network layout and pipe sizing, and a distribution grid model for ensuring grid stability and evaluating grid upgrades. A number of scenarios with different level of renewable share in the electrical grid were defined. For each scenario, we analysed how the design and operation of the urban energy system change, what is the impact on the district heating network, and the impact on the operation of the distribution grid as well as the need for grid upgrades. The results showed that only when renewable share is 100% (i.e. grid electricity is zero-carbon) it is possible to have a carbon neutral district. The only other possible solution for a district to be carbon neutral is to have either an electrical battery or seasonal heat storage (both out of scope for this work as they are still uncommon technologies). A battery enables excess PV electricity to be stored during the day and used during the night. Seasonal storage would make it possible to use the combination of PV and HP during the summer and store the excess heat generated for use in winter. When the renewable share is smaller than 55%, there is a lot of PV integrated to offset the carbon emissions of the electricity from the grid. In the carbon optimal solutions HP is used more but CHP has still a significant role in meeting the heat demand. Because of the coupling of CHP, HP and PV on a building level in the lowest carbon emissions solutions, there is no need for district heating. Also, because of the high share of PV in the grid, in these scenarios the currents in the grid are significantly higher than in the other scenarios. When the renewable share is 70% and higher, and the

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carbon factor of the grid becomes equal or smaller than the natural gas carbon factor, the use of PV decreases and the heating system becomes more electrified by producing heat from HP. In the carbon optimal solutions, the heating system is fully electricity based. As consequence, in such solutions DH is not used at all. Additionally, because PV is used less, the current peaks are smaller than in the other scenarios with lower renewable shares. Finally, district heating use and grid upgrades can be summarized as follows: in the cost optimal solutions, DH still plays an important role and is used regardless of the renewable share in the grid; as carbon emissions decrease, the potential of DH also decreases; in the carbon optimal solutions of each scenario there is no need for DH; grid upgrade is necessary only in the carbon optimal solutions when the heating systems gets more electrified; the biggest impact on the grid stability have solutions just before grid upgrade is needed. In the future work, additional technologies and options like batteries, electric vehicles and seasonal heat storage will be included as well as time-of-use electricity pricing strategies. Also, the influence on the design and operation of urban energy system of different carbon emissions calculations will be analysed.

Acknowledgment This research has been financially supported by CTI within the SCCER FEEB&D (CTI.2014.0119).

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