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Enhancing operation of decentralized energy systems by a regional economic optimization model DISTRICT

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Abstract

In this paper, a regional energy system model is introduced. The model targets the cost minimal operation of a regional energy system with the possibility of trading electricity at a spot and reserve market outside of the system borders. The system boundaries are set to be around the regional energy system, with one connection point to the rest of the system and hence the possibility to trade across the system border. Within the system boundaries, the system is divided into model areas where demand and generation are located, using a transport model approach to account for grid restrictions between the model areas. In addition to generation technologies, the model allows for demand side management and storage usage. For the trade at central markets, spot and reserve markets are integrated, using a price-taker approach. The paper shows the mathematical formulation in detail. To test the formulation and methodology of the model presented here, a case study based on real data is conducted. The case study highlights the fact that the model accounts for operational interconnections of technologies at distribution grid level. It also enables looking at effects on the grid and indicates where a more detailed power flow analysis might be required. If the proclaimed flexible energy systems come to reality, the model enables stakeholders to improve their knowledge of their distributed system, the effects of small-scale technologies and the interplay with the central system. Hence, the application demonstrates that the model adds value to closing the knowledge gap between stakeholders’ concerns about efficient operation planning of their system at distribution grid level.

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Notes

  1. The model has been extended to cover the heat sector in detail. All heat related aspects are published in a separate publication, cf. [50].

Abbreviations

a :

Model area

out :

Model area where the rest of the world is located

tec :

Technologies, consisting of all power plants, storage systems and infrastructure (distribution capacity and transformer)

pp :

Subset of tec consisting only of power plants, including all electricity generation technologies such as wind, pv, chp

re :

Subset of tec including all renewable energy plants, except biomass

stor :

Subset of tec including all storage systems

dsm :

Subset of tec only including DSM

ind :

Subset of tec including only DSM of industrial processes

t :

Time-step

\(bid\_block\) :

Bid period for the corresponding reserve product

\(\varDelta t\) :

Length of time-step in h

\(\eta _{\textit{stor}}^{\textit{ch}}\) :

Charge efficiency for storage systems

\(\eta _{\textit{stor}}^{\textit{dch}}\) :

Discharge efficiency for storage systems

\(\sigma _{\textit{chp}}\) :

Power to heat ratio for CHP

\({ cap}_{\textit{a,pp,t}}\) :

Installed plant capacity in kW

\({cap}_{\textit{a,stor}}^{\textit{ch}}\) :

Installed charge capacity in kW

\({cap}_{\textit{a,stor}}^{\textit{dch}}\) :

Installed discharge capacity in kW

\({cap}_{\textit{res}}^{\textit{res,min}}\) :

Minimum bid capacity for the corresponding reserve product in kW

\({cfr}_{\textit{res,t}}\) :

Binary call factor for offered reserve capacity

\({cp}_{\textit{res}}\) :

Call probability of corresponding reserve market product

\({{\textit{dem}}}_{\textit{a,t}}^{\textit{heat}}\) :

Heat demand in kW

\({{\textit{dem}}}_{\textit{a,t}}^{\textit{pl}}\) :

Planned demand in the corresponding area in kW

\({{\textit{dem}}}_{\textit{a}}^{\textit{pl,max}}\) :

Annual maximum of the planned demand in kW

\({dod}_{\textit{stor,t}}\) :

Depth of discharge

\({fc}_{\textit{pp}}\) :

Specific fixed operation cost in €/kW

\({fp}_{\textit{pp}}\) :

Fuel price in €/kWh

l :

Loss factor for electricity transmission

\({lf}_{\textit{a,re,t}}\) :

Load factor for renewable power plants, depending on the weather conditions in their location

\(k_{\textit{pp}}^{{{ CO}_{2}}}\) :

CO\(_{2}\) emission factor

n :

Number of time-steps

\(p^{{ {CO}_{2}}}\) :

Price of CO\(_{2}\) emission certificates in €/tCO\(_{2}\)

\(p_{\textit{pp}}^{\textit{fuel}}\) :

Fuel price in €/kWh

\(p_{\textit{res,t}}^{\textit{res,cap}}\) :

Price of offered reserve capacity for the corresponding reserve product in €/kW

\(p_{\textit{res,t}}^{\textit{res,en}}\) :

Price for called reserve energy in €/kW

\(p_{\textit{t}}^{\textit{spot}}\) :

Spot market price in €/kW

\({pot}_{\textit{a,stor}}^{\textit{ch}}\) :

Potentially installable charge capacity in kW

\({pot}_{\textit{a,stor}}^{\textit{dch}}\) :

Potentially installable discharge capacity in kW

\({soc}_{\textit{a,dsm,t}}^{\textit{max}}\) :

Maximum state of charge for the DSM storage dependent on the planned demand in kWh

\({soc}_{\textit{a,dsm,t}}^{\textit{min}}\) :

Minimum state of charge for the DSM storage dependent on the planned demand in kWh

\({tcap}_{\textit{a,aj}}\) :

Transmission capacity between areas a and aj in kW

tf :

Trading factor for spot market trades

\({tpot}_{\textit{a,aj}}\) :

Potential transmission capacity that could be installed in expansion planning in kW

\({vc}_{\textit{stor}}^{\textit{ch}}\) :

Specific variable charge cost in €/kW

\({vc}_{\textit{stor}}^{\textit{dch}}\) :

Specific variable discharge cost in €/kW

\(vc_{\textit{pp}}\) :

Specific variable operation cost in €/kWh

\({vol}_{\textit{a,stor,t}}\) :

Installed storage volume in kWh

TC :

Total cost in €

\({SoC}_{\textit{a,stor,t}}\) :

State of charge in kWh (free for all DSM storage systems, positive only for normal storage systems)

\(Y_{\textit{a,aj,t}}^{\textit{ex}}\) :

Binary decision variable for electricity export

\(Y_{\textit{a,stor,t}}^{\textit{ch,pl}}\) :

Binary decision variable for planned storage discharge

\(Y_{\textit{a,stor,t}}^{\textit{ch}}\) :

Binary decision variable for storage charge

\(X_{\textit{t,res}}\) :

Binary decision variable whether the corresponding reserve product is offered

\({{\textit{CH}}}_{\textit{a,stor,t}}^{\textit{pl}}\) :

Planned charge of storage systems in kW

\({{\textit{CH}}}_{\textit{a,stor,t}}\) :

Storage charge in kW

\({{\textit{DCH}}}_{\textit{a,stor,t}}^{\textit{pl}}\) :

Planned discharge in kW

\({{\textit{DCH}}}_{\textit{a,stor,t}}\) :

Storage discharge in kW

\({{\textit{DEM}}}_{\textit{a,t}}\) :

Electricity demand after DSM usage in kW

\(E_{\textit{t}}^{\textit{bought}}\) :

Electricity bought at the spot market in kW

\(E_{\textit{t}}^{\textit{sold}}\) :

Electricity sold at the spot market in kW

\({EX}_{\textit{t,a,aj }}\) :

Export of electricity from area a into area aj in kW

FC :

Sum of fix operation cost in €

\({FI}_{\textit{t,a}}\) :

Electricity fed into the grid from the corresponding area in kW

\({{\textit{GEN}}}_{\textit{a,chp,t}}^{\textit{heat}}\) :

Heat generation from CHP plants in kW

\({{\textit{GEN}}}_{\textit{a,pp,t}}^{\textit{pl}}\) :

Planned electricity generation in kW

\({{\textit{GEN}}}_{\textit{a,pp,t}}\) :

Realized electricity generation in kW

\({HD}_{\textit{a,chp,t}}\) :

Heat dumped in kW

\({IM}_{\textit{t,aj,a}}\) :

Import of electricity from area aj into area a in kW

\(P_{\textit{a,pp,t}}^{\textit{fuel}}\) :

Fuel power required in kW

\({RES}_{\textit{res,a,pp,t}}^{\textit{cap}}\) :

Offered reserve capacity for each reserve product from the respective plants / storage systems in kW

\({RES}_{\textit{res,a,pp,t}}^{\textit{energy}}\) :

Called reserve energy in kWh

\({REC}_{\textit{a,re,t}}\) :

Curtailment of electricity from renewable energy plants in kW

\({RES}_{\textit{res,a,stor,t}}^{\textit{energy1}}\) :

Called reserve energy affecting storage charge in kW

\({RES}_{\textit{res,a,stor,t}}^{\textit{energy2}}\) :

Called reserve energy affecting storage discharge in kW

\(R^{\textit{res}}\) :

Revenue from reserve market trading in €

\(R^{\textit{spot}}\) :

Sum of revenues from spot market trading in €

\({{\textit{WD}}}_{\textit{t,a}}\) :

Electricity withdrawn from the grid into the area in kW

VC :

Sum of variable operation cost in €

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Acknowledgements

This work has been partially supported by the German Federal Ministry for Economic Affairs and Energy in the context of the project “Netzbewirtschaftung als neue Marktrolle” (project 03ET4018A). The remaining works have been supported by a scholarship from “Studienförderwerk Klaus Murmann”. For insightful discussions and proof-reading, I thank C. Weber, N. Hussein, N. Hartmann and C. Kost.

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  1. Fraunhofer-Institut fur Solare Energiesysteme, Freiburg, Germany

    Jessica Thomsen

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Appendix

Appendix

1.1 Abbreviations

AC

Alternating current

DC

Direct current

DSM

Demand side management

PV

Photovoltaic

PTDF

Power transfer distribution factor

RE

Renewable energy

LV

Low voltage

SoC

State of charge

sn

Negative secondary reserve

sp

Positive secondary reserve

mn

Negative minute reserve

mp

Positive minute reserve

CHP

Combined heat and power

1.2 Limiting factors for the DSM sensitivity analysis

As a factor used to limit the available DSM capacity, the parameter \({lim}_{\textit{dsm}}^{\textit{cap}}\) is introduced into the original equation presented in Sect. 2.5. The factor takes on a number between one (for full capacity) and zero (i.e. no capacity).

Similarly it is used to limit the DSM potential

$$\begin{aligned} {CH}_{a,dsm,t}\le {lim}_{dsm}^{cap}\cdot ({dem}_{a}^{pl,max}-{dem}_{a,t}^{pl}) \end{aligned}$$
(4.1)
$$\begin{aligned} {DCH}_{a,dsm,t}\le {lim}_{dsm}^{cap}\cdot {dem}_{a,t}^{pl} \end{aligned}$$
(4.2)
$$\begin{aligned} {soc}_{a,dsm,t}^{max}={lim}_{dsm}^{cap}\cdot \sum \nolimits _t^{t+{dt}_{a,t}} {({dem}_{a,t}^{pl}} \cdot \varDelta t) \end{aligned}$$
(4.3)
$$\begin{aligned} {soc}_{a,dsm,t}^{min}={lim}_{dsm}^{cap}\cdot \sum \nolimits _{t-{dt}_{a,t}}^t {({dem}_{a,t}^{pl}\cdot \varDelta t)} \end{aligned}$$
(4.4)

1.3 Additional results data

The total numbers of the four base scenarios are displayed in Table 6.

Table 6 System operation cost and trade balance for the spot and reserve market in € for each scenario
Full size table

To determine the usage of single transport lines, the amount of changes in directions, represented by the sign of the difference between the power flow at t and t\(-1\), is summed up over the year and divided by the number of time-steps times two, since each direction change results in a value of two.

$$\begin{aligned}&{\textit{Direction change factor}}\\&\quad =\frac{\sum \nolimits _{\textit{t=2}}^t {(| sgn( {EX}_{\textit{t,a,aj}}-{IM}_{\textit{t,a,aj}} )-sgn({EX}_{\textit{t-1,a,aj}}-{IM}_{\textit{t-1,a,aj}}) |)} }{2\cdot n} \end{aligned}$$

The Result is displayed in Table 6.

Table 7 Share of time-steps with a change in power flow direction on each line for the different scenarios
Full size table
Table 8 Magnitude of change in power flows between time-steps on each line for the different scenarios
Full size table

To measure the changes in power flow magnitude, the following formula is used. The formula accounts of power flows between time-steps. The square prevents the direction from distorting the result.

$$\begin{aligned} {\textit{Fluctuation Factor}}=\frac{\mathop {\sum }\nolimits _{t} {(( {{\textit{EX}}}_{\textit{t,a,aj}}-{{\textit{IM}}}_{\textit{t,a,aj}} )-( {{\textit{EX}}}_{\textit{t-1,a,aj}}-{{\textit{IM}}}_{\textit{t-1,a,aj}} ))^{\textit{2}}} }{\mathop {\sum }\nolimits _{t} {({EX}_{\textit{t,a,aj}}-{{\textit{IM}}}_{\textit{t,a,aj}})^{\textit{2}}} } \end{aligned}$$

The results are displayed in Tables 7 and 8.

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Thomsen, J. Enhancing operation of decentralized energy systems by a regional economic optimization model DISTRICT. Energy Syst 9, 669–707 (2018). https://doi.org/10.1007/s12667-017-0261-9

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