A Formal Holon Model for Operating Future Energy Grids during

Blackouts

Siavash Valipour

, Florian Volk

, Tim Grube

, Leon B

ock

, Ludwig Karg

and Max M

uhlh

auser

Telecooperation Lab, Technische Universit

at Darmstadt, Hochschulstr. 10, Darmstadt, Germany

B.A.U.M Consult GmbH, Gotzinger Str. 48/50, M

unchen, Germany

Keywords:

Smart Grid, Micro Grid, Smart City, Blackout, Islanded Operation, Holon Model, Energy Network, Decen-

tralized Power Sources.

Abstract:

Modern energy grids introduce local energy producers into city networks. Whenever a city network is discon-

nected from the distribution grid, a blackout occurs and local producers are disabled. Micro grids circumvent

blackouts by leveraging these local producers to power a ﬁxed subset of consumers. In this paper, we evolve

micro grids to Holons, which overcome the need for ﬁxed subsets and power as much of the city network as

possible. We contribute a formal model of Holons and investigate the impact of the Holon concept in a simu-

lation with 10,000 randomly generated city networks. These city networks are based on parameters obtained

from a real-world test site in a medium-sized German city. Our results show that the Holon approach can

supply an average fraction of 22.08% of any city network, even when ﬁxed micro grids would fail to power

the city network as a whole.

1 INTRODUCTION

In the event of distributed small energy providers, for

example, photovoltaic systems, new challenges for

energy grids arise.

The classic scheme of combined energy trans-

mission and distribution networks (energy grids) is

given in Figure 1. The power stations that gener-

ate energy are located in and connected via the so-

called transmission grid, a network of high voltage

transmission lines. The power is transported to the

consumer, e.g., households, via the distribution grid

and city networks. Thereby, a city usually consists

of multiple city networks, all of them are indepen-

dently connected to the distribution grid. All grids are

connected with distribution substations that transform

high-voltage energy in lower-voltage energy and vice

versa.

Energy grids are undergoing paradigm changes

in producing, distributing, monitoring, and metering

electricity. Modern, so-called smart grids evolve the

traditional energy grid by the addition of communica-

tion infrastructure in order to optimize the efﬁciency

of the grid. Thus, producers and consumers can co-

ordinate their production and consumption of energy

with each other.

Especially, local energy producers are introduced

into city networks. For example, photovoltaic sys-

tems (PV systems), combined heat and power plants,

as well as wind power stations supply power to the

energy grid. Therefore, new challenges and opportu-

nities in distributing power arise for energy grid op-

erators. Our paper focuses on continued operation of

parts of city networks during blackouts.

1.1 Blackout Handling

A failing distribution substation usually cuts off the

entire city network behind it from the distribution

grid. As a consequence, the city network experiences

a power outage, a blackout. Even though local en-

ergy producers might exist inside city networks, these

producers are disabled during a blackout and cannot

supply energy on their own, as they conventionally

depend on the synchronization to the energy grid in

order to maintain grid stability. Local emergency en-

ergy sources, as, e.g., batteries and diesel generators

are only available to those households that operate the

respective sources.

1.2 Holon Approach

This paper adopts the Holon approach, as it is be-

ing developed in the project PolyEnergyNet, a project

146

Valipour, S., Volk, F., Grube, T., Böck, L., Karg, L. and Mühlhäuser, M.

A Formal Holon Model for Operating Future Energy Grids during Blackouts.

In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 146-153

ISBN: 978-989-758-184-7

Transmission

Grid

Distribution

Grid

City Network

Hospital

System

Figure 1: Combined energy transmission and distribution

network.

concerned with a resilient and secure energy supply of

tomorrow. The adopted model presented here, inves-

tigates a possibility to operate parts of city networks

independently from the distribution grid by leverag-

ing energy producers located inside the city network

(cf. Figure 2). Our aim here is to supply as many

consumers as possible with energy during a blackout.

Moreover, prospectively, Holons are thought to en-

able prioritization of consumers so that – in case of

energy scarcity – the most critical parts of city net-

works (hospitals and similar) can be kept active while

only consumers of low importance are affected by the

blackout. Furthermore, Holons should prefer renew-

able energy sources over conventional ones.

3 kW

Hospital

System

+5 kW

1 kW

(

1 kW)

(

1 kW)

Figure 2: A disconnected city network is partly supplied by

a local PV system.

1.3 Paper Structure

This paper is structured as follows: work related to

our approach is reviewed in Section 2. In Section 3,

we present a formal model of the Holon approach, in-

troduce the involved stakeholders, and discuss con-

straints. Our approach is evaluated in the subsequent

sections. Therein, Section 4 presents the evaluation

setup, including a real-world test site, which is un-

der construction in a medium-sized town in Germany.

The results of the evaluation are summarized and dis-

cussed in Section 5. Section 6 concludes and presents

our upcoming research.

2 RELATED WORK

Many approaches for evolving the energy grid to

smart grids (Amin and Wollenberg, 2005) exist. Most

of these approaches target energy-efﬁciency and de-

mand side management to achieve higher energy grid

stability and cost-reduction (Hashmi et al., 2011;

Fang et al., 2012).

This section ﬁrst reviews work related to our ap-

proach in Section 2.1 and, later in Section 2.2, dis-

cusses the approach of micro grids, which we see as

an evolutionary base for the Holon approach.

2.1 Smart Grids

The term smart grid is, ampong others, well explained

by Amin in (Amin and Wollenberg, 2005). Both

Hashmi et al. and Fang et al. survey smart grid

technologies and approaches in (Hashmi et al., 2011)

and (Fang et al., 2012), respectively.

With regards to the stability of smart grids,

erard et al. propose a grid model based on dy-

namic graphs to detect and handle network errors

within smart grids (Gu

erard et al., 2015). Our ap-

proach speciﬁcally targets network errors that isolate

city networks and require isolated operation (here: is-

landed operation) to cope with blackouts.

Farhangi criticizes missing alignment of techno-

logical evolution and legal regulations in smart grids

and presents a general road map for smart grid de-

velopment in (Farhangi, 2014). The Holon approach

requires both new technologies and new regulations,

e.g., the permission to operate local energy producers

during a blackout. In terms of technology, many

challenges are to be solved, for example, operating

multiple power producers concurrently requires them

to synchronize their frequencies during a bootstrap

phase.

A Formal Holon Model for Operating Future Energy Grids during Blackouts

147

The German Association of Energy and Water In-

dustries BDEW proposes a so-called “Trafﬁc Light

Concept” for the operation of smart grids (BDEW,

2014). The trafﬁc light concept classiﬁes smart grid

operation into three phases:

• During the green phase, the smart grid is fully

functional and stable. Market mechanisms, like

the ones proposed by Saad et al. (Saad et al.,

2011), are in control of production, consumption,

and prices.

• When the smart grid is in danger to become un-

stable (amber phase), the network operators to-

gether with the market participants enforce stabil-

ity rules (BDEW, 2015).

• In the red phase, in the event of imminent risk of

failure, the smart grid is solely managed and con-

trolled by the network operators. Market mech-

anisms are suspended in order to restore a stable

energy grid.

The Holon model comes into play during the amber

and red phases of the trafﬁc light concept.

In (Bessler et al., 2015), it is explained in detail

how demand side ﬂexibilities can be used to optimize

city networks. Similar to ﬂexibilities, in (Kausika

et al., 2015) the authors investigate the distribution

and potentials of PV systems. This is done in or-

der to achieve optimal saturation of renewable energy

sources within city networks.

2.2 Micro Grids

Micro grids, often also referred to as “cellular grids”,

are very similar to our Holon approach. By isolating

predeﬁned areas of energy grids, these areas become

able to harvest energy from local energy producers

inside the micro grids. The size of micro grid cells

varies on the given scenario. Sometimes, a micro grid

cell might only be one building, e.g., a hospital with

backup batteries, while in other scenarios, a cell can

be a whole city network, as shown in ﬁgure 3.

3 kW

Hospital

System

+7 kW

1 kW

Switch

(open)

Figure 3: A micro grid in islanded operation.

The German cities of Mannheim and Dresden practi-

cally evaluated the concept of micro grids by rolling

out such an energy grid for 1,000 households (MVV

Energie AG, 2012). The main difference of micro

grids and Holons is that micro grids are predeﬁned

areas that can be physically separated from their sur-

roundings. Holons are virtual micro grids inside city

networks that do not require physical separation and,

thus, allow dynamic service composition based on

communication infrastructure.

In Schiffer’s PhD thesis (Schiffer, 2015), he in-

vestigates practical constraints like frequency stabil-

ity and voltage stability that are introduced by oper-

ating energy producers inside city networks. Schif-

fer proposes multiple control concepts to cope with

these constraints. All these constraints also apply to

Holons.

Operating micro grids in islanded mode, i.e., op-

erating them independently from a distribution net-

work, is discussed in (Kroposki et al., 2008) as well as

in (Shaﬁee et al., 2014). While this paper at hand fo-

cuses on operating Holons in islanded mode, a mixed

operational setting for Holons that are connected to

the distribution network is planned for the future.

Schiller and Fassmann describe IT challenges for

network operators introduced by micro grids (Schiller

and Fassmann, 2010). As Holons depend on control

and communication infrastructures just as micro grids

do, the challenges discussed by Schiller and Fass-

mann apply to Holons as well.

In (Ramesh et al., 2015), the authors present a mi-

cro grid architecture that allows to identify line faults

and to isolate affected areas. They claim that their ap-

proach is able to localize a fault in less than two sec-

onds. As Holons do not require physical separation,

an isolated segment of a micro grid could continue its

operation as a Holon.

3 HOLON MODEL

In this section, we contribute a formalized Holon

model. The term holon was ﬁrst described by Arthur

Koestler (Koestler, 1967) as a modeling scheme

for autonomous entities that can consist of other,

smaller autonomous entities. Our model represents

autonomous sets of energy producers and consumers

inside city networks. The overall goal is to evolve

smart grids into more resilient energy grids by over-

coming the limitation of only having predeﬁned mi-

cro grids. Hereby, our understanding of resilience is

aimed at a system which provides a high degree of

service availability. Blackout scenarios result into iso-

lated city networks with speciﬁc energy production

SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems

148

and consumption conﬁgurations. Such a “snapshot”

of a city network is represented by one energy grid

instance as deﬁned below.

3.1 Formal Model

We model an energy grid as graph G = (N, E) of

nodes N with edges E ⊆ N × N. The whole energy

grid builds one connected component. A node n ∈ N

can be classiﬁed into one of the following sets: Pro-

ducers P = {p

| p

∈ N} that produce energy in the

grid, Consumers C = {c

| c

∈ N} that consume en-

ergy in the grid, or Junctions J = { j

| j

∈ N} that

split power cables if necessary, e.g., at crossroads.

For simplicity we deﬁne P∩C = P∩J = C ∩J =

Any object that has to be covered by more than one

class can be (virtually) split into subnodes, so that the

subnodes can be correctly classiﬁed as either produc-

ers, consumers or junctions.

The function

power : N → R : n →











if n ∈ P

0 if n ∈ J

−

if n ∈ C

returns the production or consumption of a node in an

energy grid. While the producers supply energy to the

grid and have a positive power value, the consumers

draw energy from the grid and have a negative power

value. A junction does not change the overall energy

and therefore, it has a power value of 0.

The function

cap : E → N

: e → cap(e)

returns the capacity of a power cable for transmitting

energy. Thereby, the capacity is deﬁned by the break-

ing capacity of the respective fuse that protects the

power cable.

A Holon is a connected subgraph H = (N

, E

)

with N

⊆ N and E

= {(n1, n2) ∈ E : n1, n2 ∈ N

}

and can be thought of as kind of Peer-to-Peer–Overlay

that does not alter edges. In order to transmit energy,

the Holon has to be connected, i.e., the Holon has to

form a single connected component.

Additionally, the available energy within a Holon

must be transmittable from producers to the respec-

tive consumers by the existing power cables, leading

to a valid Holon.

3.2 Valid Holons

A holon has to fulﬁll few prerequisites to be able to

supply consumers with energy in a distributed way.

• The ﬁrst important requirement is the connectiv-

ity. As stated before, connectedness is only a nec-

essary but not a sufﬁcient condition for a Holon.

• Moreover, the sum of produced and consumed en-

ergy has to be in balance:

∑

∈P

power(p

) =

∑

∈C

power(c

)

• A third requirement is the sufﬁcient capacity of

power cables. At no time shall an energy ﬂow

surpass the maximum capacity of any edge in

a Holon. Therfore, ∀e ∈ E

: f low(e) ≤ cap(e)

has to hold. This requirement can be reduced to a

max-ﬂow problem (Schroeder et al., 2004).

Max-ﬂow problems can be solved with the Dinic

algorithm (Dinic, 1970) or the Ford-Fulkerson (Ford

and Fulkerson, 1956) algorithm. In order to be able

to compute these algorithms, an additional source

as well as an additional sink are introduced into the

graph. The source is connected to all producers by

edges with their weights equaling the capacities of

the respective producers. Similar, all consumers are

connected to the sink by edges with their respective

consumption values.

4 EVALUATION

In order to evaluate the effects of applying our Holon

approach to city networks, we conducted a large-

scale simulation based on randomly generated city

networks.

These city networks are generated based on pa-

rameters we obtained from measurements and ex-

periences of a German network operator. The city

networks consist of different energy producers, con-

sumers, and power cables, each with speciﬁc capabil-

ities.

Our aim is to gather information on how the Holon

approach performs in comparison with predeﬁned,

ﬁxed micro grids. Especially, we are interested in

speciﬁcs that distinguish Holons from static micro

grids.

4.1 Real-world Test Site

The Holon approach will be evaluated in the context

of a publicly funded research project PolyEnergyNet

in a real-world test site. The test environment which

served as basis for evaluation is based on the city net-

work of a real-world, medium sized German city with

an industrial quarter with PV systems and consumers.

The setup of the following simulation is based on

time-snapshot measurements taken in the test site and

on know-how of the local network operator.

Consumer households usually draw 2–3 kW from

the city network. PV systems within city networks

A Formal Holon Model for Operating Future Energy Grids during Blackouts

149

generate 5 kW up to 60 kW under optimal conditions.

The two cable types typically used for wiring are pro-

tected by fuses that allow 150 kW or 185 kW to pass

the network. These values are used to generate ran-

dom city networks and to evaluate our approach.

4.2 Simulation Setup

As stated before, our simulation generates random

city networks based on parameters obtained from

measurements in a real-world test site and on know-

how of a network operator. All parameters are shown

in Table 1.

Table 1: Parameter values used for the generation of random

city networks.

Parameter Value

Network Size 10–25 nodes

Producers 10%

Consumers 80%

Junctions 10%

Production Values {5, 20, 30, 40, 60} kW

Consumption Values {10, 15, 20, 30} kW

Cable Capacities {150, 185} kW

4.2.1 Network Size

Every city network was chosen to have about 10–25

nodes in total. Thereby, every consumer node repre-

sents 5–10 single households sharing one power ca-

ble.

4.2.2 Node Class Probabilities

Based on our observations, we modeled the city net-

works to consist of 80% consumers, 10% producers,

and 10% junctions.

4.2.3 Consumption and Production Values

The network operator describes a consumption of 2–

3 kW as typical value for a household. Thus, con-

sumer nodes with 5–10 households consume either

10, 15, 20, or 30 kW. The production values for pro-

ducer nodes are chosen in the same fashion.

4.3 Research Questions

The simulation is used to investigate the following re-

search questions:

1. How many of the generated city networks can op-

erate in complete as micro grids?

2. How many non-functional micro grids can operate

in parts as Holons?

3. How much of a city network can covered by

Holons?

4. How does the size of city networks inﬂuence the

amount of nodes covered by Holons?

Figure 4 shows a city network consisting of seven

nodes and one additional junction. As can be seen,

there are three valid holons in the network:

• Producer 1, Consumer 3

• Producer 3, Consumer 2, and Consumer 3

• Producer 2, Consumer 1

Producer-2 (20)

Consumer-1 (-20)

Consumer-4 (-30)

Junction-1 (0)

Consumer-3 (-20)

Producer-1 (20)

Consumer-2 (-30)

Producer-3 (50)

185185

185

150

185

150

Figure 4: An exemplary city network with three Holons and

71.4% coverage.

Because of the overlap of the ﬁrst two holons, namely

in Consumer 3, the maximum coverage of this city

network with Holons is given by the ﬁve green nodes

in Figure 4. A ﬁxed micro grid would not be able

to operate in islanded operation, while the Holon ap-

proach would power 71.4% of the city grid.

5 RESULTS

The following results are based on 10,000 randomly

generated and evaluated city networks. Each city net-

work was generated according to the parameters in

Table 1.

5.1 Comparison with Micro Grids

Out of the 10,000 generated city networks, only 25

(0.25%) expose valid micro grids. Thus, these 25 city

networks also form Holons, which include all nodes

from the generated city network.

6,139 (61.39%) city networks contain valid

Holons, that is, at least one valid Holon conﬁgura-

tion is present. The number of Holons within a city

network increases with the size of the city networks.

In larger city networks, more producers and junc-

tions will appear, thus enabling more valid combi-

nations according to our model. On average, 2.46

SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems

150

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

9000

9500

10000

Coverage

Simulation Round

Figure 5: Distribution of city network supply coverage. The rounds on the x-axis are sorted ascendingly with respect to

the city network size. This result shows higher ratios of coverage with growing network sizes on average, as more nodes

contribute to a more coarse-grained distribution and promote the chances of valid Holon setups.

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Coverage

Simulation Round

Figure 6: Distribution of city network coverage, omitting city networks without valid Holons altogether. The rounds on the

x-axis are sorted ascendingly with respect to the city network size. The reverse trend can be explained by higher average

coverage values due to not considering solutions with 0 solutions.

valid holons exist in every city network. 22.08% of

all buildings can be supplied on average by the largest

possible combination of Holons within the same city

network.

5.2 Inﬂuence of City Networks Without

Holons

Substantial differences can be observed when distin-

guishing on the analysis of gathered data from city

networks with at least Holon present and complemen-

tary data from city networks allowing also 0-Holon

conﬁgurations. In cases where there is at least one

valid Holon, there are three further Holons to ﬁnd.

This means, that usually you will ﬁnd on average 4

Holons per network if you neglect networks which do

not meet the Holon criteria at all. The average sup-

ply coverage also increases from 22.08% to 35.73%

in these networks.

Table 2 summarizes the number of found holons

and the supply coverage ordered by the city net-

work size for all investigated city networks. Table 3

presents the same data for city networks with at least

one valid Holon present.

The histogram in Figure 7 shows how city net-

works without valid Holons are distributed over city

network size. As can be seen, with an increasing num-

ber of nodes, the amount of city networks without

100

150

200

250

300

350

400

City networks without holons

Nodes in city network

Figure 7: Distribution of cells without any solution in rela-

tion to cell size.

valid Holons decreases. This observation may con-

tribute to the difference between the results shown in

Tables 2 and 3.

5.3 Coverage Distribution

A look at the distribution of the overall supply cover-

age (cf. Figures 5 and 6) yields three observations:

• There appears to be a correlation between small

city network sizes and the probability of ﬁnding

either a Holon that covers the whole city network

or ﬁnding no Holon at all. However, it is much

A Formal Holon Model for Operating Future Energy Grids during Blackouts

151

Table 2: Evaluation results for all city networks, including

those without valid Holons.

Network Holons Found Supply Coverage

Size avg. med. avg. med.

10 0.70 0 17.62% 0.00%

11 0.78 0 18.17% 0.00%

12 1.06 0 20.70% 0.00%

13 1.07 1 20.19% 15.38%

14 1.37 1 21.11% 15.38%

15 1.64 1 22.02% 15.38%

16 1.87 1 22.76% 18.75%

17 1.93 1 20.43% 17.65%

18 2.23 1 21.74% 17.65%

19 2.94 1 24.76% 21.05%

20 2.80 2 23.23% 20.00%

21 3.30 2 23.64% 21.05%

22 3.42 2 22.69% 19.05%

23 3.96 2 24.22% 22.22%

24 4.71 2 24.34% 21.05%

25 5.75 2 25.52% 20.83%

Table 3: Evaluation results for city networks that include at

least one valid Holon.

Network Holons Found Supply Coverage

Size avg. med. avg. med.

10 1.79 2 45.06% 42.86%

11 1.85 1 43.28% 40.00%

12 2.20 2 42.90% 36.36%

13 2.13 2 40.11% 38.46%

14 2.52 2 38.79% 33.33%

15 2.83 2 38.00% 30.77%

16 3.17 2 38.64% 35.71%

17 3.21 2 34.02% 28.57%

18 3.54 2 34.52% 29.41%

19 4.25 2.5 35.78% 31.25%

20 4.03 3 33.38% 27.78%

21 4.69 3 33.63% 30.00%

22 4.74 3 31.46% 26.32%

23 5.10 3 31.19% 27.27%

24 6.23 3 32.20% 28.57%

25 7.33 3 32.53% 28.00%

more likely to ﬁnd no Holons in such a setting.

• When including all city networks, the overall cov-

erage by Holons increases with the city network

size (cf. trend line in Figure 5). However, leav-

ing out those city networks without any Holons,

the overall coverage decreases (cf. trend line in

Figure 6).

• Holons always have a natural number of nodes.

Thus, the coverage values for small city networks

are more coarse-grained.

6 CONCLUSION AND FUTURE

WORK

In this paper, we investigated the adopted concept of

Holons in city energy networks. Holons are regarded

as enablers for decentralized energy producers inside

city networks to supply power to consumers inde-

pendently from external energy sources, like, power

plants connected via the transmission network.

We conducted a large-scale simulation with ran-

dom city networks based on experiences from a real-

world test site to analyze the performance of the

Holon approach. As the evaluation results show,

Holons can power parts of city networks, even when

they are disconnected from the transmission and dis-

tribution network during a blackout.

Our results show that the Holon concept is able to

supply 22.08% of a city network on average. This

coverage raises with increasing city network size

while the probability of total blackouts drops.

We see this increase of coverage as an effect

of higher ﬂexibility when more producers and con-

sumers are available inside the city network. Our fu-

ture work will investigate how the ﬂexibility in city

networks can be increased. We will investigate how

inﬂuencing the consumption of energy (and, likewise,

the production of energy) by introducing lower and

upper bounds for energy consumption relates to ﬂex-

ibility. We hope that increased ﬂexibility enables

higher coverage of city networks. Moreover, our in-

vestigation will include prioritization of speciﬁc con-

sumers in order to favor critical infrastructures, like,

hospitals, over other consumers in case of energy

scarcity.

ACKNOWLEDGEMENTS

The work in this paper was performed in the context

of the PolyEnergyNet project and partially funded by

the German Federal Ministry for Economic Affairs

and Energy (BMWi) under grant no. “0325737E”.

Additionally, this work has been co-funded by the

DFG as part of project B.2 within the RTG 2050 “Pri-

vacy and Trust for Mobile Users”. The authors as-

sume responsibility for the content.

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