**On the use and production of power**

What separates us today

from the past?

We have access to power!

The question is how to obtain reliable and

sustainable power supply.

And how to use it.

**Renewable energy and it's use**

Most renewable energy on Earth is

energy from the sun:

Photovoltaics is direct

How to harness it?

It varies over the day, over season and with

clouds.

Need to quantify the use, for example:

- Household electricity use

- Electric vehicle charging

**Aims of the thesis**

Develop mathematical models for solar irradiance and photovoltaic (PV) power production

(Papers I-II)

Develop a mathematical model for household electricity use

(Paper III)

.

Develop mathematical models for electric vehicle (EV) charging

(Papers IV-V)

.

Develop, investigate and apply mathematical models regarding the combined system of PV power production, household electricity use and EV charging to study grid interaction and self-consumption

(Papers VI-VIII)

.

Investigate and analyze grid interaction and self-consumption from meter data on PV power production and EV charging

(Paper IX)

.

Joakim Munkhammar

Built Environment Energy Systems Group

Department of Engineering Sciences

Uppsala University

**Distributed Photovoltaics,**

Household Electricity Use and

Electric Vehicle Charging

Household Electricity Use and

Electric Vehicle Charging

**Mathematical Modeling and Case Studies**

**Methodology**

Mathematical modeling and data analysis of:

Solar irradiance and photovoltaic power production.

Household electricity use.

Electric vehicle charging.

(And the combination of all above)

**Modeling solar irradiance and PV power**

Bimodal Distribution model

Convolution model

**Household electricity use**

**Distribution model**

**Household electricity use**

Widén Markov-chain model (Used in this thesis, not developed)

**Electric vehicle charging**

**Distribution model: charging anywhere**

**Markov-chain model: home-charging**

Combination models

Markov chain

Distribution

**Case studies**

**Westminster, London, UK**

**Solelia Solar-charging stations**

**Some general results**

PV power production, Household electricity use, EV charging and their combination can be accurately modeled with probability distributions.

Bimodal distribution model

Convolution model

A bimodal distribution is

fit to the clear-sky index

of solar irradiance.

In turn this is used to

simulate PV power

production.

Paper I

Assumption that the

clear-sky index could

be modeled as a convolution

of stochastic variables for

direct and diffuse irradiance.

Resulted in a generalized

Ångström equation relating

irradiance to number of hours

of bright sunshine:

Assumption: Household electricity use can be modeled as a probability distribution.

By inspection: A Weibull distribution

Modeled for different time-bins:

Each hour of the day

Each day of the week

Each season

Paper III

Paper II

It was developed by Joakim Widén in:

Widén et al., Energy and Buildings 2009

Widén&Wäckelgård, Applied Energy 2010

Markov-chain EV home-charging

model

Based on the Widén Markov chain model for household electricity use.

Paper IV

Collaboration with Pia Grahn (KTH), Joakim Widén (UU), Lennart Söder (KTH) and Karin Alvehag (KTH). (IEEE Trans. Power Systems 28, 2013)

Assumption: Certain percentage when the Markov chain model

enters the state away: the EV is taken out driving. When back

home: plugged in and charged.

EV Distribution model

Observation: Charging or not

might be modeled via a

Bernoulli distribution.

Charges whenever stops.

Distribution model: Do that

based on actual driving

patterns.

Collaboration with Jesper Rydén (UU), Joakim Widén (UU) and Pia Grahn (KTH). (in proceedings of IEVC 2014)

Paper V

PV - EV - Household model

(Markov-chain)

Paper VII

PV power production was provided

from a simple linear model.

Household electricity use from

the Widén Model.

EV Charging from the

home-charging model.

Collaboration with Pia Grahn (KTH) and Joakim Widén (UU). (Solar Energy 97, 2013)

PV - Household - EV:

Probability distribution model

Paper VIII

It characterized the

variability of all

components combined.

Westminster study

Collaboration with Justin Bishop, Juan José Sarralde, Wei Tian and Ruchi Choudhary (All at Cambridge). (Energy and Buildings 86, 2014)

Paper VI

Study of the potential for PV and

EV in the City of Westminster,

London, UK.

METEONORM + Widén's PV model

Widén Markov-chain model

Home-charging EVs

Solelia solar charging station data

Paper IX

Collaboration with Joakim Widén (UU) and Per Wickman (Solelia). (In proceedings of SIW 2014)

Data analysis of:

PV power production

EV charging

Diurnal average plot for each solar charging station,

PV=Dashed, EV=Solid.

A full coverage of PV in Westminster will during no occasion cause net production.

EV charging can be modeled as an extension to the Widén Markov-chain model.

Data from EV charging reveals no unison in patterns.

Collaboration with Jesper Rydén (UU) and Joakim Widén (UU). (Applied Energy 142, 2015)

Collaboration with Jesper Ryden (UU), Joakim Widen (UU) and David LIngfors (UU). (Manuscript)

Collaboration with Joakim Widén (UU). (Manuscript)

Collaboration with Jesper Rydén (UU) and Joakim Widén (UU). (Applied Energy 135, 2014)

Viktor Vasnetsov (Wikimedia commons)

It is based on the probability of

going from one activity to another.

And electricity use associated

with each activity.

Total EV charging is about the same as the total PV power production over nearly a year.

The mismatch between load and production is less pronounced for aggregates.