SIMULATION OF ENERGY STORAGE WORK AND ANALYSIS OF

COOPERATION BETWEEN MICRO COMBINED HEAT AND POWER

(μCHP) SYSTEMS AND ENERGY STORAGE

Authors: Adrian Chmielewski, Kamil Lubikowski, Stanisław Radkowski

("Rynek Energii" - 04/2015)

Key words: microcogeneration, energy storage, load cycle, energy management, prosumer

Summary. In view of the year 2030, Poland as a member of European Union should be able to meet the require-

ments regarding both: the climate protection (reduction of CO2 emissions by 40% in comparison to the year 1990),

increase in the contribution of the Renewable Energy Sources in the energy market (up to 27 %), as well as im-

provement in the energetic efficiency (up to 27%) EUCO 169/14 [13], in view of the year 2020, the requirements

defined by the: 2009/28/WE [8], 2012/27/UE [9] directives, among others. The fact should also be emphasised that

as a result of the 2009/72/WE [10] directive, 80% of intelligent meters at consumer endpoints in Poland should be

replaced with remote reading meters (so called Smart Meters), in view of the year 2020. Smart metering and devel-

opment of smart grid open new prospects for the prosumer distributed energetics. Among the distributed generation

sources, the issue connected with adequate energy management and storage of generated energy becomes more and

more essential. In the first part of this article, using µCHP has been analysed, on the basis of the daily energy power

demand profile at the prosumer's household. In the second part of this article the cooperation of the electrochemical

cell at the given load cycle (resembling the daily power demand of the household) with the µCHP(Micro Combined

Heat and Power) has been simulated. The change in the degree of the cell charge – SOC (State of Charge), the

charge/discharge currents curves, voltage values on the cell’s terminals, emf (electromotive force), as well as the

cell’s temperature increase at charging/discharging with the preset current, have been presented for the given load

cycle. Attention has been focused on the parameters significantly influencing efficiency of the generated electric

energy storage and of its renewed use. The possibilities of managing the sales of the stored electric energy from the

micro cogeneration system to the grid, have also been discussed.

1. INTRODUCTION

The prospect of climate policy of the European Union up until the year 2030 [13] obliges the

EU member states to pursue the requirements connected with, among others: improvement in

efficiency of energy transformation from fossil fuels (27% growth in energetic efficiency),

increase of renewable energy sources share in the energy market (to nearly 27%), as well as

reduction of greenhouse gas emissions (to 40% compared with the year 1990) so as to protect

the natural environment. For these purposes to be achieved, the development and technologi-

cal progress in the scope of distributed generation sources, are needed [2]. It is also necessary

to manage the demand properly (DSM - Data Side Management) [16], as well as the end us-

ers’ active response (DR – Data Response). One of the elements of DSM and of the Smart

Grid (SG) development is, as has already been mentioned in work [4], the possession of a

smart meter (Smart metering) by the end user. A smart meter enables the reading with a de-

fined timestamp (eventually every 15 minutes) of the energy consumption in the building,

passing the information to the operator providing the services. If the end user has a micro-

installation [19], they become prosumers then, and can sell the electric energy to the low volt-

age electro energetic network (on-grid [11]) at 80% of the average energy price from the pre-

vious year on the competitive market. The prosumer can own a renewable energy source, or a

micro cogeneration system [2-5], which will generate the electric energy from the waste heat,

for example a fossil fuel boiler or a gas boiler. It should also be kept in mind that prosumers

can be divided into people running their own businesses (they can apply to receive a so called

green certificate then), and people who do not have their own company – lack of the certifi-

cate [22]. Prosumers can of course count on support from the state programmes (e.g. the “Pro-

sumer” programme run by the National Fund for Environmental Protection and Water Man-

agement – Pol NFOŚiGW [2,17].

At present, there are no acts of law in Polish legislation regulating the management of gener-

ated electric energy at the given time of the day, month, or year. The lack of such regulations

causes certain unpredictability of energy sale to the network (e.g. from wind turbines or

photovoltaic cells). The introduction of variable rates when purchasing energy at the peak or

the valley, e.g. at night, would be a good solution. It is certainly an advantage of some kind

from the point of view of operators who take the responsibility of ensuring the proper func-

tioning and reliability of energy supply for the end users, who are not prosumers, and will

never be.

In this work, in the subchapter 2, the analysis of the energy use from µCHP has been pre-

sented, as well as the simulation results of the cooperation between the electro chemical bat-

tery with the µCHP system for the load cycle similar to the real-life daily cycle of the pro-

sumer household.

2. ANALYSIS OF THE µCHP ENERGY USE IN A PROSUMER HOUSEHOLD

Households (household understood as a group of people living together and sharing the costs

of living) that amount to nearly 13.6 million [15] constitute about 20% of the energy market

[21]. From the point of view of reducing the household’s daily power demand (Figure 1), the

battery energy stores will be most appropriate to be employed. Among the battery energy

stores, batteries such as: lead-acid batteries or Valve Regulated Lead Acid batteries (VRLA),

lithium-ion batteries, nickel-cadmium batteries, sodium-sulphur batteries, or flow batteries

can be included.

Certain energy saving potential results from Figure 1, e.g. turning the washing machine after

10.00pm (in the case, when there is a dual tariff, the day and night rate). It is worth mention-

ing that in the hours between midnight – 00:00, and 6:45am, electric energy is consumed by

such appliances as: the refrigerator (about 0.02kWh), mobile phone charger (~0.015kWh),

and appliances working in a stand-by mode, such as: the TV set (0.001kWh), digital decoder

(0.015kWh), wireless router (0.018kWh).

Fig 1. Daily energy consumption in the winter month

on a working day, in a two-person household

(authors’ own study)

In the hours from 6:45am to 7:45am, the iron (2,1kWh), kettle (2kWh), then the electric stove

(~2kWh), and 2 energy-saving E27 bulbs (0.01kWh) get switched on. As follows from Figure

7, the load higher than 2kWh takes place for about four hours (between 6:45am - 8:00am,

9:00am - 9:15am, 9:30am - 10:15am, 5:15pm - 6:00pm, 6:30pm - 6:45pm, and between

7:45pm - 8:15pm). At the remaining times of the day the energy consumption does not exceed

250W/h (0.25kWh). For the ensuing consideration the authors assume that the debated house-

hold has a two-function central heating boiler fired with solid fuels (heat energy production

and water heating) and a micro cogeneration system which generates PµCHP=0.5kW/h (at the

point of maximum power for waste heat temperature of 700 oC). Additionally, the assumption

has been made that the µCHP system works in the winter 24 hours a day. The whole system

has been described in detail in works [3, 4].

Using the energy generated by the prosumer’s µCHP can occur in several different ways:

no resale to the grid, consuming the generated energy to meet the prosumer’s own needs

only. The prosumer does not have the energy storage. In such a case the unused energy po-

tential occurs, which is wasted. This situation can be described by the equation:

CHPKSEprosum PPP (1)

where:

PKSE- demand for power from KSE (Polish Power System)-Figure 2 profile,

PµCHP- electric power generated by the micro cogeneration system, the assumption has been

made that: PµCHP=500W (0.5kW/h),

Prosum- reduction of the demand for power from KSE (Polish Power System) resulting from

using the µCHP system. The analysis of the power demand shows that the Prosum value can be

both positive and negative. When:

Pprosum<0 - wasted power excess,

Pprosum>0 and Pprosum=0 effective µCHP power management (the whole generated power is

used).

Fig. 2. Curve of the reduced power demand (Pprosum)

authors’ own study

the possibility of resale to the grid (on-grid), using the generated energy to satisfy the pro-

sumer’s own needs, the excess is sold to the grid. The prosumer does not have the energy

storage. In such a case the unused energy potential, which is then wasted, does not occur.

Such a situation can be described by the equation (1), too. The area where Pprosum<0 is the

gross prosumer profit – they sell the energy to the grid (in the year 2014 it was 145.24

PLN/MWh [23]). For the end user (household) the average price for 1kWh according to [24]

amounts to 0.56 PLN/kWh. In the situation when the prosumer has an electrochemical en-

ergy storage, they also have the possibility of reselling the energy to the electro energetic

network at any time. There are a few energy management strategies possible here, among

others: the partial coverage of peak energy demand by the energy storage – up to 50% (it is

related with the increase of nominal capacity of electrochemical batteries). Depending on the

capacity of electrochemical batteries, on the basis of the adjustable tariffs, the resale of en-

ergy to the electro energetic network is also possible (when the market price is profitable). A

Smart Meter is necessary in such a household.

Majority coverage of peak power demand by the energy storage - over 50%. In this situa-

tion, the micro cogeneration system is used only to charge the energy storage and to use the

energy directly, in case when the power demand does not exceed 500W (the negative area -

red field in Figure 2). In the case of choosing the lead-acid battery for the considered house-

hold, its capacity should be higher than 600-750Ah, which with 12 cells (voltage of each cell

at SOC=1 equals 2.1V) in nominal conditions (T=20°C) results in the battery power of

15.12-18.9kWh. Of course the power demand of the presented household (Figure 1)

amounts to about 9.5kWh, nevertheless a few practical factors should be taken in considera-

tion, such as: incomplete cell discharge, losses connected with storing and losses related to

transmission – change of current flow direction in the cell (usually the lead-acid cell capac-

ity in the charge/discharge cycle ranges between 50%-70%, according to [18].

3. CHARACTERISTICS OF THE ELECTROCHEMICAL ENERGY STORAGE

The electrochemical energy storage consists of two electrodes: the cathode, the anode, and the

electrolyte. In the case of the lead–acid battery, the electrolyte is a 40% solution of sulphuric

acid. Each battery is characterised by the reversible work (charging/discharging, which are

accompanied by the reversible chemical reactions). In the case of the lead-acid battery, the

sulphuric acid is used during discharging and pure water is produced (this is also accompa-

nied by the change in electrolyte density). During charging, the reversed process takes place

(lead occurs on the negative plate with the sulphates being released; as a consequence of

chemical reactions happening, the lead oxide and sulphuric acid are produced on the positive

electrode – this corresponds with the increasing electrolyte density). A very important pa-

rameter while using the battery (charging/discharging) is the voltage change on its terminals

(e.g. with the fully charged 12V battery, the voltage on the terminals amounts to about 13.2-

13.6V). It can therefore be assumed that the voltage from the fully charged state to the fully

discharged state fluctuates within the range of 10%.

During the battery use it is particularly essential that it is not overcharged, nor overly dis-

charged to SOC=0 (state of charge), because its life becomes shortened even by half [7, 20].

Another essential element which needs to be taken into account during the battery use is the

maximum speed of its charging/discharging – usually not exceeding 3-5C (in the case of lith-

ium-ion batteries this is very important because it can lead to sudden rise of the temperature

gradient and the cell’s explosion).

Several criteria for selection of electrochemical batteries can be mentioned, including:

high energy density (among others: lithium-ion [7, 18, 20]) – the mass as little as possible

(more expensive),

low cost of purchasing of such a cell – among the available cells the lead-acid cells are the

cheapest (over 80% are maintenance-free cells with a safety VRLA valve) - lower energy

density, lower price, greater mass compared with lithium-ion cells [7],

toxicity (environmental aspects) – the most appropriate are nickel-metal-hydrid, the disad-

vantage is 30% self-discharging/month [7],

speed of charge – the best are zinc-air type (charging in as little time as 5 minutes)- low

number of charge/discharge cycles, service station required,

wysoka long life – usually for the lead-acid cell it is about 1500 work cycles, for lithium-ion

– about 600-1200 (to total discharge), in the case of incomplete discharge the number of

work cycles can be increased; the Battery management system is responsible for this, and in

an electric vehicle it informs (on the dashboard) about the range and vehicle’s charging

level. Usually the optimal charging level ranges within the cell’s linear work 0.9<SOC<0.2

[7, 20].

3.1. Mathematical model of the electrochemical battery

The Peukert relationship [1, 6, 14, 20] is often used for mathematical notation of the electro-

chemical battery traction properties. The relationship connects the battery discharge capacity,

time of the battery current load, and corresponds to the external conditions [1, 6, 14, 20]. Usu-

ally, the cell manufacturers provide the cell nominal capacity related to the standard condi-

tions (T=293K=20oC). For such an assumption the battery capacity change depending on the

load current is linear [1, 6, 14, 20]. As a consequence, the capacity change can be described

by:

)()(1

nomaknomak IiQiQ (2)

where:

nomQ - cell nominal capacity (provided by the manufacturer for standard conditions), at a given

nominal current Inom and nominal discharge time tnom (e.g. for nomnomnom tIQ AhQnom 120

one-hour discharge current 1C=120A), iak- instantaneous cell discharge current,

- the constant determined on the basis of the Peukert equation (for lead-acid batteries

6,0;3,0 ).

Dividing the equation (2) by Qnom the dependency can be obtained, describing the utility ratio

of the energy stored in the form:

)(1

nomakbat Ii (3)

For any temperature value (in the conditions different from standard), the nominal battery

capacity can be illustrated by:

|)|1( nomunomu TTQQ , (4)

where:

α- temperature cpacity ratio (according to [20] α=0,01deg-1

.

Tu- temperature in conditions different from nominal

Dividing the expression (4) by Qnom we obtain:

Tnomnomunomu cTTQQ 11|)|1( (5)

Knowing that the battery can be charged or discharged, the charge/discharge current should

be taken in consideration; therefore the relationship describing the changing utility capacity

can be formulated:

t

aknomu dttiQQ0

)(

(6)

The utility capacity change can also be set from the equations (1), (4), and (5), assuming the

cell work in normal conditions (the temperature indicator of nominal capacity changes

cT nom=1), the following can therefore be stated:

t

aknomnomaaku dttiQTiQ0

)(),(. (7)

The electromotive force in the case of the lead-acid or nickel-cadmium battery can be defined

by:

SOCUESOCE min)( (8)

where:

SOC- state of charge, described by the relationship:

1

0

)(),(

nom

t

aknomnomaak QdttiQTiSOC

(9)

The voltage on the battery terminals during discharging/charging amounts to [20]:

wewak RtiSOCESOCtU )()(),( (10)

where:

wewR - internal resistance of an individual cell.

This is a non-linear parameter and for more detailed analyses the fact should be taken in con-

sideration that it depends on the electrolyte resistance, polarisation resistance, and the elec-

trode resistance. Rwew can be shown in the following [20]:

1),,(

),(),,(

nomnomak

elektrodeleknomakwew

IQTibE

RQRQTiR

(11)

where:

elekR - electrolyte resistance,

elektrodR - electrode resistance,

1),,( aka IQibE - polarisation resistance (generally, according to [7, 20] it can be divided into

activation and concentration polarisation),

b- ratio [20], which denotes the relative change of the polarisation electromotive force on the

cell terminals during current flow Ia related to the electromotive force E for the nominal ca-

pacity.

In this work, the simulation of battery charging/discharging has been obtained by the fly-

wheel acceleration, which was connected with the electric machine by means of a mechanical

gear with the j1=1:4 ratio) loading the electric machine, which in turn discharges/charges the

electrochemical battery.

Each flywheel has [20] the torque of the motion resistance, which can be presented in the fol-

lowing form:

dwbp armM , (12)

where:

bm - flywheel mass [kg],

r- flywheel radius [m],

w - rotational mass ratio, amounting to [20]

22

21 1

1rm

Jr

jJ

b

kmsw

, (13)

where:

sJ - moment of inertia of the electric motor rotor,

kJ - moment of inertia of a driven flywheel reduced to the electric motor shaft,

1j -overall gear ratio between the driving motor shaft and the flywheel (j1=4),

m - transmission efficiency.

The power of the flywheel resistance to motion will amount to:

r

tVMtN pp

)()(

, (14)

where:

V(t)- time-varying velocity extortion (defined by the load cycle).

On the basis of [20], the equation describing the voltage on the electric motor terminals, takes

the form:

edt

diLRiuz

, (15)

where:

R - stator windings resistance,

i - stator current,

L - inductance,

eke - electromotive force (ke- electric constant,

ω- rotor angular velocity)

Electric motor torque [20] equals:

lpbs MMMM , (16)

where:

bM - torque dependent on angular acceleration and rotor inertia,

0lM - bearing torque losses.

3.2. Simulation model of the µCHP system cooperation with the electrochemical

energy storage

The simulation model shown in Figure 3 was created on the basis of the equations (1-16) and

consisted of :

the load cycle, taking in consideration the electrochemical cell load – approximating the

daily power demand cycle (Figure 4),

the dynamic model of the electrochemical battery (lead-acid type), whose input data has

been shown in Table 1,

the direct current electric machine, whose input data has been shown in Table 2,

the flywheel model, which loaded the electric machine in the defined load cycle charg-

ing/discharging the battery (Table 3),

the µCHP source model, which works under load at the maximum power point charging

the battery (Table 4).

Table 1. Electrochemical battery data

Cell voltage, V 2.1

(for SOC=1)

Capacity, Ah 600

Number of cells 12

Internal resistance of an individual cell, Ω 0.025

Temperature indicator of the nominal capacity cτ change 1

Constant determined on the basis of the Peukert equation κ 0.35

Table 2. Data for the electric machine

Nominal current, A 600

Windings resistance, Ω 0,12

Inductance, mH 5

Electric constant, Vs/rad 0,238

Mechanical constant, Nm/A 0,238

Nominal torque, Nm 60

Nominal velocity, rev/min 3000

Maximum velocity, rev/min 5200

Rotor moment of inertia, kgm2 0,032

Tabela 3. Data for the load

Flywheel mass, kg: 50

Flywheel radius, m 0,26

Moment of inertia, kgm2 0,46

Transmission efficiency 0,97

Overall ratio between the shaft of the drive motor and the flywheel 4

Table 4. Data for the µCHP system

Electric power 500 W

The model view from the Matlab&Simulink programme is presented in Figure 3.

Fig. 3. Illustration of the simulation model in the Matlab&Simulink programme

3.4. Simulation results obtained from the model

In this subchapter, the simulation results of the µCHP system cooperation with the electro-

chemical energy storage in a daily load cycle (the cycle similar to the daily power demand in

a prosumer household). Figure 4 illustrates the load cycle, which lasted 30 hours 55 minutes.

This cycle should be interpreted as the consecutive 30 hours 55 minutes, clocked from mid-

night (the 00:00 hour – midnight). For the first 6 hrs 55 min the constant battery discharge

over time takes place (the battery is fully charged in the beginning – SOC=1, Electromotive

force=25.2V). At 6:55 cell loading happens. The load cycle was purposefully prolonged by 6

hrs 55 min, so that on the next day the battery is fully charged, e.g. for subsequent iterations.

Positive extortion values denote the battery current discharge, the negative values of extor-

tion, however, denote charging the battery with the current from the micro cogeneration sys-

tem. It should be emphasised that for the first 7 hours 45 minutes during the first iteration,

when the cell is fully charged, the micro cogeneration system does not charge the cell. The

cell is charged in the period of time when the power demand is low (below 100W).

Fig. 4. Load cycle (time-varying velocity extortion)

In Figure 5, the battery charge/discharge current curve has been shown. For the positive cur-

rent values the battery discharging takes place, for the negative – the battery is charged by the

micro cogeneration system (0.5kWh with the known cell voltage equal to 25.2V). At night

(after 24 hours) the µCHP system charges the cell for the next 6 hours 55 minutes, so that the

cell state of charge would amount to SOC=1 during the next iteration (the cell fully charged).

Fig. 5. Charge/discharge current curve of the cells in the load cycle

Figure 6 illustrates the curve of voltage change on the cell terminals during the simulation.

During the load cycle (Figure 4), the change of the current flow direction takes place. During

the cell discharge (positive values of extortion and current – Figure 4 and 5), the voltage curve

in time drops, which corresponds to the real-life battery working conditions. During charging,

the voltage on the cell terminals increases. The impulse character of the voltage curve changes

results from the load cycle character occurring in the prosumer household (Figure 1).

Fig. 6. Voltage curve on the cell terminals at the load cycle

Electromotive force change curves (Figure 7), and the change in the cell state of charge (Fig-

ure 8), are also interesting, The character of the curves is similar. The change of the state of

charge in this cycle does not decrease below SOC=0.78. The authors’ intention was to present

the possibilities of using µCHP system to charge the cell in such a way so that it is fully

charged to start another iteration. Of course, to alter such a state of charge (decrease while

maintaining the µCHP system working conditions), it is enough to reduce the planned nomi-

nal capacity of the cell from 600Ah to, for example, 300Ah.

Fig. 7. Change in the cell electromotive force

at the load cycle

W In real-life objects, the charging (discharging the cell) with the given current is accompa-

nied by the cell temperature growth (this is one of the key parameters monitored while charg-

ing batteries, for example lithium-ion batteries).

Fig. 8. Change in the cell state of charge

Fig. 9. Cell temperature rise curve at the load cycle

In Figure 9, the curve of the cell temperature rise has been shown at the given load cycle

(Figure 4). It has been assumed that the temperature rise ΔT by 1oC corresponds to the

charge/discharge with the 25A current. It is essential at, for example, simulation of the so

called Fast Charge states, where usually the cell current value is regulated and controlled by

the Battery Management System (in the case of the lithium-ion batteries, charging at the con-

stant voltage value during charging to SOC=1).

This simulation is connected with many practical aspects. Implementing the appropriate load

cycle enables selection of the suitable battery capacity and prediction of the degree of the bat-

tery discharge state. Similarly, the cooperation with renewable energy sources (e.g. photo-

voltaic cells or wind farms) can be simulated. Additionally, knowing the battery specification

(e.g. the maximum current of charge, or discharge) the work of such a battery can be simu-

lated before the actual purchase. From such analyses and simulations, the degree of the most

economical management of the limited-power energy source, can be estimated. Also, the pos-

sibility should be emphasized, of parallel connecting of a super capacitor with the electro-

chemical battery (advantage superposition) which has a very high power density (instantane-

ous current peak of approximately Kilo-Amperes).

4. SUMMARY

Special attention has been drawn in this article to the prosumer household, whose daily power

demand profile has been analysed in Chapter 2. The possibility of using the electrochemical

energy storage by such a household has been taken in consideration, too. In the further part of

this work, the model of the electrochemical battery has been presented, whose load cycle re-

sembled that of a household’s daily power demand. In the model, the cooperation between the

energy storage and the µCHP system working at one point with the constant load, has also

been considered. The simulation and analysis results presented herein are particularly essen-

tial for the cooperation between electrochemical energy storage units and other sources of

distributed generation.

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energii elektrycznej na rynku konkurencyjnym za rok 2013.

[24] Zakład Energetyczny– http://zaklad.energetyczny.w.interia.pl/–aktualizacja 08.02.2015.

SYMULACJA PRACY MAGAZYNU ENERGII ORAZ ANALIZA WSPÓŁPRACY

UKŁADU µCHP Z MAGAZYNAMI ENERGII

Słowa kluczowe: mikrokogeneracja, magazyny energii, cykl obciążeniowy, zarządzanie energią, prosument

Streszczenie. W perspektywie 2030 roku Polska jako członek Unii Europejskiej powinna spełniać wymogi do-

tyczące zarówno ochrony klimatu (ograniczenie emisji CO2 o 40% w porównaniu do 1990), wzrost udziału od-

nawialnych źródeł energii na rynku energii (do 27%) oraz poprawy efektywności energetycznej (do 27%) EUCO

169/14 [13], w perspektywie 2020 wymagania określone w dyrektywach m.in: 2009/28/WE [8], 2012/27/UE [9].

Należy również podkreślić fakt wynikający z dyrektywy 2009/72/WE [10], że w Polsce w perspektywie 2020

roku powinno zostać wymienione 80% liczników u odbiorców końcowych na liczniki zdalnego odczytu (tzw.

Smart Meter). Smart metering oraz rozwój smart grid otwiera nowy rozdział dla rozproszonej energetyki prosu-

menckiej. Wśród źródeł generacji rozproszonej coraz istotniejsza staje się kwestia dotycząca odpowiedniego

zarządzania energią oraz magazynowania wytworzonej energii. W pierwszej części pracy przeanalizowano wy-

korzystanie µCHP na podstawie analizy dobowego profilu zapotrzebowania na moc w prosumenckim gospodar-

stwie domowym. W drugiej części artykułu zasymulowano współpracę ogniwa elektrochemicznego w zadanym

cyklu obciążeniowym (zbliżonym do dobowego zapotrzebowania na moc gospodarstwa domowego) z

µCHP(Micro Combined Heat and Power). Zaprezentowano dla zadanego cyklu obciążenia m.in: zmianę stopnia

naładowania ogniwa‒ SOC (State of charge), przebiegi prądów ładowania/wyładowania, napięcia na zaciskach

ogniwa, SEM (siły elektromotorycznej) oraz przyrost temperatury ogniwa przy ładowaniu/wyładowaniu zada-

nym prądem. Zwrócono uwagę na parametry szczególnie wpływające na efektywność magazynowania wytwo-

rzonej energii elektrycznej i powtórnego jej wykorzystania. Omówiono także możliwości zarządzania sprzedażą

zmagazynowanej energii elektrycznej z układu mikrokogeneracyjnego do sieci elektroenergetycznej.

Adrian Chmielewski, is a teaching assistant at the Institute of Vehicles, Warsaw University

of Technology, a graduate of the Faculty of Automotive and Construction Machinery Engi-

neering where he earned his Master of Science in Engineering degree. His scientific interests

are connected with the modelling and construction of the µCHP systems. E-mail:

a.chmielewski@mechatronika.net.pl.

Kamil Lubikowski, Master of Science in Engineering, a graduate of the Faculty of Automo-

tive and Construction Machinery Engineering, Warsaw University of Technology, Ph.D. stu-

dent at the Institute of Vehicles. His scientific interests are related to the micro cogeneration

systems research.

Stanisław Radkowski, a Professor, Ph.D., D.Sc. at Warsaw University of Technology, Dean

of the Faculty of Automotive and Construction Machinery Engineering, a Professor at the

Institute of Vehicles. His scientific interests include energy harvesting and technical diagnos-

tics of machines and appliances.