Master thesis, 30 hp
Master of science in energy engineering 300 hp
OPTIMIZATION OF A
BATTERY ENERGY
STORAGE SYSTEM
For utilization of peak shaving
and fast frequency reserve
Robert Sundgren
Sammanfattning
När Sverige går över till ökad andel förnybar elproduktion kommer kraven på energinätet och energimarknaden att bli högre. Eftersom en större del av elförbrukningen kommer från flödande energikällor kommer produktionen att bli mindre stabil och svårare att planera med förbrukningen.
Trögheten hos elnätet kommer också att minska eftersom sol- och vindkraft inte är synkront anslutna till elnätet, vilket gör systemet känsligare för störningar. För att hålla balansen så att frekvensen förblir 50 Hz har Svenska kraftnät flera reserver till sitt förfogande. Sommaren 2020 kommer Svenska kraftnät att lansera en ny reserv som kallas Fast frekvensreserv (FFR) vars syfte är att hantera snabba obalanser. Genom att komplettera en vindkraftspark med ett batteri-energilagringssystem (BESS) blir det möjligt att jämna ut vindkraftsparkens intermittenta elproduktion genom att kapa effekttoppar och sänka nätkostnaderna för vindparken. Eftersom en BESS har en full aktiveringstid under en sekund så blir ett BESS lämpligt för att tillhandahålla FFR.
För att bestämma vilken kapacitet och effekt en BESS behöver för att kapa effekttoppar hos en vindkraftspark och tillhandahålla FFR, så byggdes en optimeringsmodell i MATLAB för att studera lönsamheten för en BESS med flera kombinationer av effekt och kapacitet. Dessutom så studerades även cyklerna för BESS samt förmågan att kapa effekttoppar. Optimeringsmodellen utnyttjar uppmätt produktionsdata per timme från en vindkraftspark i Norrland.
Förutom BESS-optimeringen byggdes en till optimeringsmodell för att minimera
produktionskostnaderna genom att sänka effektuttaget från en vindturbin. Syftet med optimeringen var att undersöka om sänkning av effektuttaget skulle kunna förlänga livslängden för ett
vindkraftverk och därmed sänka produktionskostnaden mer än förlustintäkterna från elförsäljning, för att totalt sett öka nettointäkterna för vindkraftverket. Utöver nettointäkterna studerades också hur mängden elektricitet minskade vid sänkning av effektuttaget. Modellen använde en månads produktionsdata på timbasis för varje säsong under 2019.
Optimeringen för BESS visade att de lagringskostnaderna (𝐿𝐶𝑂𝑆𝐸) för närvarande är för höga för att en BESS ska kunna användas för endast kapning av effekttoppar med en vindkraftspark. För att ett BESS ska vara lönsamt tillsammans med en vindkraftpark måste 𝐿𝐶𝑂𝑆𝐸 komma ner mot 𝐿𝐶𝑂𝑆𝐸 <
6 𝐸𝑈𝑅 / 𝑀𝑊ℎ, när BESS också levererade FFR ökade intäkterna mellan 1,5 − 8% beroende på effekten på BESS. Kapaciteten var den begränsande faktorn för BESS vid kapning av effekttoppar medan FFR begränsades av effekten på grund av det låga energibehovet i FFR.
Att sänka effektuttaget för ett vindkraftverk resulterade i en ökning av nettointäkterna för varje månad mellan 10 − 90% denna ökning kommer bli uppenbar först när drift och
underhållskostnaderna sjunker efter några år men detta öppnar för en diskussion om hur en vindparksägare ska köra sina vindkraftverk.
Abstract
As Sweden switches to increasing renewable electricity production the demand on the energy grid and energy market will become higher. Since a bigger part of the electricity consumption will come from flowing energy sources the production will become less stable and harder to plan with the consumption. The inertia of the electrical system will also decrease since solar and wind power are not synchronously connected to the electrical system which will make the system more sensitive to interference. In order to keep the short-term balance so that the frequency remains at 50 𝐻𝑧, Svenska kraftnät has several reserves at their disposal. As of summer 2020, Svenska kraftnät will launch a new reserve called Fast frequency reserve (FFR) with the purpose to deal with rapid imbalances. By supplementing a wind farm with a battery energy store system (BESS), it becomes possible to even out the wind farm's intermittent electricity production by applying peak shaving and lower the grid costs for the wind farm. Because a BESS can provide power within a
fraction of a second and is therefore is suitable to provide FFR.
To study the profitability and determine what capacity and power a BESS needs for peak shaving and FFR with a wind farm, an optimization model was built in MATLAB to study the profitability of a BESS with multiple power and capacity combination. In addition, the cycling of the BESS and the limitation of peak shaving was also studied to get deeper knowledge about the limitations. The optimization model is using hourly generation data from a wind farm in northern Sweden.
Besides the BESS optimization, a separate optimization model was built in order regulate the output power to minimize the generation cost by prolonging the service life of a wind turbine (WTG). The purpose of this optimization was to study if regulating the output power could lower the generation cost, more for the WTG. In addition of the net income the loss of electricity was also studied. The optimization used hourly data during one time period every season during of 2019.
The optimization for the BESS showed that the levelized cost of storage (𝐿𝐶𝑂𝑆𝐸) is currently too high for a BESS to be used for only peak shaving with a wind farm. For a BESS to be feasible together with a wind farm the 𝐿𝐶𝑂𝑆𝐸 needs to decrease towards 𝐿𝐶𝑂𝑆𝐸< 6 𝐸𝑈𝑅/𝑀𝑊ℎ, and when the BESS also supplied FFR the income increased between 1.5 – 8% depending on the power output for the BESS.
The capacity was the limiting factor for the BESS when preforming peak shaving while FFR was limited by the power because of the low energy demand in FFR.
Lowering the power output for a WTG resulted in an increased net income for every month between 10 – 90% although this increased income will become more apparent when the operation and maintenance cost starts to drop over a couple of year but this open up a discussion of how an owner should operate there WTG.
Förord
Detta examensarbete har genomförts under vårterminen 2020 I samarbete med Vattenfall R&D.
Examensarbetet innefattar 30 hp och blir avslutningen på civilingenjörsprogrammet inom
energiteknik på Umeå universitet. Stort tack riktas till min handledare på Umeå Universitet, Anders Åstrand och även till mina handledare Jan Ukonsaari och Jens Sperens på Vattenfall för deras stöttning och inspiration under arbetet som gjorts. Jag vill även tacka Gregory Simmons och alla andra anställda inom Vattenfall som jag har varit i kontakt med under våren.
Avslutningsvis så vill jag tacka min flickvän och min familj för att ni har stöttat mig inte bara under examensarbetet utan även genom hela utbildningen.
Robert Sundgren Maj 2020.
Table of content
Introduction ... 1
1.1 Purpose ... 1
1.2 Limitation of the study ... 1
Theory ... 2
2.1 Direct current ... 2
2.2 Alternating current ... 2
2.3 Power... 2
2.4 Rotating mass ... 3
2.5 Electricity grid ... 4
2.5.1 The backbone grid ... 4
2.5.2 Regional grids ... 4
2.5.3 Local grids ... 4
2.6 Balance of the electricity grid ... 4
2.6.1 Frequency maintenance reserve for normal operation (FCR-N) ... 4
2.6.2 Frequency maintenance reserve for disturbance (FCR-D) ... 5
2.6.3 Frequency restoration reserve (mFRR) & (aFRR) ... 5
2.6.4 Fast frequency reserve (FFR) ... 6
2.7 Battery Technologies ... 7
2.7.1 State of Charge ... 7
2.7.2 Round-trip Efficiency ... 7
2.7.3 E- & C-rate ... 7
2.7.4 Self-discharge ... 7
2.7.5 Depth of Discharge ... 7
2.7.6 Lifecycle ... 8
2.7.7 Lithium-ion ... 8
2.7.8 Lead-acid ... 8
2.8 Battery energy storage system (BESS) ... 8
2.8.1 Components in a BESS ... 9
2.8.2 Implementations and studies about BESS ... 9
2.8.3 Price Development ... 10
2.9 Building regulations for installing BESS ... 12
2.10 Mechanical fatigue for a wind turbine ... 13
2.11 Different type of optimization problems ... 14
2.12 Optimization problem of a wind farm with a BESS ... 16
2.13 Optimization of power output for a WTG ... 18
Method ... 19
3.1 Literature study ... 19
3.2 Wind farm with BESS ... 19
3.2.1 Calculation process ... 20
3.3 Optimization of power output ... 22
Results ... 23
4.1 Wind farm with BESS ... 23
4.1.1 Economics ... 23
4.1.2 BESS SoC ... 27
4.1.3 Peak-shaving ... 29
4.1.4 FFR ... 33
4.2 Optimization of power output ... 34
4.2.1 Power output ... 34
4.2.2 Income and electricity loss ... 35
Discussion ... 36
5.1 Wind farm with BESS ... 36
5.1.1 MATLAB model ... 36
5.1.2 Economics ... 37
5.1.3 SoC and cycling ... 37
5.1.4 Peak shaving ... 37
5.1.5 FFR ... 38
5.2 Optimization of power output ... 39
5.2.1 MATLAB model ... 39
Conclusion ... 40
6.1 Future work ... 41
References ... 42
Abbreviations
Abbreviations
AC Alternating current
aFRR Automatic Frequency restoration reserve BESS Battery Energy Storage system
BMS Battery management system
B-TMS Battery thermal management system
DC Direct current
DoD Depth of discharge
EIA Environmental Impact Assessment
EMS Energy management system
ER Experience rate
ESS Energy Storage system
FCR-D Frequency maintenance reserve for disturbance FCR-N Frequency maintenance reserve for normal operation
FFR Fast frequency reserve
LP Linear optimization problem
mFRR Manual Frequency restoration reserve
NP Non-linear optimization
RTE Round-trip Efficiency
SoC State of charge
TSO Transmission system operators
WTG Wind turbine
𝑳𝑪𝑶𝑺𝑬 Levelized cost of storage
Introduction
As Sweden switches to increasingly renewable electricity production, the demands on the electricity grid will become higher. The electricity must be consumed as it is produced, this means that
generation must be planned according to consumption.
Since the energy generation that consists of stored energy of coal and nuclear power are being replaced by flowing energy sources such as solar and wind power, electricity production will go from being simple to plan and stable, to becoming more intermittent and unstable. There are also other features that pose challenges to the power system. Solar and wind power are not synchronously connected to the electrical grid, which means that they do not contribute to the electrical grids inertia, this makes the system more sensitive to interference [1].
Electricity prices will also be affected by the change in production. The flowing resource are available in unlimited quantities, which means that solar and wind power can therefore produce electricity at low costs when these resources are available, which will lead to reduced prices in the electricity market leading to reduced profitability for all producers in the market [1].
By supplementing a wind farm with BESS, the wind farm's intermittent electricity production can be even out and make wind power easier to plan. A BESS can also act as backup power in the grid to counteract interference.
1.1 Purpose
The purpose of this thesis is to study the possibility of supplementing an existing wind farm with BESS.
With the questions
• What power and capacity are needed for a BESS to be useful with a wind farm?
• Can a BESS be used to cut the power peaks and lower the grid costs for a wind farm?
• Can a BESS increase the profitability of a wind farm by storing energy, including auxiliary effects on machinery and equipment?
• Can the battery storage be used to assist with the frequency control through FFR and is there the opportunity to improve network stability in general? For example, support the functionality that hydropower has today.
• What are the limitations, if any? boundaries in general and for a specific wind farm.
• Impact on e.g. infrastructure, state, network, environment
• Battery performance and cost today
1.2 Limitation of the study
This thesis is focusing on BESS and is excluding other Energy Storage system (ESS) like pump storage, flywheel and hydrogen fuel cells.
Theory
2.1 Direct current
In order to generate current, a voltage source and an electrically closed circuit are required for the current to flow. When the current always flows in the same direction it’s called direct current (DC).
A common voltage source for a direct current is a battery. Here the electricity flows from the battery's positive terminal to the negative terminal of the battery, thus opposite direction to the electrons [2].
2.2 Alternating current
An alternating current (AC) is generated by a voltage source whose plus/minus poles alternate with a certain frequency. Theoretically, an alternating current could be generated by spinning a battery so that the poles change place, but in practice it would be very unwieldy. A more practical solution to generate AC can be by synchronous machines from power plants that forms a sine curve used for transmission of electricity [2].
2.3 Power
Power is a measure of how much energy is converted for every second, with the unit Watt (W).
Power developed in an AC circuit with a phase angle 𝜑 between voltage and current obtained in a pure sine form is written according to
𝑃 = 𝑈 𝐼 cos (𝜑) (1)
where U is the voltage (𝑉) and I is the current (𝐴), P can also be referred to as active power.
Reactive power performs no work, instead the reactive power is oscillating between the network and the active component. The reactive power is positive when 𝜑 > 0 and is called inductive. When the phase angle 𝜑 < 0, the reactive power is negative and is then called capacitive.
The reactive power can be described as
𝑄 = 𝑈 𝐼 sin (𝜑) (2)
and has the unit volt-ampere (𝑉𝐴𝑟) [2]. With the active power and the reactive power defined, by studying Figure 1, one can describe the apparent power 𝑆 which has the unit Volt-ampere (𝑉𝐴), through Pythagoras’s theorem 𝑆 can be shortened by Equations (1) and (2) to
𝑆 = √𝑃2+ 𝑄2= 𝑈 𝐼 (3)
Figure 1 Viewer diagram of active, reactive and apparent power [3].
2.4 Rotating mass
The rotational energy stored in turbines and synchronous generators that is rotating in our power plants is called rotating mass. The inertia constant of a turbine generator is denoted H is defined as
𝐻 =𝐽𝜔𝑛2 2𝑆𝑛
(4) Where 𝐽 is the turbine generator's moment of inertia, 𝜔𝑛 is the speed of rotation and 𝑆𝑛 is the apparent power of the generator [4].
In order to calculate the power grids moment of inertia, Equation (4) can be rewritten to 𝐻𝑠𝑦𝑠=∑𝑁 𝑆𝑛,𝑖𝐻𝑖
𝑖=𝑖
𝑆𝑛,𝑠𝑦𝑠
(5)
Where 𝑆𝑛,𝑠𝑦𝑠= ∑𝑁𝑖=1𝑆𝑛𝑖 is the apparent power for the system and 𝑆𝑛,𝑖 is the apparent power and 𝐻𝑖 inertia constant for generator 𝑖. Instead of expressing the moment of inertia of the grid for every second, it can be expressed as how much rotating mass is in the grid expressed in (𝑀𝑊𝑠) by rewriting the Equation (5) to [4].
𝐸𝑘,𝑠𝑦𝑠 = 𝑆𝑛,𝑠𝑦𝑠𝐻𝑆𝑦𝑠 (6)
If there is a lot of rotating mass in the system the frequency will not decrease much during a deficit of production, so there is a great inertia in the electricity grid. However, if there is too little inertia in the system then a deficit generation will cause the frequency to drop drastically like Figure 2 shows.
The same problem also arises in the case of excess generation, although the frequency will increase instead. In the Nordic countries, nuclear power contributes a large proportion of rotating mass. The problem is emphasized since nuclear power is phased out in Sweden, this will cause a large amount of rotating mass to disappear together with nuclear power. This makes the electricity grid more sensitive to interference [1].
Figure 2. Frequency drop when the nuclear reactor Oskarshamn 3 (14,000 𝑀𝑊) was disconnected. The lowest frequency was 49.36 Hz, which is the lowest measured during a loss in production [1].
Forecasts for from year 2020 and to 2025 show that the variation in the amount of rotating mass in the Nordic electricity system seems to decrease, as the smallest values are higher and the largest values are lower [4]. Svenska kraftnät estimates that the annual mean value of the rotating mass will decrease from 202 𝐺𝑊𝑠 in 2020 to 159 𝐺𝑊𝑠 in 2040 [5].
2.5 Electricity grid
Sweden is divided into four electricity areas which can be seen in Figure 3, electricity prices vary between the electricity areas, the electricity is the cheapest at surplus in northern Sweden and most expensive at deficit in southern Sweden [6].
Figure 3. Sweden's four electricity areas with SE1 in the north and SE4 in the south [6].
2.5.1 The backbone grid
Svenska kraftnät is responsible for the backbone grid which comprises the voltage levels 220 𝑘𝑉 and 400 𝑘𝑉. The backbone grid includes the connection of the Nordic neighboring countries. Power producers and big industries can connect to the grid for transport from power plants to users [7].
2.5.2 Regional grids
The regional grid is usually at voltage levels 70 − 130 𝑘𝑉 and are owned and operated by the power companies. The grid links the backbone grid with larger receivers for power, such as distribution companies but also larger industries [7].
2.5.3 Local grids
The local grid is owned by distribution companies and normally have a voltage of not more than 20 𝑘𝑉. From the local grid, the voltage is transformed down to the normal voltage of 400/230 𝑉 [7].
2.6 Balance of the electricity grid
The transmission system operators (TSO) are responsible for balance on the electricity grid on an hourly basis, this is accomplished by the TSOs by balancing the production with the consumption [8].
Svenska kraftnät is responsible for the short-term balance of the electricity grid in Sweden. Svenska kraftnät has several reserves that have been procured in advance. The purpose of the reserves is to balance production and consumption so that the frequency remains at 50 Hz. Historically, the power reserve has consisted of agreements with electricity companies to make additional electricity generation available, as well as agreements on reduced electricity consumption [9]. The following chapter addresses the reserves that Svenska kraftnät have at their disposal.
2.6.1 Frequency maintenance reserve for normal operation (FCR-N)
FCR-N is an active power reserve that is used to suppress frequency changes. FRC-N is active at frequencies between 49.9 𝐻𝑧 to 50.1 𝐻𝑧 [10]. The activation time is 100% within 120 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 [11].
Activation should take place within the blue area in Figure 4.
Figure 4. Activation range for FCR-N in blue, where 𝑃 is consuming power and 𝑓 is frequency. The red line is a suggestion for activation [12].
2.6.2 Frequency maintenance reserve for disturbance (FCR-D)
FCR-D is a reserve used for disturbance on the electricity grid, this reserve is used to increase the frequency. FRC-D should activate within the blue area in Figure 5, when the frequency drops below 49.9 𝐻𝑧 [10]. With an activation time of 50% within 5 seconds and 100% within 30 seconds [11].
Figure 5. Activation range for FCR-D in blue, where P is consuming power and f is frequency. The red line is a suggestion for activation [12].
2.6.3 Frequency restoration reserve (mFRR) & (aFRR)
Frequency restoration reserve with manual activation (mFRR), as well as with automatic activation (aFRR). aFRR is activated within 120 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 and is controlled by a control signal from the Svenska kraftnät. mFRR shall be activated within 15 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 following a request from Svenska kraftnät [13].
2.6.4 Fast frequency reserve (FFR)
Fast Frequency Reserve (FFR) is a reserve whose purpose is to deal with rapid imbalances. The reserve is introduced by Svenska kraftnät in the summer of 2020 [10]. The need for FFR is
concentrated around the summer and the highest need are during the night when the consumption and production is low [14], therefor the FFR reserve is active during the months July – September [15].
There are different requirements for activation time depending on which frequency the reserve is activated
A. 0.7 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 at 49.5 𝐻𝑧 B. 1 𝑠𝑒𝑐𝑜𝑛𝑑 at 49.6 𝐻𝑧 C. 1.3 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 at 49.7 𝐻𝑧.
The reserve should be fully turned on and supporting for at least 5 seconds for short activation alternatively at least 30 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 for long activation [16].
When deactivating reserves, there are no requirements for long activation or how quickly the reserve can be turned off, but for short activation the power must not decrease by more than 20% per second. After the reserve is turned off, a buffer of 10 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 is required before the reserve can start charging from the electricity grid. Charging of the reserve must not take place with more power than 25% of the available power [16]. The different periods for FFR can be seen in Figure 6.
Figure 6. FFR activation in 𝑀𝑊 along the y-axis with different time parts along the x-axis, activation time at 𝑡 = 0 [16].
A BESS can provide power within a fraction of a second and is therefore useful for grid balancing [17].
The number of times the frequency crossed the activation threshold for the FFR is very rare [18] and Table 1 shows the number of activations for 2015 − 2018 [19].
Table 1. Number of times the frequency crossed the threshold, for additional data back to 2013 see [19].
Number of activations
Alternative Activation level [Hz] 2015 2016 2017 2018
A 49.5 0 0 0 0
B 49.6 3 2 1 2
C 49.7 11 8 3 5
2.7 Battery Technologies
A battery consists of a reversible chemical process used to store electrical energy as chemical bonded energy [20]. This section presents some concepts used to describe a battery's performance and information about some common battery types.
2.7.1 State of Charge
An important concept for batteries is the State of Charge (SoC), which denotes the percentage of energy where 100% is fully charged and 0% is empty. To define SoC for a battery, imagine a fully charged battery at time 𝑡0 with the discharge current 𝐼𝑏 (𝑡) (𝐴) , the energy delivered from the battery then becomes∫ 𝐼𝑡𝑡 𝑏(𝑡)𝑑𝑡
0 and with a maximum storage capacity of the battery of 𝑄0 (𝐴ℎ) and t (ℎ), SoC can be defined as
𝑆𝑜𝐶(𝑡) = 𝑄0− ∫ 𝐼𝑡𝑡 𝑏(𝑡)𝑑𝑡
0
𝑄0 ∙ 100
(7)
To optimize the service life, the 𝑆𝑜𝐶 (𝑡) is usually limited within a given interval 25% ≤ 𝑆𝑜𝐶(𝑡) ≤ 95% [21].
2.7.2 Round-trip Efficiency
Round-Trip efficiency (RTE) takes into consideration the energy losses from power conversion in ESS [17]. RTE can be expressed as
𝜂𝑅𝑇𝐸=𝐸𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝐸𝑐ℎ𝑎𝑟𝑔𝑒
(8)
Where 𝐸𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (𝑀𝑊ℎ) is the energy that is discharged to the grid after removing auxiliary loads.
And 𝐸𝑐ℎ𝑎𝑟𝑔𝑒 (𝑀𝑊ℎ) is the energy used to charge the ESS [22]. EES with an RTE under 75% is unlikely to be cost-effective [17].
2.7.3 E- & C-rate
To describe the battery charging current, C-rate is used to normalize against battery capacity. A C- rate of 1𝐶 means that the charging current can charge the battery in one hour. This means that a battery with a capacity of 100 𝐴ℎ and a C-rate of 1𝐶 has a charging current of 100 𝐴. But if the same battery had had 0.5𝐶 then the charging current would have been 50 𝐴, the battery gets charged to 50% in an hour. E-rate works in the same way but refers to the discharge of a battery [20].
The preferred fast C-rate for a lithium-ion cell is 1𝐶 with a maximum rate of 2𝐶. This charging rate provides the shortest charge cycle without degrading to the battery pack performance [23].
2.7.4 Self-discharge
Self-discharge describes the losses in chemically bound energy when the battery isn’t connected to a circuit. The self-discharge rate for a Lithium-ion battery is very low a 𝐶/50000 but depends on cycling history, temperature and SoC [24].
2.7.5 Depth of Discharge
Depth of discharge (DoD) denotes the percentage of battery capacity that has been discharged as a percentage of maximum capacity. A discharge above 80% is called a deep discharge [20].
2.7.6 Lifecycle
A battery's life cycle is determined by how many charge/discharging cycles a battery should handle before performing under a given criterion. Lifecycle is estimated for a specific charge/discharging pattern. The actual battery life depends on the charging current for each charge/discharging and how often the cycles occur, as well as other conditions such as temperature and humidity [20]. Batteries that are discharged below a 20% 𝑆𝑜𝐶 i.e. more than 80% 𝐷𝑜𝐷 age faster. If a lithium–nickel–
manganese–cobalt (lithium–NMC) battery is discharged at 10% 𝐷𝑜𝐷 the battery can perform over 50 000 𝑐𝑦𝑐𝑙𝑒𝑠, while the same battery with a 100% 𝐷𝑜𝐷 only can perform 500 𝑐𝑦𝑐𝑙𝑒𝑠 [17]. A lithium-ion battery can handle 3000 𝑐𝑦𝑐𝑙𝑒𝑠 before losing 80% of its capacity [25].
2.7.7 Lithium-ion
The world's first lithium-ion battery was released by Sony in 1991, and since then the demand for these batteries has grown exponentially in several different markets [25]. The success is due to several different properties such as efficiency, and age on the battery cells. In addition, the energy density is high with 200 𝑊ℎ/𝑘𝑔. The biggest obstacle to large-scale batteries is the cost, since the cost is over 1200 $/𝑘𝑊ℎ [25]. The RTE for a Lithium-ion battery is between 87 − 94% [17].
Vattenfall Eldistribution is building a battery store in Uppsala that uses this type of battery, the battery storage will have an output of 5 𝑀𝑊 and a capacity of 20 𝑀𝑊ℎ [26].
2.7.8 Lead-acid
Lead-acid batteries have been used for many years for various purposes. The efficiency is relatively high between 65 − 80%, unfortunately the energy density is lower 30 − 50 𝑊ℎ/𝑘𝑔. The battery has a life of between 500 − 1000 𝑐𝑦𝑐𝑙𝑒𝑠, and requires maintenance, partly because the battery emits acidic vapors and hydrogen when charging. Which means that good ventilation is required. In addition, the battery's performance decreases at lower temperatures, which means that a heating system is required [25].
2.8 Battery energy storage system (BESS)
Using BESS within the electricity grid for frequency control is not a new technology, the world's first large-scale battery installed to control the frequency was installed in West Berlin in 1980 by Berliner Elektricitätswerke. Given the limitations within West Berlin's isolated electricity grid, only 300 MW of power plants where possible. When it was necessary to build a new power plant, it proved more profitable to build electric power plants for base-load and install a battery storage for variation rather than building a load-following plant [27]. Also, smaller islands with a high proportion of renewable production can use batteries to handle frequency regulation [27]. Since a battery can both supply a certain power and be charged with the same power from the electricity grid, a battery of 1 𝑀𝑊 can deliver from −1 𝑀𝑊 to 1 𝑀𝑊, giving an up/down regulation of 2 𝑀𝑊. Unlike a power plant of 1 𝑀𝑊 which can only supply up/down regulation of 0.5 𝑀𝑊 [27].
A BESS located in Helsinki, Finland is owned by Helen Ltd, the BESS is rated for 1.2 𝑀𝑊/600 𝑘𝑊ℎ.
During the first three years the BESS was used for research. One of the things studied was the ability to use the BESS for frequency control. The BESS provided the reserves FCR-N and FCR-D, the test as based on a frequency control curve that combines FCR-N and FCR-D to control the power from the BESS. During the test the capacity limits where reached multiple times, this had the effect that the BESS could not keep up with the desired frequency control [28].
The reductions of electric power thrue a point in the electricity grid, where the grid is under heavy load is called peak shaving and can been seen in Figure 7. Peak shaving can reduce the need to reinforce that point, therefor defer investment. Peak shaving also helps the electricity companies to meet demand without the need to start up more expensive generators [17].
Figure 7. Reducing the need of expensive generators by peak shaving using an EES [17].
2.8.1 Components in a BESS
The battery system consists of the battery pack, which connects multiple cells to achieve correct voltage and capacity. To protect the cells from harmful operation such as temperature, current voltage to achieve safe operation the battery pack is equipped with a battery management system (BMS) and a battery thermal management system (B-TMS). Figure 8 shows the different components in a BESS. In order to achieve reliable operation for the battery system an energy management system (EMS) is installed as well as a power conversion system to convert DC to AC [17].
Figure 8. Different components in a BESS where J/B is junction box [17].
2.8.2 Implementations and studies about BESS
Pia Borg describes in her report Förstudie Energilager anslutet till vindkraft [29] about the different applications that a BESS can be used for in the power grid, besides being able to even out production and make wind power more planable. It is also possible to reduce connection fees to the core grid, or regional networks, as well as increased acceptance limits. The acceptance limit is a way of
quantifying the impact that a new consumption or production plant has on the electricity grid. To study the acceptance limit, one looks at different performance indexes. For example, performance indexes may be slow voltage changes, flicker or losses. The profitability of an energy store becomes larger if it is owned and used by an energy company with balance responsibility. The preliminary study also concluded that the investment for an energy storage is relatively high compared to traditional grid planning, but since energy storage has certain characteristics that traditional grid planning lacks. For example, the opportunity to level out and plan wind energy's intermittent
generation. These attributes must be taken into account and not only focus on the cost of
investment. Errors between the forecast and actual weather conditions can lead to big deviations in power production. A BESS can stabilize the power production by discharging the BESS during high errors or during high demand, and charge the BESS when error or demand is low [17]. Greenchoice is a dutch company who owns and operate a BESS at 10 𝑀𝑊/10 𝑀𝑊ℎ together with the wind farm Hartel. The wind farm consists of 8 turbines and deliver on average 68 𝐺𝑊ℎ/𝑦𝑒𝑎𝑟. The BESS will smooth the electricity and thus ensure stability on the power grid [30].
2.8.3 Price Development
A good knowledge of future costs for battery packs and battery systems is important to increase investor confidence and enable decision makers to devise implementation strategies [31].
In the report The future cost of electrical energy storage based on experience rates [31], the authors have estimated price curves based on historical data, literature, research/industry reports, news, databases and interviews with manufacturers. Prices vary depending on the scope, size and application. Where scope means whether the price applies to single batteries, whole batteries, packages, modules or systems. Cumulative production has been identified as the variable that best shows price trends compared to other variables. The authors describe the change in price as
experience rate (ER) and is expressed in %. Figure 9 shows how the price drops the more cumulative capacity is installed. The technologies have been divided into categories where prominent
technicians have an installed capacity of < 1𝐺𝑊ℎ and for maturation < 100𝐺𝑊ℎ and mature >
100𝐺𝑊ℎ respectively. For lithium ion the degree of experience decreases as you expand the scope of the technology, which indicates that price development is driven primarily by experience from cell manufacturing and not from other components.
Figure 9. The price trend for different battery types based on cumulative installed capacity, the dashed lines show linear regression of the price trend [31].
Most technologies will achieve 1 𝑇𝑊ℎ of cumulative installed capacity within 10 − 23 years. Figure 10 shows that by 2030, stationary energy systems will cost between 290 $/𝑘𝑊ℎ and 520 $/𝑘𝑊ℎ, when accounting for uncertainty in ER the price range expands to 120 $/𝑘𝑊ℎ – 1.160 $/𝑘𝑊ℎ and is shown as a gray area. The price for lithium ion batteries for electric cars will be 120 $/𝑘𝑊ℎ. The fact that the price will be lower compared to stationary installations is explained by the expected high demand for electric cars in 2030. The demand will result in 300 𝐺𝑊ℎ installed capacity per year for electric cars compared to 50 𝐺𝑊ℎ for stationary systems [31]. Other reports indicate that the price for electric car battery packs will be around 160 $/𝑘𝑊ℎ by 2025 [32].
Figure 10. Price trends for various technologies between 2015 and 2040 [31] .
The electrical cost of storage for usable capacity (𝐸𝑈𝑅 𝑢𝑠𝑎𝑏𝑒𝑙 𝑘𝑊ℎ/⁄ 𝑐𝑦𝑐𝑙𝑒) is when the BESS is constrained by limits in 𝑆𝑜𝐶. Usable capacity is an indicator of storing and releasing 1 𝑘𝑊ℎ of electricity on top of the generation cost. In Germany 2014 a BESS with a usable capacity of 4.4 𝑘𝑊ℎ and around 3000 cycles could be bought for around 7500 𝐸𝑈𝑅. This resulting in an electrical storage cost of 0.57 𝐸𝑈𝑅 𝑢𝑠𝑎𝑏𝑒𝑙 𝑘𝑊ℎ/⁄ 𝑐𝑦𝑐𝑙𝑒 [33].
The Levelized cost of storage (𝐿𝐶𝑂𝑆𝐸) is another way to quantify the cost for energy storage. 𝐿𝐶𝑂𝑆𝐸 sums up to the total cost for the EES divided by the supplied energy during the project lifetime. And is expressed as
𝐿𝐶𝑂𝑆𝐸= ∑(𝐶𝐴𝑃𝐸𝑋𝐵𝐸𝑠𝑆+ 𝑂&𝑀𝐵𝐸𝑆𝑆) ⋅ (1 + 𝑟)−𝑡
∑ 𝑊𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑,𝑡⋅ (1 + 𝑖)−𝑡
(9)
Where 𝐶𝐴𝑃𝐸𝑋𝐵𝐸𝑆𝑆 is the investment cost (EUR) and 𝑂&𝑀𝐵𝐸𝑆𝑆 is the operation and maintenance cost (EUR). 𝑊𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 is the yearly supplied energy from the BESS (𝑀𝑊ℎ/𝑦𝑒𝑎𝑟) during the years 𝑡.
With the discount factor 𝑟 (%) and 𝑖, where 𝑖 neglects the interest rate since the energy has no momentary value [34].
2.9 Building regulations for installing BESS
In order to build a new wind farm an Environmental Impact Assessment (EIA) must be concluded for the group station, in order to evaluate the environmental impact from the wind farm. A BESS isn’t included in the group station of the wind farm, and therefor the BESS can be excluded from the EIA according to 9 chapter in Miljöbalken. If The BESS is placed on the land that is already used by the wind farm only a planning application is required for the and the BESS. If land outside of the wind farm is used by the BESS a notice must be sent to the supervisory authority according to 12 chapter 6
§ in Miljöbalken [35]. BESS must be in a protected space, where possible use electrical equipment space or locked space for electrical equipment [36].
The following factors must be considered when choosing battery space
• Protection against danger, e.g. fire, water, impacts, vibration and vermin
• Protection against danger generated by the battery, e.g. High voltage explosion hazard, electrolyte danger and corrosion
• Protection against access by unauthorized personnel.
• Protection against the influence of extreme ambient conditions, such as temperature, moisture or airborne pollutants.
Since batteries such as lithium-ion are temperature sensitive, the ambient temperature must be within the battery operating range of about 5 − 40 ℃ for the cells not to get damaged and to maintain longevity [37].
Some batteries generate hydrogen when charging. Therefore, ventilation of a battery compartment or battery cabinet is important to keep the hydrogen concentration below 4%𝑣𝑜𝑙 which is the lower explosion limit. The requirement for ventilation should primarily be met with self-contained
ventilation and otherwise with mechanical ventilation [36].
Batteries that meet the standards and regulations that are in place are considered safe and it takes a lot of time before such a BESS is to suffer such serious errors that can cause a fire [37]. External short circuits and overcharging are common causes of electrical failure. In the event of a short circuit, the discharge current will be much higher than normal current which will raise the temperature which can lead to thermal rush. A battery overcharge is usually due to failure of the battery control system [38]. When overcharged, the electrolyte can start to evaporate, and the gas is very flammable. Even if the battery shuts down when the fault is detected, there is still a risk that damaged cells will self- ignite [37]. The consequences of thermal rush are higher for an overcharged battery compared to a normally charged because the amount of chemically bound energy in an overcharged battery is higher [38]. Normal charging below the freezing point can also damage the battery, the anode can be covered by metallic lithium and there is a risk of short-circuiting. Normal charging at temperatures above 70 °𝐶 mainly affects the life cycle, but at continuous load and higher temperatures, thermal rush can occur [37].
It is important to have control of fire extinguishing function for environmental reasons. When extinguishing a fire in battery systems with water, high levels of metals as well and unusual metals have been found in extinguishing water used to fight a fire in a BESS, most of which were metals such as europium and antimony [39]. Antimony can be accumulated by plants in heavily contaminates soils and may pose a health risk to animals and humans [40]. Elevated levels of metal can be toxic to plants humans and nature. The metals are not broken down either, but remain in nature, the metal will spread to rivers and lakes. Plants, fish and microorganisms will also be damaged by these metals [41].
2.10 Mechanical fatigue for a wind turbine
A wind turbine (WTG) tends to cycle more than 100 million revolutions during the WTG service life and during this time the blades and the tower are exposed to the hostile conditions in the form of varying temperatures, humidity, rain, hail, snow, ice, solar radiation. The length and weight of the blades contributes to high bending moments due to rotational and gravitational loads [42]. It is important for a WTG to withstand fatigue in order to reach full expected life. One way to determine materials mechanical fatigue is to study S-N curves for the materials. In a S-N curve the cylindrical stress (𝑆) is plotted against cycles to failure (𝑁) on a logarithmic scale [43].
Figure 11 shows an illustration of a model for used fatigue life for a WTG depending on the power output, the curve is based on an S-N curve a wind turbine for and is adjusted to expect 100% service life at 100% of power output.
Figure 11. Used life for every power output [44].
75 80 85 90 95 100 105 110 115 120 125 130
0 50 100 150 200 250 300
Power Output (%)
Life (%)
2.11 Different type of optimization problems
When working with optimization it is important to understand what kind of problems you are working with as different types of problems need different angles of approach. A general optimization problem can be formulated by
min𝑥 𝐽(𝑥) (10)
subject to
𝐺(𝑥) < 0 (11)
𝐻(𝑥) = 0 (12)
𝑥𝑙 ≤ 𝑥 ≤ 𝑥𝑢 (13)
Where Equation (10) is the objective function to be minimized, if you want to maximize 𝐽(𝑥), you can instead minimize −𝐽(𝑥). Equation (11) and (12) represents constraints for differences and similarities that must be fulfilled. These constraints mean that the minimization will be reasonable, for example, limiting how much the solution may cost. Equation (13) limits upper and lower boundaries, for example, you can limit the mass 𝑥 to 0 ≤ 𝑥 so as not to get a solution with negative mass [45].
Optimization problems can be broadly classified into seven different aspects, knowledge of these aspects is important in order to understand whether the problem is a simple or complex, and what algorithm are needed to solve the problem.
Linear vs nonlinear
Is 𝐽(𝑥), 𝐺(𝑥) och 𝐻(𝑥) all linear or non-linear functions of 𝑥? If all functions are linear then the problem is called a linear optimization problem (LP). When the objective function or constraints is non-linear, the problem is called non-linear optimization (NP). LP is generally a simpler problem to optimize compared to NP. Especially for functions with many variables [45].
Constrained vs Unconstrained
Does the optimization task have any constrains or is it unconstrained? If there are no constraints, the problem is called an unlimited optimization problem, if there are any constraints the problem is called a limited optimization problem. Most practical problems are constrained. For an LP must be limited otherwise the solution will not be finite [45].
Discrete vs continuous
Is any of 𝑥 discrete or are all continuous? If any of the variables are discrete, the problem is no longer continuous. 𝑥 can, for example, be limited to be integers or only be 0 or 1. The latter is called binary optimization [45].
Single vs Multiobjective
An optimization allows one or more objects to be optimize. For example, you want to optimize the chassis for a car to cope with a collision, with a thicker chassis the car will be stronger but also heavier which will affect gasoline consumption which is also an object to be optimized. Thus, there are two objective functions [45].
Single vs multiple optimum
Are there one or more optimal solutions for the object function? Finding a solution for a multi- solution objective function is called global optimization. Global optimization algorithms differ quite a bit compared to local optimization [45].
Deterministic vs Nondeterministic
In recent years designers began to understand that there is a high cost associated with tight tolerances. They also understand that it is not necessary for every part to have the same tolerance.
The net result is that there are some aspects of the design that can be represented by variables that are deterministic while others might have to be treated as nondeterministic [45].
Simple vs Complex problem
Perhaps the most critical aspect of a problem is whether the problem is simple or complex. This is done by classifying the aspects mentioned above. An example of an aspect of a simple problem may be
1. The problem contains only continuous values 2. The problem is not highly non-linear
3. Local optimization is enough
4. The algorithm used to solve the problem will be able to do so within seconds or minutes [45].
2.12 Optimization problem of a wind farm with a BESS
The profitability of a BESS with a wind farm is going to be studied using an optimization model. The model uses the BESS to maximize the income for the wind farm by peak shaving. In addition to support the wind farm the BESS is also supporting the grid by providing the reserve FFR.
By using an optimization model results in a solution that shows how much the income can increase from the wind farm due to a BESS. Since most of the available data regarding electricity generation is presented in active power (𝑀𝑊) and energy (𝑀𝑊ℎ) the model will be based around these units.
The costs needs to be added in the objective function 𝐽(𝑥). Since the goal is to maximize the income the costs are positive, and the income is negative. The income from the sale of electricity to the grid can be expressed as
𝐼𝑛𝑐𝑜𝑚𝑒𝑔𝑟𝑖𝑑(𝑥) = − ∑ Δ𝑡
𝑇
𝑡=1
𝐼𝑔𝑟𝑖𝑑,𝑡𝑥𝑔𝑟𝑖𝑑,𝑡
(14)
Where Δ𝑡 is the timestep for the simulation, 𝐼𝑔𝑟𝑖𝑑,𝑡 is the income for the electricity sold
(𝐸𝑈𝑅/𝑀𝑊ℎ) and 𝑥𝑔𝑟𝑖𝑑,𝑡 is the power to the grid (𝑀𝑊). The income for providing the reserve FFR can be expressed as
𝐼𝑛𝑐𝑜𝑚𝑒𝐹𝐹𝑅(𝑥) = − ∑ 𝐼𝐹𝐹𝑅𝑥𝐹𝐹𝑅,𝑡
𝑇
𝑡=1
(15)
Where 𝐼𝐹𝐹𝑅is the income from the reserve (𝐸𝑈𝑅
𝑀𝑊) and 𝑥𝐹𝐹𝑅 is the amount of power that is sold (𝑀𝑊).
Section 2.6.4 describes that the need for FFR is concentrated around the summer and the highest need is during the night when the consumption and production is low, therefore the model is built to provide FFR every night between 00: 00 – 08: 00.
The cost to deliver electricity out to the network grid is based on the tariff PT12 in [46]
𝐶𝑜𝑠𝑡𝑔𝑟𝑖𝑑(𝑥) = 𝑇
8760∑ 𝐾𝑔𝑟𝑖𝑑⋅ 𝑥𝑔𝑟𝑖𝑑,𝑚𝑒𝑎𝑛+ 𝐾𝑆𝑡𝑎𝑟𝑡
𝑇
𝑡=1
(16)
𝐾𝑠𝑡𝑎𝑟𝑡 is a yearly fee and 𝐾𝑔𝑟𝑖𝑑is the power cost (𝐸𝑈𝑅/𝑀𝑊), where 𝑥𝑔𝑟𝑖𝑑,𝑚𝑒𝑎𝑛 is the mean between the highest power and the second highest power from 𝑥𝑔𝑟𝑖𝑑,𝑡 during the time period 𝑇. Because the time period of the optimization is less than a year the cost is normalized by dividing 𝐶𝑜𝑠𝑡𝑔𝑟𝑖𝑑(𝑥) with 8760 ℎ and multiplied with the number of hours in the time period.
The cost of storage for the BESS can be expressed as
𝐶𝑜𝑠𝑡𝐵𝐸𝑆𝑆(𝑥) = Δt ∑ 𝐿𝐶𝑂𝑆𝐸
𝑇
𝑡=1
𝑥𝐵𝐸𝑆𝑆,𝑡
(17)
Where 𝑥𝐵𝐸𝑆𝑆,𝑡 is the amount of energy discharged from the BESS (𝑀𝑊), for each timestep and 𝐿𝐶𝑂𝑆𝐸 is expressed in Equation (9).
The wind farm is limited to only deliver power to the receiving grid, so the boundary for 𝑥𝑔𝑟𝑖𝑑,𝑡 can be formulated as
0 ≤ 𝑥𝑔𝑟𝑖𝑑,𝑡 ≤ 𝑃𝑔𝑟𝑖𝑑,𝑀𝑎𝑥 (18)
where 𝑃𝑔𝑟𝑖𝑑,𝑀𝑎𝑥 is the maximum power that can the grid can receive (𝑀𝑊). To maximize the service life the 𝑆𝑜𝐶 for the BESS the 𝑥𝐵𝐸𝑆𝑆,𝑡 is limited within
𝑆𝑜𝐶𝑀𝑖𝑛≤ Δ𝑡 𝑥𝐵𝐸𝑆𝑆,𝑡≤ 𝑆𝑜𝐶𝑀𝑎𝑥 (19)
Where 𝑆𝑜𝐶𝑀𝑖𝑛= 𝑆𝑜𝐶𝑙 𝐸𝐵𝐸𝑆𝑆 (𝑀𝑊ℎ), 𝑆𝑜𝐶𝑀𝑎𝑥 = 𝑆𝑜𝐶𝑢 𝐸𝐵𝐸𝑆𝑆 (𝑀𝑊ℎ). The power for the FFR must come from the battery since the wind farm can’t deliver the power fast enough. Therefore, the upper limit for 𝑥𝐹𝐹𝑅,𝑡 is expressed as
0.1 ≤ 𝑥𝐹𝐹𝑅,𝑡 ≤ 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (20)
Where 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 is the maximum discharging power (𝑀𝑊) from the BESS. The lower limit for 𝑥𝐹𝐹𝑅,𝑡 is 0,1 𝑀𝑊 during the time period for FFR [47]. Outside the time period both the upper and lower limit is zero.
The wind farm is limited to several constraints. Since wind farm can’t sell more electricity than it is producing the constraint for the production can be expressed as
𝐻1,𝑡(𝑥) = Δ𝑡(𝑥𝑔𝑟𝑖𝑑,𝑡− 𝜂𝑅𝑇𝐸𝑥𝐵𝐸𝑆𝑆,𝑡+ 𝑥𝐵𝐸𝑆𝑆,𝑡+1) + 𝑡𝐹𝐹𝑅𝑥𝐹𝐹𝑅,𝑡= 𝐸𝑝𝑎𝑟𝑘 (21) Where 𝐸𝑝𝑎𝑟𝑘 is the generation from the wind farm (𝑀𝑊ℎ), and 𝑡𝐹𝐹𝑅 is the total time (ℎ) that the FFR is activated during Δ𝑡. From the specifications in Section 2.6.4 the support time for long activation is 30 seconds, adding on activation time and deactivation time results in roughly 35 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 from 𝑡 = 0 to start of buffer time that can be seen in Figure 6. Because the reserves need to be capable of 4 activations every hour [16] 𝑡𝐹𝐹𝑅 = 4 ⋅ 35 ≈ 1/25 ℎ.
All the electricity for the FFR needs to come from the BESS since the wind farm can’t deliver the power fast enough. Therefore, a constraint that reserves the required electricity in the BESS can be expressed as
𝐺1,𝑡(𝑥)= −Δ𝑡 𝑥𝐵𝐸𝑆𝑆,𝑡+ 𝑡𝐹𝐹𝑅𝑥𝐹𝐹𝑅,𝑡 < 𝑆𝑜𝐶𝑀𝑖𝑛 (22) The maximum power from the wind farm and the BESS can be expressed as
𝐺2, 𝑡(𝑥) = 𝑥𝑔𝑟𝑖𝑑,𝑡+ 𝑥𝐹𝐹𝑅,𝑡 < 𝑃𝑔𝑟𝑖𝑑,𝑚𝑎𝑥 (23) The charging/discharging power for the BESS is limited by the constraints
𝐺3,𝑡(𝑥) = −𝑥𝐵𝐸𝑆𝑆,𝑡+ 𝑥𝐵𝐸𝑆𝑆,𝑡+1 < 𝑃𝑐ℎ𝑎𝑟𝑔𝑒 (24) and
𝐺4,𝑡(𝑥) = 𝑥𝐵𝐸𝑆𝑆,𝑡− 𝑥𝐵𝐸𝑆𝑆,𝑡+1< 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (25) Where 𝑃𝑐ℎ𝑎𝑟𝑔𝑒 is the maximum charging power (𝑀𝑊).
2.13 Optimization of power output for a WTG
To study if regulation of the power output of a WTG can prolong the service life and thus lower the generation costs, and overall increase the net income. To do this another optimization model was built with the objective function calculates the net income from the WTG and is formulated as
𝐽(𝑥𝑊𝑇𝐺,𝑡) = Δ𝑡 ∑ 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡(𝑥𝑊𝑇𝐺,𝑡) − 𝐼𝑔𝑟𝑖𝑑,𝑡𝑃𝑊𝑇𝐺(𝑥𝑊𝑇𝐺,𝑡)
𝑇
𝑡=1
(26)
Where 𝑥𝑊𝑇𝐺,𝑡 it the fractional output power from the WTG (%) and 𝑃𝑊𝑇𝐺 is the power (𝑀𝑊).
𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡 based on the service life of the WTG and how the service life is varying with the power output in Figure 11. The 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡 can be written as
𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑐𝑜𝑠𝑡(𝑥𝑊𝑇𝐺) = 𝑅𝑢𝑛𝑛𝑖𝑛𝑔𝑐𝑜𝑠𝑡
10−5⋅log (𝑥𝑊𝑇𝐺,𝑡)+ 𝑆𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦𝑐𝑜𝑠𝑡 (27) Where 𝑅𝑢𝑛𝑛𝑖𝑛𝑔𝑐𝑜𝑠𝑡 is the cost that is depending on the power output from the WTG (𝐸𝑈𝑅/ℎ), while 𝑆𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦𝑐𝑜𝑠𝑡 is the cost for the wind turbine when the power output is zero (𝐸𝑈𝑅/ℎ).
The maximum power output is depending on the wind and is there for constraint to 𝐺1,𝑡 (𝑥𝑊𝑇𝐺,𝑡) = 𝑥𝑊𝑇𝐺,𝑡 ≤𝑃𝑤𝑖𝑛𝑑,𝑡
𝑃𝑊𝑇𝐺
(28)
Where 𝑃𝑤𝑖𝑛𝑑,𝑡 is the amount of power in the wind (𝑀𝑊). Since the wind turbine still needs to make money a constraint stating that the wind turbine needs to make more money than if the WTG always ran at maximum available power as describes in Equation (28) a nonlinear constraint based on the objective function is written as
𝐺2,𝑡(𝑥𝑊𝑇𝐺,𝑡) = 𝐽(𝑃𝑤𝑖𝑛𝑑,𝑡
𝑃𝑊𝑇𝐺 ) ≤ 𝐽(𝑥𝑊𝑇𝐺,𝑡) (29)
The WTG is limited to generate power
0 ≤ 𝑥𝑊𝑇𝐺,𝑡 (30)
An upper limit isn’t required due to the constraint in Equation (28).
Method
3.1 Literature study
Throughout the work with this master thesis relevant literature has been studied and included in the report, the aim was to gather knowledge about cost and operating conditions for BESS. Similar optimization models have been studied with the goal to achieve a model that takes additional parameters into account such as storage and grid cost.
3.2 Wind farm with BESS
To find the optimal solution for a wind farm with a BESS the calculations software MATLAB was used and the equations used for the optimization are described in Section 2.12.
In order to do the optimization a few assumptions need to be made. Because of the way the constraint in Equation (21) is designed the assumption 𝜂𝑅𝑇𝐸 = 1 is made, since the model needs to move electricity that is stored in the BESS to the next time step in order to save it for later, if 𝜂𝑅𝑇𝐸<
1 some electricity will be lost despite the BESS isn’t discharging any in practice. The
charging/discharging power for the BESS is assumed to be the same 𝑃𝑐ℎ𝑎𝑟𝑔𝑒= 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒= 𝑃𝐵𝐸𝑆𝑆. The self-discharge for the BESS is also assumed to be negligible. The price for FFR is currently under bid confidentiality [15], therefore an assumption needs to be made. The mean price FCR-D was 21 𝐸𝑈𝑅/𝑀𝑊 during September 2019 [48], so the price for FFR is assumed to 𝐼𝐹𝐹𝑅= 18 𝐸𝑈𝑅/𝑀𝑊 since.
To study if it is economically feasible to install a BESS the increased income is studied. Since the optimization model is shorter than a year the increased income needs to be extrapolated to cover a year. The currency chosen for the report is EUR with the exchange rate of 1 𝑆𝐸𝐾 = 0.09 𝐸𝑈𝑅 [49].
Calculating the 𝐿𝐶𝑂𝑆𝐸 from Equation (9) for an 20 𝑀𝑊ℎ BESS with 3000 𝑐𝑦𝑐𝑒𝑙𝑠 over a 10 𝑦𝑒𝑎𝑟 period with 𝑖 = 2% and 𝑟 = 2.16% [50] . Where 𝑂&𝑀 = 2% ⋅ 𝐶𝐴𝑃𝐸𝑋𝐵𝐸𝑆𝑆 and 𝐶𝐴𝑃𝐸𝑋𝐵𝐸𝑆𝑆 = 266 880 𝐸𝑈𝑅/𝑀𝑊ℎ based on low price for EES by 2030 from Section 2.8.3 converted to
𝐸𝑈𝑅/𝑀𝑊ℎ [51] yields a 𝐿𝐶𝑂𝑆𝐸= 167 EUR/MWh. The calculated 𝐿𝐶𝑂𝑆𝐸 where proved too high to provide advantages such as peak shaving and energy storage, therefore the LOCSE where
successively increased until the optimization model almost stops using the BESS.
3.2.1 Calculation process
For every value 𝐿𝐶𝑂𝑆𝐸 all combinations of 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 and 𝐸𝐵𝐸𝑆𝑆, MATLAB where optimized and the increased income due to the BESS was compared. This way the 𝑃𝐵𝐸𝑆𝑆 and 𝐸𝐵𝐸𝑆𝑆 of the BESS was studied based on an economic evaluation.
Figure 12 visualizes the MATLAB code that used the 𝐿𝐶𝑂𝑆𝐸 to formulate the objective function as a separate MATLAB function called fun(x), that consists of Equation (14) - (17). Then the code used a for loop to find an optimal solution for all combinations of 𝑃𝐵𝐸𝑆𝑆 and 𝐸𝐵𝐸𝑆𝑆. Because 𝑃𝐵𝐸𝑆𝑆 and 𝐸𝐵𝐸𝑆𝑆 is affecting the constraints and boundaries, a separate MATLAB script called Main.m
constructs the constraints in the matrix 𝐴 and 𝐴𝑒𝑞 with the vectors 𝑏 and 𝑏𝑒𝑞, that fmincon needs to find the optimal solution Equations (22) − (25) is in the matrix 𝐴 and vector 𝑏, while Equation (21) is in 𝐴𝑒𝑞 and 𝑏𝑒𝑞.
Figure 12. Flowchart showing how the calculation process.
Because FFR is only active during three months of the year, another optimization without FFR where made in order to include the difference in income without FFR during the rest 9 month of the year.
This was achieved by removing Equation (15) from the objective function and Equation (22) and (23) from the constraints. In order to assist fmincon, fun(x) also calculates the gradient for the objective function, this way fmincon can utilize the gradient to quickly find the optimum.
𝑃𝐵𝐸𝑆𝑆 is limited by the maximum C-rate of 1𝐶 and therefore the first value 𝐸𝐵𝐸𝑆𝑆 will increase with 𝑃𝐵𝐸𝑆𝑆. All combinations from Table 2 where optimized in order to determine the power and capacity rating for the BESS.
Table 2. Combinations of power and capacity that where changed within the optimization.
Variable From Step To
𝐾𝐵𝐸𝑆𝑆 0 𝐸𝑈𝑅/𝑀𝑊ℎ 2 𝐸𝑈𝑅/𝑀𝑊ℎ 6 𝐸𝑈𝑅/𝑀𝑊ℎ
𝑃𝐵𝐸𝑆𝑆 5 𝑀𝑊 5 𝑀𝑊 30 𝑀𝑊
𝐸𝐵𝐸𝑆𝑆 𝑃𝐵𝐸𝑆𝑆⋅ 1ℎ 𝑀𝑊ℎ 5 𝑀𝑊ℎ 180 𝑀𝑊ℎ
FOR-LOOP
Main.m fmincon Optimal
solution 𝑃𝐵𝐸𝑆𝑆 & 𝐸𝐵𝐸𝑆𝑆
𝐿𝐶𝑂𝑆𝐸 fun(x)
𝐸𝑝𝑎𝑟𝑘 is based on hourly generation during the two weeks of September from a wind farm located in SE2, the generation curve and can be seen in Figure 13. The electricity price based on Vattenfall’s projections during the same month. The constants used in the optimization can be found in Table 3.
Figure 13. Generation from a wind farm in SE2.
Table 3. Constants used in the optimization.
Variable Value Source
𝚫𝒕 1 ℎ Set value
Grid
𝑲𝒈𝒓𝒊𝒅 1170 𝐸𝑈𝑅/𝑀𝑊 [46], [49]
𝑲𝒔𝒕𝒂𝒓𝒕 104 400 EUR [46], [49]
𝑷𝒈𝒓𝒊𝒅,𝒎𝒂𝒙 100 MW Set Value
FFR
𝝉𝑭𝑭𝑹 1/25 ℎ Sec 2.6.4
𝑰𝑭𝑭𝑹 18 𝐸𝑈𝑅/𝑀𝑊 Assumption
BESS
𝑪𝒚𝒄𝒍𝒆𝒔 3000 [25]
𝜼𝑹𝑻𝑬 100% Assumption
𝑺𝒐𝑪𝒖 95% [21]
𝑺𝒐𝑪𝒍 25% [21]
3.3 Optimization of power output
WTG
(29) Figure 14 (26)
Figure 14. Turbine generation for one month during each season in 2019.
Just like the other optimization the MATLAB function fmincon will be used with a for loop to run all seasons, with the objective function described in Equation (26) with values from Table 4. The linear constraint in Equation (28) where inserted in the matrix 𝐴 and 𝐴𝑒𝑞 with the vectors 𝑏 and 𝑏𝑒𝑞.
Because Equation (29) is a nonlinear constraint fmincon require it to be written in a separate
function. There is no need for an upper limit because of the linear constraint so the upper limit is left open and the lower limit is set to zero.
Table 4. Constants used in the optimization.
Variable Value Source
𝑃𝑊𝑇𝐺 2 𝑀𝑊 [52]
𝑅𝑢𝑛𝑛𝑖𝑛𝑔𝑐𝑜𝑠𝑡 45 𝐸𝑈𝑅/ℎ Assumed
𝑆𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦𝑐𝑜𝑠𝑡 10 𝐸𝑈𝑅/ℎ Assumed
Some assumptions are made about the optimization model. First, the WTG is assumed to be designed to use 100% of the used life at 100% output power. It is also assumed that the WTG is generating as much as possible. The generation cost is hard to approximate for a wind park, so in order to get an idea of how the generation can affect the values for the generation cost where assumed.
Results
The results are divided in to two separate sections for each optimization
4.1 Wind farm with BESS
To study how the 𝐿𝐶𝑂𝑆𝐸 affects the increased income with power and capacity, increased income where plotted against the capacity for BESS with different power with and without the income from FFR.
4.1.1 Economics
Figure 15 shows the increased income for a wind farm with a BESS without the income from FFR, the income from the BESS is increasing even when the capacity is 60 𝑀𝑊ℎ. With the exception for 10 𝑀𝑊, that seems to level out at about 5%. When adding the income from the three months of FFR the increased income can be seen in Figure 16 which shows that a BESS with higher power will yield a higher income compared to a lower power BESS with the same capacity. Increasing the capacity will have a positive effect on the increased income but as the capacity grows bigger the increased income will level out and yield no difference.
When the 𝐿𝐶𝑂𝑆𝐸 ≠ 0 the increased income changes, Figure 17 shows the increased income from the wind farm with a BESS without the income from FFR the trend for the increased income is similar to Figure 15 but the income from the BESS is lower. It also becomes clear that without FFR the power isn’t affecting the increased income for small capacity, it is only until around 70 𝑀𝑊ℎ that the power starts to effect the increased income, but and a large BESS isn’t going to increase the income more than 3% .Figure 18 shows the increased income with three months of FRR follows the same trend as Figure 16, but the increased income is almost non increasing with larger capacity, this indicates that the majority increased income comes from the FFR, which is more dependent on the power rating for the BESS rather than the capacity.
𝐿𝐶𝑂𝑆𝐸 = 0 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 15. Yearly increased income without FFR where 𝐿𝐶𝑂𝑆𝐸= 0 𝐸𝑈𝑅/𝑀𝑊ℎ.
Figure 16. Yearly increased income with FFR where 𝐿𝐶𝑂𝑆𝐸= 0 𝐸𝑈𝑅/𝑀𝑊ℎ.
𝐿𝐶𝑂𝑆𝐸 = 4 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 17. Yearly increased income without FFR where 𝐿𝐶𝑂𝑆𝐸= 4 𝐸𝑈𝑅/𝑀𝑊ℎ.
Figure 18. Yearly increased income with FFR where 𝐿𝐶𝑂𝑆𝐸= 4 𝐸𝑈𝑅/𝑀𝑊ℎ.
When the 𝐿𝐶𝑂𝑆𝐸 continues to increase the increased income from the wind farm with a BESS continues to change. Figure 19 shows that without FFR the 𝐿𝑂𝐶𝑆𝐸 is too high for a BESS to increase the income much more than 1%. With FFR Figure 20 shows that the income for a BESS can vary between 3 – 8% depending on the power output for the BESS, and the capacity doesn’t have any effect on the increased income.
𝐿𝐶𝑂𝑆𝐸 = 6 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 19. Yearly increased income without FFR where 𝐿𝐶𝑂𝑆𝐸= 6 𝐸𝑈𝑅/𝑀𝑊ℎ.
Figure 20. Yearly increased income with FFR where 𝐿𝐶𝑂𝑆𝐸= 6 𝐸𝑈𝑅/𝑀𝑊ℎ.
4.1.2 BESS SoC
To get a good understanding of the wear of the BESS. The cycling of the BESS needs to be studied, the 𝑆𝑜𝐶 for constant power and different capacity where plotted. Figure 21 shows that when the 𝐿𝐶𝑂𝑆𝐸= 0 𝐸𝑈𝑅/𝑀𝑊ℎ the wind farm takes maximum advantage of the capacity, the cycling pattern and DoD looks almost identical independent of the capacity of the BESS.
To see how 𝐿𝐶𝑂𝑆𝐸 affected the cycling and the DoD of the BESS, the SoC was also plotted for 𝐿𝐶𝑂𝑆𝐸= 4 𝐸𝑈𝑅/𝑀𝑊ℎ and 6 𝐸𝑈𝑅/𝑀𝑊ℎ in Figure 22 and Figure 23. Figure 22 shows a lower amount of cycles, and with larger capacity the occurrence of the cycles is the same, but the DoD becomes smaller with larger capacity. Figure 23 shows that when the 𝐿𝑂𝐶𝑆𝐸= 6 𝐸𝑈𝑅/𝑀𝑊ℎ the wind farm avoids using the BESS for other things rather than peak shaving, but if the electricity price is especially low like for 𝑡 = 133 it’s still feasible to cycle the BESS. The small changes in 𝑆𝑜𝐶 over an eight hour period that can be seen when 𝑡 ≈ 150 for a 20 𝑀𝑊ℎ capacity, is due to the constraint in Equation (22) and the fact that the BESS is providing FFR.
𝐿𝐶𝑂𝑆𝐸 = 0 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 21. SoC for BESS when 𝐿𝐶𝑂𝑆𝐸= 0 𝐸𝑈𝑅/𝑀𝑊ℎ.
𝐿𝐶𝑂𝑆𝐸 = 4 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 22. SoC for BESS when 𝐿𝐶𝑂𝑆𝐸= 4 𝐸𝑈𝑅/𝑀𝑊ℎ.
𝐿𝐶𝑂𝑆𝐸 = 6 𝐸𝑈𝑅/𝑀𝑊ℎ
Figure 23. SoC for BESS when 𝐿𝐶𝑂𝑆𝐸= 6 𝐸𝑈𝑅/𝑀𝑊ℎ.
