Optimization of a PV + Battery system to provide grid ancillary services

Final Degree/Master Degree Project INNOENERGY RENE MASTER PROGRAMME Master of Energy Engineering Business Oriented Model for Optimization of Energy Storage Systems Author: Martim Gir˜ ao de Melo Perestrelo Coordinator: Oriol Gomis Escola T` ecnica Superior d’Enginyeria Industrial de Barcelona September 23, 2021 Executive Summary This master thesis was carried out in collaboration with the company Starke Energy with the purpose of creating a model to be used when sizing projects according to each client preferences. The objective of the model was to maximize the revenues of each individual project by optimizing the battery capacity depending on different parameters such as: the grid connection size, the availability of PV panels and its total capacity and the consumption of each building. The objective of this thesis is also to demonstrate the importance of such models for companies operating in the same area as Starke - virtual power plants performing services such as frequency containment - and to show one possible method to increase operations efficiency when delivering the project specifications to clients - to be a link between the energy storage sizing algorithms of companies and its clients inputs. The optimization model takes as input data provided by Starke Energy company, related to the best bidding strategies to participate in electricity markets. Then, it uses client´s data to evaluate the best possible solutions of a battery+pv+grid system. It does so by comparing several combinations of scenarios taking into account the current grid connection, the PV status - if it is already installed or not - and the different battery sizes available. In the end, the model outputs three different solutions: a minimizing one where the grid size is downgraded, a maximizing one where the connection is leveled up and a scenario where there are no modifications on the grid capacity. Each solution will show what is the design and size of the system, the investment needed and how it is divided, the different revenues sources and finally the ROI and payback periods. All of these parameters are demonstrated for 3 case studies. The first case study demonstrates that the expected outcome is not actually the best one, the second explains how negative results can turn into positive ones and the third shows one example for cases in which the grid size is already maximum. All in all, the three case studies are, most importantly, an illustration of the flexibility of the model since it can adapt to several different scenarios. In conclusion, although the model could be further developed to return more parameters or to adapt to more situations, its results were confirmed by specialists in the field and most importantly, it has helped the company to increase its efficiency by being able to connect its energy storage sizing algorithm with all of its clients inputs and deliver reliable and accurate information about each project specifications in a matter of days instead of weeks. 1 Acknowledgments The development of this thesis would not be possible if not for InnoEnergy Master School, in which I have studied the RENE programme in two excellent universities, KTH and UPC. I want to thank all the administration of InnoEnergy for making such an excellent programme with the purpose of creating the next energy industry leaders and entrepreneurs. I want to give out a big thank you for all the professors of both universities and for every lecture they performed. I also want to thank all of my fellow colleagues of these two years who helped me surpass many obstacles and grow as a person, who will obviously continue to be my industry colleagues after graduation. Finally, and most importantly, I want to thank my family and friends for all the support throughout the years and to always ensuring me I was on the right track. Without all of this support, this thesis would not have been possible. 2 Contents 1 Introduction 6 1.1 Purpose and Goal of the thesis ................... 7 1.2 Scope and Limitations ........................ 7 1.3 Existing Literature .......................... 8 1.4 Structure of the Thesis ........................ 9 2 Background 10 2.1 Virtual Power Plant Concept .................... 12 2.2 Electricity Market .......................... 13 2.2.1 Netherlands Electricity Market ............... 14 2.3 Starke Energy Operations ...................... 15 3 Technology 16 3.1 BESS + Inverter Description .................... 16 3.2 PV Description ............................ 17 3.3 Behind the meter concept ...................... 17 3.4 Types of Grid Connections ..................... 18 4 Method Description 22 4.1 Project Based Optimization - Method Used ............ 22 4.2 Data Used ............................... 22 4.3 The Model .............................. 23 4.3.1 FlowChart explanation .................... 24 4.4 Expected Result ........................... 26 5 Results 28 5.1 Case Study 1 ............................. 28 5.2 Case Study 2 ............................. 30 5.3 Case Study 3 ............................. 32 6 Conclusions 34 7 Annexes 36 3 List of Figures 1 Share of energy from renewable sources, 2019 (% of gross final energy consumption) source: Eurostat (Statistics Eurostat). . . 11 2 Basic elements of a Virtual Power Plant .............. 12 3 Battery and Inverter Prices ..................... 17 4 Behind-the-meter VS Front-of-meter ................ 18 5 Behind-the-meter possibilities .................... 19 6 Model Flowchart ........................... 24 7 Case Study 1 ............................. 29 8 FCR Revenues VS Battery capacity for 3 grid connections . . . . 29 9 Case Study 1 Results ......................... 30 10 Case Study 2 ............................. 31 11 Case Study 2 Results ......................... 31 12 Case Study 3 ............................. 32 13 Case Study 3 Results ......................... 33 14 Interview to Starke´s Energy Software Engineer .......... 35 15 Case Study 2 full table ........................ 37 16 Case Study 1 Results full table ................... 38 17 Case Study 2 Results full table ................... 39 18 Case Study 3 Results full table ................... 40 4 List of Tables 1 Contract Tariffs - source: Liander (Liander Rates 2021)..... 20 2 Transport Tariffs - source: Liander (Liander Rates 2021). . . . 20 3 Upgrade/Downgrade Costs from Stedin .............. 21 5 Introduction Climate change has become one of the biggest challenges of the 21st century. In order to tackle this problem, the European Commission, in line with the Paris Agreement, have made the objective of the European Green Deal to achieve an economy with net-zero green house gas emissions by 2050[1]. To accomplish such goal, innovations will be needed mostly in 4 sectors: Electricity and Heat Production; Transportation; Industry; Agriculture, Forestry, and Other Land Use[2]. In the Electricity and Heat Production sector, one of the main objectives is to increase the share of Renewable Energy generation and phase out fossil fuel power plants[3]. However, as more renewable energy is integrated in the electric grid, more difficult it is to maintain grid stability and balance. Traditionally, grid operators used to take the load for granted and change the supply accordingly: they rated the available fossil fuel plants in the so-called merit order to satisfy demand first with the cheapest option, eventually rising up the merit order until demand was completely met. Throughout the years, massive nuclear or lignite-fired units usually served at maximum capacity to cover the base load. The conventional merit order dispatch faces new obstacles in a market dependent on renewable energy. Solar and wind energy, which will form the foundation of future electricity markets, are intermittent in nature and must be used when they are available; otherwise, they will be wasted. Plant and grid operators, on the other hand, cannot order wind or solar plants to generate energy when it is required, as they might in the conventional merit order approach. This clearly demonstrates that, as more countries depend on intermittent renewable energy, new ideas for balancing load and generation are needed to maintain grid stability[4]. At the moment, energy storage has been the most talked topic as a solution to the problem of the grid imbalance. This solution however, it is not just a single battery for a single home but instead many batteries aggregated which can communicate with each other in order to optimize charge and discharge behaviors. This concept, is what experts call a Virtual Power Plant[5]. The latter, will be explained with more detail in the next sections. Starke Energy is a relatively new company which installs batteries in residential areas and connects them all to create a virtual power plant. Therefore, each new project the company has will add to the total capacity of the ”virtual battery”. Moreover, using an algorithm which focuses in optimizing battery 6 performance to ensure a higher lifetime, Starke Energy provides balance to the electricity grid by participating in the frequency reserve markets. This thesis aims to help Starke Energy optimizing even more the efficiency of their projects by building a model which, by analyzing specific clients data, will output the exact configuration of the storage system needed. This way, Starke can respond to clients in a faster and more effective way. Purpose and Goal of the thesis The Purpose of this work is to develop an optimization model to be used by Starke Energy when finished. The model will receive, as inputs, company data related to the bidding strategies in the electricity market as well as client specific data such as grid connection size, capacity of PV panels and the building consumption. The reason to perform such work is that there is little to no information on how to effectively size an energy storage system and take into account different needs from different clients while also ensuring a participation in the electricity markets. There is indeed some literature about the topic, - this will be discussed in section 1.3 - however, there is not a concrete method to do this. Therefore, this thesis purpose is to serve as an example of how sizing can be done regarding energy storage projects and as well, give Starke Energy the possibility of handling projects in a faster and more accurate way. In the end of this work, the model should be able to output the following: •The Battery Capacity needed in KWh •The lifetime of the Battery •The CAPEX associated with each project •The ROI estimation for each project •Other important parameters related to each unique project Scope and Limitations Companies with business models which consist of using energy storage to participate in markets such as the FCR, FCR-N, and others, are becoming increasingly popular over the years. Therefore, models to ensure an easy sizing of these systems can have a significant impact in helping companies to achieve their operations in a more efficient way. The scope of this thesis is to show one possible method for doing so and possibly help others develop even more better models. To develop this model, several external factors were taken into consideration, either related to each customer needs, electrical grid characteristic and availability of certain types of technology. The main objective of this work is, therefore, to show how a company can connect the desired battery storage size 7 with each individual client inputs, while maximizing the overall profit for both stakeholders. However, all projects have their own limitations and the model created in cooperation with Starke Energy is no exception. The two main limitations focus on the aspect that this work was conducted during an internship at Starke Energy company, which limits the scope of the thesis: First of all,the model was designed specifically for the company, taking into account how the company operates and using data from its clients. This means that there is the possibility that it can be difficult to adapt the methodology for other companies. Secondly, part of the model depends on Starke Energy proprietary algorithm, which is used to determine the bidding strategies to the electricity markets. This restricts the scope of the thesis as the methods the company uses cannot be disclosed for intellectual propriety reasons. Nevertheless, even though such limitations impose some restriction for the scope of this thesis, it is important to highlight that the methodology used for the development of the model will be explained thoroughly and that by the end of this work it should be clear how to adapt it to develop other similar models. Existing Literature The concept of using energy storage systems as a virtual power plant to participate in electricity markets is already known and in use by several companies and there are many research papers describing methods to do so. Strategies to participate in energy markets as a VPP are presented in [6], [7] and[8] which focus on the optimal operation of the battery systems while participating in frequency reserve markets. There are also many master thesis around the subject,[9] describes an optimization method to size a virtual power plant in the Nordic market,[5] shows how different energy resources can be aggregated to build a VPP and help the frequency reserve markets and[10] goes a little bit further in details and shows how batteries can be used for peak shaving and for trading in the markets at the same time. Although this concept is already rigorously studied, papers that focus on sizing methods for energy storage assets with the purpose of participating in energy markets while taking in consideration different company´s use cases are less common. There are indeed a lot of publications around energy storage and battery sizing methods:[11] depicts a sizing methodology for a battery system providing frequency containment reserves in a power system with large wind power penetration,[12] also shows a sizing strategy of battery systems for smoothing power fluctuations of a PV/Wind hybrid system,[13]&[14] describe methods to size storage systems tied to PV systems while taking into account optimized energy dispatch schedule and[15] does the same but with the goal of minimizing operation costs. The latter is also something that many authors take into consideration - sizing storage while reducing costs: [16] demonstrates how to economically optimize battery storage for residential areas and[17] depicts how to calculate the levelized cost of energy for battery systems and also other renewable sources. It is easy to see that there are a lot of different approaches to energy storage sizing from all these references 8 annually by ENTSO-e. It is because of this obligation that TenneT procures FCR. •Frequency Restoration Reserves (aFRR) - For maintaining the realtime power balance of the Netherlands, TenneT mainly uses bids for regulating power (aFRR) and reserve power (mFRRsa) offered by market participants to TenneT. The activation (dispatching) of FRR bids for balancing takes place in real-time operations. This regulating and reserve power is exclusively for correcting the real-time power imbalance. •Manual Frequency Restoration Reserves directly activated (mFRRda) - TenneT uses the regulating and reserve bids for maintaining balance that have been made available by market participants. In addition, TenneT can use mFRRda, or incident reserves, for maintaining the balance in case of incidents and substantial long-lasting power deviations. •Manual Frequency Restoration Reserves scheduled activated (mFRRsa)- mFRRsa is reserve power that is used for balancing purposes. In contrast to aFRR, the bid has a call time of 1 PTU (Program Time Units) instead of a ramp rate. The call is the offered volume per PTU. These bids are not contracted. Starke Energy Operations As it has been explained before, Starke Energy acts as an aggregator of energy storage and uses its available capacity to perform services to its clients and to the utility grid. The former consist of lowering electricity power costs - normally in an electricity contract each client has to pay a fixed fee per kW connected, on a monthly basis, and a variable fee per kWh used during that period of time. By adding batteries to its clients building, Starke can lower the kW fee by making it possible to reduce the grid connection capacity. As for the services for the utility grid, the available storage Starke has acts as a reserve capacity which can be used to participate in the FCR markets. 15 Technology Virtual Power Plants can integrate many different units such as renewable energy generation PV and Wind Power plants, Combined heat and power units, and also flexible storage systems, for example batteries, super-capacitors or even flywheels. Starke Energy technology consist of batteries which are integrated in each client´s building and are all connected through the cloud. This means that the reserve capacity Starke has increases for each new project developed. Typically, since the company´s most common clients have buildings with significant consumption, it is wise for both Starke and its client, to analyze the potential of adding PV panels to integrate with the battery banks. However, Starke does not provide any PV infrastructure and only analyzes the potential of it. Sometimes panels already exist(or are already being installed by the client) and its the company´s job to evaluate if they are sufficient or if more should be added, and other times the building is lacking such infrastructure so the evaluation process consists of analyzing if it should be added or not. This section will, therefore, describe which battery technology is used by Starke Energy and how does the process of PV evaluation works. BESS + Inverter Description For the battery and inverter technology,at the moment of the Internship Starke was outsourcing all the infrastructure through CE+T (CE+T). Since each client can be significantly different, the battery power goes from 20kW to 240kW. As for the inverters, there are units of 20, 25 and 30 kW which can be stacked together to sum up to the necessary capacity. All of this is illustrated in figure 3, as well as the corresponding costs. To facilitate calculations in the model, the battery and inverter costs were changed to €/kW: •Battery smaller than 60kW = 369,21€/kW •Battery between 60 and 80 kW = 331,21€/kW •Battery larger than 80kW = 288,06€/kW •Inverter cost = 126,93€/kW 16 Figure 3: Battery and Inverter Prices PV Description As stated previously, Starke does not handle any PV infrastructure. It analyzes the building potential for PV panels by studying the roof conditions and using available software to make estimations. Regardless of whether the Client already possesses Photovoltaic units or not, the process of evaluation follows the same pattern. To conduct such calculations, the software being used was either HelioScope or a more simple tool called power calculator by IBC Solar (Solar Power Calculator). Firstly, the location of each project has to be inputted to get an accurate view of the building rooftop. The second step is to evaluate the presence of objects that can prevent panels from being assembled and to highlight them so that the software knows it cannot place an unit there. The next step is to automatically place the PV panels in the remaining space available and to troubleshoot different configurations until reaching the one with more energy production expected. Finally, all that is left to be done is simply printing the configuration worksheet to get the number of units, the kW per unit and the total kWh produced during one year. For the scope of the model, PV costs had to be estimated in order to perform important calculations such as the initial investment. The assumed costs were: •Greater than 50kW = 650€/kW •Between 35 and 50kW = 750€/kW •Smaller than 35kW = 950€/kW Behind the meter concept Any gas or electricity user – whether they are big or small, a domestic user, or a commercial or industrial organization – will have meters on their premises 17 that calculate how much energy has been taken from the grid and consequently how much is owed to the utility provider. However, there are two different types of meters and both depend on the energy system’s position in relation to the electric meter[36]. A behind-the-meter (BTM) system provides power that can be used on-site without passing through a meter, while a front-of-meter system provides power to off-site locations. The power provided by a front-of-meter system must pass through an electric meter before reaching an end-user. BTM systems can provide energy directly to households or businesses without going through an electric meter and interacting with the electric grid. If electricity has to pass through an electric meter to reach a given property, that electricity came from in front of the meter, or the grid. If electricity does not need to pass through an electric meter to reach such property, that electricity came from a BTM system. All electricity end customers sit behind the meter[37]. Figure 4: Behind-the-meter VS Front-of-meter Starke Energy batteries are installed behind-the-meter since the benefits are many. Firstly, BTM batteries can help consumers decrease their electricity bill, through demand-side management. Secondly, increased demand flexibility can unlock the integration of more renewable energy technologies in the grid. Thirdly, aggregated BTM batteries can provide support for system operation, while also deferring network and peak capacity investment. Finally, by aggregating numerous batteries Starke can create a large capacity and ensure frequency containment reserves to help the utility grid[38]. Types of Grid Connections Every electricity bill takes into account two cost components: a fixed cost per month related to the connection size in kW and a variable monthly cost depending on how much energy, kWh, the consumer used. At Starke, one of the most important parts of the analyze is to determine weather it is more valuable to upgrade or downgrade a client´s kW connection in order to maximize electricity savings. Therefore, it is important to clarify which connections exist, who are the suppliers and what are the prices they charge. Most of the company´s 18 Figure 5: Behind-the-meter possibilities clients had as their utility supplier either Liander or Stedin, so this section will focus on these two suppliers. First and foremost, there are several sizes of grid connections and sometimes they differ depending on the utility. Nevertheless, Liander and Stedin have exactly the same connections available, which are: •25A corresponding to 17.3 kW approx. •35A corresponding to 24.2 kW approx. •50A corresponding to 34.6 kW approx. •63A corresponding to 43.6 kW approx. •80A corresponding to 55.4 kW approx. •100A corresponding to 69.3 kW approx. •125A corresponding to 86.6 kW approx. •160A corresponding to 110.9 kW approx. •200A corresponding to 138.6 kW approx. •250A corresponding to 173.2 kW approx. 19 Each connection has different costs associated and depending on its size upgrading and downgrading costs also change. As it was stated before, there are fixed and variable fees associated with the power and energy consumed. Inside the fixed fees, the costs include a connection and a transport tariff as it is illustrated in table 1and table 2: Contract Tariffs Capacity per Connection/month Cost € Larger than 3x80A and smaller than 100kVA 11,32€ Greater than 100kVA and smaller than 160kVA 12,59€ Greater than 160kVA and smaller than 630kVA 47,84€ Table 1: Contract Tariffs - source: Liander (Liander Rates 2021) Transport Tariffs SubMarket Contracted Transport Capacity Fixed Duty rate per month in € Per kW per month - kW contract in € kW max per month in € LS up to 50 kW 1,50 0,76 0 MS/LS Greater than 50 to 136 kW 36,75 1,93 1,74 MS Greater than 136 to 2000 kW 36,75 1,23 1,74 Table 2: Transport Tariffs - source: Liander (Liander Rates 2021) Apart from these costs, it is also crucial for Starke´s operations to understand the costs related to the upgrade or downgrade of each connection. To facilitate, in the development of the model, the values used were solely taken from Stedin´s website (Stedin Fees) since Liander´s numbers could only be known by contacting the utility company itself. Since grid connection modifications costs are mostly related to changes in meters and other infrastructure, it was assumed the prices of both utilities were similar. These are illustrated in table 3 20 Upgrading Costs Downgrading Costs Grid Connection Change Cost of Upgrade € Grid Connection Change Cost of Downgrade € From 25A,35A,50A to 35A,50A or 63A 230,19 From 80A to any low grid 230,19 From 25A,35A,50A or 63A TO 80A 297,19 From 250A,200A,160A,125A or 100A to 80A 3324 From 25A,35A,50A,63A or 80A to 100A or 125A 5482,51 From 250A,200A,160A,125A or 100A to 63A,50A or 35A 3105 From 25A,35A,50A,63A or 80A to 160A,200A or 250A 6958,71 From 250A,200A,160A,125A or 100A to 25A 2664 From 100A to 160A,200A or 250A; From 125A to 200A or 250A; 8406 From 250A,200A or 160A to 125A or 100A 6929 From 160A to 250A 8406 From 250A to 160A 8406 Upgrading/Downgrading one level in high grid connections (100A or more) 262,4 Table 3: Upgrade/Downgrade Costs from Stedin 21 Method Description This section will consist in the explanation of everything that was needed to build the model, from the data used, where it was gathered, the equations applied to get results, the parameters which were chosen to be evaluated, and most importantly, how the model interacts with the user to reach the desired output. Project Based Optimization - Method Used In optimization there are several different types of modeling that can be used to solve a particular problem. Depending on its complexity, one can choose the most simple optimization - an LP or MILP, linear programming and mixed integer linear programming - or can opt for a more complex method if there are many scenarios to evaluate - for example, stochastic programming. The model developed with Starke is divided in two parts: the first part uses Starke Algorithm to predict the best possible ways to bid into the FCR market taking into account the degradation of the battery, the clients energy consumption, the electricity prices, etc. The second part, and the one described in this thesis, uses the output of Starke´s algorithm to analyze numerous scenarios with the goal of outputting the 3 best options for the client - one in which the grid is upgraded, another in which it is downgraded and a third in which it does not suffer any modifications. Therefore, given that there are many scenarios to be tested against each other, and given the timeframe and the complexity of the model, the algorithm created for the second part was developed in python with the help of the Pandas library. It was decided not to formulate any optimization model such as the ones mentioned above because the objective was to have a simple tool which could give faster results, and modeling that with optimization techniques would take a long time. Data Used The data used for the model was collected from the company clients as well as from external sources. From the client, the model needed as input the following: •The current grid connection 22 •The average monthly energy consumption •The number of PV panels and the total kWs (if PV panels existed already) •The location of the project In the case where no PV infrastructure exist, external tools like HelioScope and IBC Solar Calculator were used to calculate the maximum amount of PV´s that could fit in the building roof and how much those numbers translated into kW and kWh. The Model As it was stated before, the entire model is divided into two parts, which interact with each other. Firstly, Starke Energy algorithm was used to compute multiple scenarios depending on the type of grid connection the client had. For example, if the current connection was 80A, then this algorithm would output all the different possible combinations of a system with battery and PV for three different grid sizes: the actual one, the size below and the size above - in this case, 80A,63A and 100A. The objective of this part is to output, for each scenario, the following parameters: •Battery sizes for each scenario •PV sizes for each scenario - if the client already had PV panels, this parameter is always the same •FCR Revenue (€) •FCR times (Number of times that were used to bid) •Energy sold (How much energy was sold to the grid in €) •Energy bought (How much energy was purchased from the grid in €) •Number of battery cycles •Energy delivered to the grid in kWh •Energy consumed from the grid in kWh •Energy supplied for FCR •Energy consumed for FCR Examples of this output are going to be shown in the Results section. Secondly, using the algorithm developed for the purpose of this thesis, it is possible to go through all the scenarios outputted by Starke´s and narrow it down until only the best options for each 3 different grid sizes are reached. In the following chart, figure 6, it is illustrated the algorithm flow which was used to accomplish such task: 23 Figure 6: Model Flowchart FlowChart explanation 1. Starke´s algorithm output is loaded to the model and organized into a DataFrame for an easier visualization; 2. To estimate the current bill, the following equation was used: Bill =EnergyBought(£) −EnergySold(£) If the client building did not have PV infrastructure yet, then the value of Energy Sold is zero; 3. After having calculated the current bill, it is possible to estimate the potential savings for each combination: Savings =CurrentBill(£) −EnergyBought(£) + EnergySold(£) 4. The lifetime of the project is determined using the number of cycles provided by the model´s first part. To avoid overestimating, the model restrains the maximum lifetime to 15 years. The calculation goes as follows: Lifetime = 6000/cycles The variable cycles corresponds to the number of cycles per year and the number 6000 is the battery maximum number of cycles, approximately; 24 Figure 10: Case Study 2 Figure 11: Case Study 2 Results 31 Case Study 3 This last case study depicts a project in which the grid connection was already the largest one possible, with 173kW. That means that the model will only output two scenarios, the current and the downsizing one. In figure 12 this is easily visible as the number of scenarios is way shorter, with only 13 combinations being tested. Another reason for this is that the client has already analyzed the PV possibilities for the building concluding therefore that 100kW would be installed. Figure 12: Case Study 3 Both results show positive outcomes and in this case, in contrast with case 1, the best solution involves the largest grid connection. The reason for such outcome is that for the same PV capacity, a smaller battery was used in the second option. Moreover, this is also due to the fact that the latter is also the current grid size of the client, which means that there are no upgrading costs involved. The results of this case are shown in figure 13. 32 Figure 13: Case Study 3 Results 33 Conclusions The objective of this thesis was to highlight the importance that business oriented models have in the daily operations. Furthermore, the model explained here was created to benefit Starke Energy but also as an example to other companies which also participate in electricity markets on how to turn their sizing techniques more efficient and to leverage their algorithms even more. In general, the conclusions of this work regard both technical and business characteristics, but most importantly, the latter. The technical conclusion is that sizing an energy storage model has many external factors and sometimes the best scenario does not much what would normally make sense in the first place. Another technical aspect that can be derived from this analyze is that there are many assumptions involved and by altering just one single one of them can give out an entirely different business case. Therefore, it is highly critical to ensure that all the assumptions were properly defined and that many cases were tested before using the model as granted. Unfortunately, since working in a Startup is a fast-paced environment, it is not 100% accurate to assume there are not any small errors in the model or that some improvements can not be made. As for the business perspective, this model gave out very promising conclusions. From feedback directly from the company Software Engineer (see figure 14), in charge of the sizing of projects, it was concluded that using the model instead of hand calculating and guessing results, increased the efficiency of the cases, making them run in a couple of days instead of weeks. Secondly, it was concluded from professionals with experience in the area that the model output is in line with what would be expected for each projected evaluated. Finally, it can also be said that using this model is in a way maximizing the overall welfare of both the company and the client, saving money, time and improving productivity. 34 Figure 14: Interview to Starke´s Energy Software Engineer 35 Annexes 36 Figure 15: Case Study 2 full table 37 Figure 16: Case Study 1 Results full table 38 Figure 17: Case Study 2 Results full table 39 Figure 18: Case Study 3 Results full table 40