Impact of Distributed Generation on Energy Loss: Finding the Optimal Mix

(1)

Impact of Distributed Generation on Energy Loss:

Finding the Optimal Mix

N.N. Croes

(s1454811)

(2)

Master Thesis Operations Research Supervisor TNO: Drs. F. Phillipson

(3)

Impact of Distributed Generation on Energy Loss:

Finding the Optimal Mix

N.N. Croes

Abstract

(4)

Preface

This thesis is the result of my graduation project for my master’s degree in Operations Re-search at the University of Groningen and is written during my internship at TNO Information and Communication Technology.

I am very thankful for the support and encouragement I have received and would especially like to thank my supervisor Frank Phillipson for his patience and guidance, and all the valuable feedback he has provided during my internship at TNO. Working at TNO gave me the opportunity to meet many fun and interesting people who gave me advice and encouragement. I would like to thank them as well.

(5)

Summary

Distributed power generation is becoming more attractive as it relies on renewable energy sources, such as solar panels, or achieve higher efficiencies in power generation. Distributed generation can increase efficiency in the grid by reducing the distance between generators and consumers of electricity. In addition, distributed generation can provide security of energy supply and contribute to a diverse energy portfolio. Since the Dutch government is promoting the use of distributed generators (DGs) by e.g. implementing a feed-in premium, it is expected that there will be a significant increase in share of DGs in the energy supply.

DGs exhibit high fluctuations in production over time, so electricity generated by DGs will probably not match load demand and can cause over- or underproduction of electricity. In this thesis we design a mathematical optimization model of the energy grid where the infrastructure, supply and demand, and their mutual effects are modeled. Using this model we find the optimal mix of DGs in a district by minimizing energy loss while making sure that all demand is satisfied. In addition, we avoid overload in cables and transformers. The DGs that we consider are micro Combined Heat and Power (micro-CHP) systems and Photo Voltaic (PV) solar cells. Note that energy grids can include the supply of electricity and heat; for simplicity we only consider the supply of electricity. This means that the results and conclusions are only for the power grid without the consideration of heat demand and production.

We focus on a district consisting of only houses. In this district all houses can generate their own power using decentralized power generation. Any overproduction is supplied back to the grid. We include a storage system in the model to help capture overproduction and if possible reduce energy loss. In addition, we model extra demand from heat pumps (that rely on electricity) and electric vehicles.

Using the data provided by TNO we construct a case study. Depending on the various assumptions, such as whether it is allowed to transport overproduction to other districts or use the storage system, and if there is additional demand from electric vehicles and heat pumps, we obtain different results. This means that we have obtained several solutions in the case study each under different assumptions. However, all results indicate that implementing an optimal mix of DGs in the district can reduce energy loss substantially.

Without the consideration of additional demand from electric vehicles and heat pumps, no overload occurs in the optimal solutions. But when these additional demands are included in the model, overload occurs where not even one electric vehicle can be charged at home without overloading the system. Hence, if we want to introduce electric vehicles and heat pumps in the districts, we must first reinforce the grid to be able to withstand such a large increase in electricity demand.

(6)

List of Abbreviations

AC Alternating Current

CAES Compressed Air Energy Storage DC Direct Current

DG Distributed Generator

DSO Distribution System Operators Energiekamer Dutch Office of Energy Regulation EV Electric Vehicle

GRG Generalized Reduced Gradient

HP Heat Pump

HV High Voltage

Hz Hertz

kVA kilo Volt-Ampere

kW kilo Watt

kWh kilo Watt hour LP Linear Programming LV Low Voltage

Micro-CHP Micro Combined Heat and Power MILP Mixed Integer Linear Programming MINLP Mixed Integer Non-Linear Programming MIQP Mixed Integer Quadratic Programming MV Middle Voltage

NaS Sodium-Sulfur NiCd Nickel-Cadmium NiMH Nickel-Metal Hydride NiZn Nickel-Zinc

PV Photo Voltaic (solar panels)

QCQP Quadratically Constrained Quadratic Programming QP Quadratic Programming

RMS Root Mean Square

SMES Superconducting Magnetic Energy Storage TSO Transmission System Operator

(10)

1 Introduction

Every year a staggering 400 million euro is lost due to transportation of electricity (Source: TNO). Distributed power generation is expected to play a crucial role in reducing transporta-tion loss and meeting future energy demand. In most cases these distributed generators (DGs) are based on renewable energy such as Photo Voltaic (PV) solar cells and wind turbines, but there are also new technologies to increase efficiency such as the micro Combined Heat and Power (micro-CHP) systems.

Another reason why distributed generation is becoming more attractive is that it can provide security of energy supply and contribute to a diverse energy portfolio. Concerns regarding environmental issues, in particular global warming and exhaustion of non-renewable energy resources, are also on the rise.

The Dutch government is stimulating the use of renewable energy sources by supplying a feed-in premium. This way they hope that consumption of renewable energy sources becomes more attractive and that greenhouse gas - primarily carbon dioxide - emissions are reduced. The aim is to increase the share of renewable energy to 20 percent of total energy supply by 2020. Since the Dutch government is promoting the use of DGs, it is expected that the share of DGs in energy supply will increase significantly.

Although the introduction of DGs looks promising, the challenge however will be to opti-mally integrate the increasing number of small generation units in an electricity system that up to now has been very centralized, integrated and planned (Pepermans et al., 2005). Since most DGs rely on exploitation of natural sources of energy they exhibit high fluctuations in production over time. This means that electricity generated by DGs will probably not match load demand and can cause over- or underproduction of electricity. The current technolog-ical solution to solve possible transport problems is to reinforce the existing grid. This is very expensive and is avoided as much as possible. Another more futuristic solution is to make the grid smarter by controlling fluctuations in production and consumption. This more ‘intelligent’ grid is referred to as the smart grid.1

The study of smart grids can be divided into three levels: the lowest level is the infras-tructure, the middle level is the coordination of production and consumption, and the highest level is the business model. We focus on the lowest level of energy grids: the infrastructure. However, smart grid technologies are far from large scale deployment. Instead of immediately deploying smart grids, it would be interesting to take a look at a step in between the transition of current grids to smart grids.

One way to avoid grid reinforcements and smart grids is to find an optimal mix of DGs while keeping network capacities in mind. We need to make sure that all demands are satisfied, by power plants and/or DGs. Each DG type has a different production pattern depending on e.g. the sun, wind or heat demand, that may complement each other. When there is sunshine (or wind) all PV solar panels (or micro wind turbines) in the district will generate electricity at the same time, leading to a sudden increase in generated electricity. If all houses in a district have the same DG type, then it will probably be less efficient compared to a district with an optimal mix of DGs. Hence, finding such an optimal mix can provide a better understanding of the effects of DGs on energy loss in the current power grid.

The thesis is organized as follows. In Section 2 we discuss the objective, importance and scope of the research. Section 3 gives an overview of energy models in the literature. The

(11)

optimization model with all it characteristics and assumptions is discussed in Section 4. The demand and production data are discussed in Section 5. In Section 6 we give an overview of solutions methods and in Section 7 we explain how the model is solved. The obtained results are discussed in Section 8. In Section 9 we give the limitations, interpretation and implementation of our results. In Section 10 we conclude and in Section 11 we give directions for further research.

2 Goal of the Study

We will design a mathematical optimization model of the energy grid where the infrastruc-ture, supply and demand, and their mutual effect are modeled. The objective of the model is to minimize energy loss. Different profiles of DGs are defined and used as input. We include capacity constraints into the model so that overload is avoided. Then from this model optimal combinations with respect to energy loss are determined. We should be able to answer the following question using this model:

What is an optimal mix of distributed power generation so that energy loss is minimized?

Note that energy grids can include the supply of electricity and heat; we only consider the supply of electricity. Aside from reducing transportation loss, finding the optimal mix of DGs in the current grid with its capacities is a way to avoid expensive grid investments or waiting for the introduction of smart grids. This model will also give more information on how these DGs work together and find out whether there are any complementaries between them. This depends on the DGs’ production patterns. By looking at the demand patterns of future electronic equipments such as electric vehicles and heat pumps2, we can additionally find out whether they can be compensated by some mix of DGs.

In smart grids supply and demand are matched as much as possible by controlling con-sumption and production. To see whether a smart grid is working optimally one would need to measure the efficiency of the grid where supply and demand are matched. Furthermore, when modeling smart grids one is looking to match supply and demand locally. In this thesis we match supply and demand in a district, which is also a local optimization. This means that by looking at efficiency and optimizing locally, our model can be used as a starting point for modeling smart grids.

This thesis is partly based on another research conducted by TNO. Due to the fact that their research is confidential, the source will not be made public. From their research we obtain a simulation model to calculate loads and losses. In addition, we incorporate many of their assumptions, such as the demand and production profiles, capacity of transformers and cables, and the average energy loss percentages. Instead of referring to the confidential sources we will reference them as: the research conducted by TNO.

2.1 Energy Loss

By looking at the efficiency of the grid we can get a good indication as to how the grid is functioning, and since energy loss and efficiency are closely related we can use energy loss

2

(12)

as a measure for efficiency. Each time electricity is transported there is energy loss. And when electricity is transported over long distances, it is transformed to higher voltage levels to reduce energy loss during transportation. But transforming electricity into higher or lower voltage levels also creates energy loss. So the smaller the distance between feeder and load, the lower the energy loss and the more efficient the system.

Distribution System Operators (DSOs) are especially interested in energy loss. Every year transportation loss costs the DSOs in the Netherlands 400 million euro (Source: TNO). They have to compensate for the actual losses, while they receive ‘standard’ - fixed by the government - loss payments from consumers. The lower the actual losses the higher their profit, so they have an incentive to reduce losses. DGs can have a big effect on energy loss in the distribution grid. The use of DGs can reduce energy loss, but too many DGs can again increase losses, as is shown in Section 3.2. DSOs will be greatly affected by the growing level of DGs in the distribution grid. Hence, it will be interesting to see how the penetration of DGs affects the efficiency of the grid.

The reason why we did not include costs in the model is that it will make the model more complex. The price of electricity consists of three elements: supply, transportation and taxes. Supply prices are set by the suppliers, and transportation costs and taxes are regulated by the government. Transportation costs are paid to the network operator for the transport of electricity and maintenance of power cables. The transport price of electricity is thus composed of several elements and is furthermore fixed by the government. This means that the price of electricity will not give us the real cost of transportation losses. Hence, minimizing cost as objective does not provide us with a better understanding of how DGs affect the grid.3

The goal of reducing energy loss can also be seen as a way to contribute to sustainability. If less energy is wasted, less energy sources are needed. This will put less strain on the environment. In addition, the demand for electricity is increasing and many are concerned on how to satisfy these additional energy demands. Reducing energy loss and finding other sustainable ways to generate electricity helps to alleviate future energy problems.

2.2 Distributed Generation

There is currently no consensus as to how to define distributed generation. A question-naire submitted by the International Conference on Electricity Distribution (CIRED Working Group No 4, 1999) to the member countries confirms this. In this research some countries defined distributed generation on the basis of voltage level or maximum power rating, while others relied on the type of prime mover (e.g. renewable or co-generation). Some countries considered distributed generation as generation which connected to the distribution grid, i.e. where consumers are connected to and are supplied directly.

It is also common to define it as a combination of these descriptors. The International Council on Large Electric Systems (CIGRE Working Group 37-23, 1998) defined distributed generation as: (i) not centrally planned, (ii) today not centrally dispatched, (iii) usually connected to the distribution network, and (iv) smaller than 50 - 100 MW, where not centrally planned or dispatched means that major influences are out of control of the system operator. Due to such a diversity in definitions, a DG can be as large as a wind park or as small as a solar panel. We only consider DGs that are expected to be widely used by 2020 and that

3

(13)

can fit in or on a house. These are solar panels, micro wind turbines and micro-CHP systems. On the demand side, we include the use of heat pumps and electric cars, which is expected to be widely used in the future.

2.3 The Dutch Power Grid

An electricity supply system comprises of three main components: power generation, trans-mission and distribution. In Figure 1 a simple diagram of the Dutch power grid is shown. The High Voltage grid will be referred to as the HV-grid, the Middle Voltage grid as the MV-grid and the Low Voltage grid as the LV-grid.

Figure 1: A Diagram of the Dutch Electricity Grid

(14)

The MV-grid connects a HV/MV substation to several MV/LV substations. In HV/MV substations a transformer converts high voltage power into middle voltage and in MV/LV substations middle voltage is transformed into low voltage. MV-grids transmit electricity with power between 10 and 20 kV.

Houses are connected in series to a single linear cable, also referred to as the trunk. Multiple trunks are then connected again to a single linear cable, which is connected to an MV/LV substation. In LV-grids electricity is transmitted at 0.4 kV.

Transmission refers to the transportation of high voltage electricity over long distances (HV- and partly MV-grids) and is managed by the Transmission System Operator (TSO). In the Netherlands TenneT is appointed as the TSO. The distribution of electricity has to do with the transportation to consumers in the grid, i.e. LV-grids and partly MV-grids. The distribution grids are managed by the DSOs.

Most power stations in the Netherlands are natural gas power plants but there are also some coal-fired power plants, biomass power plants and one nuclear power plant. There are a few offshore wind farms and a few small hydroelectric power stations.

We focus on a district connected to an MV/LV substation. This is illustrated by the selection in Figure 1. The reason that we choose to model only houses is that there are too many different types of industries and businesses, from mining to offices and swimming pools. Each have quite a different demand pattern which makes it difficult to model.

All houses can generate a part of their demand using decentralized power generation; any overproduction is sold back to the grid. So there will be a bi-directional flow of electricity in the grid. We also include storage systems in the model to help capture overproduction and if possible reduce energy loss. Whether it will actually reduce energy loss depends on how efficient storage technologies are.

3 Related Work

The aim of this section is to give an overview of energy models that have been proposed and used in the literature. Since the paper of M´endez et al. (2002) focuses on the effects of DGs on energy loss, we go more into details and discuss their key findings. In addition, we discuss several types of storage technologies that are currently available or still under development.

3.1 Overview of Energy Models

There is a wide range of different types of energy models with different approaches and objectives. The review papers by Jebaraj and Iniyan (2006) and by Hiremath et al. (2007) give a good overview of energy models presented in the literature. We also discuss the papers of Singh et al. (2008) and Mashhour and Moghaddas-Tafreshi (2009) which have some similarities to our problem.

Jebaraj and Iniyan (2006) gives an overview of energy models that have been emerging over the last few years. The following types of energy models are discussed: energy plan-ning models, energy supply-demand models, forecasting models, optimization models, energy models based on neural networks and emission reduction models.

(15)

Mixed Integer Linear Programming (MILP) and linear complementarity programming mod-els. These models are used to optimize energy production, transportation, distribution and utilization with respect to cost.

Belyaev (1990) presents an approach to the solution of decision problems using a pay-off matrix. Stochastic variables are used to represent uncertainty for data that are not precisely known. These are modeled for several scenarios and are put into a pay-off matrix. Using this pay-off matrix a decision is made.

In the articles on optimization models more often than not the objective is to minimize costs. See for example De Musgrove (1984) and Satsangi and Sarma (1988). De Musgrove (1984) uses the MARKAL, a Linear Programming (LP) model with total system discounted cost as objective, to analyze the Australian energy system during 1980-2020. Satsangi and Sarma (1988) discusses the possible options for meeting energy needs of the economy for India for the year 2000-2001. The objective is to minimize cost, based on resource, capacity and upper/lower bound constraints.

Suganthi and Jagadeesan (1992) presents the Mathematical Programming Energy-Economy-Environment (MPEEE) model, where the GNP/energy ratio based on environmental con-straints is maximized to meet energy requirements for India in the year 2010-2011. Luhanga et al. (1993) gives an overview of energy planning research on implementation of the Long range Energy Alternative Planning (LEAP) model by using optimization models in combi-nation with a forecasting model for Tanzania. Two models are presented: the first one is to find the optimum mix of energy sources at minimum cost, and the second one is to find the optimum number of end-use biomass devices and hectare of land to be afforested to minimize the wood fuel deficit.

Iniyan and Jagadeesan (1998), Iniyan et al. (1998), Iniyan et al. (2000) and Iniyan and Sumathy (2000) discuss different adaptations of the Optimal Renewable Energy Model (OREM), which has been formulated to find the optimum level of utilization of renewable energy sources. The model aims at minimizing cost/efficiency ratio and finds the optimum allocation of different sources for various end-uses. The constraints used in the model are social acceptance level, potential limit, demand and reliability.

To solve the energy resource allocation problem Chedid et al. (1999) presents a fuzzy multi-objective LP approach. The multi-objective optimization problem has the following six objectives: (i) minimizing cost, (ii) maximizing efficiency, (iii) minimizing imported petroleum resources, (iv) maximizing the use of local resources (v) maximizing energy related jobs, and (vi) minimizing emissions (COx, NOx, SOx).

Hiremath et al. (2007) gives an overview of different decentralized energy planning mod-els, with their approaches and applications. The different types of models are classified by: the purpose of energy models, the model structure (internal and external assumptions), the analytical approach (top-down or bottom-up), the underlying methodology, the mathemati-cal approach, the geographimathemati-cal coverage (global, regional, national, lomathemati-cal, or project), sectoral coverage, time horizon (short, medium, or long-term), and data requirements.

Despite of having a different objective, Joshi et al. (1992) provides an interesting and useful insight for obtaining an optimal mix of energy sources. An LP model to minimize the cost function for an energy-supply system consisting of a mix of energy sources and conversion devices is presented. The model is applied to a typical village in India for both domestic and irrigation sectors.

(16)

substantial differences between these two. For example, our objective is to minimize energy loss and thus means that we have a different objective function. Another example is the type of variables used in the optimization model. Energy sources can be petroleum or wood, and DGs can be wind turbines or solar panels. To model DGs one uses binary variables, while when modeling energy sources the decision variables are nonnegative real numbers. So these models cannot be used to solve our problem.

There are two other papers that are slightly more related to ours. Singh et al. (2008) minimized energy loss for optimal sizing and placement of distributed generation using a genetic algorithm. This paper discusses a simulation approach for the optimal sizing and placement of a DG for a minimum annual energy loss with time varying load model. It is made sure that the voltage levels are within the acceptable range and that the line flows are within limits. This paper focuses on the quality aspects of electricity, so voltage levels and reactive power are also considered (see Section B.1.1 for an explanation of these technical terms). This means that the model in Singh et al. (2008) is too complex for our purpose.

Mashhour and Moghaddas-Tafreshi (2009) presents a multiperiod optimization model for a micro grid, aimed at maximizing its benefit, i.e. revenues-costs. The optimization model includes the use of DGs relying on wind and solar, an electrochemical storage and interruptible load. DGs are incorporated into the low voltage grid where both technical and economic aspects are considered. The obtained problem is a Mixed Integer Non-Linear Programming (MINLP) problem and is solved using a genetic algorithm. Even though this model minimizes cost, we obtain a model with similar structure due to the fact that it also tries to find an optimal mix of DGs. This similarity is especially present in the constraints of the storage system and DGs. Mashhour and Moghaddas-Tafreshi have gone one step further and allow the DGs and storage system to be controllable. This creates a system resembling the smart grid.

3.2 Effect of DGs on Energy Loss

The search for the optimal penetration level4 of DGs is graphically depicted by Scheepers and Wals (2003) in Figure 2. This graph is based on a study by M´endez et al. (2002) where they modeled several scenarios of DG penetration levels, DG dispersions and DG mixes.

The idea is that because the distance between feeder and load is reduced, the transporta-tion losses decrease. But as Figure 2 shows, this only applies to a certain DG penetratransporta-tion level. Once the optimal penetration level of DGs is reached the losses increase again. Higher DG penetration levels lead to situations where local production exceeds local consumption. This overproduction has to be converted into higher voltage levels and transported further away. Converting electricity from one voltage level to another creates loss and transporting electricity also creates loss, which thus means that overproduction will ultimately create more loss. So if too many houses start generating electricity, the increase in penetration levels of DGs becomes more of a disadvantage than an advantage. This graph gives a good illustration of what we are looking for.

The study concludes that for low DG penetration levels energy loss decreases, but that for higher penetration levels energy loss starts to increase and can ultimately become higher than the losses in the base base. In addition, minimum losses are reached with high penetration levels if DG is sufficiently dispersed. Reactive power is also considered in the study and it

4

(17)

Figure 2: Variation of Distribution Losses Due to DG Penetration, Scheepers and Wals (2003)

turned out that controlling reactive power supplied by DGs have a big impact on distribution losses.

3.3 Energy Storage

Solar panels and wind turbines have high fluctuations in their production due to constantly changing weather conditions. It will be difficult to match their peak power outputs with the power requirements. In the case of micro-CHP systems, which depend on heat consumption, energy production is less fluctuating than solar panels and wind turbines, but it still is variable. Moreover, when DGs generate electricity it does not necessarily mean that there is actually a demand for it. So usually supply will not be equal to demand. A solution may be to have storage systems installed so that any overproduction can be stored and underproduction compensated. In this way the amount of energy generated by these DGs can be smoothed out over time which may help match demand and supply.

There are many types of storage technologies available, where each type is suitable for certain situations. In Appendix B.4 we discuss the most important energy storage methods available or under development. These are flywheels, battery storage, supercapacitors, Su-perconducting Magnetic Energy Storage (SMES), hydrogen storage, pneumatic storage, and pumped storage.

3.3.1 The Main Uses of Energy Storage

Energy storage systems can have different purposes and can be used in different ways. Leeds (2009) and APS (2007) have summarized four ways to use energy storage systems.

(1) The storage system can harness power of renewable energy by capturing energy that is generated when there is little demand. In this way the storage systems is used to store overproduced electricity so that overproduction does not go to waste and thus preventing unnecessary energy loss.

(18)

There are two types of power plants: one is the base-load power plant which generates electricity at a ‘cost effective’ rate, and the other one is the peak-load power plant which relies on flexible sources (mostly fossil based) to provide quick responses to fluctuating demand. Most peak-load power plants are expensive to run so they are avoided as much as possible. Storage systems can act as buffer between DGs and the main grid by filling in ‘supply valleys’ and shaving ‘supply peaks’, and thus reducing the need for building more expensive peak-load power plants.

(3) Storage systems can be used to increase the overall power quality of the grid. Power fluctuations, even for a few milliseconds, can cause computer-based systems to fail. As we are relying more and more on digital technology, the cost of outages is increasing. Many industries manufacturing computer-based systems require Uninterruptible Power Supply (UPS), also known as battery back-up, that can provide stable voltages and frequencies. So storage systems can quickly provide power to the grid and stabilize voltage levels as well as matching frequency of electricity between a storage device and the grid. See Appendix B.1.3 for further discussion on quality aspects of electricity. (4) Storage systems can also act as back-up power source for short power failures, e.g.

brownouts5 _{and blackouts, by providing power to the grid or until back-up generation}

has been started up. It is especially useful in areas that are prone to power outages and may help to delay the need for expensive investments in the grid.

Hence, energy storage systems can be used in quite different ways and energy grids with DGs need energy storage systems to be able to handle the variability in production. The other uses of energy storage systems are extra measures to increase reliability and quality of electricity. Since our focus is more on finding an efficient mix of DGs in the current grid and not necessarily on the reliability, we will only let storage systems function as a storage for overproduced energy from DGs and avoid overproduced energy going to waste.

3.3.2 Number of Storages in District

It is possible that all houses have their own energy storage system or that each district has a centralized energy storage system. The advantage of an energy storage system in each house is that for the homeowners there is more control over the retainment and release of energy from their own energy storage system. They can for example choose to make a buffer for emergency purposes or use it immediately when needed. But our goal is to balance supply and demand in the whole district and not necessarily for a house. Furthermore, it is expensive to have an energy storage system in each house, while the whole district can share one. So for our purpose one centralized storage system fits best.

Our decision for choosing one centralized storage system is supported by the Power Home project by KEMA (for Essent together with TNO), where they looked at the effect of installing storage systems in residential districts and in households (Lysen et al., 2006). It turns out that storage systems at district level is preferred over storage in households. So their research supports our decision to include only one centralized energy storage in the district.

However, we do want to add that in the near future electric vehicles are expected to be widely used. To charge their batteries these vehicles will be connected to the main grid. This

(19)

means that their batteries can also be used as storage systems for overproduced electricity from DGs; this is referred to as ‘vehicle-to-grid’. But to be able to use electric vehicles as storage systems we will have to make decisions and assumptions on many different factors. Examples are deciding when and where the storage system is used (at home, at work or only at night), and how much is allowed to be discharged (enough to be able to get to work or hospital). Since these issues are still being studied, the possibility for vehicle-to-grid is excluded from our analysis.

3.3.3 Storage Technology Type

The decision on the appropriate storage technology depends on a number of factors, includ-ing storage capacity, spacinclud-ing and environmental constraints, cost, and location of storage. As previously discussed, the purpose of the storage system is to store any overproduced en-ergy from DGs. This means that the storage system has to be able to fit in a district and should be able to retain most of the district’s overproduced energy to avoid importing and exporting. In Appendix B.4.8 we compare several storage technologies and see which ones fit our requirements best. The choice of storage technology is between lead-acid batteries, sodium-sulfur (NaS) batteries and vanadium-redox flow batteries.

4 The Optimization Model

In this section we design a mathematical optimization model to find an optimal mix of DGs such that energy loss is minimized. We focus on a district consisting of only houses, where each house can generate a part of their demand using DGs. When there is overproduction it is supplied back to the grid. We also include a storage system in the district so that overproduction can be stored. The optimization model needs to make sure that demand is always satisfied and that overload is avoided as much as possible.

We start by discussing the overall interpretation of the model, such as how variables are defined, what the assumptions are, how energy loss is estimated and how overload is avoided. Then we discuss the different parts of the mathematical model and give an overview.

4.1 Power Flow and DG Variables

To match supply and demand there are a few different possibilities as to who supplies elec-tricity to whom. We have the following entities: ‘power plants’, ‘district’, ‘other districts’, ‘storage system’ and ‘house’. The power flows between these entities are depicted in Figure 3. The entity ‘power plants’ can only supply, ‘district’ can give and receive power, ‘other dis-tricts’ can only consume, ‘storage system’ can retain and release, and ‘house’ can supply and consume.6

All variables representing power flows are denoted by P.. where the indices correspond

to the following entities: ‘p’ stands for power plants, ‘o’ stands for other districts, ‘d’ stands for district, ‘s’ stands for storage, and ‘h’ stands for house. This means that the amount of electricity imported ‘from power plants to the district’ is denoted as Ppd. Similarly, for power

flows ‘from the district to other districts’ are denoted as Pdo, power flows ‘from storage to

6

(20)

Figure 3: Power Flows in Mathematical Model

district’ and ‘district to storage’ are denoted as Psd and Pds, respectively, and for ‘district to

house i’ and ‘house i to district’, Pdh,iand Phd,i, respectively, where i = 1, . . . , n and n is the

number of houses in the district.

The demand and production of electricity are measured in time periods. Consequently, the power flows in the district are calculated for each time period. To include this in the model, we add an extra index t ∈ {1, . . . , T } which stands for the time period [t − 1, t). So all variables above representing power flows have this extra index. We have the following variables Pt

pd, Pdot , Psdt , Pdst , Pdh,i,t and Phd,it denoting power flows at time t.

For each house the decision variables are whether a DG type is present or not. This means that we have binary decision variables for each house and each DG type. Suppose that we have n houses and m DG types, then for i = 1, . . . n and j = 1, . . . , m we have

DGi,j =

1 if house i has DG type j, 0 otherwise.

4.2 Some Initial Assumptions

Since we focus on one district connected to an MV/LV transformer, we do not model power plants, neither other districts’ production and demand. Therefore we need to make some assumptions on their behavior. To make sure that there is enough electricity generated to satisfy the whole district’s demand, we assume that power plants always supply the remaining demand of electricity. And because we do not know how much electricity is generated in other districts, we assume that the district only imports electricity from power plants. Furthermore, we assume that electricity exported to outside the district can always be consumed by another district. This way we avoid the issue of whether other districts can consume the overproduced electricity or if it will be wasted energy. To summarize, power plants always make sure that demands are satisfied and the other districts always make sure that overproduced electricity is consumed.

4.3 Energy Loss

(21)

• the loss of transporting electricity from power plants all the way to the houses in the district

• the loss of exporting electricity from the houses in the district to houses in other districts • the loss of transporting within the district, i.e. (i) from one house to another and (ii)

between the houses and the storage system • the loss of using the storage system

The loss of transporting electricity consists of losses in cables and/or losses in transformers. Cable losses have to do with the heat generated in cables. The higher the resistance in cables the higher the losses. As different materials have different resistances, cable losses depend on the material used as conductor.

In transformers energy is dissipated in the windings, core, and surrounding structures. Transformer losses are divided into losses in the windings, termed copper loss, and those in the magnetic circuit, termed iron loss. Copper losses are heat losses in the coils and are considered quantitatively as most important. In both cables and transformers, loss depends on the ambient temperature. The higher the temperature, the higher the losses. So in the summer losses are higher than in the winter. See Appendix B.2 for more information on cables and transformers.

When using the storage system energy loss is created due to self-discharge and inefficiency. The latter one is the loss of transforming electricity into e.g. mechanical or chemical energy (depending on the storage technology), and then back again into electric energy.

Note that electricity from the main grid is provided as Alternating Current (AC), while some electrical equipment (such as solar panels and batteries) generates Direct Current (DC) power. To transform one to another one would need an AC-DC or DC-AC converter which induces energy loss. Also, some generators supply reactive power. This leads to an increase in reactive power in the system and creates more energy loss. For more information on AC, DC and reactive power see Appendix B.1.1. To be able to include the calculation of these losses in the model, we would have to include complex technical terms, such as voltage levels and current flows. These are beyond the scope of this thesis and will be excluded from the model.

4.3.1 Average Loss Percentages

There is limited data on the size of network losses. The total network losses are estimated by EnergieNed (1996) at 7 to 8 % of the power consumed for the entire chain, i.e. from power plants to consumers. To find out whether incorporating DGs in the district decreases energy loss, we need to make some assumptions on the power losses in High-, Middle-, and Low-Voltage grids.

(22)

These percentages are averages and exclude the effect of temperature changes and different conductor materials.

For the the calculation of energy loss from using the storage system, the efficiencies and self-discharge rates for different storage technology types are reported in Appendix B.4.8. It is expected that in the near future these technologies will be more developed and have higher efficiencies. We model a (not yet existing) storage system with a low self-discharge rate and a high efficiency. This futuristic storage system will be referred as StorageX, and we choose a self-discharge rate of 2% per month and an efficiency of 95%. We model scenarios of different self-discharge rates and efficiencies to find out how efficient a storage system should be so that it will be used in the district and how different storage efficiencies affect the optimal mix of DGs.

4.3.2 Calculating Transportation Loss

To find out how to calculate transportation loss in the model we need to use some technical electrical terms. These are briefly discussed below (see Appendix B.1.1 for more details). Electric power depends on voltage and current as is shown in the following equation

P = I · V,

where P = the electric power (in Watt), I = the electric current (in Ampere) and V = the potential difference (in Volt). This equation implies that, keeping voltage the same, a higher amount of power requires a higher current flow. Joule’s law states that

Q = I2· R · t,

where Q is heat generated (in joule) for a time t. This equation implies that, if resistance is kept the same, higher current levels lead to higher generated heat. And as heat is power loss, higher current causes more power loss. In a nutshell, more power leads to higher current (keeping voltage the same), and as a result more heat is generated and thus leads to higher energy loss.

These equations show that energy loss has a quadratic relation to load: the higher the load the higher the relative loss. So we cannot simply multiply the average loss percentages (7.5%, 6.9%, and 1.1%) with the power flows, because then the quadratic relation between loss and load will not be present in the model. Furthermore, these percentages are for the electricity grid without distributed generation. In the research conducted by TNO, they have dealt with these issues as follows:

(1) To include the quadratic relation between loss and load, one should quadratically nor-malize the power loss percentage for each day whilst making sure that it still equals the average percentage. The reason to normalize it for each day is because the daily consumer profile does not change much. Define vt as the load for time period t and

` ∈ [0, 1] as the average loss fraction. Then the power loss wt at time t is calculated as

wt= vt2× ` ×

P

t∈dayvt

P

(23)

(2) The obtained average loss percentages are for the current grid. But because we model a district with DGs, these average percentages of loss in the grid can turn out to be higher or lower. This follows from the quadratic relation between loss and load. Since we do not know the average loss percentages in a grid with DGs we will first normalize the load in the grid with DGs (xt) by the load in the current grid (vt) for each time

period t. Then we multiply it by the loss as calculated in the current grid. So the power loss in the grid with DGs yt at time t is calculated as

yt = xt vt 2 × wt = xt vt 2 × v2_t × ` × P t∈dayvt P t∈dayv2t ! = x2_t× ` × P t∈dayvt P t∈dayvt2

4.3.3 Incorporating Transportation Loss

In the method discussed above the transportation loss is calculated for each time period, where the load is multiplied by ` ×

P

t∈dayvt

P

t∈dayvt2

. This term depends on the total sum of load in the corresponding day. As a result we obtain a different loss coefficient for each day, leading to a large objective function containing many loss coefficients. While having only one loss coefficient for importing from power plants, one for exporting to other districts and one for transporting within the district leads to a much simpler and smaller objective function.

Since loss has a quadratic relation to load, we will use quadratic regression to obtain these loss coefficients. The methodology is explained as follows. Using a simulation model obtained from the research conducted by TNO (which calculates transportation loss using the method explained in the previous subsection), we calculate the loads and losses in four scenarios: the current scenario (the grid without DGs), the quarter mix scenario (a quarter of the houses have all DGs), the half mix scenario (half of the houses have all DGs) and the maxed out scenario (all houses have all DGs). In each scenario we obtain loads and losses of (i) importing electricity from power plants, (ii) exporting to other districts, and (iii) transporting within the district. To obtain the loss coefficient for each of these three cases we apply quadratic regression on the corresponding loads and losses.

We start by estimating the loss coefficient of importing electricity from power pants. The resulted load data of all scenarios and all time periods are put into one vector x to represent the different loads of import over a whole range of scenarios, from no DGs to a lot of DGs in the district. The same is done for the resulted loss data which are put into vector y representing the loss data corresponding to the loads of import in x. Then we have the following quadratic regression model

y = `px2+ , (4.1)

where lpis the loss coefficient of importing from power plants and is the residual vector. The

estimated `p is used in the optimization model to calculate losses from importing electricity

into the district.

(24)

We have obtained the following estimated quadratic coefficients of loss: for import ( ˆ`p) it is

0.00233, for export ( ˆ`o) it is 0.00229 and for within district ( ˆ`d) it is 0.00035. For comparison,

both the ‘real’ and estimated losses are plotted in Figure 4.

Figure 4: Quadratic Regression of Loss and Load (Both are in kWh’s)

The problem with this approach is that the estimated losses of transporting electricity may not be proportional to the losses of using the storage system, i.e. if we underestimate the transportation losses then it becomes less efficient to use the storage system, while if we overestimate the transportation losses then it becomes more efficient to use the storage system.

We admit that the way we estimate losses is a bit ad hoc, but there is very little data available. One can improve it by including technical electrical aspects which is beyond the scope of this thesis.

When electricity is transported from one place to another, there is energy loss. So the amount of electricity that is supplied is not the same as the amount received. This means that each time electricity is transported, an additional amount of electricity needs to be supplied to compensate the loss. But transporting this additional amount of electricity will also create energy loss. So again an additional amount of electricity needs to be imported, which again creates loss, thus creating a vicious cycle. To keep it simple we exclude these losses from the balance constraints in the model and only incur them in the objective function.

4.4 Overload

(25)

are designed it is made sure that overload does not occur and that the expected increase in load is taken into account. That overload occurs is a fact, however it is difficult to quantify as it also depends on the ambient temperature of cables and transformers.

Overload can be defined as load that is above the nominal value, i.e. above the value at which the cable or transformer is designed for. From Equation (B.3) in Appendix B.1.1, we have that heat depends on squared current, resistance and time. This means that given a resistance, the higher the current the higher the heat. The problem is that if the cable gets too hot it will damage the insulation. So overload decreases the lifetime. And actually, overload can even melt the insulation and start a fire. So overload is a serious problem and many protection mechanisms (e.g. fuses, circuit breakers and temperature sensors) are incorporated to avoid any adverse effects on the circuit. See Appendix B.2 for more information on cables and transformers.

We make the following assumptions in the model. From the MV/LV-transformer there are five to six cables connecting houses to the transformer. As explained in Appendix B.1.2 each cable has three phases. We assume that each house is connected to only one phase. To make sure that the cables are not overloaded we include capacity constraints for each phase. This means that for each group of houses (connected to a phase) the amount of power transported is not allowed to be higher than some capacity. For the transformer we make sure that the amount imported to and exported from the district is not higher than the transformer’s capacity.

4.5 Constraints

For each house we need to make sure that the demand is satisfied. The supply of electricity can come from power plants, its own generated electricity, overproduction of other houses or from the storage system. In addition overproduced electricity must be stored or exported to other districts. There are also some restrictions that we need to consider. These are the capacity constraints of cables, transformer and storage system.

4.5.1 Supply/Demand-Balancing Constraints

We need to make sure that the demand of all houses in the district is satisfied. Each house can use electricity from their own production. If there is not enough generated electricity then a house can import from the main grid. Or if there is overproduction they can deliver it back to the main grid. Then for each house i at time t we have the following constraints

m

X

j=1

si,j,t· DGi,j+ Pdh,it − Phd,it = di,t, (4.2)

where dt_i is the demand of house i at time t and si,j,t stands for the generated electricity of

house i from DG type j at time t. These constraints make sure that the demand of each house is satisfied by its own DGs and/or the main grid.

(26)

constraints n X i=1 m X j=1 si,j,t· DGi,j+ Ppdt − Pdot + Psdt − Pdst = n X i=1 di,t. (4.3)

So the demand of the whole district (P

idi,t) must be equal to the district’s production

(P

i,jsi,j,tDGi,j), plus import (Ppdt ) and/or from storage (Psdt ) if there is underproduction,

and minus export (P_dot ) and/or to storage (P_dst ) if there is overproduction. Whether the storage system is used depends on how efficient the storage system is compared to importing and exporting.

Constraints (4.2) and (4.3) imply X

i

(P_dh,it − P_hd,it )

| {z }

Net flow houses

= Z

P_pdt − P_dot Z

| {z }

Net flow external

+ Z

P_sdt − P_dst . | {z }

Net flow storage

That is, the net flow of electricity from houses should be equal to the net flow of electricity from import/export plus the net flow of electricity from the storage system.

4.5.2 Capacity Constraints

For the transformer we have the following capacity constraints for each time period t

P_pdt + P_dot ≤ cap_tra. (4.4)

So the amount imported or exported is not allowed to be higher than the capacity captra.

For cables we split the houses into groups, as discussed in Section 4.4. We have the following cable constraints for each group of houses g and time period t

X

i∈Ag

(P_dh,it + P_hd,it ) ≤ capcab, (4.5)

where Ag is the set of indices for each group of houses g ∈ {1, . . . , G} connected to one phase.

So the amount of electricity transported to or from a group of houses is not allowed to be higher than the maximum capacity capcab.

4.5.3 Storage Constraints

Storage systems have restrictions on energy and power capacity. Power is expressed in kilo-watts (kW) and energy is expressed in kilowatt-hours (kWh). The capacity at which the storage system can store or release energy is the power capacity and the maximum amount of energy that can be stored is given by the energy capacity. Define capchas the power capacity,

then the charge/discharge constraint for each time period t is

P_dst + P_sdt ≤ capch. (4.6)

Define `s ∈ [0, 1] as the self-discharge rate, E ∈ [0, 1] as the efficiency of the storage system,

B0 as the storage level at the starting period (t = 0) and capstor as the energy capacity, then

the storage capacity constraints for each time period t ∈ T are

(27)

and t X k=1 h E · P_dsk − P_sdk(1 − `s)t−k i + B0(1 − `s)t−1≤ capstor. (4.8)

The storage capacity constraints basically state that the storage level is not allowed to be negative or higher than some capacity capstor. The storage level at time t is calculated by

summing the amount of energy that is retained and release from the starting period till time t, discounted for the loss from self-discharge.

4.5.4 Binary and Non-Negativity Constraints

As discussed in Section 4.1, the DG-variables are binary. So for each house i and DG type j

DGi,j ∈ {0, 1}. (4.9)

In addition, we include non-negativity constraints for the power flow variables. For each time period t

P_pdt , P_dot , P_sdt , P_dst ≥ 0, (4.10)

and for each house i and time t

P_dh,it , P_hd,it ≥ 0. (4.11)

4.6 The Objective Function

The objective is to minimize loss, so we minimize loss of importing, exporting, transporting within district, and using the storage system. Firstly, we discuss the quadratic terms of the objective function, i.e. losses from transporting electricity. And secondly, the linear terms, i.e. losses from using the storage system.

Define ˆ`p, ˆ`oand ˆ`das the estimated coefficients from the quadratic regression model (4.1)

for 7.5%, 6.9% and 1.1% average loss, respectively. Then we have for the quadratic part

T X t=1  `ˆ_pP_pdt 2 + ˆ`oPdot 2 + ˆ`d n X i=1 P_hd,it − P_dot + P_sdt !2 . (4.12)

The first quadratic term is the loss of importing, the second quadratic term is the loss of exporting and the last quadratic term is the loss of transporting within. The first two terms are pretty straightforward. The last term is explained as follows. A power flow from house i to the district, P_hd,it , consists of transporting from house i to (i) other houses in the district, (ii) the storage system and (iii) other districts as export. Since the loss of exporting to outside the district is already incurred in the objective function, the amount exported should be subtracted. Then we still need to add the power flows from the storage system to the district.7

7_{We can also do this the other way around: subtract the flow of imports from the flows of district to houses}

and then add the flow of district to storage. In mathematical terms: Pn i=1P t dh,i− P t pd+ P t ds. This is equal to

the previous termsPn i=1P

t

hd,i− Pdot + Psdt. These equations can be deducted from the two

(28)

The linear part that describes the loss of using the storage system is calculated as T −1 X t=1 `s t X k=1 E · P_dsk − Pk sd (1 − `s)t−k+ B0(1 − `s)t−1 ! + T X t=1 (1 − E)P_dst , (4.13)

where `s ∈ [0, 1] is the self-discharge rate, E ∈ [0, 1] the efficiency of the storage system and

B0 the storage level at the starting period (t = 0). The first term represents the loss from

self-discharge, where the term between the large brackets is the storage level. The second term is the loss from converting electricity from one form to another, i.e. the inefficiency of the storage system.

4.7 Overview of the Mathematical Model

The optimization model is a Mixed Integer Quadratic Programming (MIQP) problem, due to some binary variables and quadratic objective function. A complete overview of the mathe-matical model with its objective function and constraints is given in (4.14). We also give a list of definitions of all variables and parameters.

min Ppdt , Pdot , Phd,it Psdt , P t ds T X t=1  `ˆpPpdt 2 + ˆ`oPdot 2 + ˆ`d n X i=1 P_hd,it − Pt do+ Psdt !2  + T −1 X t=1 `s t X k=1 E · P_dsk − P_sdk(1 − `s)t−k+ B0(1 − `s)t−1 ! + T X t=1 (1 − E)P_dst subject to - supply/demand-balancing constraints: m X j=1

si,j,t· DGi,j + Pdh,it − Phd,it = di,t, ∀i, t

n X i=1 m X j=1 si,j,t· DGi,j+ Ppdt − Pdot + Psdt − Pdst = n X i=1 di,t, ∀t

- capacity constraints of the transformer and cables: P_pdt + P_dot ≤ captra, ∀t

X

i∈Ag

(P_dh,it + P_hd,it ) ≤ capcab, ∀g, t,

(29)

- binary and non-negativity constraints: DGi,j ∈ {0, 1}, ∀i, j

P_pdt , P_dot , P_sdt , P_dst ≥ 0, ∀t P_dh,it , P_hd,it ≥ 0, ∀i, t

Definitions of Variables and Parameters Decision variables:

DGi,j =

(

1 if house i has DG type j, 0 otherwise.

Variables:

P_pdt = amount of electricity imported from power plants to the district at time t (in kWh) P_dot = amount of electricity exported from district to outside at time t (in kWh)

P_dh,it = amount of electricity imported from district to house i at time t (in kWh) P_hd,it = amount of electricity exported from house i to district at time t (in kWh) P_sdt = amount of electricity imported from storage system to district at time t (in kWh) P_dst = amount of electricity supplied from district to storage system at time t (in kWh)

Parameters: ˆ

`p = estimated coefficient of energy loss of importing electricity from power plants

ˆ

`o = estimated coefficient of energy loss of exporting electricity to outside the district

ˆ

`d = estimated coefficient of energy loss of transporting electricity in district

`s = self-discharge rate of storage system per 15 minutes (in [0,1])

E = efficiency of the storage system (in [0,1]) di,t = demand of house i at time t (in kWh)

si,j,t = supply of distributed generator of house i DG type j at time t (in kWh)

captra = capacity of transformer (in kW)

capcab = capacity of cables (in kW)

capstor = capacity of storage system (in kW)

capch = maximum charge/discharge rate of storage system (in kWh)

B0 = charged level of storage system at starting period (t = 0)(in kW)

Sets & Indices: i = 1, . . . , n houses

j = 1, . . . , m types of DGs t = 1, . . . , T time periods g = 1, . . . , G groups of houses

Ag is the set of indices for each group of houses.

5 Description of Data

(30)

capacities. All data are obtained from the research conducted by TNO, as discussed in Section 2.

The demand and production data are reported for every 15 minutes and are split into four seasons: winter, spring, summer and fall. We are modeling only one week per season so that the data set does not become too large while still taking the seasonal effect into account. A large data set leads to a big optimization model which cannot be solved with given computer power. So each season is represented by one week and starts on Wednesday. Wednesday is chosen as the first day of the week because it represents an average day without the influence of weekends.

Since we are only modeling one week for each season we need to make some assumptions for the storage system as the amount of electricity stored at the end of each week will probably not be the same as the amount of electricity stored at the beginning of the week in the following season. But when optimizing the use of the storage system it is important that we allow the storage to store and release energy freely without interruptions between seasons. So we assume that the storage system at the end of each week is the same as the storage level in the beginning of the week in the following season.

There is only limited data available to us. For demand of a household and production by DGs there is no real data available. But we can make some general assumptions on household demands and DGs’ performances. This way we can obtain average profiles from which we can make some general conclusions.

5.1 DG Production Profiles

The DGs that we consider are micro-CHP systems, PV solar panels and micro wind turbines. The amount of electricity that each of these DGs will generate is unknown, but one can make some assumptions and use the characteristics of these DGs to make average profiles. Micro-CHP systems depend on heat consumption, PV solar panels on sunlight and micro wind turbines on wind speed. The production of electricity by micro-CHP systems and PV solar panels is variable but still quite predictable. On the other hand, the production of micro wind turbines is very unpredictable. This is because of the intermittent nature of wind in urban areas and the different effects that obstacles, such as buildings and trees, have on wind speed and direction. The data for these three DGs are discussed in the following subsections. Monte Carlo simulations are performed on the DGs’ production profiles. For more information on how these simulations were performed, refer to Appendix A.3.

5.1.1 Micro-CHP Systems

A micro-CHP system is a household furnace for heating with the addition that it can generate electricity. Current micro-CHP systems are heat demand following. When there is a demand for heat, it simultaneously generates electricity. There is also a buffer to store overproduced heat. These micro-CHP systems will be commercially introduced in 2010. Because of the easy adaptability in existing buildings, it is expected that it will have a successful development in the market.

(31)

week are the same, so we only show the first day of each season.

(a) Micro-CHP System in Winter (b) Micro-CHP System in Spring

(c) Micro-CHP System in Summer (d) Micro-CHP System in Fall

Figure 5: Daily Production Profile of Micro-CHP systems for Each Season

These graphs show that in the winter, when heat demand is high, the micro-CHP starts producing heat at 7:00 and stops at 21:00. In spring time the production of electricity decreases a lot. In the morning the micro-CHP produces electricity between 7:00 and 8:00 and at night electricity is generated between 17:00 and 20:00. During the summer, micro-CHP systems are only used in the morning, from 7:00 to 8:00. And in fall, electricity is generated between 07:00 and 10:00 and at night between 18:00 and 22:00. We can see from these graphs that the production of micro-CHP systems are quite stable because of their capacity of 1 kW. Only start and end times vary but are still predictable.

5.1.2 PV Panels

(32)

For simplicity, only one type of PV is considered: monocrystalline silicon. Monocrystalline PV solar panels currently have higher efficiencies but also cost more. We assume that (i) all PV solar panels in the district have an angle of 0.5, (ii) all PV solar panels in the district have an efficiency of 20%, and (iii) the size of PV pointing towards the south is 8 m2. In addition, we assume that these eight square meters of PV solar panels have a capacity of 1 kW.

In Figure 5.1.2 the production profiles of PV is plotted, where for each season they are plotted for each day of the week. The thick blue line is the first day of the week, in this case a Wednesday. PV production is estimated using observed solar power in 2004. The week corresponding to each season is estimated by averaging the four previous weeks, the week itself and the four following weeks.

(a) PV Solar Panels in Winter (b) PV Solar Panels in Spring

(c) PV Solar Panels in Summer (d) PV Solar Panels in Fall

Figure 6: Daily Production Profile of PV Solar Panels for Each Season

(33)

(sunsets) of production.

5.1.3 Micro Wind Turbines

Wind is characterized by direction and speed, and is very variable and hard to predict. Micro wind turbines that are installed in urban areas have an even more intermittent generation as wind is influenced by obstacles such as buildings and trees. Since most districts are located inland and micro wind turbines are placed on lower altitudes, wind speed will also be much lower. This makes it less interesting to incorporate micro wind turbines in urban areas. In Figure 5.1.3 graphs of micro wind turbine production profiles are shown. Each graph gives the daily production of a week in each season. The thick blue line is the first day of each week.

(a) Micro Wind Turbines in Winter (b) Micro Wind Turbines in Spring

(c) Micro Wind Turbines in Summer (d) Micro Wind Turbines in Fall

Figure 7: Daily Production Profile of Micro Wind Turbines for Each Season

(34)

5.2 District Composition and Demand Profiles

The main focus is on a group of houses in a district. But as there is no one district that represents all districts and one house that represents all houses, we need to make some as-sumptions on the district composition and the different types of houses. One problem is that there is no data available on the demands of households. But as most houses have a fairly predictable demand profile we can use this as a tool for modeling the houses’ demands. 5.2.1 District Composition

Our definition of a district is a group of houses connected to an MV/LV transformer (see Figure 1). We assume that there are 250 houses in the district. Five types of houses will be considered: detached, semi-detached, terraced, apartment and maisonette. The average demands and shares of houses are reported in Table 1, where the average demand is the average year demand typical for the house type and the share of houses is the overall share of each house type in the Netherlands.

Table 1: Average Demand and Share for Each House Type Detached

Semi-Detached Terraced Apartment Maisonette Average Typical Year

Demand (in kWh) 5000 4000 3500 3000 3500 Share of Houses

in the Netherlands 14.8% 12.4% 42.6% 25.5% 4.7% Observe that more than 40% of houses are terraced and have an average demand of 3500 kWh a year. More than a quarter of the houses are apartments with a lower demand of 3000 kWh. Semi-detached and detached houses are around 12 to 15% of the total number of houses and have the highest demands for electricity, as would be expected. And less than 5% are maisonettes with an average year demand of 3500 kWh a year.

Using these data we can construct a district that represents the average composition of houses in the Netherlands. However, most of the times a district consists of only a few types of houses and are not distributed in this way. This means that in reality a district in the Netherlands may actually need more (or less) electricity depending on the composition. For example, if in a district most houses are detached or semi-detached, then the demand in this district will be higher compared to a district with mostly apartments. In the former one it is probably more profitable to have more DGs while in the latter one less DGs would be needed. To be able to make general conclusions we model a district with an average composition of the Netherlands.

5.2.2 Demand Profiles

(35)

We will be looking at electricity demand in 2020. The demand of electricity is split into a base demand and extra demand. The base demand is an average demand per household and it is estimated by increasing the average demand in 2008 by 5%.8 On top of the base demand we add the extra demand from electric vehicles and heat pumps (these technologies are discussed in Section 5.3).

We have obtained one average demand profile, which is the base demand, and it is given as a percentage of the total average year demand for every 15 minutes. This base demand profile is used to model the demand for all houses. To obtain demands for every time period, these percentages are multiplied with the total demand of the corresponding house type, as reported in Table 1. In Figure 8 a base demand is plotted for one week. This graph clearly shows the repeated pattern of demand for each day.

Figure 8: Base Demand for One Week

To create different variants of demand for each house we perform Monte Carlo simulations on the base demand. The Monte Carlo simulations are performed as follows.9 For each house and for every 15 minute time period a random number is taken from the normal distribution with the base demand as mean and 10% of the mean is taken as standard deviation. The demand in one period depends on the demand in the previous period, with a correlation of 0.6. In this way if demand is higher than average in one time period, then it is more likely that the demand in the following period will also be higher than average. In Figure 9 we show such a simulation of the base demand for one day. The simulated demand deviates quite a lot from the base demand, but it clearly follows the base demand and does not give unrealistic demand for electricity.

Electricity demand fluctuates a lot during the year due to seasonal changes. We split a year into four seasons and for every season we model one week (first week of winter, first week of spring, first week of summer and first week of fall). The first week is chosen for practical reasons: there are more input data available for these weeks.

8

This assumption is made in the research conducted by TNO.

9_{We apply Monte Carlo simulations on the data using the same assumptions as in the research conducted}

Impact of Distributed Generation on Energy Loss: Finding the Optimal Mix

Impact of Distributed Generation on Energy Loss:

Finding the Optimal Mix

Impact of Distributed Generation on Energy Loss:

Finding the Optimal Mix

Preface

Summary

Contents

List of Abbreviations

1

Introduction

2

Goal of the Study

3

Related Work

4

The Optimization Model

5

Description of Data