Nicolas Pilatte

A parametrizable, large-scale, combined,transmission and distribution test system

Semester Project

EEH – Power Systems LaboratorySwiss Federal Institute of Technology (ETH) Zurich

Examiner: Prof. Dr. Gabriela HugSupervisor: Dr. Petros Aristidou

Zurich, June 14, 2016

Abstract

With environmental and security issues such as climate change and theFukushima accident, governments are looking to diminish their usage offossil fuels and phase out nuclear power. This is leading countries to greatlyincrease the installed capacity of renewable generation. Contrary to the tra-ditional generation for which a few power plants supply large quantities ofenergy in the transmission network, renewable generation units provide amuch smaller quantity of energy and are usually spread out in the distri-bution network. This arrangement is called distributed generation (DG).However, it can create adverse effects on the existing power grid. Indeed,DG cause problems such as intermittency of supply, voltage rise, harmon-ics and high-ramp rates (duck curve). Those problems are shared by bothtransmission and distribution networks and yet they are usually studied sep-arately. In addition to that, the growing demand for an effective regulationof distributed generation requires test systems to assess the effect of policiesand the impact it has on the entire power grid.

The goal of this project is to provide a tool to model a fully combinedtransmission and distribution test system, which will enable researchers tostudy the interactions between transmission and distribution networks andaddress, among others, the problems listed above. The test system will beparametrizable and able to analyse different scenarios of the power grid.

As a result of this project, we have developed a toolbox that allowsthe user to obtain a test system designed according to certain parametersand that can be used independently of the toolbox for static, economic anddynamic analysis. Furthermore, simulation results confirm the problemsthat we addressed before, such as a voltage rise and reverse power flow ifthe penetration level of renewable generation is too high.

i

Contents

List of Acronyms iv

List of Symbols v

List of Figures vi

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Test systems 42.1 Transmission network . . . . . . . . . . . . . . . . . . . . . . 42.2 Distribution network . . . . . . . . . . . . . . . . . . . . . . . 42.3 Transmission & Distribution network . . . . . . . . . . . . . . 7

3 Methods and data formats 93.1 Data formats . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Matpower . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 ARTERE . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.3 RAMSES . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1 Power flow calculation . . . . . . . . . . . . . . . . . . 103.2.2 Optimal power flow . . . . . . . . . . . . . . . . . . . 11

3.3 Load tap-changing transformers in Matpower . . . . . . . . . 12

4 Toolbox description 154.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 Static analysis . . . . . . . . . . . . . . . . . . . . . . 164.2.2 Economic analysis . . . . . . . . . . . . . . . . . . . . 184.2.3 Dynamic analysis . . . . . . . . . . . . . . . . . . . . . 18

4.3 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

ii

CONTENTS iii

5 Results 215.1 Voltage limits . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2 Influence of parameters . . . . . . . . . . . . . . . . . . . . . 215.3 Reverse power flow . . . . . . . . . . . . . . . . . . . . . . . . 245.4 Computational performance . . . . . . . . . . . . . . . . . . . 255.5 Open source availability . . . . . . . . . . . . . . . . . . . . . 26

6 Conclusion and outlook 28

Appendix A - How to run the toolbox 29

Bibliography 32

List of Acronyms

DN(s) Distribution Network(s)TN Transmission NetworkT&D Transmission and Distribution networkDG Distributed GenerationLTC Load Tap-Changing transformerPF Power FlowOPF Optimal Power FlowPV Photovoltaicp.l. Penetration LevelARTERE Analyse des Reseaux de Transport de l’Energie electrique en Regime EtabliRAMSES RApid Multiprocessor Simulation of Electric power SystemsIEEE Institute of Electrical and Electronics EngineersSEDG Centre for Sustainable Electricity and Distributed GenerationPSAT Power System Analysis Toolbox

iv

List of Symbols

x state vectorθ bus voltage angleU bus voltage magnitudeP (x) active power flowing out of the nodeQ(x) reactive power flowing out of the nodePinj active power injection by generators or loadsQinj reactive power injection by generators or loadsJ(x) Jacobian matrix of the systemfp cost function for active power generationfq cost function for reactive power generationngen Number of generators in the systema, b, c cost function coefficientsSfrom(θ, U) apparent power leaving the nodeSto(θ, U) apparent power arriving to the nodeSmax apparent power rating of the lineθref voltage angle referenceN complex turns ratio of phase-shifting transformersτ magnitude of the transformer turns ratioPDG active power generated by the distributed generationPd active power demand of loads in the DN

v

List of Figures

1.1 Power grid schematic [1] . . . . . . . . . . . . . . . . . . . . . 2

2.1 One-line diagram of the transmission network [2] . . . . . . . 52.2 One-line diagram of the distribution network . . . . . . . . . 62.3 Aggregated loads replaced by DNs in parallel . . . . . . . . . 8

3.1 Switching operation under load of LTC [3] . . . . . . . . . . . 133.2 Branch model in Matpower [4] . . . . . . . . . . . . . . . . . 14

4.1 Flow chart of the program . . . . . . . . . . . . . . . . . . . . 20

5.1 Over-voltages in the TN . . . . . . . . . . . . . . . . . . . . . 225.2 Voltage profile of a distribution network without DG . . . . . 225.3 Voltage profile of DN for low penetration levels . . . . . . . . 235.4 Voltage profile of DN for high penetration levels . . . . . . . 235.5 Voltage profile of DN for different generation weights . . . . . 245.6 Power flow from the transmission to the distribution network 25

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Chapter 1

Introduction

1.1 Motivation

Test-systems are very important in research to draw conclusions on thevalidity and the performance of proposed algorithms, control schemes, ornew components. They allow researchers to test ideas in a realistic butcontrolled environment, before proceeding to more expensive laboratory orfield testing. It is also important for researchers to use the same test-systemsto be able to reproduce results and enable comparison between solutionstackling the same problem. Several professional organizations have createdgroups dedicated to developing standard models, recent examples can befound in [2] and [5]. These models need to be realistic, accessible to allresearchers, and appropriately documented.

Unfortunately, while there is an abundance of smaller test-systems, thereis currently a significant lack of (and demand for) large-scale power systemmodels. Moreover, the available models focus only on the transmission net-work (high voltage) and are not suitable for testing new technologies emerg-ing from active distribution networks (see figure 1.1). Finally, they are oftendedicated to a specific application and one then needs to use different mod-els for static, dynamic or economic simulations. Thus, there is an urgentneed for a well-documented, open-source, realistic, universal, large-scale testsystem, including both transmission and distribution network levels.

1.2 Objectives

The goal of this project is to develop, analyse and document a parametriz-able large-scale transmission and distribution (T&D) network that can beused for static, dynamic and economic simulations and that will be madeavailable as an open-source model. A transmission network model (TN) anda distribution network model (DN) will be chosen. An automatic procedurewill then combine the two models by replacing the aggregated transmission

1

CHAPTER 1. INTRODUCTION 2

Figure 1.1: Power grid schematic [1]

CHAPTER 1. INTRODUCTION 3

loads with DNs scaled and fitted to the given loads, using multiple DNs whenneeded to avoid voltage and current violations. Also, the operating pointsof the various DNs will be randomised to avoid artificial synchronisation.

The provided tool will receive some user-selected parameters, such asthe amount of penetration of renewable resources, the scaling factors forloads and generators as well as the existence of uncertainty in the system.Based on these parameters, a procedure will provide a valid T&D test-system for a selected number of applications (power flow, economic analysis,dynamic security assessment,etc.) in a selection of data formats (ARTERE,Matpower, RAMSES,etc.). In the end, the program will be open-source,free to use and modify by anyone.

1.3 Structure

The report is structured as follows:

Chapter 2: Test systems. The different test systems used in the projectare introduced and their interaction is explained.

Chapter 3: Methods and data formats. The programs used to solvepower flow and optimal power flow problems are presented. The differentformats in which the output data is available are also outlined.

Chapter 4: Toolbox description. Detailed explanation of the input pa-rameters of the toolbox as well as a complete description of the program.

Chapter 5: Results. Analysis of simulation results and display of theinfluence of certain parameters. Brief description of where this toolbox hasbeen made available and what is provided.

Chapter 6: Conclusion and outlook. The contributions of this projectare presented and potential future improvements are addressed.

Chapter 2

Test systems

2.1 Transmission network

The transmission network is based on the model documented in [2]. It isa variant of the Nordic32 test system that has been used by the IEEE onseveral occasions (see [6] - [7]). As you can see on the one-line diagram infigure 2.1, the network is highly meshed and has long transmission lines of400 kV with some regional lines operating at 220 and 130 kV. The system,which operates at a frequency of 50 Hz, is separated into four zones: Equiv,North, Central and South. Most of the generation is situated in the NorthRegion with hydro power plants. The rest of the generation, in the Centraland South areas, consists of thermal power plants. Most of the consumptionis located in the Central and South areas. Equiv is an equivalent of anexternal system connected to the North area. In this model, the distributionnetworks are represented as aggregated loads. The goal of this project isto split them up into several distribution networks in parallel in order toproduce a large-scale system containing both transmission and distributionnetworks.

2.2 Distribution network

The model used for the distribution network developed by the SEDG and canbe found online [8]. It represents an 11kV urban network fed from a 33kVsupply point. Its one-line diagram is represented in figure 2.2. The topologyis radial with lines comporting both loads and distributed generation (DG).There are two kinds of DG in the system. The short feeders representbigger consumers and their generation is done via micro-turbines whereas thelong feeders represent residential consumers whose generation is done withrooftop solar panels. This distinction will be of importance in the programsince several parameters are influenced by that topology (see section 4.1).

4

CHAPTER 2. TEST SYSTEMS 5

Figure 2.1: One-line diagram of the transmission network [2]

CHAPTER 2. TEST SYSTEMS 6

Figure 2.2: One-line diagram of the distribution network

CHAPTER 2. TEST SYSTEMS 7

Symbol Description

Load tap-changing transformer linking the transmission net-work to the distribution network

PQ buses of the distribution network

Micro-turbines used for distributed generation on the shortfeeders

Residential PV panels to cover the rest of the distributedgeneration on the long lines

Shunt reactance added if the penetration level is 0, tomake sure that the total reactive power demand of the DNsmatches the original aggregated load (see section 4.2.1)

Table 2.1: Elements of the distribution network

2.3 Transmission & Distribution network

The main objective of this project is to provide a large-scale transmissionand distribution (T&D) network. To achieve that, it is necessary to replacethe aggregated loads in the TN by several DNs in parallel. To limit thenumber of nodes in the system, it is necessary to scale up the DNs in such away that a maximal power demand is achieved while respecting the voltagesand current limits. This requires several changes in the topology of thesystem. The transformer present in the DN model is removed, and the DNsare linked with the TN by the tap-changing step-down transformer alreadypresent in the TN. The turns ratio of the load tap-changing transformer thenhas to be calculated to allow the correct amount of active and reactive powerto be fed into each DN but also to prevent under-voltages. The combinationof the transmission and distribution networks is thus not as straightforwardas it seems and will be investigated in the next chapter.

Once all of this is taken care of, we have the final topology of the T&Dsystem. Now, we can introduce the distributed generation and run powerflow calculations according to the user parameters.

CHAPTER 2. TEST SYSTEMS 8

Figure 2.3: Aggregated loads replaced by DNs in parallel

Chapter 3

Methods and data formats

3.1 Data formats

Several programs can be used to do power flow calculation. This projectfocused on three of them : Matpower, ARTERE and RAMSES. All thepower flow and optimal power flow calculations were done in Matlab withMatpower solvers (see section 3.2). Therefore, the toolbox that we provideis composed only of Matlab files. However, to ensure compatibility withARTERE and RAMSES, several scripts have been made to be able to exportthe data in a format that can be chosen by the user.

3.1.1 Matpower

Matpower is a package that can be used with Matlab and can be downloadedfor free from [9]. If the export format parameter is set to matpower, theprogram will create a .mat file containing a struct which, itself, containsall the information needed to run a power flow or an optimal power flowin Matlab. As long as matpower is properly set up, the user can use thisstruct completely independently of the toolbox and change the topology ashe wishes. For more information on the matpower data format, please referto [4].

3.1.2 ARTERE

ARTERE is a software developed by the ”Universite de Liege” that can bedownloaded for free from [10]. It can perform power flow calculations withthe Newton-Raphson method and provides some features that are not avail-able in Matpower, such as load tap-changing transformers. If the exportformat parameter is set to artere, a .dat file will be created and all the infor-mation will be saved as text. This file can then be modified with a simpletext editor and run with the ARTERE software. Additional information onthe data format of ARTERE can be found in [11].

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CHAPTER 3. METHODS AND DATA FORMATS 10

3.1.3 RAMSES

RAMSES is developed by the same team and can be downloaded from [10].It is used for dynamic simulations of power systems, a feature that is notavailable in Matpower. If the user selected the dynamic export option,another .dat file is created with the dynamic information of the system.This file has to be linked with an ARTERE file that includes the static dataand can be run with the RAMSES software.

3.2 Solvers

3.2.1 Power flow calculation

The default solver of Matpower for power flow calculations is based on theNewton-Raphson method, which is explained in detail here [12]. First, aslack bus must be defined to fix the angle reference. In our system, the slackbus is g20 (see figure 2.1). The state vector x contains the unknown voltageangles (PU and PQ buses) and magnitudes (PQ buses only).

x =

(θU

)(3.1)

A non-linear function f is composed of the active and reactive powermismatches (i.e. the difference between the power flows out of the node andthe power injections from generators and loads).

f(x) =

(P (x)− PinjQ(x)−Qinj

)(3.2)

Where P (x) and Q(x) are respectively the active and reactive powerflows out of the node and Pinj and Qinj are the active and reactive powerinjections into the node.

The goal is, of course, to have f(x) = 0. To do this, we linearize f(x)with a Taylor expansion of the first order

J(x)

(∆θ∆U

)+ f(x) = 0 (3.3)

with J(x) being the Jacobian matrix of the system, which is equal to

J(x) =

∂P∂θ

∂P∂U

∂Q∂θ

∂Q∂U

(3.4)

The solution is found with an iterative process, starting from an ini-tial state x0 and updating it with ∆x at every iteration until the powermismatches are smaller than a given tolerance. During this process, the

CHAPTER 3. METHODS AND DATA FORMATS 11

Jacobian is recomputed at every step and the equation (3.3) is solved for∆x.

3.2.2 Optimal power flow

The goal of an OPF is to get a power flow optimization under certain con-straints. Generally, we want to minimize generation costs and losses in thesystem. A detailed explanation of the different kinds of OPF that exist canbe found in [13] and the description of this particular model comes from [4].The general definition of an OPF is

minxf(x) = 0 (3.5)

subject to

g(x) = 0 (3.6)

h(x) ≤ 0 (3.7)

xmin ≤ x ≤ xmax (3.8)

In this formulation, x is the optimization vector and contains the systemstate (as before) but also the available controls on which we can act. In ourcase, the system state is the voltage angles and magnitudes and the controlsare the active and reactive power injections of generators.

x =

θUPinjQinj

(3.9)

The equation (3.5) that we want to minimize is called the objective func-tion. It is the sum of all the individual cost functions fp and fq, respectivelyof active and reactive power injections for every generator.

f(x) =

i=ngen∑i=1

f ip(Piinj) + f iq(Q

iinj) (3.10)

For this project, we neglected the reactive power cost functions and usedquadratic cost functions, as defined in equation (3.11), for the active powergeneration. The value of the three coefficients a, b and c depends on thetype of generators used. For the TN, we used values from [14] and for themicro-turbines in the DNs, we took them from [15].

fp(Pinj) = a+ bPinj + cP 2inj (3.11)

The equality constraints (3.6) are the power flow balance equations,which must hold for every node in the system.

CHAPTER 3. METHODS AND DATA FORMATS 12

P (x)− Pinj = 0 (3.12)

Q(x)−Qinj = 0 (3.13)

The inequality constraints (3.7) indicate security limitations. Here, theyillustrate the fact that the apparent power flowing through a line cannotexceed the power rating of this line. They are separated in two sets ofequations: one for the power leaving (Sfrom) the node and the other forpower arriving (Sto) to the node (excluding the power injections).

|Sfrom(θ, U)| − Smax ≤ 0 (3.14)

|Sto(θ, U)| − Smax ≤ 0 (3.15)

Finally, the limits imposed on the optimization vector in equation (3.8)refer to the upper and lower limits on voltage magnitude and angle for busesand on active and reactive power generation for generators.

For the slack bus only

θref ≤ θ ≤ θref (3.16)

For all the busesUmin ≤ U ≤ Umax (3.17)

For all the generators

Pmin ≤ P ≤ Pmax (3.18)

Qmin ≤ Q ≤ Qmax (3.19)

Now that the problem is properly set, we use the step-controlled versionof the default Matpower solver to find the solution: Matlab Interior PointSolver (MIPS). It is written entirely in Matlab and uses the primal-dualinterior point method. We will not go more into details about this solver inthis report but detailed information can be found in [4].

3.3 Load tap-changing transformers in Matpower

Load tap-changing transformers (LTC) are a crucial part of this project.They are used to join the TN with the DN and can change their turns ratiowhile maintaining energy supply. This particularity is very useful to keepthe voltages of the DN within bounds. These transformers have a voltage setpoint on the low-voltage side and adjust their turns ratio in order to keep theactual voltage within some deadband around the set point. Since the currentflowing through the transformer cannot be interrupted, this adjustment isnot trivial. Figure 3.1 is taken from [3] and explains the switching operation

CHAPTER 3. METHODS AND DATA FORMATS 13

Figure 3.1: Switching operation under load of LTC [3]

CHAPTER 3. METHODS AND DATA FORMATS 14

Figure 3.2: Branch model in Matpower [4]

of an LTC. If the actual voltage is lower than the set point, the turns ratio isdecreased and, if it is higher than the set point, the turns ratio is increased.

Unfortunately, load tap-changing transformers cannot be represented inMatpower. As shown in figure 3.2, the turns ratio of such a transformer isa parameter that can be changed manually but only outside of power flowcalculations. This means that we cannot impose a voltage set point andswitch during the operation as explained in figure 3.1. The only way to stillget the characteristics of an LTC in Matpower is then to check the voltageof the node at the low-voltage side after the power flow calculation, updatethe value of the turns ratio accordingly and run a power flow calculationagain. This loop is repeated until the voltage set point is reached. In theend, we get a power flow configuration exactly identical to what we wouldhave had if LTC could be implemented in Matlab. The big disadvantageof this method is that the computation time is greatly increased becauseseveral power flow calculations have to be run in order to get the solution ofone system. For standard power flows, it is not a very significant drawbacksince they are quite fast. However, for optimal power flow calculations, itdoes create a substantial increase in computation time which is discussed inmore details in section 5.4.

Chapter 4

Toolbox description

4.1 Parameters

The toolbox works the following way: the user chooses certain parametersand a T&D system is created according to those parameters and exportedin the desired format. The user can then use the system independently ofthe toolbox. This section will explain the most important input parametersof the program.

• Penetration level : This value defines the percentage of the active powerdemand to be generated by the DG inside each DN. It is defined asthe ratio between the total active power injected by the DG and thetotal power demand of the DN.

p.l. =

∑PDG∑Pd

(4.1)

• Constant load : This Boolean is used to define which possible vision ofthe future of the power grid we want to apply to the system. The firstone (constant load=’false’) is that the growth of distributed genera-tion through renewable energies will outpace the growth of electricitydemand. In this case, the loads in the DN will remain constant andthe generation will increase. If we look at this from the TN point ofview, we see that the total demand will be decreased since part of thatdemand will be covered by DG. This means that, if the penetrationlevel is high enough, one might see a reverse power flow going from theDN to the TN instead of the opposite. The second scenario (constantload=’true’) is that, despite the DG increase, the electricity demandwill also increase (because of electric cars for example). This impliesthat the excess demand will be covered by the DG and the TN willsee the same total demand from the DNs (hence ’constant load’).

15

CHAPTER 4. TOOLBOX DESCRIPTION 16

• Random: If this is set to ’true’, all the distribution networks will haveslightly different power demands around a given set point to avoidartificial synchronisation.

• Generation weight : This value gives the percentage of the renewableenergy to be generated by the micro-turbines (on the short feeders ofthe DN) instead of the solar panels.

• Large system: When replacing the aggregated loads by DNs, two op-tions exist. Either we replace all of them (’true’) and get a very largesystem (about 22k nodes) or, only replace the loads in the central area(’false’) and get a system a bit smaller (about 15k nodes).

• Oversize: If 15k nodes are still too much for the user, there is stillthe option to overload the DNs by multiplying their power demandby this variable. This allows us to reduce the number of DNs neededto replace the aggregated nodes and therefore reduce the number ofnodes but it can create severe voltage problems. It can go up to afactor of 2, giving a system of about 7k nodes.

• Export format : Chooses the format in which the power flow data isexported (Matpower or ARTERE)

• Export dynamic: Determines if the dynamic data is needed. If so, thedata is exported in a RAMSES file

• Run OPF : Determines if the user wants to run an OPF. If this optionis activated, then the OPF data will be exported and not the staticdata. Note that this cannot be activated when constant load is trueor if penetration level is 0. More information in section 4.2.2.

4.2 Operation

Below is a detailed description of the program and the three options that weprovide: static power flow, optimal power flow and dynamic analysis. For amore visual approach, figure 4.1 is a flow chart representing the main stepsof the program.

4.2.1 Static analysis

Since the complete system is very large, we used a master-slave approach toresolve the power flow algorithm. This allows the TN and the DNs to besolved separately and to decrease the computation time. First, the topologyof the TN (the master) is loaded and a power flow is calculated. Then, theDN (the slave) is loaded and its total power demand is maximized whilethe voltages are kept under constraints. This step is necessary to limit the

CHAPTER 4. TOOLBOX DESCRIPTION 17

number of DNs in the system and prevent having too many unnecessarynodes. The number of DNs needed to replace every aggregated load canthen be calculated easily by dividing the power demand of the aggregatedload by the power demand of one DN.

The DNs are then modified according to the parameters defined by theuser. The amount of renewable generation is defined by the penetration level,and its allocation is changed through the generation weight parameter. Thegeneration weight parameter allows the user to generate more power throughthe micro-turbines on the short feeders and less through the residential PV.Also, if the user asked for it, a randomisation is applied to make sure thatall the DNs that we will use in the future are not identical. Finally, if theconstant load parameter is set to true, the active power demand of the systemis increased in such a way that the excess power demand will match the newlyintroduced distributed generation. Whatever the parameters chosen, in theend we get a collection of DNs that will be integrated into the transmissionnetwork.

The integration is done by replacing the aggregated loads in the TN byseveral DNs in parallel. Tap-changing transformers make the link betweenthe TN and the DNs. These are used to regulate the voltage inside the DNs.Indeed, if the voltages in the DN are too low, a reduction of the turns ratioof the transformer will cause all the voltages in the DN to increase. Unfor-tunately, matpower does not support load tap-changing transformers. Thus,we had to implement that function ourselves by looping over the voltagesand correct the turns ratio of the transformer if necessary before recalcu-lating a power flow, which led to a significant increase in the computationtime of the program. It should also be noted that those boundary conditionchanges caused by the load tap-changing transformers make this integrationstep quite complex.

If there is no distributed generation, the total active and reactive powerdemand of the DNs have to match the original aggregated load. This is donein two different ways for the active and the reactive power. For the activepower, the last DN is scaled down and dimensioned in such a way that itsactive power demand is equal to the difference of active power between theaggregated load and the sum of all the previous DNs. For the reactive powerdemand, the goal is to divide it equally between all the DNs. This can bedone by adding shunt reactances on the first node of each DN with a valueequal to the difference between the reactive power demand of the loads andthe desired one.

Once the topology of the full T&D is defined, a power flow is calcu-lated and tap-changing transformers are adjusted to make sure that all thevoltages are acceptable.

Another approach can also be chosen by the user. If he wants fewer nodesin the system, the oversize parameter can be given a value larger than 1.That allows the DNs to be overloaded (i.e. increasing the power demand and

CHAPTER 4. TOOLBOX DESCRIPTION 18

lifting the voltage constraints). In that situation, the total power demandof the DN will be higher and the number of DNs needed to replace theaggregated loads will decrease. A power flow solution can be reached if theoversize parameter does not exceed 2, which means that the number of nodesin the system can be decreased to ca. 7k. However, a trade-off has to bemade since this configuration will certainly lead to under-voltages and somefeatures, like the OPF, will not work in such conditions.

4.2.2 Economic analysis

If the user wants, an optimal power flow can also be run. To do an OPF, costfunctions are needed for the generators. For this project, we used a quadraticmodel and the coefficients used can be found in [14] and [15]. In the system,we assumed that only the generators of the TN and the micro-turbines of theDNs would be considered as adjustable generators. Therefore, we did notinclude cost functions for the residential PV and assumed that they wouldalways work at maximal capacity.

Similar to the static analysis, the load tap-changing transformers are notsupported by Matpower and cause some problems in the convergence of theOPF. To make it work, we had to solve the system in four steps, restrictingthe limits and updating the turns ratio at every step. Again, that limitationled to an increase in computation time. In the end, the OPF gives a powerflow solution within the limits and at least cost of generation.

The OPF does not work with every combination of parameters, however.If the penetration level is set to zero or if constant load is true (which, fromthe TN point of view, is the same situation), the OPF will not find a solution.This is due to the fact that the system is very large (ca. 15k nodes) andthe only way to solve under-voltage problems in the DNs is by acting on thelarge generators that are situated very far away and cannot have much ofan impact. Another situation in which the OPF might not converge is whenthe oversize parameter is set to more than one. This is simply because thisparameter is intended to reduce the number of nodes in the system whilelifting the voltage constraints. Consequently, if the DG capabilities are nothigh enough, they might not be able to fix the voltage problems and theOPF will not converge.

4.2.3 Dynamic analysis

Another functionality of the toolbox is that it can export dynamic data ofthe system to be used in RAMSES. It is important to point out that ourprogram does not run a dynamic analysis, it only provides the data to runit with another software. The reason why a dynamic analysis of the systemcannot be carried out in Matlab is because PSAT (the matlab library fordynamic analysis [16]) does not run on Matlab versions older than 2014a.

CHAPTER 4. TOOLBOX DESCRIPTION 19

Therefore, we chose instead to provide the files needed for compilation inRAMSES.

4.3 Nomenclature

Matpower only allows integers as bus names. Therefore, a very specificsystem had to be put in place in order to name the nodes of the system andstill recognize their role easily.

Firstly, the generators start with the letter ’g’ in the original data (seefigure 2.1). This ’g’ was replaced a 9. Sometimes, two generators are put inparallel. In that case, the second generator has the letter ’b’ appended tohis name. If a ’b’ is present, it is replaced by a 1 and if there is no ’b’, thelast number is a zero. Here are some examples:

g1→ 9010

g18b→ 9181

Secondly, the aggregated loads in the original data are just representedby an integer going from 1 to 72. Since we cannot use letters but we wouldstill like to recognize those nodes easily, we added a 5 in front of the busname. Note that only the loads that will be replaced by DNs have their namechanged. Then, the aggregated loads are replaced by several DNs. The firstnode of each DN (right after the LTC) will be represented by adding twomore digits at the end of the name. In the end, a single number will lead toa collection of 5-digit numbers designating the first node of every DN.

1→ 50101, 50102, 50103...

Lastly, for the nodes inside the DNs, two more digits are needed sincethere are 75 nodes per DN. For example, to represent the buses inside theDN whose first bus is 54302, two digits going from 01 to 75 are appendedto the name.

54302→ 5430201, 5430202, ..., 5430275

For this reason, buses in the T&D system tend to have long names butit is a simple way to recognize the position of the bus just by looking at hisname.

CHAPTER 4. TOOLBOX DESCRIPTION 20

Figure 4.1: Flow chart of the program

Chapter 5

Results

5.1 Voltage limits

One of the main problems associated with distributed generation is the volt-age rise it creates. We have observed this first-hand in our system. For thepower flow calculation, the voltage limits are 1.15 pu and 1.03 pu for the TNand DN respectively. As shown in figure 5.1, the penetration level increases,more and more buses in the TN experience over-voltages. Similar problemsarise in the DNs and are treated in the next section.

Nevertheless, if an OPF calculation is made, those over-voltages are nota problem anymore. All the voltages in the TN can be brought down below1.10 pu and those in the DN below 1.03 pu.

5.2 Influence of parameters

Another interesting thing to look at is the influence that parameters hason the voltage profile in the distribution network. Figure 5.2 represents thevoltage profile of a DN without any DG. We can see that the voltage setpoint of the LTC is around 1.03 pu. We also observe a series of voltagedrops. These are the radial lines leaving the main bus. Since there is nogeneration and all the nodes are connected with loads, it is normal that weobserve such a decline. Obviously, the longer the line, the bigger the voltagedrop.

Now, if we introduce some DG, the voltages will have a tendency toincrease. If the penetration level is not too high, as displayed in figure5.3, this can help mitigate the voltage drop. However, as the penetrationlevel gets higher we begin to see over-voltages, as shown in figure 5.4. Onthe short feeders, production has exceeded consumption which caused theseover-voltages.

The next parameter that we can change is the generation weight. Thisvalue represents the fraction of power to be generated by the micro-turbines

21

CHAPTER 5. RESULTS 22

Penetration level0 10 20 30 40 50

Nu

mb

er

of

ove

r-vo

lta

ge

bu

se

s

0

1

2

3

4

5

6

7

8

9

10

Figure 5.1: Over-voltages in the TN

Bus number10 20 30 40 50 60 70

Bu

s v

olta

ge

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Penetration level = 0

Figure 5.2: Voltage profile of a distribution network without DG

CHAPTER 5. RESULTS 23

Bus number10 20 30 40 50 60 70

Bu

s v

olta

ge

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

Penetration level = 0Penetration level = 5%Penetration level = 10%Penetration level = 20%

Figure 5.3: Voltage profile of DN for low penetration levels

Bus number10 20 30 40 50 60 70

Bu

s v

olta

ge

0.96

0.98

1

1.02

1.04

1.06

Penetration level = 0Penetration level = 25%Penetration level = 50%Penetration level = 75%

Figure 5.4: Voltage profile of DN for high penetration levels

CHAPTER 5. RESULTS 24

Bus number10 20 30 40 50 60 70

Bu

s v

olta

ge

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Generation weight = 25%Generation weight = 50%Generation weight = 75%

Figure 5.5: Voltage profile of DN for different generation weights

on the short feeders. The default value is 50%, which means that the micro-turbines produce as much power as the PV panels. But, since there aremore PV panels than micro-turbines, the individual contribution of everysolar panel is much lower than the production of every micro-turbine. Wesee in figure 5.5 that a high value of the generation weight exacerbates theover-voltages on short feeders while a low value does not create such a bigincrease in voltage and also decreases the voltage drop on long lines.

5.3 Reverse power flow

As the penetration level increases, the power demand of the DNs decrease.If it goes above a certain level, the DG will generate more energy than whatis required for the DN which will lead to a reverse power flow. This indicatesthat the power will flow from the DN to the TN instead of the opposite. Aswe have already seen, it can cause voltage violation and increased voltagestress of the equipment but it can also be dangerous if special protectionsystems are not put in place [17].

The evolution of the power flow with an increase in penetration level ofrenewables is displayed in figure 5.6. We see that, for a penetration levelof about 115%, a reverse flow is observed. There are several reasons whythis change does not happen exactly at 100%. First of all, the DG doesnot need to only compensate the power demand, it should also cover the

CHAPTER 5. RESULTS 25

Penetration level

0 20 40 60 80 100 120

Pow

er

flow

fro

m T

N to D

N

-5

0

5

10

15

20

25

30

35

Figure 5.6: Power flow from the transmission to the distribution network

Operation Run-time

Power Flow 30 secondsOptimal Power Flow 200 secondsExport data 15 seconds

Table 5.1: Approximate run-time of every part of the program

losses, which are not considered in the penetration level. Secondly, due tothe randomization of the system, the penetration level is not exactly equalto the value displayed in the graph, so the actual value might be a bit loweror higher than what is shown here. These also explain why the graph is nota linear function.

5.4 Computational performance

Depending on the choice of parameters, the run-time of the program canvary a lot. The longest part is by far the OPF calculation, especially sinceit is composed of a loop to account for the LTC (see section 3.3). In thetable below are the approximate times that one should expect when usingthe toolbox with a given set of parameters. According to this, if the userwants to use the toolbox fully, he would get a total run-time of about 4minutes.

CHAPTER 5. RESULTS 26

Name Description

README.txt basic introduction to the toolboxinput data/

tn template.mat topology of the TNdn template.mat topology of the DNdynamic data.txt dynamic data of the system

output data/ARTERE/ folder containing the automatically generated

ARTERE and RAMSES filesMatpower/ folder containing the automatically generated

Matpower files

Table 5.2: Files present in the toolbox

5.5 Open source availability

The goal of the project was to make this toolbox available as an open-sourceprogram. As a result, the published code can be changed and distributedto anyone and for any purpose. It has been posted in Bitbucket [18] andcan be downloaded from this address: https://bitbucket.org/apetros/

parametrizable-combined-transmission-and-distribution-system. Ta-bles 5.2 and 5.3 describe the files and functions that can be found in theonline repository.

CHAPTER 5. RESULTS 27

Name Description

main.m parent script of the programparameters.m script in which all the parameters are definedfunctions/

add costs.m adds the cost coefficients for the OPFcalc opf.m runs an OPF algorithm on the T&D systemdnbus2int.m converts the aggregated load name into a DN

nameexport artere.m exports the data into the ARTERE formatexport data.m gets the system data ready for exportexport ramses.m exports the data into the RAMSES formatfinal dn.m recalculates the power flow in the DNs with data

from the T&D systemgenbus2int.m converts the string generator name into an intget dn.m applies the parameters on the DNs and calcu-

lates a power flowint2genbus.m converts the int generator name into a stringinternal dn node.m creates the name of nodes inside the DNsloop opf.m solves the OPF step-by-step to meet the voltage

limitsmerge td.m creates the final topology as a combined T&D

networkpf withpv.m introduces distributed generation inside the DNstd topology.m replaces the aggregated loads by DNs in parallelvoltages 103.m checks the set point of the LTC and updates the

turns ratio accordingly

Table 5.3: Functions present in the toolbox

Chapter 6

Conclusion and outlook

During this project, a program generating a parametrizable, large-scale,combined, transmission and distribution test system was developed. Usingexisting test systems for transmission and distribution networks, we com-bined them in order to get a combined transmission and distribution testsystem, which required the implementation an appropriate model for loadtap-changing transformers in Matpower. The final program was made insuch a way that it could be useful to a large number of people. Therefore,it is open-source and the output data can be exported to different formatsaccording to the user preferences. In the end, the T&D system is suitableto study operation and planning problems and test new control methods inlarge-scale. It also allows researchers to freely have access to a common,large-scale, test-system, in order to compare their results.

With the simulation results, we were able to demonstrate the key changesinduced by distributed generation as well as the problems they cause. Anincrease in penetration level can have great environmental benefits but itcan also lead to over-voltages and reverse power flows between TN and DN.Additionally, the fact that load tap-changing transformers are not availablein Matpower forced us to define loops over power flow and optimal powerflow calculations, which greatly increased the run-time of the program. IfLTC were implemented directly in the PF and OPF methods, the complexityof the algorithm, and thus the run-time, would be significantly decreased.

Future developments in the power grid will surely include more instal-lation of distributed generation but also new technologies such as energystorage. Adding these technologies in the model will certainly prove to beuseful. Furthermore, another feature could be added to the toolbox: thestochastic OPF. A stochastic OPF is a method that adds new constraintsduring the OPF calculation, such as the stochastic availability of intermit-tent renewable sources, the presence of lossy storage resources and rampingcosts.

28

A - How to run the toolbox

1. Go to http://www.pserc.cornell.edu/matpower/, download mat-power 5.1 and unzip

2. Go to https://bitbucket.org/apetros/parametrizable-combined-transmission-and-distribution-system, download the toolbox andunzip

29

A - HOW TO RUN THE TOOLBOX 30

3. Inside the toolbox repository, you will find two subfolders, two matlabfiles and a README file. It is not obligatory but it might be moreconvenient to paste the matpower folder here.

4. Open the file named ’parameters.m’ and change the first variable todefine the path to your matpower folder. If they are in the same folder,this variable is simply the name of the matpower folder.

A - HOW TO RUN THE TOOLBOX 31

5. Change the other variables according to the system that you want togenerate

6. Run the script ’main.m’

7. Find the exported data in the ouput data folder, either in the mat-power subfolder or the artere subfolder depending on the option chosen

Bibliography

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[2] IEEE Power System Dynamic Performance Committee. “Test Systemsfor Voltage Stability Analysis and Security Assessment”. Technical re-port, IEEE Power & Energy Society, Aug. 2015.

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[4] Ray D Zimmerman and Carlos E Murillo-Sanchez. “Matpower5.1-User’s Manual”. Power Systems Engineering Research Center(PSERC), 2015.

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[10] Thierry Van Cutsem. “Web page of Thierry Van Cutsem”. http://

www.montefiore.ulg.ac.be/~vct/software.html. [Online; accessed11-06-16].

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[12] Goran Andersson. “Power System Analysis”. EEH - Power SystemsLaboratory, ETH Zurich, 2015.

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