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International Conference on Smart Energy Grid Engineering (SEGE’14) 1
Copyright © 2014 Inderscience Enterprises Ltd.
A toolbox for the modelling and
simulation of islanded microgrids
Shivam Saxena*, Hany E.
Farag and Amir Asif
Department of Electrical Engineering and
Computer Science, York University,
Toronto, Ontario, M3J 1P3, Canada
E-mail: shivam@cse.yorku.ca
E-mail: hefarag@cse.yorku.ca
E-mail: asif@cse.yorku.ca
*Corresponding Author
Abstract: This paper proposes a simplified toolbox for the modelling
and simulation of large microgrids operating in islanded mode. The
toolbox integrates an easy to use user interface built in LabVIEW with
MATLAB’s stiff Ordinary Differential Equations (ODEs) solver to
allow a user to model custom microgrid models for test purposes. For
smaller models, the user is able to drag and drop network components
onto a custom drawer and visualize the network as it is being built. For
larger models, a configuration file can be used which contains all the
necessary component data for the simulation. This flexibility and ease
of use allows for rapid prototyping and testing of microgrid dynamics
and steady-state behaviours at different operating conditions.
Keywords: Microgrids; Islanded microgrids; distributed generation;
power electronics; inverters; power generation; nonlinear systems;
Smartgrid; power sharing; LabVIEW; MATLAB
1 Introduction
The demand for power in North America continues to grow at a steady rate and is
projected to increase 28% by the year 2040 (Campillo, 2012). This ever increasing load
on the electric power grid is placing a great deal of strain on an ageing and outdated
infrastructure. Due to the centralized and hierarchical nature of the electric power grid, a
major component fault can cause an outward spiralling effect, which can leave many
consumers without power. This was in clear evidence during the Northeast power
blackout of 2003 in United States and Canada, in which a combination of multiple
Saxena et al.
transmission lines became faulted and a race condition in the control software of the EPG
left upwards of 50 million consumers without power for over 24 hours (Andersson and
Donalek, 2005).
As such, the promise of an electrical power network which is decentralized, automated,
and distributed has come to realization with the concept of the Smart Grid. The Smart
Grid seeks to decentralize the massive power grid into a network of smaller, more
manageable subsystems, each of which service a smaller demand for power. These
smaller grids, true to their name, are known as Microgrids. Microgrids generate power
locally through distributed generation and distribute it among local loads. The term
microgrid has been created to be the building block of smart grids (IEEE Guide for
Design, Operation, and Integration of Distributed Resource Island Systems With Electric
Power Systems, 2011). A microgrid should be able to operate in two modes of operation:
grid-connected or islanded. The successful implementation of the microgrid concept
demands a proper definition of the regulations governing its integration in distribution
systems. In order to define such regulations, an accurate evaluation of the benefits that
microgrids will bring to customers and utilities is needed. Therefore, there is a need for
careful consideration of microgrids in the assessment, operation, planning and design
aspects of smart grids (Abdelaziz et al., 2013).
The motivation behind this research is to build a toolbox for the modelling and
simulation of inverter based microgrids. Such toolboxes have been well established for
conventional power networks (Milano, 2005; Larsson, 2004), however, there exists a lack
of a realistic simulation platform used to model large, custom microgrids. Simulink and
PSCAD are the most popular tools in which to model microgrids (Panigrahi et al., 2006),
however, creating large networks using these tools can be a complex and time consuming
process. The modelling of the distributed generator (DG) in particular is difficult as all
the internal components and controllers must be modelled. This toolbox uses a simplified
model for the DG as a set of five differential equations in which the constant parameters
are enabled to be customized by the user. The accuracy of this model has been verified in
previous research (Farag et al., 2013). Using an intuitive user interface built in
LabVIEW, a user can drag and drop a customized DG and model a microgrid with
transmission lines and loads which are similarly customizable. The LabVIEW User
Interface is integrated with a MATLAB ODE solver which is then used to solve the
custom network modelled as a system of nonlinear differential equations. The traditional
approach in modelling power networks and Microgrids is to linearize the nonlinear
differential equations, which define the system (Pogaku et al., 2007; Bottrell, 2013).
However, electrical power networks are highly nonlinear in nature, and thus this is not an
optimal strategy for capturing system dynamics. This toolbox preserves the non-linearity
of the ODEs and allows a user to define a custom microgrid for the purposes of
simulation.
2 Inverter Based Microgrids
Traditionally, power is generated in large, centralized power plants which are located
close to natural resources (coal, natural gas). However, as touched on before, the
equipment used to generate electricity is ageing and becoming increasingly more prone to
faults. Secondly, and most importantly, emissions from these power plants are extremely
harmful to the environment. As such, there is a great deal of research and implementation
geared towards harnessing renewable energy sources which are efficient to use and also
environmentally friendly. These energy sources could be solar panels, photovoltaic
A Toolbox for the Modelling and Simulation of Islanded Microgrids
panels, and fuel cells etc. These sources are low cost, low voltage, high reliability, and
most importantly, have minimum impact on the environment.
Distributed generation is a concept of aggregating a variety of small energy sources
(less than 100 kW) and using the combined power to satisfy larger power demands
(Lasseter, 2002). However, the voltages produced by these microsources are DC, and are
converted to AC using a voltage source inverter. Thus, an inverter based microgrid is an
electrical power network comprised of microsources which produce power locally. The
generation units which produce the power are called Distributed Generators (DGs), and
they are connected to a bus (node) on the network through transmission lines. The system
is finalized by attaching local loads to the nodes (Figure 1).
Figure 1 An example of a test microgrid network
As mentioned before, the microgrid can operate in two modes – Grid Connected and
Islanded. When the microgrid is operating in grid connected mode, the overall system
dynamics are dominated by the main grid itself (Farag et al., 2013). Traditionally, EPGs
try to handle an increase in power demand by turning on smaller, more expensive
generators to balance the load. In this case, the microgrid’s power supply can be used
instead to save cost. In islanded mode, the microgrid services only its local loads and is
an individual, self-sufficient network. The system dynamics are governed by all three
components: DGs, Lines and Loads. The focus of this paper will be on microgrids
operating in islanded mode, and their modelling and state space representation is covered
in the next section.
3 Islanded Microgrid Modelling
3.1 Distributed Generators (DG)
The DG is responsible for producing power for the network to use and uses a voltage
source inverter to provide AC power. As such, the DG is modelled by a set of non-linear
ordinary differential equations that include the DG and inverter (Figure 2).
Saxena et al.
Figure 2 Block Diagram of the Distributed Generator and Inverter
The model for the combined DG and inverter is split into several control loops as
indicated in Figure 2. The most important controller is the Power Controller, whose
primary objective is to efficiently share the load of the network among the DGs. This is
achieved by introducing a droop gain as a system parameter and allows the DGs to share
power appropriately in the network. It receives the output voltage and current of the LC
Filter (Vo and Io) of the LC Filter and sets the output magnitude and phase of the voltage
(Vo*). The Voltage and Current Controllers, which are designed to reject high frequency
disturbances and provide adequate damping for the output LC Filter (Pogaku et al.,
2007), are then used to compute the final DC Voltage (VI*). The Inverter then converts
the DC Voltage to AC. The LC Filter, which provides stability to the system and is used
to attenuate the frequency ripple of the inverter (Micallef, 2012) then produces the output
voltage and the current which feeds into the node. The addition of RN at the node is to
ensure that the numerical solution to the system is well defined. Since the Power
Controller and Output LC Filter dominate system dynamics for the DG, the voltage and
current controllers can be omitted to simplify the DG model (Farag et al., 2013).
The state variables of interest for the modelling of the DG are: δ - the angle of the DG,
PG - the active power generation of the DG, QG – the reactive power generation of the
DG, Iod – Output current in the dth dimension, and Ioq – Output current in the qth
dimension. It is important to mention that the state space modelling done in this paper is
in the DQ frame (Figure 3). Each DG (say n) is rotating at its own angular frequency, ωn,
on the axis (dn, qn). This can be calculated by taking the difference δn between the angles
associated with the individual DG and the original DQ reference frame on axis (D, Q). As
such, an arbitrary DG is appointed as the ‘common’ DG and is aligned to the DQ axis.
The angle for this DG is set to zero, and its rotational frequency is a parameter named
ωcom which is then used to calculate the angle of all the other DG’s. When modelled
together in a single network, all DG’s (and by extension all other network state
variables), must be translated to the DQ frame by using the following transformation:
(1)
A Toolbox for the Modelling and Simulation of Islanded Microgrids
Figure 3 Block Diagram of the Distributed Generator and Inverter
The set of nonlinear differential equations describing the modelling of the common DG
unit (in this case, DG 1 is assigned as common) is given hereunder in equations (2)-(5).
δ1 ΄= 0 (2)
PG1 ΄=
ωc1[Vo1*Iod1 - Nq1QG1Iod1] - ωc1PG1 (3)
QG1 ΄= -
ωc1[Vo1Ioq1 – Nq1QG1Ioq1] - ωc1QG1 (4)
Iod1 ΄ = (-Rc1/Lc1) Iod1 + ωcomIoq1 + (Vod/Lc1) - (Vbd/Lc1) (5)
Ioq1 ΄ = (-Rc1/Lc1)Ioq1 - ωcomIod1 + (Voq/Lc1) - (Vbq/Lc1) (6)
where Vod = Vn* and Voq = 0
Similarly, the nonlinear differential equations represent the rest of DG units connected
to the microgrid network are given below in terms of unit n identified by inserting an
additional subscript n in each variable.
δn ΄= ωn* - MpnPGn – ωcom (7)
PGn ΄=
ωcn [Vn*(Ioqn sin(δn) + Iodn cos(δn))
- NqnQGn (Ioqn sin(δn) + Iodn cos(δn))] - ωcnPGn (8)
QGn ΄= -
ωcn [Vn*(Ioqn cos(δn) - Iodn sin(δn))
- NqnQGn (Ioqn cos(δn) - Iodn sin(δn))] - ωcn QGn (9)
Iodn ΄ = (-Rcn/Lcn)* Iodn + ωcom * Ioqn + (Vod/Lcn) - (Vbd/Lcn) (10)
Ioqn ΄ = (-Rcn/Lcn)* Ioqn - ωcom * Iodn + (Voq/Lcn) - (Vbq/Lcn) (11)
Saxena et al.
3.2 Lines
Lines are physical transmission lines which connect one node to another. In this paper,
transmission lines comprises of a resistor and inductor. The state variables of interest are
the currents of the line in the DQ frame (ILineD, ILineQ), and differential equations
describing the line connecting two buses are given as follow:
ILineD,n ΄= - (RLine,n* ILineD,n)/ LLine,n + ωcom * ILineQ,n
+ (VbjD/ LLine,n) - VbkD/ Lline,n (12)
ILineQ,n ΄= - (RLine,n* ILineQ,n)/ LLine,n - ωcom * ILineD,n
+ (VbjD/ LLine,n) - VbkQ/ LLine,n (13)
where subscripts j,k represent the to and from node, respectively, and subscript n
represents the nth Line in the network.
3.3 Loads
In this work, loads are represented by their equivalent admittance. The state variables of
interest are the currents of the load in the DQ frame (ILoadD, ILoadQ), and the differential
equations are given as:
ILoadD,n ΄= - (RLoad,n* ILoadD,n)/ LLoad,n + ωcom * ILoadQ,n + (VbjD/ LLoad,n) (14)
ILoadQ,n ΄= - (RLoad,n* ILoadQ,n)/ LLoad,n - ωcom * ILoadD,n + (VbjQ/ LLoad,n) (15)
3.4 Nodes
A node, or a bus, is a connection point within the microgrid which connects together a
DG, line, and/or load. The voltage at each node is calculated and is needed for both the
line and load modelling, where Rn is a virtual resistor. The introduction of the virtual
resistor (and its relatively high value), is to ensure that the numerical solution of the
system is well grounded and that the node dynamics do not interfere with the overall
system dynamics (Pogaku et al., 2007).
VbDi = RN*( IoDi - ILoadDi + ILineDi,j) (16)
VbQi = RN*( IoQi - ILoadQi + ILineQi,j) (17)
Where the subscripts i,j represent the to and from node, respectively.
A Toolbox for the Modelling and Simulation of Islanded Microgrids
3.5 Overall System Model
The network, or overall system model, can then be modelled by combining the set of
differential equations of all DGs, Lines, and Loads into an overall state vector. The state
variables for all the DGs are modelled first, followed by the Lines, followed by the
Loads. Although the order can be defined in any such way for the MATLAB ODE solver,
this order is preferred when it comes to creating an index map of the state vector. As can
be seen in equation (17), there are 5 state variables for each DG unit, 2 state variables for
each load, and 2 state variables for each load.
X = [δn, PGn, QGn ,Iodn ,Ioqn, ILineD,n, ILineQ,n, ILoadD,n, ILoadQ,n] (18)
4 Software Design of Toolbox
4.1 Framework
The objective of the toolbox is to provide an easy to use interface in which the user can
solve an n node, n DG, and n Load microgrid network operating in islanded mode. As
shown in Figure 4, the software consists of two platforms – LabVIEW and MATLAB.
The general framework is written in LabVIEW which includes the user interface, main
state machine, and main data storage objects. MATLAB is then called from within the
LabVIEW framework to solve the set of differential equations generated by the custom
network.
Figure 4 LabVIEW and MATLAB data communication
4.2 LabVIEW
LabVIEW is a graphical programming language and system design platform which is
widely used in both academic and research institutions. LabVIEW is chosen for writing
the general framework because it is naturally inclined towards a multithreaded style of
programming. Multiple threads can be statically or dynamically created and interprocess
communication is easily facilitated through built in queues and notifiers. LabVIEW also
supports object oriented style programming. Since the toolbox is modelled as a system of
objects, and in the future has the potential for the aggregation of more network
components, object oriented programming is an important consideration when it comes to
Saxena et al.
the maintenance and expansion of the code in the future. Most importantly, LabVIEW
offers an excellent interface to facilitate communication with MATLAB.
4.3 MATLAB ODE Solver
When the terms of a differential equation cause rapid variation in the solution, the
differential equation is classified as a stiff differential equation (Schadenko, 2003).
MATLAB specializes in solving stiff, nonlinear differential equations, and provides a set
of special solvers for this purpose. The ODE solver ode15s is a variable order solver
which uses two methods to integrate a system of differential equations: Numerical
Differentiation Formulas (NDFs) or Backward Differentiation Formulas (BDFs)
(Shampine and Reichelt, 1997). The ode15s solver is also a variable step solver, and will
attempt to decrease the step size when rapid variations occur to capture dynamics as
accurately as possible. The solver also provides parameters for defining relative and
absolute tolerances, which allow the user to specify constraints on the eventual solution
of the system of differential equations.
4.4 Object Model
Central to the idea of the toolbox is the idea of a network. A single network is custom
created by the user and represents all the components that make up the network: DGs,
Lines, Loads, and Nodes. An object diagram of the software model is shown in Figure 5.
As can be seen in the figure, it follows that a network consists of many nodes, while the
nodes themselves can have many DG’s, Lines, and/or Loads.
Figure 5 Object Model of toolbox
A Toolbox for the Modelling and Simulation of Islanded Microgrids
4.5 System Architecture
Figure 6 shows the system architecture of the proposed toolbox. As shown in the figure,
the system architecture is divided into three separate threads – the User Interface (UI)
Thread, the Main State Machine Thread, and the MATLAB ODE thread.
The User Interface Thread is responsible for capturing all user events and forwarding
relevant data to the main state machine. The user uses the user interface to
add/modify/remove nodes, DGs, Lines, and Loads. The User Interface thread captures the
specific option, services the user request, and forwards the updated data to the main state
machine where the network data is stored.
The Main State Machine Thread facilitates the program state and holds the latest copy
of the Network data. It receives state change instructions from the User Interface Thread
(state could go from idle, to running a simulation, to exiting) and also updates the
network according to the user’s changes. It also sends instructions and data to the
MATLAB Loop when the simulation is ready to be run and receives the data back when
the simulation is complete. It is implemented as a queued state machine whose default
state is simply idle. The UI thread interrupts the main state machine whenever the user
engages with the program to make a request.
The MATLAB ODE thread is used to execute the time domain simulation of the
network and return the results back to the Main State Machine
Figure 6 System Architecture of the toolbox
Interprocess communication is managed through the use of single element queues.
Once instantiated, a reference (pointer to the memory location) to the queue can be called
from anywhere in the program to either enqueue or dequeue an element in the queue.
Two queues are used for each communication link between thread (UI Thread to State
Machine, State Machine to MATLAB) to facilitate a send/receive interface. Screenshots
of the user interface can be seen in Figures 7 and 8.
Saxena et al.
Figure 7 Main UI of the toolbox, where user can add/remove/modify any network component
Figure 8 The user configures a custom DG and can visualize the addition to the network
4.6 Index Map
Since the toolbox should be able to solve any network, the state vector fed to the
MATLAB ODE solver must be dynamically created depending on the network the user
has made. The ODE solver must also then be able to execute the correct equation
depending on the state variables in the vector. This requires the use of an index map
which can be used to hold information about each state variable. A simple object is made
which contains the type of component (DG, Line, Load), it’s component index (there
could be multiple DG’s, Lines, Loads), and the relevant state variable for that component
(angle, power, current etc.). When an equation needs a particular state variable, it can
A Toolbox for the Modelling and Simulation of Islanded Microgrids
then find the correct index of where it resides in the state vector by searching through the
index map by component index and state variable.
4.7 Simulation Algorithm
Figure 9 shows a flowchart for the proposed simulation algorithm of the custom
network generated by the LabVIEW framework. As can be seen in the figure, first: ωcom
is calculated by using the angle equation for the common DG. Since the angle of this DG
is always set to zero, ωcom can be solved for by using the state values from the previous
time iteration. Second, voltage calculation is done for every node in the system by
applying KCL at each node. The currents from the DG and To Node are considered
positive, while the currents from the From Bus and Load are considered negative. Third,
the equations for the DGs, Lines, and Loads are solved simultaneously depending on the
custom network. For this, the index map is traversed one by one until all the state
variables have been solved. Fourth, the ODE solver checks if the time step has surpassed
the simulation time set by the user. If it has, the simulation is stopped and the data is
returned to the user. If not, the simulation increments to the next variable time step.
Figure 9 Flowchart of the proposed simulation algorithm
Saxena et al.
5 Simulation Results
5.1 Case Study – 8 Node/Bus Model
The toolbox was tested on a 8 bus, 5 DG microgrid operating at 110V and 60Hz
frequency as shown in Figure 10.
Figure 10 8 Bus Microgrid
Simulation and network parameters are included in Table 1. The experiment involved
setting the droop gains of each DG to the same value so that the real power can be shared
equally. Due to line impedance mismatches, the voltage at the nodes of the bus are not
equal, and as such equal reactive power sharing cannot be achieved since the bus voltages
affected by the droop gains settle at different values (Micallef, 2012). This does not affect
equal real power sharing since the frequency of the microgrid is set constant by the
operator. The microgrid is also set configured to be tested from a blank start, which
indicates that all state variables are set to zero.
As can be seen from Figure 11, the power generated by all the DGs converge to the
same value, which indicates that the DGs are indeed sharing the responsibility of the 5
attached loads equally. The reactive power output of the DGs is also included for
reference in Figure 12. In the second trial, the droop gains for the first two DGs are set to
25% more capacity than the second three DGs. This scenario ensures that the first two
DGs, which are presumed closer to the substation, will take more of the load than will the
other DGs. As can be seen in Figure 13, the power supplied by the first two DGs are
equal, and are significantly higher than the power supplied by the last three DGs. To test
the accuracy and stability of the system, active and reactive power losses were calculated
at each node by using the following formulas:
Active Power Loss = I2R (18)
Reactive Power Loss = I2X (19)
The steady state value of all the currents flowing into the nodes (Iod,Ioq,ILineD,
ILineQ, ILoadD, ILoadQ) was summed together and multiplied by the resistance and
inductance at that particular node to find the active and reactive power loss. It was found
that the calculated value for active and reactive power loss was approximately zero.
A Toolbox for the Modelling and Simulation of Islanded Microgrids
Considering the negligible resistance of the lines and high virtual resistor value at the
nodes, the power loss of the network is indeed expected to be close to zero.
Figure 11 Active Power Generation from the 5 DGs converging to the same value
Figure 12 Reactive Power Generation from the 5 DGs
0 1 2 3 4 5
0
50
100
150
200
250
300
350
400
450
Active Power (W)
Time (s)
Active Power Generation of DGs
P1,P2
P3,P4,P5
0 1 2 3 4 5
0
100
200
300
400
500
Rective Power (W)
Time (s)
Reactive Power Generation of DGs
Q1,Q2
Q3,Q4,Q5
Saxena et al.
Figure 13 Active Power sharing with unequal droop settings
6 Future Work
Future steps to extend the simulations of the toolbox include: Modelling the omitted
current and voltage controllers, modelling several varieties of loads instead of a simple
RL load, and performing state estimation within the microgrid. State estimation in
particular is an important research aspect within electrical power grids since sampling is
only done approximately every 10 minutes (Blood, 2011).. Modelling larger networks,
such as the well-known 69 bus microgrid system, is also a priority. It is noted that the
drawing the 69 bus system using the toolbox can be a tedious task. As such, a spreadsheet
file with relevant data regarding the DGs, Lines, Loads, and nodes is also accepted within
the toolbox which will populate the Network object and run the simulation exactly as if
the user had drawn the network.
0 1 2 3 4 5
0
50
100
150
200
250
300
350
400
450
500
550
Active Power (W)
Time (s)
Active Power Generation of DGs
P1,P2
P3,P4,P5
A Toolbox for the Modelling and Simulation of Islanded Microgrids
6 Conclusion
The objective of this paper is to present a dynamic toolbox for the modelling and
simulation of islanded microgrids. A user is able to create custom networks using a user
friendly user interface as well as to input larger networks to the system by file. This
toolbox therefore does not require the user to have any programming experience since the
components are modelled internally and the state matrix is dynamically created based on
the custom network. Furthermore, the intuitive user interface allows the user to quickly
design, develop, and prototype a variety of custom microgrids, allowing each one to be
saved to file and loaded back at a later time. Finally, the non-linearity of the system of
differential equations is preserved, thus providing a more accurate reflection of the
dynamics of an electrical power system. An eight bus test model is also developed and
droop gain tests are done in order to ensure that the model is in working order. This
toolbox has also been tested on a variety of network configurations, including three, five,
and six bus models.
Appendix
Table 1 Constants for 8 Bus Model
Parameter
Value
Units
ω1*,ω2*,ω3*,ω4*,ω5*
377.045
rad/s
Mp1,Mp2,Mp3,Mp4,Mp5
1.8 e-5
-
Nq1,Nq2,Nq3,Nq4,Nq5
1.0 e-4
-
ωc1,ωc2,ωc3,ωc4,ωc5
37.7
-
Vo1*,Vo2*,Vo3*,Vo4*,Vo5*
110.25
V
Rc1*,Rc2*,Rc3*,Rc4*,Rc5*
0
ohms
Lc1*,Lc2*,Lc3*,Lc4*,Lc5*
0.401,0.423,0.423,0.423,0.423
ohms
RLine,1,RLine,2,RLine,3
RLine,4,RLine,5
0
ohms
LLine,1,LLine,2,LLine,3
LLine,4,LLine,5
0.0226,0.0339, 0.0226,
0.0226,0.0226
ohms
RLoad,1, RLoad,2, RLoad,3,
RLoad,4, RLoad,5
13.104, 13.104, 26.208,
39.312, 39.312, 52.416
ohms
LLoad,1, LLoad,2, LLoad,3,
LLoad,4, LLoad,5
15.76, 15.76, 31.52, 47.28,
47.28, 63.04
ohms
Saxena et al.
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