MURDOCH UNIVERSITY
Thesis Report Voltage and Frequency Droop Control of a
Microgrid in Islanded Modes
Zhaoyi Liu
1/13/2016
Supervisor: Dr. Gregory Crebbin
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Abstract
Nowadays, there are increased amount of distributed generation and renewable resources
(including geothermal, ocean tides, solar and wind) used in the microgrid systems, which are
connected via the power inverters. Microgrid is a concept that the systems include at least one
distributed generation resources and local loads can switch to islanded power distributed
systems, [1]. Duo to the small scale of microgrid, the voltage and frequency of system will
carry more severe fluctuations then the larger grids, which will be able to stable these
fluctuations via the wider systems, [9]. The inverters can provide the stability and redundancy
to the power systems. For the normally working of the high current electronic devices, it is
deviation that several inverters operate in parallel in the systems, [3]. The inverter control
methods which should be able to bring the reliable and efficient electricity to microgrid
system have attracted much attention in recent years. Various droop control methods are
regarded as the effective solving technique in conventional generation system.
The droop control strategy is associated with using local power to detect the load changes of
complex powers in the system and adjusting the outputs, automatically, [2]. The advantage of
droop control method is to allow the distributed generators in the system can operate without
external mechanism communications, [3]. No mechanical communication means the system
can adjust and share the loads among distributed generators (connected via inverters)
automatically when the loads change happen. This is based on the calculation of droop
control characteristics. The droop control uses the real power to adjust the frequency of
loads, and vary the reactive power to vary the voltage of loads. However, droop control
scheme are different when the impact of complex impedance is considered. The experimental
simulation results will be presented to illustrate how the droop control scheme impacts the
power distributions of parallel-connected inverters.
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Disclaimer
I declare all the information and knowledge has been developed are all my works except the
parts had been referenced.
Signature:
January 2016
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Acknowledgements
It is a great self-study opportunity that finishing a thesis research project to gain the
knowledge before finishing my bachelor degree of engineering at Murdoch University. It will
be beneficial to my engineer career and any type of futures learning.
I would first like to thank my supervisor Dr. Greg Crebbin for not only provide the chance to
study under his guidance but also the patience and academic knowledge that provided over
the course of thesis. He donates a big amount of time to recommend me and support
questions to run my thesis smoothly and correctly.
I would also acknowledge all my friends from the School of Engineering and Information
Technology at Murdoch University, for providing direct and indirect helps towards the
completion of this thesis period.
Lastly, I would like to thank my family that supporting me on getting an overseas bachelor
degree. They spend much of the patience to guide me to be beneficial to the society.
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Contents
Abstract ...................................................................................................................................... 1
Acknowledgements .................................................................................................................... 3
Contents of table ........................................................................................................................ 6
1.0 Introduction .......................................................................................................................... 8
1.1 Introduction ...................................................................................................................... 8
1.2 Aims description .............................................................................................................. 9
1.3 Thesis Structure ................................................................................................................ 9
2.0 Background ........................................................................................................................ 11
2.1 Microgrid Concept ......................................................................................................... 11
2.2 Microgrid Technologies ................................................................................................. 12
2.3 Distributed Generation ................................................................................................... 13
2.4 Distributed Storage ......................................................................................................... 14
2.5 Interconnection Switch ................................................................................................... 15
2.6 Filters Selection .............................................................................................................. 15
3.0 Droop Control .................................................................................................................... 23
3.1The reasonable justification of the droop control approach ............................................ 23
3.2 Theoretical background .................................................................................................. 24
3.3 Droop controller among inverters .................................................................................. 27
4.0 Modelling and Simulation.................................................................................................. 30
4.1 Theoretical concept of droop controller construction .................................................... 30
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4.2 Average Active Power ................................................................................................... 33
4.3 Average Reactive Power ................................................................................................ 34
4.4 Software Introduction ..................................................................................................... 35
5.0 Implementation .................................................................................................................. 36
5.1 Design of a Single Controller to Achieve Resistive Output impedance. ....................... 36
5.2 Design of a Double Controller with Resistive Output impedance to achieve 2:1 power
sharing. ................................................................................................................................. 39
5.3 Single Inverter Controller Simulations of inductive Output Impedance........................ 40
5.4 Double Inverters Controller Simulations of inductive Output Impedance .................... 42
6.0 Simulation Results ............................................................................................................. 44
6.1 Single Inverter Controller Simulations of Resistive Output Impedance ........................ 44
6.2 Two Inverters Controller Simulations of Resistive Output Impedance ......................... 46
6.3 Single Inverter Controller Simulations of inductive Output Impedance........................ 48
6.4 Two Inverters Controller Simulations of inductive Output Impedance ......................... 50
7.0 Conclusions and Future Works .......................................................................................... 52
7.1 Conclusion ...................................................................................................................... 52
7.2 Future Works .................................................................................................................. 53
Bibliography ............................................................................................................................ 54
Appendix A SPICE Netlist for Signal Inverter Resistive Case ............................................... 56
Appendix B SPICE Netlist for Double Inverters resistive Case .............................................. 59
Appendix C SPICE Netlist for single Inverters inductive Case .............................................. 63
Appendix D SPICE Netlist for Double Inverters resistive Case.............................................. 66
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Contents of table
Figure 1 Simple RC Circuit Figure.1 Simple RC Circuit ........................................................ 16
Figure 2 Bode plots of the second order low-pass filter .......................................................... 18
Figure 3 Simple LC low pass filter circuit ............................................................................... 19
Figure 4 Simple LC low pass filter circuit .............................................................................. 20
Figure 5 Second Order Low Pass Filter Block Input Setting................................................... 21
Figure 6 Bode plots of Second Order Low-pass Filter ............................................................ 21
Figure 7 Power Flowing through a Line .................................................................................. 24
Figure 8 Classic droop control characteristic plots .................................................................. 27
Figure 9 Inverters with same droop characteristics ................................................................. 28
Figure 10 Inverters with different droop characteristics .......................................................... 29
Figure 11 Two parallel-connect inverters with resistive output impedances .......................... 30
Figure 12 Droop control characteristic Line Graph ................................................................. 32
Figure 13 Droop control Block Diagram (Resistive Case) ...................................................... 32
Figure 14 Single phase inverter controller scheme .................................................................. 37
Figure 15 Single Phase Inverter Controller Equivalent Circuit ............................................... 38
Figure 16 Single Phase Two Inverters Controller Scheme (Resistive Case) ........................... 39
Figure 17 Droop control Block Diagram (Inductive Case) ..................................................... 40
Figure 18 Single Phase One Inverter Controller Component (Inductive Case) ....................... 41
Figure 19 Single Phase Two Inverters Controller Scheme (inductive Case) ........................... 42
Figure 20 RMS value of load voltage for single inverter (resistive case) ............................... 44
Figure 21 Single Inverter Controller Frequency Variation (Resistive Case) ........................... 45
Figure 22 Single Inverter Controller Amplitude Variation (Resistive Case) .......................... 45
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Figure 23 Load voltages for Two Inverters (Resistive Case) .................................................. 47
Figure 24 Two Inverters Controller Amplitude Variation (Resistive case) ............................. 47
Figure 25 Two Inverters Controller Frequency Variation (Resistive case) ............................. 47
Figure 26 Single Inverter Controller Output Variation (Inductive Case) ................................ 49
Figure 27 Load voltages for Two Inverters (Inductive Case) .................................................. 50
Figure 28 Two Inverters Controller Amplitude Variation (Resistive case) ............................. 50
Figure 29 Two Inverters Controller Frequency Variation (Resistive case) ............................. 50
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1.0 Introduction
1.1 Introduction
Nowadays, the distributed generations and renewable energy resources (solar panels, variable
speed wind turbines, and ocean tidal power plants) have been more and more prevalent in the
modern electrical power generations. With the development of this, the power inverters
technology has been applied in terms of connecting the energy resources to the main power
grids. However, it is inevitable that several inverters connected in parallel. Therefore, how to
control these parallel-connected inverters to has become a significant problem. The control
method can make the system can detect the outages and finish the maintaining work
automatically.
There is another problem is that how to share the power among these inverters, [3]. It will
happen when the load demand change. A conventional technology named droop control is
used widely to achieve the power sharing goal. There is no external mechanical
communication requirement needed to achieve sharing power automatically, [3]. In addition,
the microgrid system is regarded as a useful way to provide the advantages to the reliability
and stability of the systems, which is discussed in paper, [1]. The microgrid can operate in
both grid-connected and autonomous (islanded) modes, [11] [12].
Islanding mode is one system disconnected to main power grid and can operates
independently, [11]. The independent system can satisfy the local load requirement.
Disconnecting from the main grid is used to protect the components when the fault occurs,
[11]. This thesis project will investigate the microgrid technology and the performance of
droop control approach. These control approach are used to achieve the proportional power
sharing among the inverters without external mechanical communications. In the thesis, a
simplified microgrid circuit in standalone mode will be researched. The simplification
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process will use the voltage sources represent the complicated elements such as the
renewable resources or distributed generators. The simplified circuit will be easier to evaluate
the response duo to the load changes. In addition, the relevant information includes filter
selection and mathematical block diagrams calculations will be investigated in future
research progress.
1.2 Aims description
The aims of the thesis project are to get familiar with the principle of frequency droop control
method operating in the purely inductive and purely resistive network. In additon, the project
is developed to simulation a simple two parallel-connected inverters circuit. What is more,
the reason for the droop control method is used widely to control the distributed generation
resources will be explained.
The project is to evaluate the various frequency and voltage controller options with the
objective of minimize the energy losses and matching the proportional load sharing
throughout the microgrid power system. In addition, to investigate the control and
management of mircogrid, the strategy of frequency and voltage droop control which will
impact frequency and amplitude of output voltage in the islanded mode will be simulated.
In addition, to evaluate the performance of the droop control method, several simple test
electrical circuits will be constructed for SPICE simulations. Therefore, the test system
components which include various elements will be demonstrated by the suitable method in
order to get the final results.
1.3 Thesis Structure
This thesis will evaluate the performance of simple droop control scheme in the case of
purely inductive and purely resistive. The report is divided into 7 chapters. The first chapter
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is going to introduce the whole thesis work, the second chapter reviews the significant
background information, which includes the microgrid concept and its technologies that keep
the system running regularly. In addition, the filter selection will be discussed in the chapter 2.
Chapter 3 illustrates the reasonable justification and theoretical calculations of the traditional
droop control method. In this chapter, the basic information about the droop control works
process will be explained. Throughout chapter 4, the droop control schemes’ mathematical
block diagram will be developed with the aid of data and information provided in Zhang’s
example technical article, [3]. In this chapter, the descriptions are using the mathematical
model that is easier to understand to represent the physical technique. The computer software
introducing is also covered in this part. Chapter 5 is going to show the several conditional
experiments’ implementation in the SPICE. Chapter 6 provides all the results of the projects,
including the case of two inverters systems that are simple microgrids. Chapter 6 concludes
the project and propose the improvements to the conventional droop control. The Appendices
list all of the Netlist used in Icap 4 SPICE.
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2.0 Background
2.1 Microgrid Concept
It has been claimed that the microgrid technology can provide the advantages of reliability
and stability of the systems. A microgrid is defined as “a subsystem of distributed energy
sources and their associated loads”, [1]. The microgrid grid concept is described as resources
which include the distributed generation and renewable energy resources connected to the
local electric power networks via the power inverters. [4] The usage of microgrids has
increased to a large extent due to its largest advantage which is to provide higher reliability
electric energy and higher quality to the system load, [1]. To achieve the objectives, a mini
robust system using the distributed generations which utilize the local information to
maintain system operations will be constructed, [2]. This approach can be a stand-alone
system or connected to the main intelligent power grids, which correspond to the islanding
mode and grid-connected mode, respectively. In addition, most microgrid system
implementations associate loads and from the intentional islanding, the available waste heat
of system is trying to be used, [5]. These concepts are all depending on the complex
communications among system components and various control methods, [5]. Microgrid
concept is to create generator-base controls which can run in “plug- and-play” mode without
mechanical communications, [5].
The microgrid can provide the three main benefits over the traditional centralised distributed
generations [2]:
Opportunities to increase efficiency of the total energy supply system
Practical optimum utilizing of the waste thermal recovery technologies
Improvement of system stability and power quality
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According to [5], the overall fuel-to-electricity efficiency of current power plants which
includes the distributed and central type can be only kept in the range of 28%-32%. This
means that the approximately 70% of energy. To increase system efficiency, both fuel-to-
electricity efficiency and waste heat recovery technologies are utilized in practical. By using
the combined power cycles technology, the entire system efficiency can attain as 60%, [5]. In
addition, based on [5], the waste heats which carry low total fuel-to-useful efficiency (28%-
32%) as mentioned above can be enhanced to greater than 80% by use the “heat exchangers”,
“absorption chiller” and “desiccant dehumidification”. [5] To the biggest extent, the fuel-to-
use energy frequency can get higher than 80% currently by use 60 kW microturbines to warm
the water, [5].
Combined heat and power (CHP) and co-generation technologies are utilized to finish the
waste heat recovery and electricity delivery from the energy resources. [5] Generally, heat is
in the form of steam or hot water in the generation systems, which is hard and not economical
to transmit over the long distance, [5]. Therefore, the heat generation locations should be
constructed near the location of heat requirement load rather than the electricity requirement
load. According to [5], the heat recovery efficiencies are 20% to 80% in a typical combine
heat and power (CHP) system which is near the heat load. This advanced generation
technology should be placed near the heat loads. Lasseter mentioned that the fuel cells are
placed in the each floors of a hospital. The fuel cells can satisfy the requirements of
electricity load and heat water, [5].
2.2 Microgrid Technologies
The microgrids normally are the loacalized grids which are able to disconnect from the main
power gird. [9] In recent years, the mcirogrid technology has been developed and could be
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able to finish the combiniation of clean generations (wind source, solar source or tidal energy
etc.) and traditional generations (diesel and natural gas sources).[9] In addition, the system
can deliver electric and heat at the same time to solve the problem of low efficiency.
Microgrid architecture consists of several technologies to achieve the objective of operating.
Microgrid systems, as a kind of Distributed energy resources (DER) must include distributed
generation (DG) and distributed storage (DS), which can play a role on manage current of
systems, [5]. In addition, microgrids consist of interconnection switches and control systems,
[1] As mentioned in the [5], the biggest challenge is associated with usage and design of low-
cost technology when operate a microgrid system.
2.3 Distributed Generation
Distributed energy resources which include the distributed generation and distributed storage
have amount of advantages such as system reliability improvement when distributed energy
resources can operate properly in the electrical power systems. [6] The distributed energy
resources is defined as “are source of energy located hear local loads and can provide a
variety of benefits including improved reliability if they are properly operated in the electrical
distributed system”, [1]. Distributed generation source are typically include photovoltaic (PV),
wind turbines, traditional resources such as fuel cells, [1]. Either of fossil and renewable
resources can supply the regular operation of the power system. As mentioned above, some
kinds of distributed generation of microgrid have the function of heat recovery by recover the
wasted heat. This technique can increase the efficiency of heat and electric combination
system. It is necessary for most of the distributed generation technologies that a power
electronic used to converter the energy to main grid, [1]. The power electronics required both
rectifier and inverters or just inverter, [1]. The converter can harmonize the voltage and
frequency of components of systems. In addition, the necessary output filter is also demanded
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between the inverter and girds. The protection will also be provided by the power electronics
to the distributed generations and the local electric systems, [1].
2.4 Distributed Storage
It is deviation that the generation and local loads cannot harmonize exactly in some
conditions. To handle this technical problem, the distributed storage devices will be applied
in microgrid, [1]. Normally, the capacity applications which can categorize in terms of energy
density requirement or in term of power density requirement can play a positive role on
system performance in the 3 terms [1]:
1 It can stabilize the fluctuation of the distributed generation to run at a constant output.
2 It offered the necessary capability which is used to keep stable when the variation of load
occurs.
3 It benefit the operation of distributed generation as the seamlessly delivery unit in the
systems.
In addition to the benefit of distributed storage, it can solve the short-time power disturbances
and provide the energy reservation for the future demand. [1] Several types of the storage
applications can be utilized in the microgrid. Basically, the batteries, capacities and flywheels
are used widely. Batteries can store the electrical energy in forms of the chemical energy.
Batteries require a power converter to transfer DC power to the AC power used in the
intelligent girds, [1]. Suppercapacitors which are named ultracapacitors in some reference can
storage the electrics and enhance the density of power and high cycling capacity, [1].
Moreover, due to its quick respond compared to traditional electrical storage, the flywheels
systems came back to the public vision and play an effective role in terms of supply the
critical load demand when the system interruptions occurs, [1].
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2.5 Interconnection Switch
The interconnection switch is used to connect and disconnect the mirogrid and the rest of
distributed generation systems. Advanced technologies can combine the consolidates the
powers and switch functions which include the protection relays, metering, switching and
communications functions provided by the traditional relays and other electronic interfaces.
Specifically, the design plan of interconnection switches should match the requirements of
gird design standard. [1]
2.6 Filters Selection
According to the Zhong’s literature article [3], the low pass filter is appeared as significant
component in the simulation model. It plays an important role in terms of cutting high
frequency and passing low frequency. Therefore, the suitable value of low pass filter should
be demonstrated in the process of constructing simulation models.
2.6.1 Theoretical background
In a linear electrical system, sinusoidal input signals, can be represented used to evaluate the
frequency response in the system. This evaluation can be divided into the following steps:
1. Convert the sinusoidal input source to use phasor equivalent:
𝑥𝑖𝑛(𝑡) = 𝑋𝑖𝑛 cos(𝑤𝑡 + 𝜃𝑖𝑛) → 𝑋𝑖𝑛 = 𝑋𝑖𝑛𝑒𝑗𝜃𝑖𝑛
2. Convert all inductors and capacitors to their impedance:
𝑍𝑙 = 𝑗𝜔𝐿
𝑍𝐶 =1
𝑗𝜔𝐶= −𝑗(
1
𝜔𝐶)
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3. Calculate the voltages and currents of unknown phasors by using KVL and KCL
equations.
4. Transfer the output phasor back to sinusoids:
𝑋𝑜𝑢𝑡 = 𝑋𝑜𝑢𝑡𝑒𝑗𝜃𝑜𝑢𝑡 → 𝑥𝑜𝑢𝑡(𝑡) = 𝑋𝑜𝑢𝑡 cos(𝑤𝑡 + 𝜃𝑜𝑢𝑡)
It also should be noted that, there should be a phasor that is selected as the reference phasor.
Normally, the input phasor will be selected but the specified phasor should lead a simpler
calculation. In addition, the phasors can be represented by the either polar (magnitude, angles)
or rectangular forms (real, imaginary numbers). The phasor analysis suit the situation where
there are multiple same-frequency input sources.
The phase analysis is very effective in terms of understanding amplitudes and phase shifts
relevant to the input signals and determining the expressions for amplitude and phase changes
as function of frequency.
A simple example will be developed to determine the transfer functions:
Figure 1 Simple RC Circuit Figure.1 Simple RC Circuit
The capacitors in the simple RC circuit can be converted to 1/j𝜔C, and following equation
was gained by the impedance divider rules:
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𝑉𝑜 =
1𝑗𝜔𝐶
𝑅 +1
𝑗𝜔𝐶𝑅
𝑉𝑖𝑛
𝑉𝑜
𝑉𝑖𝑛=
1
1 + 𝑗𝜔𝐶𝑅
The ratio of output phasor and input phasor is called transfer function. The transfer function
can be represented in polar form:
H(ω) =𝑉𝑜
𝑉𝑖𝑛
=1
1 + 𝑗𝜔𝐶𝑅
=1
√1 + (𝜔𝐶𝑅)2 < 𝑡𝑎𝑛−1(𝑤𝐶𝑅)
= H(ω) < 𝜃𝐻(𝜔)
The output voltage will be giving by
𝑣𝑖𝑛(𝑡) = 𝐻(𝜔𝑜)𝑉𝑠𝑖𝑛(𝜔𝑜𝑡 + 𝜃𝐻(𝜔𝑜))
The transfer function can play a significant role in terms of evaluating the amplitude and
phase deviation between input and output. The plots of the amplitude and phase shown in
figures are called Bode plots. In addition, the Bode plot in this case is for a second order low
pass filter.
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Figure 2 Bode plots of the second order low-pass filter
As seen in Figure.2, the amplitude decrease from low frequency level as frequency increase.
In figure, the circuit passes low frequency but blocks high frequency sinusoids. Therefore, the
circuit play a role as a low-pass filter. In this plot, the frequency area where the signal was
passed and broken to a very small extent is named as passband region. The area where
attenuations occur to a very big extant is called stopband region. The main objective of the
low pass filter is to cut the unwanted high frequency, automatically. The critical region that
lies between the stopband and passband is named as transition region. The low pass filter is
regarded as key equipment in the convention of analog to digital.
2.6.2 Filter selecting
An LC low pass filter has components of shunt capacitor and a series inductor as shown in
fugure 3. At low frequency, the inductor and capacitor acts like short circuit and open circuit,
respectively.
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Figure 3 Simple LC low pass filter circuit
The transfer function at low frequency is given by:
H(0) =𝑉𝑜
𝑉𝑖𝑛
(0) =𝑅𝐿
𝑅𝑠 + 𝑅𝐿
At high frequencies, the inductor and capacitor act as the open circuit and short circuit,
respectively. Both of the two elements have the function of blocking the high frequency.
The first-order low pass filter given in figure 1 has a transfer function which is defined as
H(ω) =𝐴
1 + 𝑗𝜔𝜔𝑐
H(ω) =𝐴
√1 + (𝜔𝜔𝑐
)2
In this equation, A =1 and𝜔𝑐 =1
𝑅𝐶. In addition, the transfer function of second order low pass
Butterworth filter is given:
H(ω) =𝑉𝑜
𝑉𝑖𝑛(ω)
=𝑅
√(2𝑅 − 𝜔2𝐶𝐿𝑅 + 𝜔2(𝐶𝑅2 + 𝐿)2
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=1/2
√1 + (𝜔
𝜔𝐶)4
WhereR = √𝐿
𝐶 , 𝜔𝐶
4 =4
𝐶2𝐿2 and 𝜔𝑐 = √2
𝐿𝐶
Converting the gain to decibel the second-order response: at high frequencies
H(ω) = −6.02 − 10 log10(1 + (𝜔
𝜔𝐶)4)
In this equation, the slope is -40 dB/decade. The objective of the calculation is to get suitable
value of inductor, resister and capacitor which suit the situation of filter low frequency and
block high frequency. The design calculations of low pass filter will be used in the droop
control simulations.
2.6.3 Filters development in SPICE
To evaluate the performance of the filter, a modelling of second order Butterworth low pass
filter, a model can be built and simulated on SPICE, as shown in figure. All the parameters
for the filter are taken from Zhong’s paper, [3].
Figure 4 Simple LC low pass filter circuit
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It should be noted that Resistor R1 is only includes in order to make sure that two elements
are connected to model, is required by SPICE analysis rules. In this SPICE simulation, the
voltage source is set to supply 1 Volt AC voltage, while the load resistance is given as 1 ohm
to illustrate the response of frequency. The input settings of the filter block are shown in
figure 5:
Figure 5 Second Order Low Pass Filter Block Input Setting
Figure 6 Bode plots of Second Order Low-pass Filter
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The bode plots shown in figure 6 shown the result of the second order low pass filter. It can
be noted that the filter works effectively. It cut the high frequency sinusoids above 5 Hz, the
cut off frequency is approximately -5.01 dB.
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3.0 Droop Control
3.1The reasonable justification of the droop control approach
Due to the sharply increased use of the renewable resources, more and more parallel
connected inverters are being used in both utility grids and microgrids, [3]. Even in the
microgrid system, it is inevitable that several generators operate in parallel to supply the local
load. Normally, the distributed generators or renewable resources are connected to the grid
using inverters, [3]. A significant issue with using is how to solve the problem of power
sharing among inverters in parallel-connected inverters system.
An optimum active power P and reactive power Q is need by a steady power system, [7].
The conventional droop control is spending the active power and reactive power to achieve
proportional power sharing among several uninterruptible power supplies (UPS).
The reason why use droop control method is to allow the distributed generators in the system
to operate without external mechanism communications. It is a symbol of zero mechanism
communications system can adjust and share the loads among distributed generators
(connected via inverters) automatically when the loads changes occur is a symbol of zero
mechanism communications, [3]. This is based on the calculation of droop control
characteristics. Specifically, one of challenge problem is frequency control. In islanded mode,
the frequency harmony of system is based on rotating masses in the large grid, which is
significant to enhance the internal stability of systems, [1]. However, microgrid is the system
entirely controlled by converters, which is relevant to rotating mass, [1]. Therefore, the
control of frequency is based on the converters’ management. The converter control systems
must be adjusted to get respond before getting respond from rotating mass.
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In addition, f-P and V-Q control can use droop character to distribute unbalanced load
requirement among the inverters which are connected to the distributed generators or
renewable resources. This simple and reliable method can guarantee the unity of whole
system’s frequency and voltage in standalone model. Droop control of adjusting active power
and reactive power to control frequency and voltage separately.
3.2 Theoretical background
To get familiar with the original approach of droop control, the complex impedance of
transmission lines model is going to be considered below. The most essential assumption
which is used below is that the inductive value is much greater than the resistive value. This
assumption is suitable for high-voltage transmission lines. microgrid may operate in the
situation of low voltage cables which have resistance, so obviously. For these cases resistance
cannot be ignored.
The relationships between power flow and voltages can be derived by considering the power
flow through a transmission line between two buses, as shown in Figure.7 is described [8]
Figure 7 Power Flowing through a Line
The power flow through the line from point A to point B which is shown in the Fig.7 is
described [8]:
P + jQ = 𝑆∗ = 𝑉1𝐼∗ = 𝑈1 (𝑉1−𝑉2
𝑍)*
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= 𝑉1(𝑉1 − 𝑉2𝑒𝑗𝛿
𝑍𝑒−𝑗𝜃)
=𝑉1
2
𝑍𝑒𝑗𝜃 −
𝑉1𝑉2
𝑍𝑒𝑗(𝜃+𝛿)
Therefore, the active power and reactive power flow into lines should be illustrated in the
equation below:
P =𝑉1
2
𝑍𝑐𝑜𝑠𝜃 −
𝑉1𝑉2
𝑍cos (𝜃 + 𝛿)
Q =𝑉1
2
𝑍𝑠𝑖𝑛𝜃 −
𝑉1𝑉2
𝑍sin(𝜃 + 𝛿)
Substituting the equation𝑍𝑒𝑗𝜃 = 𝑅 + 𝑗𝑋, the real power and reactive power of the
transmission line is [8]:
𝑉2𝑠𝑖𝑛𝛿 =𝑋𝑃 − 𝑅𝑄
𝑉1
𝑉1 − 𝑉2𝑐𝑜𝑠𝛿 =𝑅𝑃 + 𝑋𝑄
𝑉1
When it comes to the purely inductive transmission lines, inductive impedance X is much
greater than the resistive impedance R. That means R can be neglected, the equation should
be rewritten:
𝑃 ≈𝑉1𝑉2𝑠𝑖𝑛𝛿
𝑋
𝑄 ≈𝑉1
2 − 𝑉1𝑉2𝑐𝑜𝑠δ
𝑋
Droop Control of Micrigrid
26
According to De Brabandere [8], if the power angle δ is small, then the reactive power and
active power are proportional to the Voltage V1 and angle speed δ, respectively. Therefore,
the P-w and Q-u are both feedback loops:
𝛿 ≅𝑋𝑃
𝑉1𝑉2
𝑉1 − 𝑉2 ≅𝑋𝑄
𝑉1
From these two equations that varying active power can be used to control the angle 𝛿 while
vary the reactive power Q to control inverter voltage U1 can be adjusted by the Q. However,
in the droop control method, the frequency is used instead of the power angle δ, [2] [13]. The
reason for not use the power angle or phase angle is to do with unknown initial value of phase
of the other elements in the standalone systems. [2]
Then, we get the basis well-known droop control formulae:
𝑓 − 𝑓0 = −𝑘𝑝(𝑃 − 𝑃0)
𝑉1 − 𝑉0 = −𝑘𝑞(𝑄 − 𝑄0)
The frequency and voltage droop associate with the P and Q increasing figure are shown in
figure 8:
Droop Control of Micrigrid
27
Figure 8 Classical droop control characteristic plots
The droop control characteristic plots can be used to explain the conventional droop control
method. The control method can fix the fault frequency to the normal frequency when the
frequency errors occur. [8]
However, the frequency restoration of inverter in practice is not easily to be done. This is
because all formulas are based on the assumption that impedance is purely inductive. In
practice, the transmission lines have both resistive and inductive parts. When increase the
active power, the current will be increased. This is because system voltage is constant.
3.3 Droop controller among inverters
In real situations, there are usually two or more inverters in the system. They share the load
demand together. The inverter droop controls can be divided into two situations below. The
first situation is under the condition that two inverters controllers have same droop
characteristics. In this case, the load changes are shared equaling between two inverters,
which means the droop proportion is 1:1. Figure 9 below indicates the tendencies of the
droop characteristics of two parallel-connected inverters with same load power sharing
proportion. It can be clarified that the trends of 2 curves are same. This is duo to the
proportion of load sharing is designed as the 1:1. In contrast, from the figure 10, it should be
noted that if active power (reactive power) is increased same value, frequencies (voltages)
will decreased to a different extent. This is due to the difference in the inverters
Droop Control of Micrigrid
28
characteristics when they are operating in parallel. In addition, the frequency and voltage
deviations will increase when the active power and reactive power increase.
Figure 9 Inverters with same droop characteristics
Therefore, the design procedures should be considered based on the mean load sharing and
deciation extent. The inverters in figure 10 use the different droop characristics. It can be
used when the rated loads of inverters are different. The inverters can share loads according
Droop Control of Micrigrid
29
to the unit rated values. By setting the suitble set points and droop characteristics, the
propertions of load sharing can be achieved easily without external or internal mechanical
comunications among the distributed generation. In addtion, it should be noted aht the figure
10 construction are base on the [14].
Figure 10 Inverters with different droop characteristics
Droop Control of Micrigrid
30
4.0 Modelling and Simulation
4.1 Theoretical concept of droop controller construction
To simulate the droop control method among parallel-connected inverters, a droop control
scheme model should be created and analysed.
In this chapter, a reactive power-angle speed (Q-𝜔) and active power –voltage (P-V) droop
model will be created according to [3], which is easily to export to the Q-E and P-w. The Q-E
and P-w droop model is described in section 3.0. The purely resistive base circuit of two
generators operating in parallel will be analysed.
Figure 11 Two parallel-connect inverters with resistive output impedances
The Figure 11 is constructed base on [3]. Each impedance includes both of generator
impedance and the impedance of transmission lines which connected the generator and loads.
The active power and reactive power injected to loads will be given in the chapter 3.2:
P =𝑉1
2
𝑍𝑐𝑜𝑠𝜃 −
𝑉1𝑉2
𝑍cos (𝜃 + 𝛿)
Q =𝑉1
2
𝑍𝑠𝑖𝑛𝜃 −
𝑉1𝑉2
𝑍sin(𝜃 + 𝛿)
Droop Control of Micrigrid
31
Generally, the inductive inverter output impedance is used a lot in the transmission lines, [3].
However, when the inverter output impedance is resistive which is applied in the low-voltage
conditions, the equation above change to the formulas below [3]:
𝑃𝐿 =𝑉𝐿𝐸1𝑐𝑜𝑠𝛿1 − 𝑈𝐿
2
𝑅1
𝑄𝐿 = −𝑉𝐿𝐸1𝑠𝑖𝑛𝛿1
𝑅1
If the power angle δ is small, the simplified equations become:
𝐸1 ≈ (𝑅1
𝑉𝐿) 𝑃𝐿 + 𝑉𝐿
𝛿1 ≈ −𝑅1
𝑉𝐿𝐸1𝑄𝐿
According to the equation above in order to achieve the demand of changing active power of
loads P, increase active P can lead to increasing of voltage E. Similarly, an inverse response
between reactive power Q and power angle δ can occur, so that increase power angle δ can
finish by decreasing reactive power Q. It should be noticed that in order to keep the feedback
loops of P-E negative, the droop characteristic should be adjusted to negative value.
To achieve the objective of maintaining an optimal operating point, a droop controller should
be designed to oppose the characteristic trend of P-E. For instance, the figure below shows
that the Voltage of droop controller decreases versus active power P.
Droop Control of Micrigrid
32
Figure 12 Droop control characteristic Line Graph
The equations for a conventional droop controller in the purely resistive conditions are given
by [3]:
𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑃𝑖
𝑤𝑖 = 𝑤∗ + 𝑚𝑖𝑄𝑖
, where the E*and w* is rated voltage and frequency, respectively. [3] The droop control
scheme block diagram is shown in figure 13 [3] [4]:
Figure 13 Droop control Block Diagram (Resistive Case) [3]
It should be noticed that the output of this diagram is 𝐸𝑖 ∗ sin (𝜔𝑡 + 𝜑𝑖), which is the voltage
of output impedance.
Droop Control of Micrigrid
33
4.2 Average Active Power
The first step of the droop controller is to take the continuous voltage V and current I signals,
and calculated average values of active power and reactive power. The continuous value for
voltage and current and the input to the controller are given by [15]:
𝑣0(𝑡) = 𝑉0sin (2𝜋𝑓0𝑡)
𝑖1(𝑡) = 𝐼1sin (2𝜋𝑓0𝑡 + 𝜑)
The relationship with input power P is described [15]:
p(t) = 𝑣0(𝑡)𝑖1(𝑡)
p(t) = 𝑉0𝐼1sin (2𝜋𝑓0)sin (2𝜋𝑓0𝑡 + 𝜑)
The equation can be simplified to the formula below [15]:
p(t) = 𝑉0𝐼1[cos(−𝜑) − cos(4𝜋𝑓0𝑡 + 𝜑)]
According to this, the waveform includes a DC component and a time vary compound with
frequency that is twice the frequency of the initial voltage and current sinusoidal waveforms.
The averaging operating can be carried out by using a low pass filter (LPF) with a cut of
frequency that is less than 2f0. The area from 0 to 2f0 should be chosen as the band-edge of
filter. This filter shown passes the average (DC) value. However, the birck-wall filter which
can eliminate the AC (sinusoidal) waveform does not exist in real situations. According to
earlier discussion, a simple first-order low past filter has a frequency response is described
[15]:
|H(f)| =1
√1 + (𝑓𝑓𝑐
)2
Droop Control of Micrigrid
34
To make the gained at f=100Hz be as small as possible, the smallest cut-off frequency fc
should be used. However, if fc is too low, the filter will respond too slowly when changes in
power demand occur over time. The changes happen when the faults occur or when load
demands change. Therefore, the value of cut-off frequency should trade off these two
requirements. The selection of a higher order level filter means the sharper characteristic of
filter response. The second order Butterworth filter has a magnitude response which can
present by the equation is described [15]:
|H(f)| =1
√1 + (𝑓𝑓𝑐
)4
4.3 Average Reactive Power
The output of the reactive power is given by [15]:
q(t) = 𝑣0(𝑡)𝑖1(𝑡)
q(t) = 𝑉0𝐼1sin (2𝜋𝑓0 + 90°)sin (2𝜋𝑓0𝑡 + 𝜑)
It should be noted that the waveform has been phase shift by 90 degrees from the active
power expression. The equation can be simplified [15]:
q(t) = 𝑉0𝐼1[cos(90° − 𝜑) − cos(4𝜋𝑓0𝑡 + 90° + 𝜑)]
The requirement of voltage phase shift by 90 degrees can easily satisfied by using an all-pass
filter in the SPICE model construction. The transfer function of this strategy is given by [15]:
Droop Control of Micrigrid
35
H(f) = −1 − 𝑗(
𝑓𝑓0
)
1 + 𝑗(𝑓𝑓0
)
Substituting frequency f=f0 + 50 Hz the transfer formula becomes [15]:
H(50) = −1 − 𝑗1
1 + 𝑗1
H(50) = (1 180°)√2 − 45°
√2 45°
H(50) = 1 90°
4.4 Software Introduction
ICAP/4 SPICE (Simulation Program with Integrated Circuit Emphasis) circuit analysis
software is developed by Intusoft. It should be noted that SPICE was developed by university
of California Berkeley, [10]. ICAP by latusoft is a commercial vision of SPICE. It is used to
simulate the analog and mixed signal circuits, [10]. The benefit of ICAP is able to simulate
both electrical circuits and systems. In this project, the SPICE is used to combine the droop
controllers which are analog signals and data collecting circuit of droop controller which are
represented at a system level. The SPICE can be used to check and evaluate the transient and
frequency response of the circuit networks over a range of operating conditions.
Droop Control of Micrigrid
36
5.0 Implementation
The control algorithms have been installed in a SPICE Netlist. In the example given in [3],
two single phase inverter with 42 volts supply voltage, which is controlled by dSPACE kits.
As mentioned in section 3.4, an IGBT bridge controlled by PWM technology was used to
construct the continuous sinewave. The filter values of the inductor and capacitor are 2.35mH
and 22μF, respectively. [3] The switching frequency of PWM circuit is 7.5 kHz, and rated
frequency of system is 50 Hz. The switching frequency of PWM circuit is 7.5 kHz. The rated
voltage is 12V, [3].
5.1 Design of a Single Controller to Achieve Resistive Output
impedance.
Based on the main works of the project, the droop control scheme of resistive output
impedance is installed in the SPICE netlist. To illustrate the accuracy of the droop control
strategy, a single-phase inverter with different load demands system will be tested using
SPICE. This model is based on the assumption that the load impedance is purely resistive.
Droop Control of Micrigrid
37
Figure 14 Single phase inverter controller scheme
The Netlist is given in the Appendix. It can be seen from the corresponding schematic
diagram in figure that network can be divided into 2 components: the controller and that
electrical circuit. There are two feedback loops in that controller. The top side feedback loop
adjusts the amplitude of output sinewave signals via controlling the active power P and
system voltage V signals. In contrast, the bottom feedback loop is controls the frequency of
output sinusoid waveform by controlling the reactive power Q and system frequency signal.
As mentioned above in section 4.3, there is an all-pass filter is applied to achieve the phase
shift when calculating the reactive power delivered to the load. There are two feedback loops
designed to achieve the objectives of controlling amplitude and frequency of output sinewave
signals at the same time. In addition, the line current of the controller can be gotten by
measuring value of a dummy voltage source which corresponds to the voltage source Vind1
in the electrical circuit. The load voltage at node 8 is returned to the input of the controller
A
B
K*A*B
8
10
3
MUL
S^2+AS+B K
- 4
X2
POLE2
SUM2
K1
K22
1
X3
SUM2
RE
1
V1
12
9
5
X5
SWITCH
Vswitch
Rload2
9
Rload1
9
C1
22uF
6 7
L1
2.35mHVind1
8
8
K=1
B1
Voltage
1.4142*V(1)*cos(V(16))
H1
1
A
B
K*A*B
11
12
X4
MUL
S+A
S+B
X6
PZ
S^2+AS+B K
- 13
X7
POLE2
16
Rw
1
14
V4
314.295
Vo
SUM2
K1
K2
15
X8
SUM2
K/S
X9
SINT
Droop Control of Micrigrid
38
using, the continuation element. The electrical network, with test points for node voltage and
line current, is shown in Figure 15
Figure 15 Single Phase Inverter Controller Equivalent Circuit
All the parameters in the equivalent circuit are provided in the [3]. The circuit is installed in
ICAP SPICE simulation. The switch is used to connect and disconnect an additional load at
specific time. The value of voltage source Vind1 is set to 0 V. Generally, measure the current
value of dummy voltage source is an effective way to identify and adjust the line current
value. The controller generates the amplitude and frequency of the output voltage according
to the equations:
𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑃𝑖
𝑤𝑖 = 𝑤∗ + 𝑚𝑖𝑄𝑖
, where the E*and w* is rated voltage and frequency, respectively. [3]
It should be noted that the reactive power Qi is proportional to -δi if the power angle is small.
In order to make sure all the feedback loops of this strategy are negative, the signs before
𝑚𝑖𝑄𝑖 has been set to positive, [3]. In the single inverter simulation, either frequency droop
characteristic or voltage droop characteristic is set to 1. The results of this simulation will be
illustrated in the section 6 experiment results.
Droop Control of Micrigrid
39
5.2 Design of a Double Controller with Resistive Output impedance to
achieve 2:1 power sharing.
The main objective of this project is to use droop control to achieve proportional power
sharing among inverters. Therefore, the core experiments are designed to research the
performance of multiple inverters. Firstly, the simulation set up for two parallel-connected
inverters was constructed in SPICE; the schematic diagram for this set- up is shown in
figure.17
Figure 16 Single Phase Two Inverters Controller components (Resistive Case)
A
B
K*A*B
8
10
3
MUL
S^2+AS+B K
- 4
X2POLE2
SUM2
K1
K22
1
X3SUM2
RE1
Erated12
9
5
X5SWITCH
Vswitch
Rload29
Rload19
C122uF
6 7
L12.35mH
Vind1
8
8
n1=0.4
B1Voltage
1.4142*V(1)*cos(V(16))
H11
A
B
K*A*B
11
12
X4MUL
S+A
S+B
X6PZ
S^2+AS+B K
- 13
X7POLE2
16
Rw1
14
Vrated314.295
Vo
SUM2
K1
K2
15
X8SUM2
K/S
X9SINT
Line current
C222uF
17
Vind2
18
L22.35mH
B2Voltage
A
B
K*A*B
19
20
-xMUL
n2=0.8
S^2+AS+B K
- 21
X11POLE2
SUM2
K1
K222
23
X12SUM2
REx1
Eratedx12
8
H21
Line current
A
B
K*A*B
24
25
X13MUL
S+A
S+B
X14PZ
S^2+AS+B K
- 26
X15POLE2
27
Rwx1
28
Vratedx314.295
SUM2
K1
K2
29
X16SUM2
K/S
X17SINT
1.4142*V(23)*cos(V(27))
Vo2
m1=0.1
m2=0.2
Droop Control of Micrigrid
40
As can be seen clearly, the two inverters are connected in parallel. In this concept, there are
two controllers for each inverter. The droop coefficients of inverters are set to n1= 0.4 and
n2= 0.8; m1= 0.1 and m2= 0.2. It can be confirmed that P1=2 P2, and Q1= 2Q2 which is 1:2
power sharing. In addition, the two inverters share the same output voltage and load
impedance. The test point was also placed to demonstrate the output voltage of the second
inverter. The results of this experiment will be described in the section 6.2.
5.3 Single Inverter Controller Simulations of inductive Output Impedance
Generally, the impedance of power grid with high voltage cables have is inductive. The
traditional droop control method can easily satisfy the conditions of purely inductive. A
modelling of inductive output impedance will be established in SPICE. can be used to
evaluate the frequency and voltage response of a circuit. The mathematical blocks diagram
which rewrite base on the Figure, 13 is given above:
Figure 17 Droop control Block Diagram (Inductive Case)
Hence, the detail circuit component according to the concept of block diagram is shown:
Droop Control of Micrigrid
41
Figure 18 Single Phase One Inverter Controller Component (Inductive Case)
To compare with the case of resistive, the droop feedback loops are much different.
According to the theoretical background knowledge of droop control, the active power Pi is
proportional to the δ, while reactive power Q corresponds V. The rest parts of this modelling
follow the same concept as resistive case, which is indicated above. It should be notice that,
the conventional droop controller equation of purely inductive is given:
𝐸𝑖 = 𝐸∗ − 𝑛𝑖𝑄𝑖
𝑤𝑖 = 𝑤∗ − 𝑚𝑖𝑃𝑖
, where the E*and w* is rated voltage and frequency, respectively. In the single inverter
simulation, either frequency droop characteristic or voltage droop characteristic is set to 1.
The results of this simulation will be illustrated in the section 5 experiment results.
A
B
K*A*B
11
10
3
MUL
S^2+AS+B K
- 4
X2
POLE2
SUM2
K1
K22
1
X3
SUM2
RE
1
V1
12
8 9
5
X5
SWITCH
Vswitch
C1
11uF
6 7
L1
1.36mHVind1
8
8
K=1
B1
Voltage
1.4142*V(1)*cos(V(16))
H1
1
A
B
K*A*B12
X4
MUL
S+A
S+B
X6
PZ
S^2+AS+B K
- 13
X7
POLE2
16
Rw
1
14
V4
314.295
Vo
SUM2
K1
K2
15
X8
SUM2
K/S
X9
SINT
L2
8mH
L3
8mH
Droop Control of Micrigrid
42
5.4 Double Inverters Controller Simulations of inductive Output Impedance
According to the single controller operation concept, a double inverters controller component
can be easily constructed in the SPICE, which is shown in Figure. 19:
Figure 19 Single Phase Two Inverters Controller components (inductive Case)
In the double inverters of resistive case, the droop characteristics are set as: n1= 0.4 and n2=
0.8; m1= 0.1 and m2= 0.2. The controllers are set to share the power in the proportion of 1:2.
In addition, from the output-voltage results of single inverter (inductive case), it has been
A
B
K*A*B
11
10
3
MUL
S^2+AS+B K
- 4
X2POLE2
SUM2
K1
K22
1
X3SUM2
RE1
Erated12
8
C144uF
6 7
L15mH
Vind1
8
8
n1=0.4
B1Voltage
1.4142*V(1)*cos(V(16))
H11
A
B
K*A*B12
X4MUL
S+A
S+B
X6PZ
S^2+AS+B K
- 13
X7POLE2
16
Rw1
14
Vrated314.295
Vo
SUM2
K1
K2
15
X8SUM2
K/S
X9SINT
Line current
9
5
X5SWIT CH
V2
L28mH
L38mH
19
B2Voltage
17
L45mHVind2
C211uF
A
B
K*A*B
18
20
21
-xMUL
n2=0.8
S^2+AS+B K
- 22
X11POLE2
SUM2
K1
K223
24
X12SUM2
REx1
Eratedx12
8
H2Vind2
Line current
A
B
K*A*B25
X13MUL
S+A
S+B
X14PZ
S^2+AS+B K
- 26
X15POLE2
27
Rwx1
28
Vratedx314.295
SUM2
K1
K2
29
X16SUM2
K/S
X17SINT
1.4142*V(24)*cos(V(27))
V8
m2=0.2
m1=0.1
Droop Control of Micrigrid
43
demonstrated that the frequency of output voltage is pretty high. That means the low pass
filter dose not works well. This is because the value of inductor and capacitor that is the
components of filter is too small. Therefore, the values of low-pass filter are increased to
5mH and 44uF, respectively to cut the high frequency and pass low frequency. The results of
inductive controllers will be illustrated in chapter 6.
Droop Control of Micrigrid
44
6.0 Simulation Results
To prove the accuracy of the droop control strategy among parallel-connected inverters
described in the project, a series of droop control feedback loops were tested using the same
constructing concept of block diagram. The results are detailed as follows. The output
sinusoid waveforms are given firstly, while the frequency variation figures and amplitude
variation figures are given in the second place.
6.1 Single Inverter Controller Simulations of Resistive Output Impedance
The result from the single inverter controller with droop characteristic =1 is indicated in the
figure.20 while the frequency and amplitude results from conventional droop controller is
indicated from figure.21 to figure22. Obviously, there are two steady states. During 0.5
seconds, the load demand is doubled. The system need rework and get the new amplitude and
frequency to achieve the new steady state.
Figure 20 RMS value of load voltage for single inverter (resistive case)
Droop Control of Micrigrid
45
Figure 21 Frequency Response of Single Inverter (Resistive Case)
Figure 22 Amplitude Response of Single Inverter (Resistive Case)
1 v(1)
100m 300m 500m 700m 900mtime in seconds
7.50
8.50
9.50
10.5
11.5
v(1
) in
vo
lts
Plo
t1
1
Droop Control of Micrigrid
46
In this concept, the amplitude measurement can be done by measure the voltage of node 1 in
controller, while the amplitude performance demonstrated by the measurement of voltage of
node 15. The voltage node 15 corresponds the2πf + φ; (2πf + φ)x t should be calculated by
the integrator and measured by voltage node 16. The proposed block diagram strategy was
able to achieve the goal of varying the RMS value of output voltages. In addition, it should be
noticed that the unit of frequency in Figure 21 are volts. This is the voltage is used as the
controllers signals. Therefore, it can be transferred to the Hz by using the equationω = 2πf.
From the figures above, it can be clarified that both of frequency and voltage dropped at the
beginning and get the first steady state at approximately 0.15 seconds. After that, the load
impedance was doubled. The consequence of that is frequency’s fluctuation again and getting
the steady state at finals. The system frequency value of finally steady state is around 314.06
rad/s. When it comes to the amplitude variation, the tendency as a whole is decreased to a
small extent, which satisfies inverse proportion response. The final value of amplitude
decreased to approximately 5.5 Volts when the load power increased because load impedance
is doubled.
6.2 Two Inverters Controller Simulations of Resistive Output Impedance
There are two sinusoid waveforms in the Figure 23. The line 1 represents the inverter 1 while
line 2 represents the inverter No.2.
Droop Control of Micrigrid
47
Figure 23 Load voltages for Two Inverters (Resistive Case)
Figure 24 Amplitude Response of two inverters (Resistive case)
Figure 25 Frequency Response of Two inverters (Resistive case)
Droop Control of Micrigrid
48
The results of the two inverters with 2:1 proportions power sharing was indicated above. The
figures include the output voltages, amplitudes and frequency. In detail, the amplitudes
variations of inverter No.1 and inverter No.2 are measured by measuring the Voltages of
node 1 and node 23, respectively. The Figure.23 demonstrates same trends of two controllers.
However, the value of V (1) is dropped to 11.9364V that is the first steady state and decrease
to 11.8751V. The difference between first and final steady state is 0.06. On the contrary, the
value of V (23) changed approximately 0.03 which is from 11.96 to 11.93. Hence, it can be
clarified that the inverter No.1 which corresponds V (1) shared 2 times power as Inverter
No.2 that corresponds V (23). The results satisfied the goals which 2:1 proportional power is
sharing. When it comes to the amplitudes, by measuring the values of voltage node 15 and
voltage node 29, the amplitudes of controller 1 and controller 2’s output sinusoid voltage can
be evaluated, respectively. The first steady state of inverter No.1 occurred in approximately
0.15 second. The RMS value of V (15) can be obtained as 314.2923Vand decrease to the
314.2918V. On the other hand, the RMS values of another inverter’s frequency have changed
0.0002 Voltage. Although the frequencies of inverters ran smoothly and changed to a slight
extent, the power sharing ratio of this system is 2:1, which is satisfied the initial settings.
6.3 Single Inverter Controller Simulations of inductive Output Impedance
The results of single inverter controller strategy are indicated in Figure.26, which include the
performance of output voltage, amplitude and system frequency.
Droop Control of Micrigrid
49
Figure 26 Single Inverter Controller Output Variation (Inductive Case)
As can be seen clearly, the system fluctuated a while after started and get the first steady state
at approximately 0.15 second. The value of droop characteristic Ki was chosen as 1 to
intentionally look forward the performance of feedback loops when the load doubled. A
linear load of inductor that is about 8 mH was connected in parallel to the initial circuit at 0.5
second to achieve load increasing. In addition, it can be demonstrated from the figure.26 that
both the amplitude and frequency feedback loops are negative. That means the performance
of specified system works well and satisfied the theoretical background of Figure 8 Classic
droop control characteristic plots. In addition, the losses in the transmission lines are ignored
in this simulation. This is because the impedance of cables in this circuit is much greater than
the output impedance. The attention should be paid to the response of output impedance.
Droop Control of Micrigrid
50
6.4 Two Inverters Controller Simulations of inductive Output Impedance
Figure 27 Load voltages for Two Inverters (Inductive Case)
Figure 28 Two Inverters Controller Amplitude response (Resistive case)
Figure 29 Two Inverters Controller Frequency response (Resistive case)
The results of double controller with inductive output impedance are shown above. To
compare with the single controller condition, the filter can provide a better performance in
terms of decrease the frequency. In addition, the results of both amplitude and frequency have
Droop Control of Micrigrid
51
the same trends among two inverters. The amplitude dropped to a big extent when the load
demand is doubled. On the contrast, the frequency decreased to a very small extent. When it
comes to the accurate value, the frequency of inverter no.1 dropped from 3.14294 to 3.14282,
while the frequency of no.2 inverter decreased from 3.14294 to 3.14288. In terms of
amplitude scope, the value of inverter 1 decreased from 8.27 to 8.21, while the value of
another inverter dropped from 9.22 to 9.16. The frequency of inverter 1 dropped
approximately 0.00012, while the frequency of inverter 2 dropped approximately 0.00006.
Both of amplitude and frequency response satisfy the 2:1 droop ratio. In terms of amplitude,
the amplitude of inverter1 dropped 0.12, while the amplitude of inverter 2 dropped 0.06. Both
of amplitude and frequency response satisfy the 2:1 droop ratio.
Droop Control of Micrigrid
52
7.0 Conclusions and Future Works
7.1 Conclusion
With the rapid growth in size and number of renewable resource generation system connected
to the power grids, the utility and the control approach of parallel-connected inverters become
more significant to develop. This trend leads to an increasing utilize of microgrid technology
due to its main advantages, which are reliability and stability of the systems. In the microgrid
system, it is hard to avoid the need for inverters connected in parallel. Therefore, how to
solve the problem of power sharing among inverters when the load demands changed has
triggered much attention.
The goal of sharing the power in proportional without mechanical communications led to the
droop control approach being researched in this thesis. The algorithm that was developed in
this thesis is based on the DC power flow assumption, which ignored any power losses in the
transmission progress. Based on the assumption, the droop control algorithms for resistive
and inductive case are explained in the thesis. In addition, as necessary components of the
test network, the low pass filter selection is also discussed.
The results indicated in chapter 6 illustrate the response of output voltage, which include the
amplitude and frequency scopes. There are four series of results show the single and double
inverters in parallel and purely resistive and inductive impedance, respectively. The single
inverter experiments are used to test basic control schemes in the SPICE, while the double
inverters cased is to test whether supplies can achieve proportional power sharing. The
proportion of power sharing is set to 2:1 in this project. It is matched to a big extent, which
means the simulations show that the proportional power sharing is achieved by using the
theoretical algorithm of conventional droop control.
Droop Control of Micrigrid
53
In summary, the purpose of this thesis report is to evaluate the performance of droop control
in the simple microgrid in standalone mode. The thesis has been completed focusing on the
two inverters circuits with purely inductive and purely resistive loads. The power sharing
satisfies the droop control algorithm and the objective 2:1 proportion.
7.2 Future Works
The control strategy that simulated in the thesis achieved the proportional power sharing
successfully. Therefore, future work could investigate an innovative method of reducing the
losing throughout transmission lines, which increases the accuracy of proportional power
sharing among parallel-connected inverters. According to Zhang’s paper [3], the per-unit
resistive or inductive output impedance and voltage set point (Ei) will impacts the
improvement of accuracy of power sharing.
It also could investigate the multiple output impedance condition. As mentioned in the report,
the inverter output impedance and the transmission lines are inductive. The droop control
algorithm discussed in the section 3.2 is used widely. On the contrary, in low-voltage
applications, another droop algorithm discussed in section 4.1 is applied due to the purely
resistive output impedance. However, there is also the third condition that the components
include both inductive and resistive impedance; the droop control algorithm suit combination
condition should be investigated in the future. What is more, the grid-connected mode of
microgrid should be investigated because the power grid will also impact the performance of
local standalone system. To sum up, much work can be done to understand the control and
maintaining method of microgrids. To finish the future research work will lead the full
potential of droop control in the standalone mode of microgrid concepts.
Droop Control of Micrigrid
54
Bibliography
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[2] Andrew Mark Bollman, “An Experimental Study of Frequency Droop Control In a Low-
Inertia Microgrid”, College of the University of Illinois, 2009 [online] Available:
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=2
[3]Qing-Chang Zhong “Robust Droop Controller for the Accurate Proportional Load
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pp.1281-1290, Apr, 2013
[4] Josep M. Guerrero et al, “Decentralized Control for Parallel Operation of Distributed
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[5] R. Lasseter and P. Piagi, “Microgrid: A conceptual solution” in Proceedings of the 35th
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[6] J. DunCan Glover, Mulukutla S. Sarma, Thomas J. Overbye, “Power System Analysis and
Design” 5th ed. Cengage Learning, pp.32-33, 2012.
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[8] Karel De Brabandere, Bruno Bolsens, Jeroen Van den Keybus, Achim Woyte, Johan
Driesen, Ronnie Belmans, “A Voltage and Frequency Droop Control Method for Parallel
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[11] Travis Wilson. “Control and Management of a Microgrid and the use of Droop
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[12]Jinwei He et al, “An Islanding Microgrid Power Sharing Approach Using Enhanced
Virtual Impedance Control Scheme.” IEEE Transactions on Power Electronics covers
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[14] Anuroop.P.V at el, “Droop Control of Parallel Inverters with LCL Filter and Active
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[15] Gregory Crebbin “Droop controllers for Power sharing” Murdoch University
November 2016
Appendix A SPICE Netlist for Signal Inverter Resistive Case
.TRAN 1m 1 0 1m UIC
.OPTIONS acct
.PRINT TRAN Vo
X- 8 10 3 MUL { K=1 }
.SUBCKT MUL 1 2 3 {K=???}
B1 3 0 V = V(1) * V(2) * {K}
.ENDS
X2 3 4 POLE2 { K=-0.04 FN=5 Z=0.707 }
.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}
*PARAMS ARE: DC GAIN = {K}
* FREQ = {FN}
* DAMPING = {Z}
*
*TRANSFER FUNCTION: K*WN^2/(S^2 +2*Z*WN*S + WN^2)
* WHERE WN=2*PI*FN
Droop Control of Micrigrid
57
RI 1 0 1E12
E1 3 0 1 0 {K}
R1 3 4 1MEG
E2 5 0 0 4 1E6
C1 4 5 {.159155U/FN} IC=0
RZ 4 5 {.5MEG/Z}
R2 5 7 -1MEG
E3 2 0 0 7 1E6
C2 2 7 {.159155U/FN} IC=0
R3 2 4 1MEG
.ENDS
X3 4 2 1 SUM2 { K1=-1 K2=1 }
.SUBCKT SUM2 1 2 3 {K1=??? K2=???}
B1 3 0 V = {K1}*V(1) + {K2}*V(2)
.ENDS
RE 1 0 1
V1 2 0 DC=12
X9 15 16 SINT { K=1 }
.SUBCKT SINT 1 2 {K=???}
* INTEGRATOR
*PARAMS ARE GAIN={K}
RIN 1 0 1E12
E1 3 0 0 1 {K}
C1 2 4 1U IC=0
R1 3 4 1MEG
Droop Control of Micrigrid
58
E2 2 0 0 4 1E6
.ENDS
X5 8 9 5 SWITCH { }
.SUBCKT SWITCH 1 2 3
R1 1 2 1E10
G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1
.ENDS
L1 6 7 2.35mH
Vswitch 5 0 PULSE 0 100 0.5 1m 1m 10 20
Rload2 9 0 9
Rload1 8 0 9
C1 8 0 22uF IC=6V
Vind1 7 8
B1 6 0 V=1.4142*V(1)*cos(V(16))
H1 10 0 Vind1 1
X4 11 10 12 MUL { K=1 }
X6 8 11 PZ { K=-1 FP=50 FO=-50 }
.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}
*PARAMS ARE DC GAIN = {K}
* POLE FREQ = {FP} HERTZ
* ZERO FREQ = {FO} HERTZ
*
E1 0 3 1 0 {K}
RI 1 0 1E12
R1 3 4 1MEG
Droop Control of Micrigrid
59
R2 4 2 1MEG
C1 3 4 {1U/(6.28319*FO)}
C2 2 4 {1U/(6.28319*FP)}
E2 2 0 0 4 1E6
.ENDS
X7 12 13 POLE2 { K=-0.05 FN=5 Z=0.707 }
Rw 16 0 1
V4 14 0 DC=314.295
X8 13 14 15 SUM2 { K1=-1 K2=1 }
.END
Appendix B SPICE Netlist for Double Inverters resistive Case
.TRAN 0.01m 1 0 0.01m UIC
.OPTIONS abstol=10n itl4=200 method=GEAR
.OPTIONS reltol=0.02 vntol=10u vsectol=1.00u
.OPTIONS acct
.OPTIONS Bypass=0
.PRINT TRAN Vo
.PRINT TRAN Vo2
X- 8 10 3 MUL { K=0.4 }
.SUBCKT MUL 1 2 3 {K=???}
B1 3 0 V = V(1) * V(2) * {K}
.ENDS
X2 3 4 POLE2 { K=-1 FN=5 Z=0.707 }
.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}
Droop Control of Micrigrid
60
*PARAMS ARE: DC GAIN = {K}
* FREQ = {FN}
* DAMPING = {Z}
*
*TRANSFER FUNCTION: K*WN^2/(S^2 +2*Z*WN*S + WN^2)
* WHERE WN=2*PI*FN
RI 1 0 1E12
E1 3 0 1 0 {K}
R1 3 4 1MEG
E2 5 0 0 4 1E6
C1 4 5 {.159155U/FN} IC=0
RZ 4 5 {.5MEG/Z}
R2 5 7 -1MEG
E3 2 0 0 7 1E6
C2 2 7 {.159155U/FN} IC=0
R3 2 4 1MEG
.ENDS
X3 4 2 1 SUM2 { K1=-1 K2=1 }
.SUBCKT SUM2 1 2 3 {K1=??? K2=???}
B1 3 0 V = {K1}*V(1) + {K2}*V(2)
.ENDS
RE 1 0 1
VErated 2 0 DC=12
X9 15 16 SINT { K=1 }
.SUBCKT SINT 1 2 {K=???}
Droop Control of Micrigrid
61
* INTEGRATOR
*PARAMS ARE GAIN={K}
RIN 1 0 1E12
E1 3 0 0 1 {K}
C1 2 4 1U IC=0
R1 3 4 1MEG
E2 2 0 0 4 1E6
.ENDS
C2 8 0 22uF IC=6V
L1 6 7 2.35mH
Vswitch 5 0 PULSE 0 100 0.5 1000m 1m 10 20
Rload2 9 0 9000
Rload1 8 0 9.0
C1 8 0 22uF IC=6V
Vind1 7 8
B1 6 0 V=1.4142*V(1)*cos(V(16))
H1 10 0 Vind1 1
X4 11 10 12 MUL { K=0.1 }
X6 8 11 PZ { K=-1 FP=50 FO=-50 }
.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}
*PARAMS ARE DC GAIN = {K}
* POLE FREQ = {FP} HERTZ
* ZERO FREQ = {FO} HERTZ
*
E1 0 3 1 0 {K}
Droop Control of Micrigrid
62
RI 1 0 1E12
R1 3 4 1MEG
R2 4 2 1MEG
C1 3 4 {1U/(6.28319*FO)}
C2 2 4 {1U/(6.28319*FP)}
E2 2 0 0 4 1E6
.ENDS
X7 12 13 POLE2 { K=-1 FN=5 Z=0.707 }
Vind2 17 8
Rw 16 0 1
Vrated 14 0 DC=314.295
X8 13 14 15 SUM2 { K1=-1 K2=1 }
L2 17 18 2.35mH
B2 18 0 V=1.4142*V(23)*cos(V(27))
X-x 8 19 20 MUL { K=0.8 }
X11 20 21 POLE2 { K=-1 FN=5 Z=0.707 }
X12 21 22 23 SUM2 { K1=-1 K2=1 }
REx 23 0 1
VEratedx 22 0 DC=12
H2 19 0 Vind2 1
X13 24 19 25 MUL { K=0.2 }
X14 8 24 PZ { K=-1 FP=50 FO=-50 }
X15 25 26 POLE2 { K=-1 FN=5 Z=0.707 }
Rwx 27 0 1
Vratedx 28 0 DC=314.295
Droop Control of Micrigrid
63
X16 26 28 29 SUM2 { K1=-1 K2=1 }
X17 29 27 SINT { K=1 }
X18 8 9 5 0 SSWITCH { RON=0.1 ROFF=1MEG VON=1 VOFF=0 }
.SUBCKT SSWITCH 1 2 3 4 {RON=1 ROFF=1MEG VON=1 VOFF=0}
*Connections + - NC+ NC-
*Parameters: Ron On Resistance in Ohms, Roff Off Resistance in Ohms
* VON On Current in Amps, VOFF Off Current in Amps
* IF V(3,4) > VON THEN RSwitch=RON, IF V(3,4) < VOFF THEN RSwitch=ROFF, ELSE
* RSwitch will smoothly transistion between the on and off states
A1 1 2 3 4 SMOOTH
.MODEL SMOOTH VSWITCH RON={RON} ROFF={ROFF} VON={VON}
VOFF={VOFF}
.ENDS
.END
Appendix C SPICE Netlist for single Inverters inductive Case
.TRAN 1m 1 0 1m UIC
.OPTIONS acct
.PRINT TRAN Vo
X- 11 10 3 MUL { K=1 }
.SUBCKT MUL 1 2 3 {K=???}
B1 3 0 V = V(1) * V(2) * {K}
.ENDS
X2 3 4 POLE2 { K=1 FN=5 Z=0.707 }
.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}
Droop Control of Micrigrid
64
*PARAMS ARE: DC GAIN = {K}
* FREQ = {FN}
* DAMPING = {Z}
*
*TRANSFER FUNCTION: K*WN^2/(S^2 +2*Z*WN*S + WN^2)
* WHERE WN=2*PI*FN
RI 1 0 1E12
E1 3 0 1 0 {K}
R1 3 4 1MEG
E2 5 0 0 4 1E6
C1 4 5 {.159155U/FN} IC=0
RZ 4 5 {.5MEG/Z}
R2 5 7 -1MEG
E3 2 0 0 7 1E6
C2 2 7 {.159155U/FN} IC=0
R3 2 4 1MEG
.ENDS
X3 4 2 1 SUM2 { K1=-1 K2=1 }
.SUBCKT SUM2 1 2 3 {K1=??? K2=???}
B1 3 0 V = {K1}*V(1) + {K2}*V(2)
.ENDS
RE 1 0 1
VErated 2 0 DC=12
X9 15 16 SINT { K=1 }
.SUBCKT SINT 1 2 {K=???}
Droop Control of Micrigrid
65
* INTEGRATOR
*PARAMS ARE GAIN={K}
RIN 1 0 1E12
E1 3 0 0 1 {K}
C1 2 4 1U IC=0
R1 3 4 1MEG
E2 2 0 0 4 1E6
.ENDS
X5 8 9 5 SWITCH { }
.SUBCKT SWITCH 1 2 3
R1 1 2 1E10
G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1
.ENDS
L2 9 0 8mH
L1 6 7 1.36mH
V2 5 0 PULSE 0 100 0.5 1m 1m 10 20
C1 8 0 11uF IC=6V
Vind1 7 8
B1 6 0 V=1.4142*V(1)*cos(V(16))
L3 8 0 8mH
H1 10 0 Vind1 1
X4 8 10 12 MUL { K=1 }
X6 8 11 PZ { K=-1 FP=50 FO=-50 }
.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}
*PARAMS ARE DC GAIN = {K}
Droop Control of Micrigrid
66
* POLE FREQ = {FP} HERTZ
* ZERO FREQ = {FO} HERTZ
*
E1 0 3 1 0 {K}
RI 1 0 1E12
R1 3 4 1MEG
R2 4 2 1MEG
C1 3 4 {1U/(6.28319*FO)}
C2 2 4 {1U/(6.28319*FP)}
E2 2 0 0 4 1E6
.ENDS
X7 12 13 POLE2 { K=1 FN=5 Z=0.707 }
Rw 16 0 1
Vrated 14 0 DC=314.295
X8 13 14 15 SUM2 { K1=-1 K2=1 }
.END
Appendix D SPICE Netlist for Double Inverters resistive Case
.TRAN 1m 1 0 1m UIC
.OPTIONS acct
.PRINT TRAN Vo
.PRINT TRAN V8
X- 11 10 3 MUL { K=1 }
.SUBCKT MUL 1 2 3 {K=???}
B1 3 0 V = V(1) * V(2) * {K}
Droop Control of Micrigrid
67
.ENDS
X2 3 4 POLE2 { K=0.4 FN=5 Z=0.707 }
.SUBCKT POLE2 1 2 {K=??? FN=??? Z=???}
*PARAMS ARE: DC GAIN = {K}
* FREQ = {FN}
* DAMPING = {Z}
*
*TRANSFER FUNCTION: K*WN^2/(S^2 +2*Z*WN*S + WN^2)
* WHERE WN=2*PI*FN
RI 1 0 1E12
E1 3 0 1 0 {K}
R1 3 4 1MEG
E2 5 0 0 4 1E6
C1 4 5 {.159155U/FN} IC=0
RZ 4 5 {.5MEG/Z}
R2 5 7 -1MEG
E3 2 0 0 7 1E6
C2 2 7 {.159155U/FN} IC=0
R3 2 4 1MEG
.ENDS
X3 4 2 1 SUM2 { K1=-1 K2=1 }
.SUBCKT SUM2 1 2 3 {K1=??? K2=???}
B1 3 0 V = {K1}*V(1) + {K2}*V(2)
.ENDS
RE 1 0 1
Droop Control of Micrigrid
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V1 2 0 DC=12
X9 15 16 SINT { K=1 }
.SUBCKT SINT 1 2 {K=???}
* INTEGRATOR
*PARAMS ARE GAIN={K}
RIN 1 0 1E12
E1 3 0 0 1 {K}
C1 2 4 1U IC=0
R1 3 4 1MEG
E2 2 0 0 4 1E6
.ENDS
L2 0 8 8mH
X5 8 9 5 SWITCH { }
.SUBCKT SWITCH 1 2 3
R1 1 2 1E10
G1 1 2 POLY(2) 1 2 3 0 0 0 0 0 1
.ENDS
L3 0 9 8mH
L1 6 7 5mH
Vswitch 5 0 PULSE 0 100 0.5 1m 1m 10 20
X-x 17 18 19 MUL { K=0.8 }
X11 19 20 POLE2 { K=0.4 FN=5 Z=0.707 }
C1 8 0 44uF IC=6V
Vind1 7 8
B1 6 0 V=1.4142*V(1)*cos(V(16))
Droop Control of Micrigrid
69
X12 20 21 22 SUM2 { K1=-1 K2=1 }
H1 10 0 Vind1 1
X4 8 10 12 MUL { K=0.1 }
X6 8 11 PZ { K=-1 FP=50 FO=-50 }
.SUBCKT PZ 1 2 {K=??? FP=??? FO=???}
*PARAMS ARE DC GAIN = {K}
* POLE FREQ = {FP} HERTZ
* ZERO FREQ = {FO} HERTZ
*
E1 0 3 1 0 {K}
RI 1 0 1E12
R1 3 4 1MEG
R2 4 2 1MEG
C1 3 4 {1U/(6.28319*FO)}
C2 2 4 {1U/(6.28319*FP)}
E2 2 0 0 4 1E6
.ENDS
X7 12 13 POLE2 { K=0.5 FN=5 Z=0.707 }
REx 22 0 1
Rw 16 0 1
V4 14 0 DC=314.295
X8 13 14 15 SUM2 { K1=-1 K2=1 }
V3 21 0 DC=12
H2 18 0 Vind2 1
X13 8 18 23 MUL { K=0.2 }
Droop Control of Micrigrid
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X14 8 17 PZ { K=-1 FP=50 FO=-50 }
X15 23 24 POLE2 { K=0.5 FN=5 Z=0.707 }
Rwx 25 0 1
V5 26 0 DC=314.295
X16 24 26 27 SUM2 { K1=-1 K2=1 }
X17 27 25 SINT { K=1 }
B2 28 0 V=1.4142*V(22)*cos(V(25))
L4 29 28 5mH
Vind2 29 8
C2 8 0 44uF
.END
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