学号：2016326660013
Power flow analysis and calculation of
distributed generation
School: Electrical Engineering
Major: Electrical Engineering and Automation
Name: Mendigaliyeva Aray (爱芮)
Abstract I: Distributed generation system and network of regional power grid flow
calculation presents new challenges and requirements. Based on the distributed
generation system and network structure and control characteristics, the establishment
of micro gas turbine, photovoltaic, wind power, fuel cell several typical distributed
generation system and network system in the flow calculation mathematical model. In
view of the complexity of the numbering of the branches of the forward and backward
generation method and the lack of adaptability to the change of the operating mode, a
forward and backward generation method based on the “leaf node” is proposed from
the implementation method. The results show that this method can solve the problem
of grid-connected power flow of distributed generation system, and it has strong
versatility and practicability.
Key words: distributed generation; power flow calculation
Abstract II: Power system power flow calculation is a study of the steady-state
operation of the power system, which is based on a given operating conditions and the
limits of the system to determine the operating status of the entire power system of the
various parts: the voltage of each bus. Each element flоwing through the pоwеr, the
power loss of thе system and so on. Power flow cаlculation is the basis of powеr
system stеady state analysis, transient analysis and fаult analysis.
Key words: power system; power flow calculation
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CONTENT
1 PREFACE……………………………………………………………………..4
1.1 PURPOSE AND SIGNIFICANCE OF RESEARCH POWER FLOW
ANALYSIS
AND
CALCULATION
OF
DISTRIBUTED
GENERATION............................................................................................4
1.2 DEVELOPMENT TRENDS AND CURRENT SITUATION OF
DISTRIBUTED GENERATION AT HOME AND ABROAD…………..5
1.3 WORK DONE DURING THE RESEARCH……………………………12
2 INTRODUCTION……………………………………………………………14
2.1 ABOUT DISTRIBUTED GENERATION...…………………………….14
2.2 TYPES OF DISTRIBUTED NETWORK……………………………….16
2.3 WHAT IS POWER FLOW CALCULATION AND ANALYSIS………17
3 DEVELOPMENT HISTORY.………………………………...……………..20
3.1 DEVELOPMENT HISTORY OF DISTRIBUTED GENERATION……20
3.2 DEVELOPMENT HISTORY OF POWER FLOW CALCULATION….22
4 POWER FLOW CALCULATION…………………………………………..25
4.1 TYPES OF POWER FLOW CALCULATION…………………………25
4.1.1 NEWTON-RAPHSON METHOD……………………………....25
4.1.2 GAUSS-SEIDEL METHOD…………………………………….26
4.1.3 BACKWARD / FORWARD SWEEP METHOD……………….27
4.1.4 OTHER METHODS……………………………………………..27
4.2 BUS CLASSIFICATION……………………………………………......27
4.3 POWER
FLOW
ALGORITHM
FOR
NETWORKS
WITH
DISTRIBUTED GENERATION………………………………………...28
4.4 MATHEMATICAL MODELS FOR DISTRIBUTED GENERATION...30
4.5 EQUIVALENT MODEL OF DISTRIBUTED POWER SUPPLY……...32
5 COMPARISON OF NEWTON-RAPHSON METHOD AND GAUSSSEIDEL METHOD………………………………………………………......36
6 SIMULATION AND ANALYSIS OF COMPARISON…………………….38
7 CALCULATION OF POWER FLOW OF DISTRIBUTION NETWORK BY
FORWARD AND BACKWARD SWEEP METHOD……………………...41
8 CALCULATION OF POWER FLOW OF DISTRIBUTION NETWORK BY
PQ DECOMPOSITION METHOD……………………………………….....45
9 COMPARATIVE SIMULATION…………………………………………...49
10 CONCLUSION……………………………………………………………....52
11 REFERENCES……………………………………………………………….53
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1 PREFACE
1.1 PURPOSE AND SIGNIFICANCE OF RESEARCH POWER
FLOW ANALYSIS AND CALCULATION OF DISTRIBUTED
GENERATION
Purpose: using the knowledge gained at the undergraduate level, research on power
flow analysis and calculation of distributed generation.
Significance: Distributed generation is an approach that employs small-scale
technologies to produce electricity close to the end users of power. DG technologies
often consist of modular (and sometimes renewable-energy) generators, and they offer
a number of potential benefits. In many cases, distributed generators can provide
lower-cost electricity and higher power reliability and security with fewer
environmental consequences than can traditional power generators.
The current model for electricity generation and distribution is dominated by
centralized power plants. The power at these plants is typically combustion (coal, oil,
and natural) or nuclear generated. Centralized power models, like this, require
distribution from the center to outlying consumers. Current substations can be
anywhere from 10s to 100s of miles away from the actual users of the power
generated. This requires transmission across the distance.
This system of centralized power plants has many disadvantages. In addition to the
transmission distance issues, these systems contribute to greenhouse gas emission, the
production of nuclear waste, inefficiencies and power loss over the lengthy
transmission lines, environmental distribution where the power lines are constructed,
and security related issues.
Many of these issues can be mediated through distributed energies. By locating, the
source near or at the end-user location the transmission line issues are rendered
obsolete. Distributed generation (DG) is often produced by small modular energy
conversion units like solar panels. As has been demonstrated by solar panel use in the
United States, these units can be stand-alone or integrated into the existing energy
grid. Frequently, consumers who have installed solar panels will contribute more to
the grid than they take out resulting in a win-win situation for both the power grid and
the end-user.
Power flow, or load flow, is widely used in power system operation and planning. The
power flow model of a power system is built using the relevant network, load, and
generation data. Outputs of the power flow model include voltages at different buses,
line flows in the network, and system losses. These outputs are obtained by solving
nodal power balance equations. Since these equations are nonlinear, iterative
techniques such as the Newton-Raphson and the Gauss-Seidel methods are commonly
4
used to solve this problem. The problem is simplified as a linear problem in the DC
power flow technique.
The difference between the distribution network tidal flow calculation with DG and
the normal tidal flow calculation is that the tidal flow calculation model of DG is not
the same as that of the traditional generator. Distributed power can be divided into
micro-gas turbine , wind power generation, fuel cells, and photovoltaic cells.
1.2 DEVELOPMENT TRENDS AND CURRENT SITUATION OF
DISTRIBUTED GENERATION AT HOME AND ABROAD
DEVELOPMENT TRENDS
Distributed energy systems in China's development is mainly concentrated in Beijing,
Shanghai and Guangdong, and more rely on CCHP technology, natural gas is a
strategic resource of distributed energy systems in China. Today, DES has entered the
stage of engineering development by theoretical exploration, the government has also
taken appropriate policy measures, but the relevant policy is not perfect, there is a lot
of room for improvement, in the pilot stage. Many of the DES projects that have been
put into operation reflect good energy saving, economic and environmental benefits,
such as Pudong International Airport in Shanghai, Huangpu Central Hospital,
Minhang Central Hospital and Beijing Capital International Airport. Before China's
natural gas distributed energy installed capacity of about 5 million kilowatts, less than
1% of the total installed capacity of the country, is still in its infancy. In April 2010,
the National Energy Board proposed to 2011 to build 1000 natural gas distributed
energy projects; by 2020, the promotion of the use of distributed energy systems in
large cities, the installed capacity of 50 million kilowatts, and to build about 10 types
of typical characteristics of distributed energy demonstration area. According to the
National Development and Reform Commission plan, China's total installed power
capacity in 2020 will reach 17 billion kilowatts, and the installed capacity of natural
gas distributed energy projects will account for 3%.This shows that China is about to
enter the stage of large-scale development of distributed energy.
Distributed generation (distributed generation, DG) access to the distribution network,
changing the characteristics of the system power flow, the system network loss and
steady-state voltage distribution had a great impact. The power flow of distributed
generation system is related to the access location, load size and network topology. It
is also the basis of other theoretical research work to analyze the influence of
distributed generation on the static stability of the power grid. Therefore it is
necessary to carry out in-depth research on the power flow calculation method with
distribution network. Distributed generation as a frontier research direction of the
international power system, it researches focuses on its impact on the power system.
Research including distributed power grid power flow calculation method is mainly
for different types of Distributed Power model, so that it can be simulated to the
existing calculation methods to go. Its future research trends are: making the
5
algorithm can handle distributed power systems with different performance in
different operating states, the calculation process is more efficient, more versatile.
Research Status of Distributed Power Flow Calculation Algorithms at Home and
Abroad.
(I)
China
When the traditional large grid and distributed power supply and run later, will
introduce a lot of power electronics and inductors, capacitors, this will change the
original topology of the power system network, leading to the trend of distribution of
the grid also will change, so that the stability of the grid has brought uncertainty.
Since the distributed power to the grid has brought a great impact, so scholars at home
and abroad in the trend of the network containing the distributed power of the
algorithm has been studied, there is a problem is the trend of distributed power
computing models and traditional generators different. The model of a traditional
generator consists of P, PQ, and balanced nodes, but the node type of the distributed
power supply needs to take what type is required as the case may be
At present, the trend for the further development of distributed power computing
algorithms, scholars at home and abroad put forward more suitable for distributed
power flow algorithm, and also proposed a number of innovative methods are worth
learning. In order to be able to solve the actual flow calculation problems, Dariush
proposed this method of real-time analysis of three-phase flow calculation of the kind
of elementary distribution system of weak Ring network flow calculation has been
extended to strengthen the control of distributed power.In addition, Wang Chengshan,
Zheng Haifeng et al., for wind power, solar power and other random power generation
model proposed the corresponding flow calculation method using the probability and
statistical methods to deal with factors in the system of random variation, given the
probability distribution of the system running voltage branch flow, etc., can more
clearly show the health of the system, to provide a more complete data information.
Distributed energy systems are diverse in terms of technology categories, applications,
capacity, and many other factors. The following summarizes the definition of
distributed energy systems for different categories in some European and American
institutions.
Distributed energy (distributed energy, DG): exists outside the traditional public grid
any system that can generate electricity, including the prime mover to a variety of
energy types for power generation systems.
Distributed power (distributed power, DP): on the basis of DG technology, energy can
be stored by the battery, flywheel, regenerative fuel cells and other electrical energy
system.
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On the concept of DG, which includes a system connected to the Public Power Grid,
users can sell local excess power through the network to the public power company, is
a broader concept.
The International Energy Agency (IEA) (2002) defines a distributed energy system as
a service that provides on-site production or support to a distribution network
connected to a distributed voltage level. The global Distributed Energy Association
(Wade, formerly the New Energy Alliance), in its 2004 statistical report, pointed out
that distributed energy systems generate electricity and heat in or near the user's place
of consumption, which consists of three main components: first, high-efficiency
cogeneration; second, renewable energy systems; Third, Energy recycling system.
In the understanding of the meaning, the site close to the user, the use of energy
cascade, to provide a variety of forms of energy is a part of the meaning of distributed
energy system can not be missing, so we can be distributed energy system
(DistributedEnergySystem, DES) definition summarized as: built in the vicinity of the
user, can use a variety of
Second, the status of distributed energy development in developed countries
The concept of a distributed energy system was introduced in the United States after
the publication of the United States Public Utilities Policy Act of 1978, and later
accepted by other developed countries. In recent years, some developed countries are
vigorously develop, promote gas fuels such as natural gas and renewable energy as
the power, distributed in the end user energy supply system, especially in the
cogeneration (CHP) or CCHP as the main technology of distributed energy supply
system, to achieve direct energy cascade to meet user needs.
(II)
United States
Since the development of distributed energy systems, the United States DES site has
more than 6,000 seats, with a total installed capacity of more than 90 million kilowatts,
the government plans to 2020 will be more than 50% of the new office or commercial
buildings using CCHP Energy Mode, 15% of the existing buildings for energy
transformation completed. The United States DES power generation accounts for
about 14% of the total domestic power generation, mainly natural gas CCHP (4.1% of
the total power generation), the other including small and medium-sized hydropower,
solar energy, wind energy and so on. The United States Department of Energy
believes that the United States distributed energy development potential of 11 to 15
million kilowatts, including industrial areas 7 to 9 million kilowatts, commercial areas
4 to 6 million kilowatts. Most of the world's commercial DES equipment
manufactured by the United States. In support of distributed generation related
policies, the United States in 2001 promulgated the IEEE-P1547 / D08 " on the
distributed power and power system interconnection standard draft”, and passed the
relevant laws and regulations for distributed generation systems and network
operation and sale of electricity to the grid. The US Department of energy in 2005 to
7
develop the domestic micro-grid technology development roadmap to 2005 to 2015
for basic research and demonstration application period, 2015 to 2020 for the
application of micro-grid technology development period.In 2009, the United States
vigorously promote the development of smart grid and renewable energy development,
and distributed generation developed the corresponding preferential policies: the
reduction of distributed power generation project part of the investment tax; shorten
the depreciation period of distributed power generation project assets; simplify the
distributed power generation project operating permit approval procedures. In
addition, the United States in the distributed energy also uses a renewable energy
quota mechanism (RPS) and other systems for distributed energy to provide a fair,
open market conditions, to ensure the economic benefits of distributed energy has
played an important role.
The rapid development of DES in the United States is closely related to its own power
supply pattern and measures taken. United States power supply and demand to a small
range of balance, Cross-district Power Exchange is small, and the urban industrial,
commercial, residential functional areas of space layout determines the size of most of
the DES project is too small. Its advanced power generation technology is an
indispensable part of the development of DES, in recent years, the United States has
increased efforts to promote distributed generation mode of renewable energy.
(III)
Japan
Due to Japan's high price of natural gas, so the gas power generation is very
economical, its distributed generation to CHP and solar photovoltaic power
generation. Japan DES total installed capacity of about 36 million kilowatts,
accounting for 13.4% of the country, by the end of 2000 has established more than
1400 distributed CHP system. Photovoltaic distributed generation is not only used for
utilities, but also carried out residential roof photoelectric application demonstration
project. By the end of 2006, users of photovoltaic systems installed cumulative
capacity of 1.254 million kilowatts, the world's first. Japan plans to generate 20% of
its electricity supply by 2030. Japan has enacted relevant laws and preferential
policies to ensure the development of the cause, conditions, limited access to the
internet to allow these distributed power generation systems, through preferential
Environmental Protection funds to support the construction of distributed power
generation systems, including urban distributed power units tax reduction or tax
exemption; encourage banks, consortia of distributed power generation system
funding, financing;
(IV)
EU
European countries actively promote distributed energy systems, and the use of
renewable energy as the main technology applications. Denmark, the Netherlands,
Germany's distributed energy generation accounted for 53% of the total domestic
power generation, 38%and 38%, the EU distributed energy market accounted for an
8
average of 10%, dominated by natural gas, and closely integrated with the
development of renewable energy.
1.Denmark. The Danish government began to carry out power reform in 1999, is the
world's largest country to promote the Des, its share in the entire energy system is
close to 40%, the proportion of the electricity market has reached 53%, in 2010 the
Danish government announced the laying of the world's longest intelligent grid
infrastructure. The development direction of wheat CHP technology is mainly the
transformation of scale and traditional coal fuel. The coal / electricity conversion
efficiency is more than 50%, and the total efficiency is up to 90%.The Danish
government has introduced a number of laws and regulations to encourage DES, such
as the "heating Act" and "electricity supply Act", respectively, the DES explicitly
proposed to encourage, protect and support, and the development of compensation
policy and preferential loans.
2.England.The United Kingdom, like Denmark, began gradually opening the
electricity market in 1999, and the development of distributed generation policy is
more focused on environmental protection, especially the impact of climate change.
In addition to policies that support renewable energy, there are many policies that
support the development of CHP. The UK is exempt from the climate change tax on
the fuel used in CHP, from the business tax on the company, and from the support of
modern heating systems. In order to mobilize the enthusiasm of each power plant to
balance its own power generation capacity, its "new electricity trading rules" to make
clear the power generation.
3.Germany. Germany enacted the renewable energy law in 2000, and has been revised
several times, the use of “flexible” price adjustment mechanism " guide the orderly
development of DES. In 2002, Germany passed a new "thermoelectric law",
encourage and support the development of CHP, photovoltaic installed large-scale
financial subsidies. Germany plans in 2020 renewable energy generation to account
for 35% of the total power consumption, and determine the total installed photovoltaic
power generation new plans. As of 2011, Germany photovoltaic power generation
capacity reached 24.7 million kilowatts, which distributed photovoltaic power
generation system capacity accounted for nearly 80%, the main application form for
the roof photovoltaic power generation system. In addition, Germany has more than
300 MW of biogas and other biomass power stations. Germany has also developed the
release of access to the low-voltage distribution network, distributed power grid
technology standards, from the legal clear and strict network technology standards, to
ensure the safety and stability of the public power grid, for the promotion of
distributed energy systems to remove technical barriers to market.
4.Netherlands. Most distributed power plants in the Netherlands are jointly invested
by the power distributor and industry, and the liberalization of the electricity market
has increased competition. Through some of the early incentives, the Netherlands's
CHP generation capacity has risen rapidly, including government investment
9
subsidies, power generation company purchase obligation and preferential price of
natural gas and so on. In 2000, a new round of measures to solve the financial
difficulties faced by the CHP unit, including increased energy investment subsidies,
exemption from regulatory energy taxes and corresponding financial support.
The development of the European Union (EU) DES relies on policy support, focusing
on planned market pricing, development goals and standards. In addition, the
Organization, member states to carry out microgrid project, the establishment of
different sizes of microgrid experimental platform, to further promote the
development and application of DES.
(V)
Russia
In Russia, in contrast to foreign countries, the predominant value in Centralized
systems will be available in the foreseeable future. The unified energy system (UES)
of Russia covers almost the entire inhabited territory of the country and is the world's
largest centrally managed energy unit. However, up to 70% of Russia's territory (Far
North, far East, Siberia, Buryatia, Yakutia, Altai, Kuril Islands, Kamchatka) is not
covered by centralized power supply. These are regions with low population density,
harsh climatic conditions, heavy and expensive cargo delivery conditions, and remote
from power supply centers. In these territories, the construction of large power plants
is either economically unjustified or impossible due to the lack of funds for the
construction of expensive heating plants and power lines. Thus, the livelihoods of
more than 20 million people living in these regions are provided mainly by smallscale energy resources. In addition, these energy sources are widely used as a backup
(emergency) power supply to consumers that require increased reliability and do not
allow interruptions in the supply of energy in case of accidents in the areas of
centralized power supply (objects of social significance).
There are also a number of prerequisites for the development of distributed energy in
Russia. The current state of the electric power industry is characterized by a
significant increase in tariffs of network companies for services for the transmission
of electric energy and power, as well as payments for overspending and
underutilization of the declared capacity. Increasing prices is the strongest incentive
for industrial producers to develop their own small generation and refuse to buy
electricity and capacity in the energy market.
CURRENT SITUATION
80%of China's wind energy resources distributed in three North and Southeast
offshore, suitable for centralized development; 20% distributed in the Middle East
region, most of which is still focused on the development of the main, a small amount
of suitable distributed generation. Similar wind energy resources, solar energy
resources in the Northwest and North China desert areas, suitable for centralized
development. In terms of natural gas, although with the gradual establishment of
Central Asia, China and Myanmar, China and Russia and the sea channel, natural gas
10
supply has been basically able to meet the demand, but the full spread of pipeline
network facilities still need time, coupled with the uncertainty of gas prices, the
current existence of the development of high enthusiasm, but the. Our country is rich
in small hydropower resources, can develop resources up to 128 million kW, better
than the European conditions.
Overall, China's wind energy, solar energy resources are mainly concentrated in the
"three North" area, mainly in large-scale development, distributed development
conditions less than Europe and the United States; the development of multi-linked
natural gas supply uncertainty; small hydropower resources rich, better than Europe
and the United States.
China's small hydroelectricity implements the mechanism of cost accounting for
electricity price. Wind power, biomass power generation using benchmark price
policy. The main implementation of photovoltaic power generation investment
subsidies and benchmark price, but not perfect. The multi-supply tariff mechanism of
natural gas is still blank.
Overall, China's small hydropower, wind power, biomass power generation and
comprehensive utilization of resources power policy has been more complete.
In terms of power system infrastructure, China is in the stage of industrialization,
urbanization, rapid economic growth, energy supply, the average annual growth rate
of electricity consumption as high as 11.7%, outstanding power supply and demand.
Сhina's per capita electricity consumption is only 1/5 of the developed countries, a
huge growth space, and the proportion of industrial electricity more than 70%, must
be concentrated by large-scale long-distance power generation and transmission to
meet current and future electricity demand. At the same time, China's distribution
network is relatively weak, limited capacity to accept distributed power. When a large
number of distributed power access, distribution network from passive network into
an active network, large-scale transformation requires human, financial and material
input, takes a long time. In terms of the Power Industry Foundation, China's PV
module annual production capacity of more than 30 million kW, accounting for about
3/4 of the world, nearly half of excess capacity, the price decline of more than
50%.Inverter, control and complete sets of design and other core technologies are still
a certain gap with foreign countries. Wind power equipment manufacturing capacity
gradually improved, with an annual output of more than 15 million kW, but the unit
design, key control components and other core technology has yet to be a
breakthrough. Natural gas internal combustion engine power generation technology
has been basically mastered, but the micro-combustion engine units are imported. In
January 2012, the National”863 plan " micro gas turbine key projects made a major
breakthrough, the first 100 kW miсroturbine successfully developed and stable
operation in Harbin, China's initial grasp of the independent research and
development capabilities of microturbine.
11
Power distribution network trend calculation is an important foundation of power grid
economic operation and System Analysis. Not only was the radial distribution
network operating structure, and more branches, basically no contact between the
various feeders, there are significant differences in the structure of the transmission
network, the normal operation of the distribution network with a radial network
structure, a lot of load nodes, line R / X larger features, so the traditional flow
calculation methods such as: Newton method, PQ
In recent years, many scholars on the distribution network power flow calculation to
expand a lot of research, and the emergence of a number of distribution network
power flow calculation algorithm, there are: Loop impedance method [8],[9], improved
Newton method [10],[11], fast decoupling method [12], before pushing back generation
method[13] and so on. Аlthough some scholars to make rapid decoupling method can
continue to be applied in the distribution network and made some useful attempts,
such as the application of compensation technology to handle R / X larger lines, but
these methods are complicated algorithms, the loss of the original Fast decoupling
algorithm small amount of computation, convergence reliable features. Trend
algorithm varied, but generally to meet the four basic requirements: reliable
convergence, computing speed, easy to use and flexible, less memory footprint. They
are also the main basis for the evaluation of the trend algorithm. Front push back
generation method in the distribution network flow calculation is simple and practical,
all the data are stored in vector form, thus saving a lot of computer memory, for any
kind of distribution network as long as there is a reasonable R / X value, this method
can guarantee convergence. Stability of the algorithm is also an important indicator to
evaluate the distribution network flow algorithm. Under normal circumstances, the
higher the convergence order of the algorithm, the worse the stability of the algorithm,
before pushing back the convergence order generation method for the first order, so it
also has good stability. In compаrisоn, the front push back generation method takes
full advantage of the structure of the network was rаdiative features, simple data
processing, high computational efficiency, has good convergence, is recognized as
one of the best algorithm for solving radial distribution network power flow problems.
1.3 WORK DONE DURING THE RESEARCH
During the research the following work was done:
1) Examined the literature on the topic
2) A comparative analysis of the development of small power engineering in China
and other countries
3) Studied the methods of calculation
4) Was made a comparison of methods and conclusion
5) The Conclusion has been proven by examples
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6) Carried out simulation calculation of different distributed networks
7) The General conclusion for the whole work.
13
2 INTRODUCTION
The topology and location of DG in distribution networks are two very interrelated
factors. The location of generation is very important in terms of losses, because the
closer to the place of consumption, the greater the reduction in losses. For mesh
networks, it will depend on the distribution of threads in the grid to know what the
impact on losses is. In radial distribution networks, it seems obvious that the effect on
losses is not the same if the generator is connected to the feeder head when it is
connected at points close to the flow rate.
2.1 ABOUT DISTRIBUTED GENERATION
Distributed generation refers to a variety of technologies that generate electricity at or
near where it will be used, such as solar panels and combined heat and power.
Distributed generation may serve a single structure, such as a home or business, or it
may be part of a microgrid (a smaller grid that is also tied into the larger electricity
delivery system), such as at a major industrial facility, a military base, or a large
college campus. When connected to the electric utility’s lower voltage distribution
lines, distributed generation can help support delivery of clean, reliable power to
additional customers and reduce electricity losses along transmission and distribution
lines.
In the residential sector, common distributed generation systems include:

Solar photovoltaic panels

Small wind turbines

Natural-gas-fired fuel cells

Emergency backup generators, usually fueled by gasoline or diesel fuel
In the commercial and industrial sectors, distributed generation can include resources
such as:

Combined heat and power systems

Solar photovoltaic panels

Wind

Hydropower

Biomass combustion or cofiring

Municipal solid waste incineration

Fuel cells fired by natural gas or biomass
14

Reciprocating combustion engines, including backup generators, which are
may be fueled by oil
In contrast to the use of a few large-scale generating stations located far from load
centers--the approach used in the traditional electric power paradigm--DG systems
employ numerous, but small plants and can provide power onsite with little reliance
on the distribution and transmission grid. DG technologies yield power in capacities
that range from a fraction of a kilowatt [kW] to about 100 megawatts [MW]. Utilityscale generation units generate power in capacities that often reach beyond 1,000 MW.
In recent years, energy demand and Environmental Protection have contributed to the
development of distributed power and micro-grid. Distributed power (distributed
resources DR) refers to the load is located near the smaller installed capacity, the
nearest access to low-voltage power distribution network, including distributed
generation (distributed generation DG) and energy storage (energy storage
ES).According to the form of the use of primary energy division, DR is divided into
gas turbines, internal combustion engines and other clean energy power generation
unit and photovoltaic, wind power, hydropower, biomass and other renewable energy
power generation unit; according to the grid interface type division, DR is divided
into synchronous and asynchronous motors and other rotating electrical grid power
generation unit.
The development of distributed generation can make full use of distributed forms of
widespread renewable energy, improve energy efficiency, energy conservation.
Distributed power and micro-grid nearby into the low-voltage distribution network,
can reduce line losses, improve power quality at the end of the grid, ease the use of
voltage stress, improve grid resilience, to ensure reliable power supply for important
users. Independent micro-grid can also solve the problem of electricity in remote
inland or island areas. But DR or microgrid into the distribution network will bring a
series of impact on the operation of the grid, control and protection. To this end, we
must develop a unified grid standard to standardize the grid requirements for
distributed power supply, to ensure safe and reliable operation of the system.
At the same time, in the "consumer — local energy source" system, there are regular
imbalances between the production and consumption of energy or between the need
for its types, for example:
The power of solar panels and wind generators varies depending on weather
conditions, and the electricity consumption may not depend on the weather or change
in the opposite direction.
In winter, the consumption of heat energy remains constantly high, and the
consumption of electricity varies according to the time of day.
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Connected to the public power grid to compensate for lack of electricity due to its
consumption of the total network, and in the case of surplus production of electricity
from own source, to give in, to obtain the appropriate income.
This approach allows you to:
Reduce energy losses during transportation due to the maximum proximity of power
generators to electricity consumers, up to their location in the same building;
Reduce the number, length, and required capacity of main transmission lines;
Mitigate the consequences of accidents at Central power plants and main transmission
lines by using your own energy sources;
Provide mutual multiple redundancy of power generating capacities (partially);
Reduce the impact on the environment through the use of alternative energy resources,
more complete use of the potential energy of fossil fuels.
2.2 TYPES OF DISTRIBUTED NETWORK
Distribution network classification
In the power grid plays an important role in the distribution of electrical energy
network is called distribution network.
Distribution network according to the voltage level, can be divided into high-voltage
distribution network (35-110kV), medium voltage distribution network (6-10kV,
Suzhou has 20kV), low-voltage distribution network (220 / 380V); in large cities with
large load rate, 220kV power grid also has distribution function[1].
In modern power systems, large power plants are usually away from the center of the
load, power plant delivery, generally tend to be sent to the center of the load through
the high voltage or EHV transmission network, and then in the center of the load by
the relatively low voltage level of the network to power distribution to different
voltage levels of this distribution network in the power grid mainly from the role of
the network called distribution network. Distribution network according to the
geographical location or service object is divided by the urban distribution network
and rural distribution network composed of two parts. To a city and its suburbs
distribution and supply of electric power grid called urban distribution network.
Urban distribution network together with its power transmission lines and substations,
collectively referred to as the city power grid, referred to as the city grid.Supply
County (county-level city)within the rural, township, county electricity power grid,
called rural distribution network, referred to as agricultural network.
In urban power system, the main network is 110kV and above the voltage level of the
power grid, mainly from the connection area high voltage (220kV and above) the role
of the grid.
16
Distribution network refers to the 35kV and below the voltage level of the power grid,
the role is to the city in each distribution station and all kinds of electricity load
supply power.
From the perspective of investment, China and foreign advanced countries of power
generation, transmission and distribution investment ratio is very different, basically
is more than the power grid investment abroad power plant investment, transmission
investment is less than the distribution investment. China just from the heavy
generation of light-powered State Transit change over, and in the power supply
investment, transmission investment is greater than the distribution of investment.
From the transformation of China's urban network, will gradually transfer from the
transmission investment to the power distribution construction.
The distribution network generally includes the balancing of the nodes and the nodes
of PQ. The output node of a transformer station is usually considered a balance node,
and the other nodes are considered PQ nodes.And since various DGS are included in
the distribution network, new node types will appear in the system.Since DG is
usually not involved in frequency control of the system, it can be considered to
operate in a constant active power mode, and the reactive power and voltage must be
analyzed depending on the situation.
2.3 WHAT IS POWER FLOW CALCULATION AND ANALYSIS
Load flow (power flow) analysis is a basic analysis for the study of power systems. It
is used for normal, steady-state operation. It gives you the information what is
happening in a system.
It is an answer to some fundamental questions, which power system engineer or
electrical engineer can have:
What are voltage levels in all power system nodes during operation?
Are power system elements (transformers, generators, cables etc.) overloaded?
What are the weakest points of network?
Load flow analysis is an important prerequisite for whatever you do in power systems,
whether you do fault studies, stability studies, economic operation etc.
The load flow helps in continuous monitoring of the current state of the power system,
so it is used on daily basis in load dispatch/power system control centers. It can also
be a support during examining effectiveness of the alternative plans for future system
expansion, when adding new generators or transmission lines is needed. You can refer
to the description of different load flow cases for more information.
Load flow objective
17
The objective of load flow calculations is to determine the steady-state operating
characteristics of the power system for a given load and generator real power and
voltage conditions. Once we have this information, we can calculate easily real and
reactive power flow in all branches together with power losses.
What are the inputs and outputs of load flow analysis?
Minimum input data for power flow analysis:
Bus data (types of buses explained in bus types):
 For PV buses:

Real power (generation and demand),

Reactive power (demand),

Voltage magnitude.
 For PQ buses:

Real power (generation and demand),

Reactive power (generation and demand).
 For slack bus:

Voltage magnitude (usually 1 per unit),

Voltage angle(specified to be zero),

Real power (demand),

Reactive power (demand).
Line data:
 Transmission lines:

Resistance,

Reactance,

Capacitance (can be negligible).
 Transformers:

Winding resistances on low and high voltage side,

Leakage reactance on low and high voltage side,

Magnetization reactance,
18

Iron loss admittance.
Power flow analysis provides following output data for each node/branch:

Voltage magnitude,

Voltage angle,

Real and reactive power,

Power losses.
19
3 DEVELOPMENT HISTORY
3.1
DEVELOPMENT
GENERATION
HISTORY
OF
DISTRIBUTED
The development of distributed generation has gone through three main stages:
(1) Early power systems using distributed power generation that is to establish a small
capacity in the vicinity of the load hair
Power plants, mainly due to the underdevelopment of technology at that time, low
electricity consumption.
(2) The early 20th century, as the load increases and technology advances, large units,
large power grids, high voltage is the main feature of a centralized single power
supply system to become the mainstream power generation, its large capacity, giant
power generation to meet the needs of society and the development of users at that
time. However, in recent years, frequent power crises and large-scale power outages,
exposing a huge power system exists "clumsy" and " fragile shortcomings".
(3) By the late 20th century, people recognized the importance of flexible and reliable
power generation, so the combination of distributed and centralized not only to
overcome the lack of a single centralized power supply, but also to meet the growing
demand for energy and solve environmental pollution problems. Since the 90s of the
last century, renewable energy has been rapid development, many countries in the
world will be renewable energy as the basis of energy policy, and the development of
distributed energy is considered to be the world's sustainable development scale.
Distributed generation prospects.
In the United States, some countries of Europe, their industrial development, large
power load, Distributed Power Development happened earlier than in China, but the
development is also part of the initial stage. In recent years, the government attaches
great importance to the use of renewable energy development, the "total energy
control" focus on the control of the total amount of coal, and incorporated into the
"five-second" energy planning, which marks the distributed generation in China will
reach a new milestone. Renewable energy in the 12th five-year plan proposed “ten
renewable energies”.
The project includes tens of millions of kilowatts wind power projects, renewable
energy Demonstration Cities, etc. Construction target: wind turbine installed capacity
target 90 million kW (including offshore wind 5 million kW), electricity 180 billion
kWh. Natural gas distributed energy installed 5000kW. The installed capacity of
biomass energy will reach 13 million kW and 65 billion kWh of electricity. Solar
power will reach 500000 kWh, generating capacity of 7.5 billion kWh. Distributed
power generation in China's future development direction: to distribute multi-supply
20
technology as the core, combined with renewable energy to build “a small regional
energy network", the formation of smart grid and intelligent heat and cold network
complementary multi-energy integration approach; regional energy system advantage
is that you can improve energy efficiency, through the introduction of efficient
thermoelectric units, to achieve the optimal matching of electricity, gas, heat, cold; to
achieve the connection between buildings, between enterprises and energy sharing,
effectively integrate into some clean energy, such as: solar power, biomass power
generation geothermal utilization, so as to effectively inhibit carbon dioxide emissions.
Now China is in a period of rapid economic development, how rational development
and utilization of renewable energy and new energy and improve energy efficiency,
while strengthening environmental protection is the key to China's energy industry to
achieve sustainable development, to support national modernization.
Overall, the scale of development of distributed power is not backward. But by
resource conditions, incentives and industrial base of the impact, there are obvious
differences in the type of technology. At present, China's distributed power to small
hydropower-based, with a total size of 22.66 million kW, installed capacity and power
generation are ranking first in the world; in recent years, heat, residual pressure, more
than gas and other resources utilization and biomass power generation has grown
rapidly, with a total size of 8.21 million kW, ranking first in the
As of the end of June 2012, the total number of distributed power supply in the State
Grid Corporation of China operating area access 35 kV and below the voltage level of
about 15,600, the total installed capacity of 34,360,000 kW, the total generating
capacity of 103.3 billion kWh, the average annual utilization hours of 3006 h. Among
them, the most distributed use of small hydropower, the total installed capacity of
23.76 million kW, accounting for 69.2% of the total capacity of Statistics; followed
by heat and pressure than gas resources comprehensive utilization of power
generation capacity of 7.3 million kW, accounting for 21.2% of the total capacity of
Statistics; agriculture and forestry biomass power generation the total capacity is 3.0%,
1.4% and 1.1%.
In addition, the State Grid Corporation of China operating area approved under
construction distributed power installed capacity of 4.85 million kW, in the predistributed power installed capacity of 3.41 million kW. Among them, distributed
photovoltaic power generation and natural gas for the approval of the multi-joint
construction and pre-work of the largest installed capacity, with a total size of more
than 3 million kW, will become the main force of the future growth of distributed
power.
Distribution networks typically include distribution substations, primary distribution
lines, secondary distribution lines, distribution transformers, relay protection facilities,
etc., is an important link connecting hair, transmission systems and users. Urban
distribution network is one of the important infrastructure of urban modernization, is
an essential power supply system of modern city. The quality of its construction
21
directly affects the speed of urban economic development, the improvement of
people's living standards, the optimization of the investment environment and so on.
At present, the state attaches great importance to the power system reform work, the
introduction of competition mechanisms in the power industry, and carry out the
construction of the power market. Research on the distribution network issues, greatly
improve the quality and reliability of power supply, to improve the economic
efficiency and competitiveness of power companies, reducing power grid power loss,
energy conservation has great practical significance.
With the all-round development of China's economy, the problem of low-voltage
distribution network power supply reliability and backward development is becoming
more and more prominent. Urban low-voltage distribution network in the city
accounted for most of the market in the sale of electricity, but its development is
lagging behind, no longer adapt to the needs of the city, and therefore become the
main object of customer complaints. These problems are mainly as follows: First, the
power grid power outages too many times; the second is a long time outage; three is a
long time newspaper; Four is the voltage instability.
In order to solve the above distribution network problems, the inevitable requirement
of timely and accurate distribution network flow analysis results, of course, which
requires more efficient and reliable flow calculation, analysis methods. In order to
solve the above distribution network problems, the inevitable requirement of timely
and accurate distribution network flow analysis results, of course, which requires
more efficient and reliable flow calculation, analysis methods. Тhe most basic
important calculation is the power system operation, planning and safety, reliability
analysis and optimization of the foundation, but also a variety of electromagnetic
transient and electromechanical transient analysis of the foundation and starting point.
As the network structure of the system becomes more complex and perfect, power
flow calculation as one of the basic calculation of the power network analysis, but
also constantly improved and improved.
In the study of power system planning and design and operation mode of the existing
power system, we need to use the power flow calculation to quantitatively analyze the
rationality, reliability and economy of the power supply scheme or operation mode. In
addition, the power system flow calculation is the basis for the dynamic stability and
static stability of the computing system. So the power flow calculation is one of the
most important and basic operation of the power system.
3.2 DEVELOPMENT OF POWER FLOW CALCULATION
Distribution network power flow calculation is the basis of the distribution network
analysis[2],the distribution network in the structure and transmission network there are
significant differences: it is generally closed-loop design, open-loop operation, the
network structure is radial, the line resistance and reactance ratio is larger[3],[4].As
science and technology and power system development, the distribution network
22
power flow calculation research has gone through three stages of Development; handcount phase, symmetrical flow calculation phase and three-phase power flow
calculation stage.
Although the study of the power system trend as early as the Sixties have already
begun, but because of the distribution system in the power industry has not been fully
taken seriously, until the end of the seventies, the distribution network trend
calculation is still in the hands of the stage. This phase of the current calculation for
the former Push Back generation method, namely: suppose the whole network node
voltage initial value of the rated voltage, tributary power calculation from the end to
the first end of the trend against the direction, and then from the head-end to the end
of the tide along the direction of each node voltage calculation. This method is simple,
a small amount of calculation, there is no convergence problem, but only for a single
power Open Network, in addition to large networks is not easy to program [5].
From the early Eighties to the mid-nineties, against the development of the power
industry, people began to pay attention to the distribution system line loss calculation
and planning issues, trend calculation as a basis for attention, people began to study
the distribution trend of computer algorithms, in this phase trend research methods are
mainly for symmetric load[6]. There have been many symmetrical flow algorithm for
special network structure of distribution network. Such algorithms can be roughly
divided into two categories, the first category is the calculation method of the
transmission grid has been applied to improve the distribution network, such as
implicit Gauss method, the second is based on the computer algorithm before the push
back generation method, such as power distribution coefficient method, the second set
pressure method.
The implicit Gauss method is the 1991 T.H.Hey, Chen.M.S.Chen and other proposed,
the method according to the network structure to form a node admittance Matrix, node
voltage is calculated by using the principle of superposition of power and load alone
in each node generated voltage superposition obtained. Тhe principle of the method is
simple, relatively easy programming, according to changes in the distribution network
structure, forming a new node admittance Matrix, and admittance matrix is a
symmetrical and highly sparse matrix, memory is very economical. Нowever, the
convergence is slow, the number of iterations will increase with the number of nodes
in the network computing rises, resulting in a sharp increase in the amount of
computation. Thus this method is only applicable to fewer nodes in the distribution
network.
The principle of computer algorithm and hand algorithm is basically the same, is the
branch network loss as the state quantity of a typical algorithm. Тhe key issue of this
type of algorithm is how to use the characteristics of the distribution network structure
to generate a network matrix, so that the network matrix not only save memory in the
grid calculation, improve the calculation speed, and easy to modify when the network
structure changes. There are two methods of forming a network Matrix, one is the
23
node branch Association Matrix method, which uses manual numbering method, the
establishment of the node and branch Association Matrix, clear and simple, but the
memory is large, difficult to track changes in the network, the other is to calculate the
sequence method, which automatically generates a sequence of network topology
information
In the late nineties, the development of distribution automation has entered the
implementation stage, the measured three-phase load serious asymmetry, so that
people began to pay attention to the three-phase power distribution network
calculation method. In dealing with three-phase asymmetric approach, three-phase
power distribution network can be divided into court: sequence component method
(also known as symmetric component method) and phase component method. Еach
element parameter is a 3 ×3-order sub-matrix, the diagonal elements of each phase of
self-impedance and self-admittance, non-diagonal elements of each sequence between
the mutual impedance or mutual admittance. The relationship between the three-phase
current and voltage of the equivalent circuit in the symmetrical part of the system can
be decoupled by the sequential component method, and the calculation amount is
small. However, due to the load node of the distribution network a lot, and therefore
need more points of decomposition, but the greater the amount of change in the
calculation[7].
Phase component method, each element in the system are expressed in Phase
parameters, the parameters of each element is a 3 ×3 order sub-matrix, the diagonal
elements of each phase of the self-impedance or self-admittance, non-diagonal
elements of each phase of the mutual impedance or mutual admittance. Phase
component method is easy to handle three-phase asymmetric load, but when the threephase current flowing through the system imbalance (for distribution systems often
so), the system can not be decoupled between the three-phase symmetrical
components, such as, between the three-phase line, due to the three-phase current
asymmetry between the inevitable phase and phase coupling, resulting in mutual. At
present, most of the power flow distribution network algorithm adopts the phase
component method. Three-phase power flow calculation can be classified from the
flow calculation algorithm can be divided into loop impedance method, pushback
generation method. Вoth methods belong to the phase component method.
24
4 POWER FLOW CALCULATION
4.1 TYPES OF CALCULATION
The most important load flow methods, which can be applied to new distribution
networks, are categorized to six groups: NR based methods, Gauss-Seidel based
methods, super position based methods, compensated backward/forward sweep
methods, optimization based methods and artificial intelligence based methods.
Improved power flow calculation method for the above problem, we can solve it
through the following two programs: first, research and analysis of a new and
effective distribution network flow calculation method, and to ensure that the
calculation method for those who contain distributed power distribution network is
also effective; the second is the scientific deal with distributed power distribution
system.
4.1.1 Newton-Raphson Method
Newton method is a typical method of solving nonlinear equations in mathematics,
there is a good convergence.Since the mid-1960s, the use of the best order elimination
method, Newton method in convergence, memory requirements, computational speed
than other methods have become until now is still widely used method.
This is a powerful tool for solving a set of non-linear equations, the advantages of this
method are that it is not sensitive to the assumption of the solution vector made. The
solution in this case converges in most cases as compared to the Gauss-Seidel method
and it is done in a fewer number of iterations. The drawback of this method is
increased computational burden and the need of additional storage space since it
involves calculation of Jacobian matrices and storage of values of previous iterations.
At any iteration, the function is approximated by a tangent hyperplane and the
problem is linearized into a Jacobian-matrix equation. The Jacobian matrix consists of
slopes of the tangent hyperplanes.
F(X)⁡=⁡—⁡J.ΔX
The problem is solved for the correction ΔX - the correction solved is then added to
the previous value of X, so the new updated value is closer to the solution and this
iteration process continues until an acceptable accuracy is obtained and the correction
values in subsequent iterations are very small.
The application of this method to the power system will be as follows:
1. For a PQ bus for which the values of active and reactive power are known (Pi and
Qi), an initial assumption of the solution for Vi and δi is made. The calculated values
for Pi and Qi are obtained then the corrected values are calculated.
𝛥𝑃𝑖=⁡𝑃𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑⁡−⁡𝑃𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
25
𝛥𝑄𝑖⁡=⁡𝑄𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑⁡−⁡𝑄𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
2. At the slack bus the values of vоltage magnitude and angle Vi and δi is fixed. Hence,
there would be no equations pertaining to the slack bus in the Jacobian.
3. Once the corrected values ΔVi and Δδi are obtained, the next iteration is carried out
by adding these corrected values to the previous values of Vi and δi and step 1 is
repeated. This process continues until the corrected values are very small pertaining to
an accuracy that is acceptable.
4. PV buses have constant voltage magnitude and active power at every bus and the
iterative process is carried out to obtain values for reactive power and voltage angle.
4.1.2 Gauss-Seidel Method
The Gauss-Seidel method, based on conduction matrices and applied to Gauss-Seidel
iterations, is one of the first current calculation methods to be applied in power
systems, and the Gauss-Seidel method is rarely used today.
This method is used for solving a set of nonlinear algebraic equations. This is an
iterative method that starts with an assumption about the solution vector. This
assumption is made for practical reasons. The revised value of the variable is obtained
by substituting the other variables present in the solution vector into one of the
equations. The solution vector is then immediately updated with this new revised
variable. This process is performed for all variables in the solution vector in a single
iteration. Iterations continue until a certain degree of accuracy of the solution vector is
obtained. The Gauss-Seidel method is very simple in terms of its use for solving
nonlinear equations, and there is no need to store data from previous iterations to go
to the next iteration. On the other hand, this method is very sensitive to the initial
assumption of the solution vector, hence the rate of convergence depends on the
proximity of the solution vector to the actual solution. In some cases, when the
assumption is very inaccurate, the method may not converge.
The application of this method to the power system is as follows:
1.First, load requirements (Pdi and Qdi) are obtained on all buses, then, subject to the
corresponding constraints, active and reactive power generation (Pgi and Qgi) is
distributed to all generating stations, and since the largest generating station is
retained as the reference bus, the active and reactive power generation on this bus can
change over iterations.
2. The Ybus tolerance Matrix is assembled with the available line and shunt tolerance
data.
𝑣𝑖𝑝+1−𝑣𝑖𝑝<⁡ℇ
3. Once the voltage values of all buses are known then active and reactive power at
the slack bus is obtained.
26
4. The last step of the process involves calculating the losses of the system using the
line and shunt admittance data along with the known voltage values.
These steps describe the method to obtain all parameters for PQ buses since it begins
with an assumption of active and reactive power demand and consumption at every
bus. For PV buses the iterative method is different with regard to the assumptions
made at the beginning of the iterative process.
4.1.3 Backward / Forward Sweep Method
There are many algorithms based on the idea of the forward and backward sweep
method. The initial voltage and end load of the distribution network are usually set in
the feeder as the base unit of calculation. Depending on the load power from the end
to the beginning of the output, only calculate the power loss in each element without
calculating the voltage to get the current and power loss of each branch, and
accordingly get the initial power, this is the sweep process; then according to the
upper initial voltage and the initial voltage obtained to the end, calculate the voltage
to the end to get the voltage of each node, this is the forward and backward process.
Backward / forward scan (BFS) methods are usually used in practice. BFS methods
do not need a Jacobian matrix, unlike NR methods. However, the usual BFS is not
useful for modern active distribution networks. The future of retail networks, smart
networks integrated with high penetration of DG units.
Moreover, modern networks are not radial in contrast to conventional ones. In fact, to
increase the penetration of DG blocks, modern distribution networks must enable
multiple loops. Thus, simultaneous modeling of mesh and DG is the main task for
new load-flow distribution networks.
DG blocks are modeled relative to their operation and their type of connection to the
grid. They are usually modeled as PQ or PV nodes in load flow studies.
BFS conventional methods fail if the DG units are modeled as PV nodes. Therefore,
some modifications are required to update the BFS methods. Recently several new
methods of studying energy flows taking into account DG blocks are proposed. Each
method has its advantages and disadvantages. Comparing these methods can be useful
to choose the best method for a typical network. In this paper, we analyze and
compare the most important methods for studying the load flow. distribution networks,
including DG units.
4.1.4 Other methods
Newton-Downhill (ND) load flow.
The disadvantage of the NR method is dependence of the final result on the starting
point. The starting point is usually one for the voltage value and zero for the stress
angle. However, this starting point can not suitable for load flow distribution networks
27
and NR cannot be reduced to a solution. ND method it includes two phases. At the
first stage, some linear search is used to find a good source solution for second phase .
As a result, the ND decision was received the method does not depend on the starting
point.
PQ decomposition method
The main idea is to represent the node power as a voltage vector in polar form, with
the active power error as the basis for correcting the angle of the voltage vector, with
the reactive power error as the basis for correcting the voltage amplitude, the active
and reactive power iteration separately, the main characteristics of the (n-1) Order and
m-order invariant, symmetric coefficient matrix instead of the original (n+m-1) order
of change, the asymmetric coefficient matrix M, So the P-Q decomposition has a
significant increase in the calculation speed.
4.2 BUS CLASSIFICATION
In power flow research, a bus is defined as a vertical line where several components
are connected, such as generators, loads, and transformers. Each bus is associated
with four variables: the voltage value, the voltage phase angle, and the active and
reactive power. Two of the four variables are specified, and the other two are
unknown. Two unknown variables are determined by solving nonlinear power flow
equations. These buses are classified into three categories:
- Load (PQ bus): the generator is not connected to the bus. The load attracted by these
tires is determined by the real power-PLi and the reactive power QLi, in which a
negative sign is placed for the power flowing from the tire. The task of the load flow
is to find the value of the bus voltage Vi and its angle δi.
- Generator bus: input power PGi and bus voltage Vi are kept constant. We have to
find the unknown angle δi of the Bus voltage and the generated reactive power QGi
through the load flow solution.
- Slack tire (swing): this generator bus is usually numbered 1 for load flow studies.
This bus sets the angular reference for all the other tires. Since it is the angle
difference between the two voltage sources that determines the actual and reactive
power flow between them, the specific slack angle of the bus is irrelevant. However,
it sets a standard against which the angles of all other bus voltages are measured. For
this reason, the angle of inclination of this tire is usually chosen equal to δ1=0. In
addition, it is assumed that the voltage value V1 of this bus is known.
4.3 POWER FLOW ALGORITHM FOR NETWORKS WITH
DISTRIBUTED GENERATION
In this work, the algorithm proposed by gen Hao (PFJ) was used as a basis [14]. This
method has been used in numerous studies [15], [16], where, for example, it has been
28
used to calculate load flows with uncertainty in mind using fuzzy set theory. Research
has shown that this algorithm is reliable and fast with good convergence
characteristics.
To explain the PFJ algorithm, we use the network shown in figure 1 [14]..The PFJ
method is based on the ratio of two matrices that are formed by applying Kirchhoff's
laws to the network. For bus i, the input net current is expressed as (1)
(1)
where n is number of buses, Ii is the net current injected in bus i, in [pu], with i = 1,...,
n. PGi and PDi are active power generated and consumed in bus i. QGi and QDi are the
reactive power generated and consumed in bus i. Finally, Vi is module of voltage in
bus i, in [pu].
Fig. 1. Simple distribution system.
Applying the fundamental laws of electrical circuits, Teng [14] showed that it is
possible to obtain a simple equation that relates the net current injected at the nodes
with the voltage drop in feeders. Equations (7) and (8) show these relationships,
[Δ𝑉] = [𝐷𝐿𝐹][𝐼]
(2)
[𝑉] = [𝑉1]0 + [Δ𝑉]
(3)
where [𝑉1]0 is a column vector of order n-1 and contains the voltage of the reference
bus in each element. In this method, the reference bus corresponds to bus 1. The DLF
matrix relates bus voltages with currents from buses.
The solution to the power flow can be obtained through following steps:
1. With the data of the line impedances and topological configuration of the network,
obtain DLF matrices;
2. Calculate the bus net currents using (1); i = 2, ..., n
3. Calculate the voltage drops and voltages in each bus with (2) and (3):
[Δ𝑉]k+1 = [𝐷𝐿𝐹][𝐼]k
(2)
29
[𝑉]k+1 = [𝑉1]0 + [Δ𝑉]k+1
(3)
4. Equation (4) will give the stopping criterion. If it is not met, go back to step 2;
𝜀 ≤ |𝑉i𝑘+1 − 𝑉i𝑘|
(4)
As can be seen from the PFJ method, the DLF matrix remains constant throughout the
calculation process. This fact gives advantages in calculating time, since the tolerance
bus matrix and the Jacobian matrix are not required.
4.4
MATHEMATICAL
GENERATION
MODELS
FOR
DISTRIBUTED
In this section, we analyze mathematical models of distributed generation (DG)
sources that are used in the study of energy flows. In particular, the method in which
they are included in the PFV-maximum forward voltage method is described. For
space reasons, only DC and DC power factor models will be considered in more detail,
as they are more relevant to this study.
A. Constant power factor
A model widely used for DG is to keep the power factor constant. This model can be
used for synchronous generators, where the reactive power can be adjusted by
controlling the excitation current and in DG sources that use power electronics
equipment (wind, PV), where the control is made by adjusting the firing angle.
Considering a constant power factor, the reactive power and current injected into the
bus must be calculated and then integrated into the process described in the PFJ
algorithm. The procedure [15] consist in calculate the reactive injected power using (5):
(5)
where 𝑝𝑓𝐺𝑖 is the power factor specified in the DG i. Then the injected net current
associate at DG i is calculate using (1).
When we using (5) and (1) to represent a DG, the bus where it is connected will be
considered as a PQ bus that injects energy into the network.
B. Constant current
In this model, the DG is considered as an element that supplies energy with a constant
current. This case is common in photovoltaic plants, because inverters can work in
constant current mode. In the iterative process, these busbars initiate the process with
an active and reactive power specified. In the first iteration, the current calculations
are performed using (1). In the following iterations, the module is kept constant and
only the angle of current is updated. The net current injected into the bus will not
30
remain constant, only the component that is contributed by the DG will. The treatment
of these buses is similar to the case of load with constant current
Photovoltaic plants (PV) are connected to the distribution network through inverters.
The inverters can inject voltage or current signals according to their construction or
internal topology. The semiconductors used and the circuit topology in the design of
the inverters determine the type of signal they will inject into the network [15]. When
the inverter injects a current signal into the system, the photovoltaic plant can be
modeled as a constant current source in a power flow study. Below is the modification
that is necessary to do in the PFJ algorithm to consider DG modeled as constant
current:
For k=1 calculate the current, module and angle, in the bus containing DG modeled as
constant current, as shown in (6), (7) and (8). In equation (7), the negative sign
indicates that the load current comes out from the bus.
For k=2,...,n the voltage of iteration k-1 is taken and the current is calculated using
(10). Then the angle is updated according to (11)
(6)
(7)
(8)
(9)
(10)
(11)
The net current in bus i will be calculated with (12)
(12)
The introduction of buses, where a portion of the magnitude of the net current remains
constant, does not significantly alter the iterative solution process, given that the
procedure to obtain DLF is not modified.
C. Constant voltage
31
Until now, only DG models that inject power into the network in PQ mode have been
presented. As mentioned, according to how the DGs are connected to the electricity
grid, the model that will be used in a study of power flows must be chosen. For
example, in large photovoltaic plants, depending on the inverter, it might be desirable
to maintain the magnitude of constant voltage; therefore, it will function as a PV bus
[18]
. In smaller plants, it could be opted to operate in constant current mode.
Considering that the treatment of this type of bus requires an extensive mathematical
model, those interested can find more information in [15] .
D. Models for wind farms
Wind farms with asynchronous generators will mostly act by varying the reactive
power [15]. The active power will depend on the available wind curve [19] and the
reactive power should be calculated as a function of the active power consumed or
generated, the voltage and the impedance.
If the dependence of reactive power on voltage and impedance is considered, the
calculation becomes difficult and becomes cumbersome, losing efficiency. For studies
in steady state, the reactive power of a wind farm can be represented as a function of
active power [21]. An alternative for asynchronous wind generators is the operation in
constant reactive power (PQ) mode. These models are described in [21], [20].
4.5 EQUIVALENT MODEL OF DISTRIBUTED POWER SUPPLY
Distributed generation system and network, generally do not participate in the system
of frequency regulation, it can be considered that they run at a certain active power
situation. Because of its different control characteristics and operating mode,
distributed generation system and network node equivalence model in the trend
calculation also vary.
A. micro gas turbines
Micro gas turbine power generation system is divided into sub-shaft structure and
uniaxial structure.
Sub-shaft structure of the power turbine and gas turbine with different shaft, power
turbine through the transmission gear connected to a synchronous generator, can be
directly connected to the network. Generator excitation control mode has the ability to
adjust the excitation voltage and power factor type, voltage control type gas turbine in
the trend calculation of the equivalent interface model can handle the PV node, power
factor type gas turbine in the trend calculation of the equivalent interface model can
handle PQ node, single-axis structure of the compressor, gas turbine and generator.
Converter current and voltage type two, current-type converter can be seen as the
active output and injected into the grid current constant PI node. To calculate the DG
corresponding reactive output can be calculated as follows[22]:
32
(13)
Wherein, PDGS is DG active output, V is the voltage DG access point. Vоltage-based
converters can be seen as PV nodes in grid-connected operation.
B. photovoltaic power generation system
Grid-connected photovoltaic power generation system is the main development trend
of photovoltaic power generation. The output of the photovoltaic power generation
system is a random output proportional to the light intensity. Photovoltaic power
generation system and network can always run in the case of a power factor of 1, can
also be controlled by the converter, in the case of the loss of part of the active power,
the regional power grid reactive
The power grid more stable economic operation[23].Photovoltaic systems can be used
to limit the output of the converter to model. Converter is divided into current type
and voltage type. For the current control type, the output of the active power grid and
note the current is constant, in the trend calculation can be equivalent to the PI node.
For voltage inverter, the output of the active and voltage constant, in the power flow
calculation can be seen as a PV node.
C. wind power generation system
Common wind power generation system in China there are two kinds of common
asynchronous motor and double-Fed asynchronous motor, due to the different
operation mode and control strategy, its equivalent model is not the same.
Early, wind power generation generally use ordinary asynchronous generator and
network operation, the induction motor itself is no excitation device, and by the power
grid to provide reactive power to establish a magnetic field, no voltage regulation. In
order to reduce network losses, generally at the end of the machine reactive power
compensation, to ensure that the wind turbine power factor to meet the
requirements[24].For the use of asynchronous motors wind power generation system,
the output of the active decision by the wind, the trend in the calculation can be
considered a given value, then absorbed reactive power Q and the machine terminal
voltage V and slip S related. Therefore, in the trend calculation, the ordinary
asynchronous motor is the equivalent of PQ (V)node.
(14)
(15)
33
In formula, XM is the magnetic reactance, X1 is the stator leakage resistance, X2 is the
rotor leakage resistance, Xe is reactive power compensation equivalent reactance, R2
is the rotor resistance, the stator resistance is ignored.
Double-Fed wind turbines can be obtained by the wind speed power characteristics of
the generator at a certain wind speed of the total active power injection system, which
is issued by the stator winding active power and the rotor winding emitted or absorbed
active power of two parts. When the speed is higher than the synchronous speed, the
rotor winding issued active power; when the speed is lower than the synchronous
speed, the rotor winding active power absorption. The reactive power of the doubleFed wind generator is composed of the generator stator side and the converter, which
emits and absorbs the reactive power on the rotor side of the generator. Double-Fed
generator control operation in two ways: constant power type and constant voltage
type. When using a constant power factor operation mode, the trend calculation stroke
power generation system can be equivalent to PQ node; when using a constant voltage
operation mode, the wind power generation system can be seen as PV nodes.
D. fuel cell power generation system
Fuel cell power generation is under certain conditions of hydrogen, natural gas or gas
and oxidant electrochemical reaction, the chemical energy into electrical energy
process. At present, the most efficient power generation in distributed power
applications is a solid oxide fuel cell[25].Grid-connected fuel cell power generation
system is mainly composed of a fuel cell, power conditioning units, power
conditioning unit is mainly composed of DC/AC converter, voltage control link and
power control links. The equivalent circuit of the connected fuel cell and the grid is
shown in the following figure:
Fig. 2. a schematic diagram of a fuel cell power generation system incorporated into the grid
In figure 2: U FC is the battery output DC voltage, U A C is the inverter output AC
voltage, VS for the fuel cell power generation system access to the grid bus voltage.
So φ=δ-θ, φ is the ignition angle of the inverter, the flow rate of the fuel is controlled,
in order to achieve the output of the active power of the fuel cell control.
UAC amplitude and UFC has the following relationship[22]:
34
UAC=MUFC (M is the regulation index of the inverter to control the reactive output
of the fuel cell).
(16)
(17)
Fuel cell power generation system without prime mover governor and excitation
regulator, its active and reactive power control by controlling the parameters φ and M
to achieve. Therefore, in the flow calculation of the fuel cell may be equivalent to PV
nodes.
35
5 COMPARISON OF NEWTON-RAPHSON
METHOD AND GAUSS-SEIDEL METHOD
The Gauss-Seidel method is relatively easy to program, but Programming the
Newton-Raphson method is more complex and becomes more complicated mainly if
the tires are randomly numbered and the storage requirements are greater (Jacobian
elements).
The iteration time in the Newton-Raphson method is longer than in the Gauss-Seidel
method. In the Newton-Raphson method, the iteration time increases directly as the
number of buses increases.
The number of iterations is determined by the convergence characteristic of the
method. The Gauss-Seidel method demonstrates a linear convergence characteristic
compared to the Newton-Raphson method, which has quadratic convergence.
Therefore, the GS method requires more iterations to obtain a converging solution
compared to the NR method. In the GS method, the number of iterations increases
directly as the system size increases. In contrast, the number of iterations is relatively
constant in the NR method. They require about 10 iterations for convergence in large
systems.
To sum up the comparison, we can make this conclusion:
Type of Method
Newton-Raphson
Advantages
1. the convergence Rate is
fast, if you choose a good
initial value, the algorithm
will have a convergence
square, usually iterations
of 4-5 times can converge
to a very accurate solution.
And its number of
iterations
is
almost
independent of the size of
the
network
being
calculated.
2. with good convergence
reliability,
Newton's
methods converge reliably
for previously mentioned
systems where the GaussSeidel
method
is
pathological based on
nodal conduction matrices.
3. the amount of memory
required for the Newton
method and the time spent
Disadvantages
The reliable convergence
of the Newton method
depends on having a good
initial value. If the initial
value
is
selected
incorrectly, the algorithm
may not converge at all, or
it may converge to a
solution that doesn't work.
36
Gauss-Seidel
on each iteration is greater
than the above-mentioned
Gauss-Seidel method, and
is closely related to
programming skills.
1. The principle is simple,
programming is very easy.
2. the conduction Matrix is
a symmetric and very
sparse matrix, so it saves
memory very much.
3.
the
Number
of
calculations required for
each iteration is the
minimum
among
the
various current algorithms
and is proportional to the
number of nodes contained
in the network.
1.
The
speed
of
convergence is very slow.
2. for systems with
pathological conditions, it
is often difficult to
calculate convergence: for
example, systems with a
large difference in phase
angles between nodes,
systems with negatively
stable
branches
(for
example,
some
transformers with three
windings or capacitors of a
series of lines, etc.),
systems
with
longer
radiant lines, long and
short lines connected to a
single node, and systems
with a large ratio of the
length of long lines.
3. Various options for the
location of the nodes
balance also affect the
performance
of
convergence.
37
6 SIMULATION AND ANALYSIS OF
COMPARISON
To clearly show the difference between these two methods, I made a calculation of an
IEEE 9 Bus System.
The simulation for Newton-Raphson Method, Gauss-Seidel Method is carried out
using MATLAB Software for test cases of IEEE 9. The simulation results are shown
in Table 1, Table 2 for Newton-Raphson Method and Gauss-Seidel Method
respectively.
Table 1. Number of iteration = 5
Bus
Voltage
Angle
P
Q
1
1.0300
0
-1.3975
0.1899
2
1.0200
1.6837
0.1000
-0.4019
3
1.0300
2.7222
0.2500
-0.0889
4
1.0511
2.1250
0.6000
0.4000
5
1.0480
2.0508
-0.7000
0.0500
6
1.0500
3.7179
1.0000
-0.4371
7
1.0635
2.5855
0.8000
0.6000
8
1.0300
1.5256
-0.8000
-0.3252
9
1.0415
2.9129
0.2000
0.1000
Table 2. Number of iteration = 45
Bus
Voltage
Angle
P
Q
2
1.0253
0.1687
1.6194
0.5249
3
1.0254
0.0849
0.8463
0.3804
4
0.9959
-0.0403
0.0304
0.0115
5
0.9661
-0.0652
-0.9195
-0.3042
6
1.0045
0.0365
0.0170
0.0051
38
7
0.9795
0.0144
-0.9999
-0.3517
8
0.9978
0.0690
0.0009
0.0045
9
0.9510
-0.0723
-1.2485
-0.4902
DISCUSSION
The selected tolerance value used for the simulation is 0.001/0.1. This is used to
determine the accuracy of the solution. Thus, using a high tolerance value for
modeling increases the accuracy of the solution whereas when a low tolerance value
is used, it reduces the accuracy of the solution and number of iterations.
Table 3 show the number of iterations for the power flow solution of IEEE 9 BUS
system using selected tolerance value of 0.001 and 0.1 respectively to converge for
the two load flow methods.
Table 3.
Tolerance Value of
0.1
0.001
Gauss-Seidel
45
12
Newton-Raphson
5
2
By the results showing in Table 3, we can make a conclusion that Gauss-Seidel has
the highest number of iterations before it converges. The number of iteration increases
as the number of buses in the system increases. We can see an example of this
statement in the Table 4.
Table 4.
Test System
IEEE 30 BUS
IEEE 30 BUS
IEEE 57 BUS
IEEE 57 BUS
Tolerance
of
0.1
0.001
0.1
0.001
Value Gauss-Seidel
113
36
176
17
Newton-Raphson
9
5
11
10
CONCLUSION:
Comparing different methods for solving the load flow problem gives the following
results: the Gauss-Seidel method takes less time to perform one iteration compared to
the Newton-Raphson method, this is due to fewer arithmetic operations associated
with completing the iteration, since the Jacobian calculation is an integral part of
calculations for the Newton-Raphson method. The Newton-Raphson method has a
39
higher convergence rate due to its quadratic convergence characteristics. This
technique, as they say," home-in " to the solution.
For the Gauss-Seidel method, the number of iterations increases with the network size,
i.e. the larger the number of buses in the network, the longer it takes the method to
find a solution. The Gauss-Seidel method is relatively easier to implement and does
not require a lot of memory, whereas the Newton-Raphson method is complex to
implement and does require higher memory and processing capacity.
The Gauss-Seidel method is very sensitive to the selection of the slack bus, In some
cases the method is also known to not converge to a solution hence, making the first
step of choosing a solution vector very crucial. Inversely, the Newton-Raphson
method is not so sensitive to the selection of the slack bus and almost always
converges to a solution.
40
7 CALCULATION OF POWER FLOW OF
DISTRIBUTION NETWORK BY BACKWARD /
FORWARD SWEEP METHOD
Backward / Forward Sweep Method was not compared with Newton-Raphson
Method and Gauss-Seidel Method, but it is worth considering it in more detail.
For the analysis of the trend of the algorithm to start from a simple distribution
network, trunk feeder distribution network can be understood as the entire network is
only one feeder, only one injection current on each node feeder, two output current.
Figure 3 shows a standard trunk feeder distribution network, also known as a simple
distribution network. Distribution network has n nodes, N-1 branch. Under the root
node voltage, system rated voltage and node load is known by the following steps can
be obtained the whole network node voltage and power distribution.
Fig. 3. Simple radiation network
Fig.3 shows that the injection of active and reactive power separates to：
(18)
Among them i= 1, 2, ......,N-1, N-number of nodes, LP(i) - active load power of the ith node; LQ (i) - reactive load power of the i-th node；
is active power loss on ith segment;
is loss of reactive power on the i-th segment. Formula for
calculating active and reactive power losses for the i-th feed segment:
(19)
Where, i=1, 2,......n, n is the number of branches.
Example: when i=2, as shown in the figure 4:
41
Fig.4. Three point grid
Injected active and reactive power of node 2, respectively:
(20)
Formula for calculating active and reactive power losses for the 2nd feed segment:
(21)
CALCULATION EXAMPLE
Using MATLAB software, a program for calculating the currents of a distribution
network with distributed power sources was compiled, and a calculation example of
the IEEE33 node system was performed. Calculation was made with the forward and
backward sweep method. This network has 32 branches, 5 branches of the contact
switch. A power supply network head-end reference voltage 12.66 KV, three-phase
power standard value of 10MVA, network total load 5084.26 + j2547. 32kVA. The
system structure is shown in Figure 5:
Fig.5. structure of IEEE33 node system
The program code is shown in appendix 1.
The result of calculation is shown in Table 5:
42
Table 5.
Nod
ei
0
Nod
ej
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
7
8
11
17
24
20
14
21
32
28
Branch
impedance
0.0922+j0.04
7
0.4930+j0.25
11
0.3660+j0.18
64
0.3811+j0.19
41
0.8190+j0.70
70
0.1872+j0.61
88
0.7114+j0.23
51
1.0300+j0.74
00
1.0440+j0.74
00
0.1966+j0.06
50
0.3744+j0.12
38
1.4680+j1.15
50
0.5416+j0.71
29
0.5910+j0.52
60
0.7463+j0.54
50
1.2890+j1.72
10
2+j2
2+j2
2+j2
0.5+j0.5
0.5+j0.5
Load of j Node Node Branch
node
i
j
impedance
100+j60
16
17
0.3720+j0.57
40
90+j40
1
18
0.1640+j0.15
65
120+j80
18
19
1.5042+j1.35
54
60+j30
19
20
0.4095+j0.47
84
60+j20
20
21
0.7089+j0.93
73
200+j100
2
22
0.4512+j0.30
83
200+j100
22
23
0.8980+j0.70
91
60+j20
23
24
0.8960+j0.70
11
60+j20
5
25
0.2030+j0.10
34
45+j30
25
26
0.2842+j0.14
47
60+j35
26
27
1.0590+j0.93
37
60+j35
27
28
0.8042+j0.70
06
120+j80
28
29
0.5075+j0.25
85
60+j10
29
30
0.9744+j0.96
30
60+j20
30
31
0.3105+j0.36
19
60+j20
31
32
0.3410+j0.53
62
Contact
switch
Load of
j node
90+j40
90+j40
90+j40
90+j40
90+j40
90+j50
420+j20
0
420+j20
0
60+j25
60+j25
60+j20
120+j70
200+j60
0
150+j70
210+j10
0
60+j40
Summary: by the results shown in Table 5, we can see that each node voltage
amplitude decreases, active power, reactive power is gradually reduced, this is quite
logical. This algorithm can solve the currents of a PQ-type DG system alone, without
43
increasing the number of iterations or increasing the calculation time compared to
when there is no DG grid.
44
8 CALCULATION OF POWER FLOW OF
DISTRIBUTION NETWORK BY PQ
DECOMPOSITION METHOD
A fast decomposition algorithm based on the modified Newton-Raphson method is
proposed to solve problems related to the insufficient speed of calculations using the
Newton-Raphson method and the requirements for implementing online power
system management. The fast decoupling algorithm is derived from the polar form of
the Newton-Raphson method, also known as PQ decomposition. The main idea is to
represent the node power as a voltage vector in the polar equation to catch the main
contradiction, the active power error as the basis for correcting the angle of the
voltage vector, the reactive power error as the basis for correcting the voltage
amplitude, the active power and the reactive power iteration separately. It closely
combines the characteristics inherent in the power system, both in terms of memory
capacity and in terms of computing speed, significantly improved compared to the
Newton and Raphson method. Simplicity, speed, memory savings, and reliable
convergence have become outstanding advantages of the algorithm, which is a
priority domestic and foreign algorithm based on the three conditions of the
hypothesis.



In the high-voltage grid reactance parameters of the element much greater than
the resistance, the change in active power depends mainly on the change of the
phase angle of the voltage and the change of reactive power is mainly
dependent on changes in voltage amplitude.
Consider not long distances and not overloaded circuits, the phase angle at
both ends of the line is not much different.
The guidance element corresponding to the node's reactive power is usually
much smaller than the node's pickup.
SIMULATION
To show an Example of using PQ decomposition method, a calculation of IEEE14
node system was performed. The system structure is shown in Figure 6:
45
Fig.6 Structure of IEEE14 node system
Results of calculation can be seen in Table 6 and Table 7.
Branch number - 20
Iteration number - 20
Table 6.
Number
of node
I
j
r
x
b/2
1
1
2
0,01938
0,05917
0,0264
2
1
5
0,05403
0,22304
0,0246
3
2
3
0,04699
0,19797
0,0219
4
2
4
0,05811
0,17632
0,017
5
2
5
0,05695
0,17388
0,0173
6
3
4
0,06701
0,17103
0,0064
7
4
5
0,01335
0,04211
0
11
6
11
0,09498
0,1989
0
12
6
12
0,12291
0,25581
0
13
6
13
0,06615
0,13027
0
14
7
8
0
0,17615
0
15
7
9
0
0,11001
0
46
16
9
10
0,03181
0,0845
0
19
12
13
0,22092
0,19988
0
20
13
14
0,17093
0,34802
0
4
14
9
0,12711
0,27038
0
5
10
11
0,08205
0,19207
0
Table 7.
Number of PG-Active
node
Power
QG-Reactive PL-Active
Power
Load
QLReactive
Load
1
60
0
0
0
2
65
42,4
21,7
12,7
3
0
23,39
94,2
19
4
0
0
47,8
-3,9
5
0
0
7,6
1,6
6
85
12,24
11,2
7,5
7
0
0
0
0
8
0
17,36
0
0
9
0
0
29,5
16,6
10
0
0
9
5,8
11
0
0
3,5
1,8
12
0
0
6,1
1,6
13
0
0
13,5
5,8
14
0
0
14,9
5
47
Summary: Using the PQ decomposition method, the calculation is faster, the
calculation is more efficient. But from the experimental results, we can see that the
accuracy is not more accurate, there may be an error when the accuracy is too small,
as well as a slowdown due to too many iterations, which contradicts the original
intention of using pq decomposition.
48
9 COMPARATIVE SIMULATION
To make a comparative example, I performed a calculation of IEEE30 node system,
using two methods: Newton-Raphson and PQ decomposition.
Results are shown in Tbale 8 and Table 9
Table 8. Results os IEEE30 using Newton-Raphson method
Number of Iterations - 28
Number
of node
2
3
4
5
6
7
8
9
10
13
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
i
1
2
3
2
2
4
5
6
6
9
12
12
12
12
14
16
15
18
19
10
10
10
10
21
15
22
23
24
25
25
27
j
3
4
4
5
6
6
7
7
8
11
13
14
15
16
15
17
18
19
20
20
17
21
22
22
23
24
24
25
26
27
29
r
0.0452
0.0570
0.0132
0.0472
0.0581
0.0119
0.0460
0.0267
0.0120
0.0
0.0
0.1231
0.0662
0.0945
0.2210
0.0524
0.1073
0.0639
0.0340
0.0936
0.0324
0.0348
0.0727
0.0116
0.1000
0.1150
0.1320
0.1885
0.2544
0.1093
0.2198
x
0.1652
0.1737
0.0379
0.1983
0.1763
0.0414
0.1160
0.0820
0.0420
0.2080
0.1400
0.2559
0.1304
0.1987
0.1997
0.1923
0.2185
0.1292
0.0680
0.2090
0.0845
0.0749
0.1499
0.0236
0.2020
0.1790
0.2700
0.3292
0.3800
0.2087
0.4153
b/2
0.0204
0.0184
0.0042
0.0209
0.0187
0.0045
0.0102
0.0085
0.0045
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
49
27
29
8
6
9
37
38
39
40
41
30
30
28
28
10
0.3202
0.2399
0.0636
0.0169
0.0
0.6027
0.4533
0.2000
0.0599
0.1100
0.0
0.0
0.0214
0.0065
0.0
Table 9. Results of IEEE30 using PQ decomposition method
Number of iterations - 27
Number
of node
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
i
1
2
2
2
3
4
-4
5
6
6
-6
-6
6
8
9
9
10
10
10
10
12
12
12
12
14
15
15
16
18
19
j
3
4
5
6
4
6
12
7
7
8
9
10
28
28
10
11
17
20
21
22
13
14
15
16
15
18
23
17
19
20
r
x
b/2
0.045200
0.057000
0.047200
0.058100
0.013200
0.011900
0
0.046000
0.026700
0.012000
0
0
0.0169
0.0636
0
0
0.0324
0.0936
0.0348
0.0727
0
0.1231
0.0662
0.0945
0.221
0.1073
0.1
0.0524
0.0639
0.034
0.165200
0.173700
0.198300
0.176300
0.037900
0.041400
0.256
0.116000
0.082000
0.042000
0.208
0.556
0.0599
0.2
0.11
0.208
0.0845
0.209
0.0749
0.1499
0.14
0.2559
0.1304
0.1987
0.1997
0.2185
0.202
0.1923
0.1292
0.068
0.020400
0.018400
0.020900
0.018700
0.004200
0.004500
0.932
0.010200
0.008500
0.004500
0.978
0.969
0.0065
0.0214
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
21
22
23
24
25
25
27
27
27
29
32
33
34
35
36
37
38
39
40
41
22
24
24
25
26
27
-28
29
30
30
0.0116
0.115
0.132
0.1885
0.2544
0.1093
0
0.2198
0.3202
0.2399
0.0236
0.179
0.27
0.3292
0.38
0.2087
0.396
0.4153
0.6027
0.4533
0
0
0
0
0
0
0.968
0
0
0
SUMMARY:
By results in Table 8 and Table 9 we can see that the results are almost the same,
except for the number of iterations and b/2.
This is because:
1. PQ decomposition method uses two diagonal matrix instead of the previous
large matrix, a small amount of storage.
2. Matrix attack is a constant coefficient, instead of the Ox-pull method becomes
the coefficient matrix, the calculation amount is small.
3. PQ decomposition matrix is a symmetric matrix, Newton-Raphson is an
asymmetric Matrix.
4. PQ decomposition zd single operation fast, but the calculation is linear
convergence, increasing the number of iterations; Newton-Raphson single
operation is very slow, but the square of convergence. Overall, the pq
decomposition rate is faster than Newton-Raphson.
51
10 CONCLUSION
In the thesis analyzed a few types of the power flow calculation of distributed
networks with distributed generation, bus classifications, the history of development
of distributed energy and power flow calculation and analysis as well. Also I analyzed
the mathematical model of power flow calculation. Made a comparison between
Newton-Raphson method and Gauss-Seidel Method. An example of comparison was
made, and results were analyzed as well. Using MATLAB software, made an example
calculation of IEEE33 node system by forward and backward sweep method and
analyzed the results. After analyzing the General model of several distributed power
sources in current calculations, based on the forward and backward sweep method, the
proposed injection reactive power compensation method, which is used in a 33-node
distribution system for a large number of tests, the following conclusions were
obtained:
(1) wind generators usually use asynchronous generators that are permanent, P with
erosion, and PV systems connected via a current-controlled inverter that are
permanent P that can be processed in PQ nodes on each iteration. Photovoltaic
systems, fuel cells, and mini-gas turbines can be processed into PV units using
voltage-controlled inverters.
(2) introduction of the injection reactive power compensation method in the forward
backward sweep method, can effectively handle PV nodes, suitable for calculating
many types of DG networks
(3) mini gas turbine has the strongest ability to maintain the system voltage, the least
network loss; second, through the current control inverter connected to the
photovoltaic system network; wind Power through the parallel capacitor block on the
machine side after reactive power compensation, the system voltage also has some
support ability, the network loss is also reduced. And the further the DG network
position is from the root node, the greater the system voltage support. The effect of
the DG network on system network losses is not only related to the position of the DG
network, but also to the relative size of the DG capacity and load.
Also using PQ decomposition method made a calculation of IEEE14 node system as
an example. And made an analysis and summary as well.
Made a comparative example of IEEE30 node system using Newton-Raphson method
and PQ decomposition method and analyzed results and made a comparison.
52
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