Download penetration level assessment of distributed generation

PENETRATION LEVEL ASSESSMENT OF DISTRIBUTED GENERATION
BY MEANS OF GENETIC ALGORITHMS
G. CELLI
F. PILO
Department of Electrical and Electronic Engineering
University of Cagliari
Italy
ABSTRACT
The large amount of Distributed Generation (DG), that
will be installed in the near future, drastically changes the
behaviour of the typical passive MV distribution network.
If it is not correctly applied, it can cause degradation of
power quality, reliability and control of the power system,
vanishing the advantages it can introduce. This context
determines the need of new tools that help the planner to
correctly evaluate the DG impact on the distribution
network and to find the best size and location of the DG
for feeder voltage support and loss reduction. For these
reasons, the paper proposes a software procedure, based
on a Genetic Algorithm, able to establish the optimal
distributed generation allocation on an existing MV
distribution network, considering all technical constraints
like feeder capacity limits, feeder voltage profile and
three-phase short circuit current. The objective function
implemented includes among its terms the costs of buying
energy from the transmission system and from the DG
units. This allows assessing the more convenient
penetration level of DG in a distribution network.
Application examples are presented to illustrate the
algorithm effectiveness.
KEYWORDS
MV Distribution Networks, Distributed Generation,
Genetic Algorithms, Distributed Generation Planning.
INTRODUCTION
The need for more flexible electric systems, changing
regulatory and economic scenarios, energy savings and
environmental impact are providing impetus to the
development of Distributed Generation (DG), that is
predicted to play an increasing role in the electric power
system of the near future. Studies have calculated that DG
may account for up to 20% of all new generation going
online by the year 2010 [1].
DG offers an alternative that utility planners should
explore in their search for the best solution to electric
supply problems. In fact, if DG units are properly placed
in a MV distribution network, they can reduce power
losses cost and defer utility investment for enforcing its
system. But, if it is not correctly applied, it can cause
degradation of power quality, reliability and control of the
power system, vanishing the advantages it can introduce
[2-4]. For these reasons, it is essential to provide useful
tools for the MV distribution networks planning task, able
to take into consideration the presence of DG units.
Undeniably, one of the goal of the planner is to find
the optimal number and position of DG generators to
install in a given network. Independent power producers,
seeking interconnection under open access rules, may
dictate the location, and the utility planner may not have
much choice. However, a planning methodology able to
solve the siting DG problem may be used to evaluate any
additional credits the utility might offer if the DG is in an
appropriate location to have real benefits for the network
[5]. Besides, with the liberalization of electricity market,
many public administration in different countries have to
arrange their regional energy development plans and,
consequently, decide how much distributed generation to
authorize on their grid and where to locate it.
Therefore, the paper proposes a new software
procedure, based on a Genetic Algorithm, able to establish
the optimal distributed generation allocation on an
existing MV distribution network, considering all
technical constraints like feeder capacity limits, feeder
voltage profile and three-phase short circuit current.
In previous works, this goal has been reached
minimizing the typical objective function used in planning
studies, that is the total cost of the network: building,
maintenance, losses and costs of disruptions [6, 7]. To
allow assessing the more convenient penetration level of
DG in a distribution network, in this paper the costs of
buying energy from the transmission system and from the
DG units have been added to the objective function
implemented. In fact, by acting in this way, the
advantages introduced by the distributed generators are
balanced by the higher cost of the energy produced, and
the optimal equilibrium can be found.
OPTIMAL ALLOCATION PROCEDURE
GAs are a family of computational models that rely on
the concepts of evolutionary processes [8]. It is a well
known fact that according to the laws of natural selection,
in the course of several generations, only those
individuals better adapted to the environment will manage
to survive and to pass on their genes to succeeding
generations. Correspondingly, GAs operate on a set
(population) of possible solutions (individuals) of a
generic problem, applying selection and reproduction
criteria whereby new solutions (offspring) are generated
containing the information enclosed in the solutions from
which they originated (parents). Clearly, the better the
solution, the more possibilities there are of reproducing
and passing on genes to the offspring.
The first step to be taken in implementing these
algorithms is to encode a potential solution in a simple
data structure of the chromosomal type (generally a
vector) in which each element is represented by means of
a specific alphabet (usually binary). Once the initial
population has been randomly generated, every solution is
evaluated by means of the objective function.
The strategy followed by GAs is very simple. To
ensure an amelioration in the population, in each
generation a selection operator sees that the solutions with
higher fitness have greater possibilities of reproducing. At
this point some individuals are coupled and cross-bred,
with a generally high probability, by means of a crossover
operator, which recombines the salient information
brought by the parent structures in a significantly nondestructive way. The crossover operator produces
offspring, that will then replace some of the old
individuals of the population. Lastly, the strings can
undergo mutation, which involves selecting, with little
probability, a string element and changing the symbol
contained therein with another symbol of the alphabet
being used.
Once the procedures performed by the three operators
have been completed, the offspring produced are
evaluated, by using a fitness function, and compared with
their parents. If the GA is generational, then the offspring
will replace all their parents, creating a new population.
On the other hand, if the GA is steady state then the
offspring will replace their parents only if they are better.
Several parameters normally influence the search for
the optimum solution by GAs: population size, the
probability of mutation, the maximum number of
generations to be explored, etc.. These parameters should
be accurately calibrated, adapting them to the size of the
problem in question.
In this paper, a GA optimization technique has been
developed for finding the optimal sizing and location of
DG in a given MV distribution network; it is briefly
described in the following sections.
Coding of the solution
The first important aspect of a correct implementation
of the GA is the coding of the potential solution.
Considering that the network structure is fixed, all the
branches between nodes are known, and the evaluation of
the objective function depends only on size and location
of the DG units. For this reason each solution can be
coded by using a vector, whose size is equal to the
number of nodes, in which each element contains the
information on the presence or not of a DG unit. In order
to perform not only the siting but also the sizing of DG, a
prefixed number (NDG) of generator sizes have been
assumed and classified (e.g. size number 1 corresponds to
a 100 kVA DG unit, size number 2 corresponds to a 200
kVA DG unit, etc.). Therefore, each element of the vector
solution is represented by means of the following
alphabet:
0
no DG located on the node;
1, … , NDG size index of the DG installed in the
node.
Of course, the vector elements corresponding to the
HV/MV primary substations are fixed to 0.
The type of code used is suitable for every kind of
network structure (radial, meshed, etc.), that influences
only the assessment of the usual technical constraints
(voltage profile and thermal feeder capacity) considered
during the evaluation of the objective function, but does
not affect the optimal allocation procedure. In the paper
the algorithm has been applied to “open loop” distribution
networks, that are commonly used in Italy.
GA Implementation
The implementation of an optimization problem of GA
is realized within the evolutionary process of a fitness
function. The fitness function adopted is given as:
 Objectivei  Penaltyi
Fitnessi   log 
Objectivemax




(1)
where the objective function (OF) is the total cost of the
network. For each solution, all technical constraints are
checked: if one of them is not verified, a penalty term is
added to the OF value.
The genetic algorithm procedure to solve the optimal
DG units allocation problem is described below.
In the first phase, an initial population of possible
solutions is randomly generated by means of the
following procedure:
 for each solution a value of DG penetration is
selected between 0 and 100% of the total amount of
power requested by loads;
 a number of DG units of different sizes is randomly
chosen until the DG penetration level assigned is
reached;
 the DG units are randomly located among the nodes
of the network;
 the fitness for each solution is evaluated and scaled
by using the fitness function.
Regarding the population size, the best results have
been found assuming it equal to the dimension of the
problem, i.e. the number of nodes in the network.
In the second phase, the genetic operators are applied
in order to produce the new solutions. In this paper the
following implementation details for the operators have
been considered:
 Selection: the “remainder stochastic sampling without
replacement” scheme has been adopted, whereby the
number of selections of each individual is calculated
in the following way: expected individual count
values are calculated as a fraction between the OF
value of the individual and the average of OF value of
the whole population. Then integer parts of the
expected numbers are assigned, and fractional parts
are treated as probabilities.
 Crossover: the “uniform crossover” is adopted, by
which each allele is swapped with probability 0.5.
The probability of crossover between two individuals
has been kept high (about 0.95).
 Mutation: all the vector elements are mutated,
according to a small mutation probability (0.01),
choosing a different value in the defined alphabet.
Scaled the fitness of each offspring using the fitness
function, the new population is generated as follow: a
portion of the new individuals consists of the best
solutions between parents and offspring (Steady State
model); the remaining individuals to complete the new
population are chosen only among the offspring,
independently they are or not better than their parents
(Generational model).
The procedure terminates when a maximum number of
generations has been explored.
COSTING OF DG SITING SOLUTIONS
The goodness of the solutions provided by an
optimization procedure strictly depends on the definition
of an objective function that correctly represents the
problem to solve. Therefore great attention must be paid
on modelling the main aspects that can influence the DG
units allocation in an existing distribution network.
Traditional Objective Function
The main goal of planning studies is finding the
optimal network structure that allows supplying loads
minimizing the generalized cost. Thus, the objective
function to be optimized within the technical constraints
generally refers to the total cost of the network which
considers [9, 10]:
 site of the substations and loads
 geographical, geological and urbanistic features of the
area concerned
 power demands of the loads and their growth versus
time
 duration of the planning period
 some cost parameters such as inflation and interest rates
 unit cost of kWh lost due to Joule effect (cost of losses)
 construction and maintenance costs of feeders of
different cross-sections and for different types of lines
(overhead, underground).
Due to the current Italian standard, that does not admit
islanded portion of MV network directly supplied by DG,
the most common reliability indices for long interruptions
are not modified by DG units and thus no service quality
improvements can be achieved by normal customers [11].
For this reason, the costs of disruptions are not considered in
the objective function. Of course, each customer with DG
units can use them to supply, totally or partially, its loads
during grid faults or scheduled interruptions, increasing
the availability of energy and reducing the number and
duration of interruptions.
More generally, service interruptions due to overloads
should also be taken into account as well as those due to
outages or scheduled interruptions. Thus, among the
benefits introduced by DG, the reduction of overload
costs, treated like expected unserved energy (EUE),
should be considered. It is trivial to observe that by
estimating overload costs with the EUE, which is much
more higher than retail sales rate, investments decisions
are made and timed such that they to emphasize the
reliability of the system in areas where the value of
service is higher [5]. In this paper, overload costs are
disregarded because the power flow implemented
considers only an annual growth of the load energy
demand. Surely, in order to improve the proposed
planning tool, individual hourly characteristics should be
included in the OF, but this does not reduce the generality
of the described optimization algorithm. Furthermore, it
should be noticed this planning tool is suited for the
standards of the Italian public distribution company about
“open loop” networks that consider as emergency limit
the maximum continuous current-carrying (at the time of
peak load).
The objective function to be minimized is thus
represented by the total cost C0G of the generic network,
with present value taken at the beginning of the whole
planning period of N years. This cost can be expressed by
using the sum:
C 0G 
NTot  NCp
 C0 j ,
(2)
j 1
where NTot is the number of network nodes, NCp is the
number of substations, NTot-NCp the number of branches in
the network and C0j the present cost of the jth branch.
The cost of every branch j is the sum of the construction,
residual, management costs, and cost of losses in the
subperiods, transferred to the cash value at the beginning of
the planning period by using economical expressions based
on the inflation rate, the interest rate and the load growth
rate (all of them constant) [9] .
The cost of every branch can be expressed by using:
m
C 0 j  C 0 j '   C 0 pjk ,
(3)
k 1
where C0j is the total cost of the branch j, C0j' the portion of
cost independent of power flow, C0pjk the cost term
proportional to the power flow through the branch in the kth
subperiod (cost of losses) and m is the number of subperiods
into which the planning period of N years has been divided.
Denoting with C0cj the construction costs, R0j the
residual value, C0gj the management costs and ej a binary
factor (equal to 1 for a resized branch and 0 for an existing
one), the cost C0j', independent of power, can be written by
using:
(4)
C0 j '  e j  (C0cj  Roj )  C0 gj
The cost of resizing the jth branch C0cj takes into account
the year of reconstruction to transfer the cash value to the
beginning of the planning period, while the residual value
Roj considers the fact that the planning period does not
coincide with the life duration of the component.
The cost of Joule losses in the kth subperiod C0pjk can be
calculated transferring, to the cash value at the beginning of
the planning period, the annual cost of such losses Cpjk,
evaluated by using:
C pjk  C kW h  (3  8760  coeff  r j  L j  ccp j  I 2jk ) (5)
where:
 CkWh is the cost of kWh,
 coeff is the utilization factor of energy losses under full
load, different for overhead and underground,
 8760 are the number of hours per year,
 rj is the resistance per km of line [Ω/km],
 Lj is the branch length [km],
 Ijk is the phase current in the jth branch [A] at the
beginning of the kth subperiod,
 ccpj is a corrective coefficient of the losses due to the
simultaneity of loads.
New Objective Function
By using the traditional objective function described in
the previous paragraph, whichever optimization procedure
tends to place a very large number of generators. In fact,
equation (2) exalts exclusively the advantages introduced by
DG (reduction of losses and deferment of investments for
grid upgrade), and consequently the optimization process
evolves towards configurations with DG penetration levels
near 100% of the total amount of power requested by loads.
For this reason, in a previous work the genetic algorithm
procedure, to solve the optimal DG units allocation
problem, was used to perform studies with prefixed DG
penetration levels [6, 7].
In order to overcome this drawback and to allow
assessing the more convenient penetration level of DG in
a given distribution network, in this paper the costs of
buying energy from transmission system, (CkWh)Tr, and
from DG units, (CkWh)GD, have been added to the
traditional objective function:
is easy to calculate the terms (CkWh)Tr and (CkWh)GD,
opportunely transferred to the cash value at the beginning of
the planning period so that they can be comparable with the
other costs of the objective function.
An objective function like that expressed by (5) allows
better estimating DG impact on MV distribution networks
and also determining which DG penetration level is
considered more convenient for the distribution company. In
fact, the limit will be reached when the further benefits
introduced by adding new DG units no more compensate
their relative costs.
Distribution Network Structure
Distribution networks always have a radial structure
and are often subdivided into two different levels: trunk
feeders and lateral branches. The degree of reliability
obtainable with this network arrangement is limited by the
fact that a fault in one part of the network results in outage
in a large number of load points. To improve service
reliability, emergency ties provide alternative routes for
power supply in case of outages or scheduled
interruptions. Emergency ties end with an open switch so
that radial structure is maintained during normal
conditions; furthermore trunks are subdivided in some
segments by means of normally closed switches, generally
positioned in MV/LV nodes. During emergencies,
segments can be reswitched to isolate damaged sections
and route power around faulted equipment to customers
who would otherwise have to remain out of service until
repairs were made [12]. An important class of such
networks are the “open loop networks” which are usually
employed in urban power distribution systems. If there are
no laterals (“pure open loop networks”) then service
restoration is ensured through the emergency tie that
connects the ends of the feeder. An intermediate
alternative is to install laterals (“spurious open loop
networks”) in which top priority customers are supplied
through the main feeder and can be completely reenergized in the event of a fault. The main characteristic
of both “open loop networks” is that only two branches
can converge in a trunk node (topological constraint) [13].
Automatic switching devices along trunk feeders and
NTot  NCp
C0 G 
 C0 j  CkWh Tr  CkWh GD .
(5)
Emergency connection
j 1
In presence of a liberalized electricity market, it needs to
consider different retail sales rate of the energy produced by
a DG unit, that depends on the technology adopted (mini gas
turbine, CHP, wind turbine, etc.), and of the energy coming
from the transmission system.
Assuming a constant power demand growth rate and a
fixed amount of energy generated per year by DG, it is
possible to evaluate the energy that an hypothetical
distribution company has to buy from both the
transmission system and the DG installed in its network in
the whole planning study period. By resorting to an
average value of the energy rate in the planning period, it
A) Pure “open loop network” with no lateral MV nodes
Emergency connection
B) Spurious “open loop network” with lateral MV nodes
Fig. 1 – “Open loop” networks
emergency ties may reduce both the duration of service
interruption and the number of customers affected thereby
(Fig. 1) [12, 13].
Technical Constraints
Each individual produced by GA operators has to
comply with all technical constraints usually adopted by
planning engineers, i.e. the voltage profile along the
network trunks and the three-phase short circuit currents
in the network nodes [1, 14].
Indeed, the presence of generation nodes in the
distribution system can cause a voltage drop or an
overvoltage in some points of the network. Due to the
absence of any dispatch strategies and ancillary services
in the MV distribution networks, the connection of a
generator to a network can result in an increase in the
voltage that depends only on the power supplied by the
generator. For this reason, in the proposed methodology
the voltage profile is checked and those DG allocations
unable to maintain the voltage within prefixed ranges both
in normal and emergency situations are penalized.
Calculations are performed by determining the impedance
matrix Z of each feeder examined and by calculating the
voltage in each node of the network. The calculation of Z
can be noticeable simplified considering the particular
network architecture (“open loop” network).
The presence of DG can change the magnitude,
duration, and direction of the fault current. The fault
current is modified since the connection of rotating
generators modifies the characteristics (impedance) of
distribution networks. In this context, one needs to verify
that the alteration in magnitude, duration and direction of
the fault current due to dispersed generation groups does
not affect the selectivity of protection devices. In fact, the
selectivity must be checked for each connection of a new
generator to the distribution network. In the paper, fault
currents are calculated for each DG configuration
examined by using the diagonal elements of the short
circuit matrix and the voltages in each node. Again a
penalty is inflicted to all those situations which do not
comply with this technical constraint.
RESULTS AND DISCUSSION
In order to show the capability of the proposed
methodologies, an area of the real MV Italian network has
been considered. As shown in Fig. 2, it is constituted by 148
nodes divided into 3 HV/MV substations and 145 MV/LV
trunk nodes. The whole chosen area covers a surface of
about 600 km2. The period taken into consideration for the
planning study is 20 years long, with all nodes existing at
the beginning of the period. The period of study is longer
than those normally considered (5-10) in distribution
planning, but this choice allows showing significant results
even in a small case. For each MV/LV node, a constant
power demand growth rate of 3% per year has been
assumed; the size of the installed transformer ranges from
100 kVA to 630 kVA. The annual medium active power
delivered to MV nodes is, at the beginning of the planning
period, 6.6 GW. The majority of the branches is of the
HV/MV primary substation
MV/LV node
MV/LV node with DG unit
Fig. 2 – 148 nodes test network and DG siting results.
overhead type, but some buried cables exist. The thermal
capacity constraint is verified for all the branches at the
beginning of the planning period, but some of them will
have to be resized according to the growing energy demand.
In order to test the proposed methodology, DG units
have been considered, ranging between 100-300 kVA. It is
straightforward noticing that there are no limits on the size
of DG units that can be treat by the optimization procedure
proposed. The cost of Joule losses has been taken as 0.05
US$/kWh, the cost for section unity has been assumed 0.3
US$/mm2 for buried cables and 0.5 US$/mm2 for overhead
lines (no adjunctive costs for digging or poles, considering
that no new paths are built). The cost of buying energy from
T&D is 4¢ while the cost of energy from DG has been
varied within the range 5¢÷6¢.
In Table I, the costs of investments for grid upgrade
and of power losses are reported for the network in Fig. 2,
without DG and with the optimal arrangement of DG
units obtained with the proposed GA. Energy costs are
evaluated considering 5¢ for the energy bought from DG.
The DG penetration level is 22.1% of the total amount of
power requested by loads. It is worth noticing that DG
units allow reducing all costs considerably. In particular,
the greater saving is represented by the reduction of the
investments for upgrading the existing branches. This is
really an important result, considering that T&D costs
represent almost 30-50% of the kWh cost and the
deferment of investments will produce benefits to both
utilities and final customers regardless the type of
distribution energy market adopted.
In Fig. 3 is reported the voltage profile along the
highlighted feeder for the same case, clearly showing DG
benefits in voltage regulation. Without DG, despite high
building investments, the feeder voltage is dangerously
close to the lower bound limit (8%) and, thus, not
foreseen growths in load demand can lead to poor quality
of service. By using DG, voltage profile along the feeder
can be drastically improved and the higher engineering
margin leads to a more robust solution.
Table I.
Comparison between costs for the MV distribution network in Fig. 2
Without DG
With DG
7953.9 kUS$
Cost of investments
Cost of losses
Cost of energy from T&D
Cost of energy from DG
Total cost
3646.3 kUS$
626.9 kUS$
542.0 kUS$
45688.0 kUS$
37670.2 kUS$
--------------
10022.3 kUS$
54268.8 kUS$
51880.7 kUS$
Different simulations have been performed in the same
network varying the cost of energy from DG. Obviously,
when the retail sales rate increases lower levels of DG
penetration have been found. Indeed, variations in the
energy cost have a great impact in planning and this
impact increases with the increment of the planning
horizon. Anyway, nevertheless the cost of energy from
DG, the optimization algorithm has detected in which
feeders it is always more convenient to install generators.
This is a very important information for the utility, which
can use it to force independent power producers, by
means of discounts or additional credits, to interconnect
their generators in the more convenient locations.
assessed accurately so that these DG units can be applied
in a manner that avoids causing degradation of power
quality, reliability, and control of the utility system. On
the other hand, DG has much potential to improve
distribution system performance and it should be
encouraged. For this reason DG should be incorporated
into distribution planning as an option along with
traditional feeder and substation options.
On the basis of these considerations, the paper deals
with the important task of finding the optimal siting and
sizing of DG units for a given network so that the cost of
power losses during a prefixed period of study can be
minimized and investments for grid upgrades can be
deferred. Retail sales rates for energy have been also
considered so that the optimal DG penetration level in a
given distribution network can be automatically assessed.
Since much of the value inherent in DG is its ability to
hedge against uncertain load growth, a typical planning
study would analyze the cost curves for a number of
growth scenarios defined by the utility. Thus, further
studies will deal with the application of probabilistic
techniques in order to improve power flow calculations
and better treat uncertainties introduced by loads and DG.
ACKNOWLEDGMENT
The authors wish to acknowledge CESI for funding
this activity with research contracts focused on DG.
REFERENCES
CONCLUSIONS
DG is predicted to play an increasing role in the
electric power system of the near future. In fact, studies
have predicted that distributed generation may account for
up to 20% of all new generation going online by the year
2010. With so much new distributed generation being
installed, it is critical that the power system impacts be
Voltage profile with DG
Voltage
profile
[kV]
Voltage profile without DG
Lower bound of voltage drop (8%)
11.6
11.4
11.2
11.0
10.8
10.6
10.4
emergency tie
Fig. 3 – Effect on the feeder voltage profile of the presence of DG.
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