PLANNING OF THE DISTRIBUTION GRIDS WITH DISTRIBUTED GENERATION AND DEMAND SIDE MANAGEMENT

PLANIFICACIÓN DE LAS REDES DE DISTRIBUCIÓN CON GENERACIÓN DISTRIBUIDA Y
GESTIÓN ACTIVA DE LA DEMANDA
Autor: Fernández López, Beatriz
Director: Trebolle Trebolle, David
Entidad Colaboradora: Unión Fenosa Distribución
RESUMEN DEL PROYECTO
Introducción
El objetivo fundamental de las redes de distribución es conducir la energía eléctrica desde las
redes de transporte al consumidor final al mínimo precio pero verificando, tanto en condiciones
normales como ante el fallo de un elemento del sistema (escenario n-1), los siguientes criterios de
seguridad: Mantenimiento de los niveles de tensión y sobrecargas dentro en los límites
establecidos (±7% y ±20% respectivamente), maximización de la continuidad de suministro y
minimización de las pérdidas técnicas en la red. Por ello, y con el fin de garantizar el correcto
funcionamiento del sistema y la calidad de los clientes finales, es fundamental conseguir una
planificación eficiente de las redes de distribución.
Hasta el momento la forma más habitual empleada por las compañías distribuidoras en caso de
incumplimiento de estos criterios de seguridad, y en particular en el caso de la sobrecarga, es
decir cuando la demanda bruta excede la capacidad efectiva del sistema, situación en la que nos
centraremos en el proyecto, ha consistido en la inversión en elementos de red. Sin embargo, esta
inversión tradicional conlleva un importante exceso de capacidad infrautilizada durante muchas
horas al año por lo que sería deseable buscar alternativas.
Una de estas alternativas, aparte, de la de no satisfacer las necesidades de los clientes, es decir,
no invertir y pagar la penalización consecuente, podría consistir en la integración de los recursos
energéticos distribuidos en la red. Estos a su vez engloban a la Generación Distribuida (GD) y a la
Gestión Activa de la Demanda (GAD). Se denomina generación distribuida a un conjunto de
generadores conectados a la red de distribución que se caracterizan por su pequeño tamaño y por
estar localizados cerca de los puntos de consumo, mientras que por gestión activa de la demanda
nos referimos a la implementación de las medidas necesarias para influir en el modo de consumir
energía.
La ventaja más importante de la integración de la GD y GAD es que permitiría retrasar las
inversiones en red al mismo tiempo que se suministra la potencia requerida. Sin embargo, la
distribución de energía eléctrica debe verificar además de los criterios seguridad mencionados,
una serie de requisitos adicionales de firmeza, seguridad, fiabilidad y suficiencia y puesto que
estos recursos energéticos distribuidos no contribuyen, al menos hoy en día, a la firmeza del
sistema, las distribuidoras (siendo éstas las últimas responsables de la calidad de suministro) no
están dispuestas a considerarlos en la planificación de la red.
Por tanto, el objetivo fundamental del proyecto ha consistido en determinar si es posible integrar
eficientemente la GD Y GAD en la planificación de las redes de distribución y comparar la
viabilidad de este método junto con las otras alternativas, inversión en red o no inversión, en el
contexto de una red real. Para ello, la metodología empleada ha consistido en primer lugar en
caracterizar el problema de sobrecarga. A continuación se han analizado tanto las opciones
tradicionales de invertir en red y de no invertir así como la posibilidad de invertir en recursos
energéticos distribuidos. La viabilidad de cada una de estas opciones se ha comparado en una red
real con el fin de determinar si realmente la integración de la GD y GAD puede ser considerada
una alternativa válida.

Metodología
Caracterización del problema. Para caracterizar el problema de sobrecarga, hemos analizado los
perfiles anuales y diarios de la demanda para la región objeto de estudio, junto con la capacidad
disponible en la red. A partir de estos perfiles y aplicando un crecimiento vegetativo se han
obtenido el número de MWs adicionales que serían necesarios para dar respuesta a la demanda
en el año siguiente.
En nuestro caso particular se ha considerado una red de distribución de 132kV/45kV situada a las
afueras de Madrid a la que están conectados en calidad de generadores distribuidos tres
cogeneradores, un generador eólico y dos fotovoltaicos. Hemos estudiado dos posibles
escenarios: Uno inicial (n) en el que toda la capacidad del sistema está disponible y un segundo
escenario n-1, en el cual se pierde el elemento de mayor potencia (Figura 1). Además dado que
hay una diferencia significativa entre la demanda en los meses de invierno frente al resto de
meses del año, se ha decidido analizar dos curvas diarias representativas correspondientes a los
meses de diciembre y abril respectivamente. De esta forma se estableció que para el escenario n
la demanda bruta excedía a la capacidad efectiva de 9 a 13 y de 19 a 23h, durante los meses de
diciembre a febrero mientras que para el n-1, se producía el exceso durante las 24 horas del día
tanto en invierno como en el resto del año.
Figura 1. Curva de demanda bruta junto con escenarios n y n-1
Inversión en elementos de red. Considerando la inversión tradicional como primera opción para
hacer frente a las sobrecargas se han identificado los elementos de inversión necesarios, (1 línea
de 132kV, una de 45kV, un transformador de 132kV/45kV, dos posiciones de 132kV y otras dos de
45kV para nuestro caso particular) y se ha calculado el coste incurrido por las compañías
mediante la siguiente fórmula:
Donde:
El término Costs 2000LF representa los costes del marco legal estable español publicados en el
año 2000 para los items considerados, actualizados por la variación del índice de precios de
consumo, la variación del índice de precios industriales y la variación del precio del aluminio para
el 2013 (término aplicado únicamente aplica al calcular las líneas, y no para los transformadores o
posiciones). Los costes ascendieron a un total de 18 millones de euros.
No inversión. En el caso de no inversión, por un lado los distribuidores cuentan con un coste de
oportunidad asociado a esta decisión pero por otro incurrirán un coste, como consecuencia de la
potencia que quede sin suministrar, calculado como el producto de la energía esperada no
suministrada (ENSE) por un factor de penalización (PEN):

Como factor de penalización hemos considerado el valor establecido por el marco legal español
(1€/Kwh) y, con respecto al término ENSE, ha sido calculado empleando el modelo probabilístico
de coste de producción, determinando para ello la convolución de la demanda eléctrica y la
indisponibilidad de las plantas generadoras. La convolución de ambas variables se realiza
despachando las diferentes plantas generadoras en orden creciente de coste marginal, es decir,
en orden creciente de indisponibilidad de las plantas generadoras, de forma que el área bajo la
última curva, una vez que se han despachado todos los grupos representa el término ENSE
buscado (Figura 2).
Figura 2. Despacho de las plantas generadoras en orden creciente de coste marginal
Es importante recalcar que para este caso estamos considerando la red como un grupo más
inyector de potencia. De esta manera, en primer lugar de despachará la red y a continuación
entrarán los grupos de cogeneración, seguidos del eólico y por último los fotovoltaicos,
obteniéndose así, para nuestro ejemplo particular, un coste total de 3000€.
Inversión en GD Y GAD. Con el fin de solventar el inconveniente fundamental de esta opción,
(falta de firmeza por parte de los recursos energéticos distribuidos como se mencionó
anteriormente), hemos establecido un método que busca alcanzar un compromiso entre las
compañías distribuidoras y los recursos energéticos distribuidos. Este método, denominado de
opciones de fiabilidad (Reliability Options for Distributed Energy Resources, RODER), hace
parcialmente responsables a la GD y a la GAD de la firmeza, de forma que los distribuidores
adquieren la potencia firme necesaria para dar respuesta a sus clientes. Los distribuidores a
cambio proveen incentivos económicos por la provisión de este servicio.
Por tanto, la idea que se ha propuesto está basada en subastas anuales de potencia. Para todas
las regiones en las que se prevean problemas de escasez de capacidad, las compañías
distribuidoras publicarán la capacidad requerida
y convocarán subastas de cara al año siguiente.
Hemos establecido que los recursos energéticos
distribuidos oferten sus MWs de forma
voluntaria a cambio de una compensación
económica, pero que una vez que decidan
participar en dichas subastas, tanto la GD como
la GAD asuman la obligación de producir los
MWs acordados. Si por el contrario, fracasan y
no son capaces de suministrar la potencia
pactada deberán pagar una penalización
vinculada al coste de energía no suministrada. El
resultado, por tanto es un conjunto de bloques
de potencia ordenados en orden creciente de
precio (Figura 3).
Las compañías contarán con todos los recursos energéticos distribuidos necesarios hasta que se
cumpla la capacidad firme requerida y pagarán a todos aquellos que son finalmente considerados,
el precio del último MW que entra en la subasta (conocido como prima). De este modo logramos
Figura 3. Bloques de potencia en orden
creciente de precio

que ambos recursos sean parcialmente responsables de la firmeza y que los beneficios se
repartan entre ellos y las compañías distribuidoras.
Por tanto, el siguiente aspecto que tenemos que contemplar es el precio al que ofertarán los
recursos energéticos distribuidos sus MWs en las subastas. Para ello hemos empleado la siguiente
fórmula con la que queremos representar el riesgo que incurrirían ambos recursos en caso de no
suministrar la potencia acordada:
Donde:
es el precio al que los generadores y consumidores ofrecen potencia a los
distribuidores en la subasta [€/MW].
es la tasa entre las horas en un año en las que se requiere capacidad firme y el número
total de horas anuales. Dado que hemos calculado el precio por hora .
PEN factor de penalización aplicado vinculado a la energía no suministrada. Se ha tomado
1€/kWh según lo establecido en la legislación española
representa la tasa de disponibilidad de cada generador y consumidor y se ha calculado
de forma distinta para la GD que para la GAD. En el caso de la GD y con el fin de representar el
riesgo de no cumplir con la potencia inicialmente acordada debido a la intermitencia de su fuente
primaria, se ha obtenido como el producto de dos sucesos no correlacionados: fiabilidad y
firmeza. La fiabilidad es una característica
técnica propia de cada tecnología mientras
que la firmeza ha sido considerada como la
confianza de que los generadores produzcan
los MW a los que se comprometen. Se han
tomado por tanto 4 posibles niveles de
confianza elegidos al azar (0,95; 0,80; 0,65;
0,30) de forma que cada generador puede
ofertar bloques de potencia a distintos precios
en función del riesgo incurrido (Figura 4). En el
caso de la GAD tomamos =1 pues
consideramos que no existe riesgo de
incumplimiento por parte de que los
consumidores.
Finalmente queda por determinar es la cantidad de potencia firme ofertada por cada recurso. En
el caso de la GD hemos empleado un estudio probabilístico, basado en el teorema central del
límite, el cual afirma que la distribución de un número grande de variables aleatorias se aproxima
a una distribución normal. Aplicando este concepto a los datos de producción horarios,
obtenemos la media muestral de cada hora en la que se requiere un aumento de capacidad, así
como sus respectivos intervalos de confianza. Cabe destacar que los MWs que pueden ser
ofertados por la GD en estos periodos de sobrecarga se han obtenido como el límite inferior de
los intervalos de confianza y no empleando las producciones medias, para reflejar de algún modo
el riesgo de no suministrar el servicio adecuado a los consumidores.
En el caso de la GAD hemos empleado un método de descomposición porcentual, que ha
consistido básicamente en estimar los posibles desplazamientos y reducciones que los
consumidores pueden alcanzar en función de la naturaleza de las cargas. Supusimos que la curva
de la demanda estaba constituida por la suma de los consumos del frigorífico, lavadora,
lavavajillas, secadora, agua caliente, cocina/horno iluminación y climatización (calefacción en
invierno y aire acondicionado en verano), y se identificaron todos aquellos equipos susceptibles
de admitir cambios (resultaron ser todos a excepción del frigorífico y del horno pues ambas
Figura 4. Bloques de potencia de un
cogenerador según niveles de confianza

acciones resultaban insostenibles para los usuarios), obteniéndose así los porcentajes totales de
consumo gestionable en cada hora o lo que es lo mismo: Los MWs que podían ser ofertados.
A modo ilustrativo se representa en la Figura 5 el conjunto de bloques en orden creciente de
precio obtenidos para la subasta de las 11 de la noche de un día de invierno. Se observa como
aquellas tecnologías con perfiles de producción más constantes, tales como los cogeneradores
ofertan a menores precios, mientras que los fotovoltaicos que están íntimamente ligados a la
dependencia del sol lo hacen a precios más altos. También cabe destacar que dado que el para
la ecuación del precio de la GAD ha sido estimado como 1, el precio al los consumidores ofertan
sus MWs es de 0€, desplazando así hacia la derecha los bloques de los generadores. Esto produce
una reducción de un 12% aproximadamente en el coste total que las compañías distribuidoras
incurrirían frente a una subasta formada exclusivamente por generadores distribuidos.
Figura 5. Subasta 23h para día de invierno
Conclusiones. Futuros desarrollos
A partir de los resultados obtenidos se ha concluido lo siguiente:
- La inversión en GD y GAD puede ser válida desde el punto de vista de la consecución de la
firmeza y desde un punto práctico, ya que la inversión en elementos en red llevaría al menos unos
5 años desde que se obtienen las licencias pertinentes hasta que llega a ser operativa, mientras
que la inversión en recursos energéticos distribuidos podría implementarse a corto plazo.
Sin embargo, para que la contratación de recursos energéticos distribuidos sea rentable es
necesario que los periodos en los que se exige firmeza sean bajos. De lo contrario, el precio se
verá muy incrementado y dejarán de ser competitivos. Además, para que la continuidad de
suministro se vea favorecida sería conveniente tener el máximo número de generadores
distribuidos conectados a la red de distribución, de forma que ante el fallo de uno se cuente con
el servicio de otros.
Otro aspecto importante es el factor de penalización (PEN) de los recursos energéticos
distribuidos asociado al incumplimiento de su contrato. Si éste es demasiado elevado los recursos
energéticos no se verán atraídos a participar en las subastas. Si por el contrario es demasiado
reducido, el distribuidor incurre el riesgo de firmar contratos de firmeza con generadores y
consumidores que luego pueden no cumplir cuando se les exige.
- La rentabilidad de cada una de las opciones dependerá del tipo de regulación vigente, dado que
los ingresos que recibirá el distribuidor vendrán determinados por ella.
Finalmente en cuanto a futuros desarrollos cabe destacar que a la hora de analizar las sobrecargas
se tomó como hipótesis una curva diaria representativa para los meses de invierno y otra para el
resto del año. Se podría mejorar este aspecto clasificando por ejemplo según días laborables y
días festivos. Por último, en cuanto a los MWs ofertados por la GAD, se estudió únicamente el
aporte del consumo doméstico, por lo que sería conveniente estudiar también la contribución del
sector servicios.

PLANNING OF THE DISTRIBUTION GRIDS WITH DISTRIBUTED GENERATION AND ACTIVE
MANAGEMENT OF THE DEMAND
SUMMARY
Introduction
Distribution grids are in charge of conducting electric energy from the transmission networks to
the final consumers at the lowest price, but verifying at the same time, both under normal
operation circumstances and in the case of an element’s failure (scenario n-1), the following
security criteria: Maintenance of the voltage and overloading levels within the established limits
(±7% and ±20% respectively); maximization of the continuity of supply and minimization of the
technical losses in the grid. Therefore, and in order to ensure the proper functioning of the system
as well as the quality of the final clients, it is essential to achieve an efficient planning of the
distribution grids.
Up to the moment, distribution companies have invested in system facilities such as transformers,
positions or lines whenever they have had to deal with the failure of any of these security criteria,
especially in the case of over loadings (situation which will be studied deeply throughout the
project). However, this traditional investment implies a significant excess of unused capacity for
many hours during the year, and thereby it would be desirable to find other alternatives.
One of these alternatives, apart obviously from not satisfying the customers’ needs (not invest
and pay the corresponding penalty), would be to integrate distributed energy resources in the
grid, which include both Distributed Generation (DG) and Demand Side Management. Distributed
Generation is the name given to a set of generators connected to the distribution network which
are characterized by their small size and because they are located close to the consumption
points, whereas Demand Side Management refers to the planning and implementation of the
measures needed to influence the way of consuming energy so that the demand curve
experiences the necessary changes.
The greatest advantage that the integration of the DG and DSM could bring to the system is the
delay of the investments in system infrastructures while supplying the required power.
Nevertheless, there is a big drawback behind, it being that distributed energy resources do not
contribute, at least for the moment, to the firmness of the system (one of the four requirements
that the distribution of electric energy must verify in addition of the security criteria
aforementioned) and considering that distributors are the ones ultimately responsible for the
quality of supply they are not willing to consider them in the planning of the grid.
Therefore, the main objective in our project has been to determine if it is possible to efficiently
integrate both DG and DSM in the distribution grids and compare the viability of this method with
the other two alternatives (Investment in system facilities or no investment) in the context of a
real network. To do this, the methodology used has been to characterize in the first place an
overloading situation and then analyze the three options (Investment in system facilities, no
investment at all or investment in DG and DSM). The feasibility of each of the options has been
compared in a real grid in order to verify whether or not the integration of the DG and DSM can
be considered as a valid alternative.
Methodology
Problem characterization. In order to determine the overloading problem, we have evaluated the
annual and daily demand profiles for the region under study, together with the available capacity
in the grid. By applying a vegetative growth to these profiles we have obtained the number of
additional MWs that would be required in order to fulfill next year’s demand.

For our particular example we have considered a 132kV/45kV distribution grid located in the
outskirts of Madrid in which the DG technologies connected are: Three co-generators, one wind
generator and two photovoltaic generators. We have studied two possible scenarios: An initial
one (known as n) in which the whole capacity of the system is available and a second one
(scenario n-1), in which the element with the highest power is lost (Figure 1). In addition, and
considering that there is a significant difference between the demand in the winter months
compared to the rest of the year, we have analyzed two daily representative curves
corresponding to the months of December and April respectively. In this way it was established
that for scenario n gross demand exceeded the effective capacity from 9 to 13 and from 19 to 23,
during the months from December to February, whereas for scenario n-1, the excess occurred
during the 24h a day for both winter and the rest of the year.
Figure 1. Gross demand curve together with scenarios n and n-1
Investment in system facilities. Considering traditional investment as the first option to address
overloads, we have identified the necessary elements that must be bought (a 132kV line, a 45kV
line, a 132kV/45kV transformer, two 132kV positions and two other 45kV positions for our
particular case) and have calculated the cost incurred by the companies according to the following
formula:
Where:
The term Costs 2000LF refers to the costs published in the legal framework in Spain in year 2000
for the different items considered, updated with the variation of the consumer price index, the
variation of the industrial price index and the variation of the Aluminium price for year 2013 (term
only applied when calculating lines and not for transformers or positions). The costs incurred
amounted to a total of 18 million Euros.
No investment. In case of not investing at all, distributors will on the one hand, count with an
opportunity cost associated with this decision but, on the other hand, will incur a cost as a
consequence of the power that remains unsupplied, calculated as the product of the expected
energy non supplied (ENSE) times a penalty factor (PEN):
The PEN value is obtained from the Spanish Regulation, whereas the ENSE term is calculated using
the Probabilistic Production Cost (PPC), determining the convolution of the electric demand and
the unavailability of the generation plants. The convolution of both variables is done by
dispatching the different generation plants in increasing marginal order, that is, in order of
increasing unavailability of the generation plants, so that the area below the last curve, once all
the groups have been dispatched, represents the ENSE term sought (Figure 2).

Figure 2. Dispatching of the generation plants in increasing marginal order
It is important to remark that for this case we are considering the grid as an additional injector
group. In this way, the first element to be dispatched is the grid, then followed by the co-
generation groups, the wind generator and finally the photovoltaic generators, obtaining for our
particular case a total cost of 3000€.
Therefore, the idea that has been proposed is based on annual power auctions. For all the regions
in which capacity shortages are forecasted, distribution companies will publish the required
capacity and will convene auctions for the following year.
We have established that the distributed energy
resources offer their MWs in a voluntary way in exchange
for an economic compensation, but once they decide to
take part in the auctions, both the DG and DSM assume
the obligation to produce the established MWs. If on the
contrary, they fail and are unable to supply the agreed
power, they must pay a penalty linked to the cost of
energy not supplied. The result, thereby, is a set of power
blocks sorted out from the lowest to the highest price
according to their merit order (Figure 3).
Distribution companies will count on all the necessary
distributed energy resources until the firm capacity required is fulfilled and will pay to all of those
who are finally considered, the price of the last MW entering the auction (referred to as premium
fee). In this way we manage to make both resources partially responsible for the firmness and
that the benefits are shared between them and the distribution companies.
Therefore, the next aspect to be considered is the price at which the distributed energy resources
will bid their MWs at the auctions. To do this, we have used the formula below, which tries to
represent the risk incurred by the resources in case of not supplying the agreed power:
Where:
is the price at which each generator and consumer offer MWs to the distributors in
the bid [€/MW].
Investment in DG and DSM. With the objective of solving the main disadvantage of this option
(lack of firmness as afore mentioned), we have established a method which aims to find a
compromise between the distribution companies and the distributed energy resources. This
method, known as Reliability Options for Distributed Energy Resources (RODER), makes the DG
and DSM partially responsible for the firmness, in such a way that distributors acquire the
necessary firm power needed to supply their customers. As a response, distributors provide
economic incentives for the provision this service.
Figure 3. Power blocks in increasing
order of price

is the rate between the hours in a year in which firm capacity is required and the total
number of hours in a year (8760). Since we are calculating the price per hour .
PEN is the penalty applied to the different generators and consumers for not fulfilling
their power commitment. We have established for our particular grid 1€/kWh.
represents the availability rate of each generator and consumer and has been
differently calculated for the DG and the DSM. In the case of the DG and in order to represent the
risk of not fulfilling the power initially established due to the intermittency of its primary source,
has been obtained as the product of two uncorrelated events: Reliability and firmness.
Reliability is a technical feature of each
generator, whereas firmness has been
considered as the confidence that the
generators will produce the MWs agreed. We
have therefore considered 4 possible confidence
levels chosen randomly (0,95; 0,80; 0,65; 0,30)
so that each generator can offer power blocks at
different prices depending on the risk incurred
(Figure 4). In the case of the DSM and
considering that there is no risk of not supplying
the power agreed, has been established as 1.
Finally, the last aspect that remains to be
addressed is the amount of firm power that the
distributed energy resources will offer. In the case of the DG we have carried out a probabilistic
study based on the central limit theorem, which states that the distribution of a large number of
random variables can be approximated by a normal distribution. Applying this concept to the
hourly production data, we have obtained the average, the standard deviation and the confidence
intervals associated. It is important to notice that the MWs offered by the DG in these overloading
periods have been obtained as the lower limit of the confidence intervals, and not by using the
average productions in order to represent somehow the risk of not providing the correct service
to the customers.
In the case of the DSM, the MWs that can be offered have been calculated using a percentage
decomposition method, which basically consists on estimating the possible reduction and
displacement percentages that customers can achieve as a function of the nature of the loads. We
assumed that the demand curve was made up of the fridge, washing machine, dish washer, drier,
water-thermo, kitchen/oven, lightning and heating/air-conditioning consumptions and we
identified the equipments susceptible of admitting changes (all proved to admit changes except
the fridge and the oven because both actions were unsustainable for the users). With this it was
possible to obtain the total percentages of manageable consumption or in other words: the MWs
that could be offered.
As a representative example Figure 5 shows the set of power blocks in increasing order of price
obtained for the 23h auction of a winter day. It is observed how firmer technologies such as co-
generators offer their MWs at a lower price, whereas photovoltaic generators, which are
intimately linked to the solar energy, bid at higher prices. It is also important to remark that since
has been determined as 1 in the case of the DSM, the price at which consumers will offer their
MWs is 0€, displacing therefore the blocks of the distributed generators to the right. This
produces a reduction of approximately 12% in the total cost that distributors would incur if the
auction was exclusively made up of distributed generators.
Figure 4.Co-generator: Power blocks
according to the confidence levels

Figure 5. 23h auction of a winter day
Conclusions. Future developments
From the results obtained we have concluded the following:
- Investing in DG and DSM seems to be a valid option from a practical point of view, since
investing in grid facilities would take at least 5 years (since the relevant licenses are obtained until
they are finally operational), whereas investing in distributed energy resources could in
implemented in the short term.
However, it is important to observe that investing in distributed energy resources is only
economically profitable when the periods in which firm capacity is required are low. Otherwise,
the total price per bid will increase significantly and investing in distributed energy resources will
no longer be competitive. In addition, in order to favour continuity of supply it is convenient to
have the maximum number of distributed generators connected to the distribution grid, so that if
one fails we are able to count with others’ service.
Another important fact that has to be studied in detail is the PEN factor associated with not
providing the power initially established. If this PEN value is too high, distributed energy resources
will not be attracted to take part in the auctions. If on the contrary, it is far too low, distributors
face the risk of signing contracts with generators and consumers who will not be able to provide
the MWs required when needed.
- The profitability of each of the different options will depend on the type of regulatory
mechanism, as the revenues distributors receive are a function of the current regulation.
Regarding future developments it is important to remark that in order to calculate the regions
with overloading problems we only analyzed two representative curves. Thereby, this aspect
could be improved by analyzing more curves, or by classifying them for example according to
working days and weekends. Finally, in terms of the MWs offered by the DSM we only evaluated
the input of the domestic sector, so it would also be very interesting to study the possible
contribution of the service sector.

1
ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)
INGENIERO INDUSTRIAL
PLANNING OF THE DISTRIBUTION GRIDS
WITH DISTRIBUTED GENERATION AND
ACTIVE MANAGEMENT OF THE
DEMAND
Author: Beatriz Fernández López
Director: David Trebolle Trebolle
Madrid
May 2013

3
Index
1. Introduction 1
2. Distribution regulation
2.1 Cost of service regulation
2.2 Incentive-based regulation
2.3 Quality supplied by the distributors
3
3
5
7
3. Planning of the distribution network
3.1 High Voltage (HV) distribution network
3.2 Medium Voltage (MV) distribution network
3.3 Low Voltage (LV) distribution network
3.4 Planning of the distribution grid
3.5 Drawbacks of the actual system. Needs for change
11
13
16
18
18
20
4. Firmness and characterization of the distributed energy resources
4.1 Identification of hours in which there is an excess of demand
4.2 Calculation of the MWs that can be offered to the distribution
companies
22
23
25
5. Methodology. Possible investments
5.1 Investment in system facilities
5.2 Investment in DER
5.3 No investment
5.4 Profitability of the options
37
37
38
45
51
6. Real case
6.1 Characterization of overloading problem
6.2 Investment in system facilities
6.4 No investment
54
54
56
57
77
7. Conclusions 79
8. Bibliography 81
9. Annex 83

1. Introduction
Distribution grids are in charge of conducting electric energy from the transmission networks
to the final consumers at the lowest price, but verifying at the same time, both under normal
operation circumstances and in the case of an element’s failure (scenario n-1), the following
security criteria:
-Maintenance of the voltage levels within the established limits (±7% )
-Maintenance of the overloading levels within the established limits (±20%)
-Maximization of the continuity of supply
-Minimization of the technical losses in the grid
Therefore, and in order to ensure the proper functioning of the system as well as the quality of
the final clients, it is essential to achieve an efficient planning of the distribution grids.
Up to the moment, distribution companies have invested in system facilities such as
transformers, positions or lines whenever they have had to deal with the failure of any of
these security criteria, especially in the case of over loadings (situation which will be studied
deeply throughout the project). However, this traditional investment implies a significant
excess of unused capacity for many hours during the year, and thereby it would be desirable to
find other alternatives.
One of this alternatives, apart obviously from not satisfying the customers’ needs (not invest
and pay the corresponding penalty), would be to integrate distributed energy resources in the
grid, which include both Distributed Generation (DG) and Demand Side Management.
Distributed Generation is the name given to a set of generators connected to the distribution
network which are characterized by their small size and because they are located close to the
consumption points, whereas Demand Side Management refers to the planning and
implementation of the measures needed to influence the way of consuming energy so that the
demand curve experiences the necessary changes.
The greatest advantage that the integration of the DG and DSM could bring to the system is
the delay of investments in system infrastructures while supplying the required power.
Nevertheless, there is a big drawback behind, it being that distributed energy resources do not
contribute, at least for the moment, to the firmness of the system (one of the four
requirements that the distribution of electric energy must verify in addition of the security

2
criteria aforementioned) and considering that distributors are the ones ultimately responsible
for the supplied quality they are not willing to consider them in the planning of the grid.
Therefore, the main objective in our project has been to determine if it is possible to efficiently
integrate both DG and DSM in the distribution grids and compare the viability of this method
with the other two alternatives (Investment in system facilities or no investment) in the
context of a real network. For such a purpose the project has been divided into the following
chapters:
- Chapter 2, Distribution regulation: Study of the possible regulatory mechanisms (cost
of service and incentive-based regulation) that condition the revenues distributors
receive and thereby, the planning of the distribution network.
- Chapter 3, Planning of the distribution grid: Analysis of how the high, medium and low
voltage distribution grids are structured and identification of the actual system’s
problems.
- Chapter 4, Firmness and characterization of the distributed energy resources:
Modeling of how the distributed energy resources can contribute to provide firm
power and assure energy production even in times when a very high demand can
overload the grids.
- Chapter 5, Methodology: Feasibility Assessment from a theoretical background of the
three options (Investment in system facilities, no investment at all or investment in DG
and DSM) considered in the project.
- Chapter 6, Real case: Characterization in the first place of an overloading situation and
then analysis of the profitability of each of the options (investing in system facilities,
not investing at all or investing in DG and DSM) in order to verify whether or not the
integration of distributed energy resources can be considered as a valid alternative.
- Chapter 7, Conclusions and future developments: Comparison of the results obtained
and discussion of future studies.

3
2. Distribution Regulation
In 1997 the deregulation and liberalisation of the electric industry took place. From
then the generation and sale of electric power were viewed as competitive market activities,
whereas network activities (transmission and distribution) were considered as natural
monopolies still in the need of regulation. A monopoly exists when a given company becomes
the sole supplier of a product or service and is therefore in a position of charging prices to
customers that are much higher than the actual production costs. However, there is a
justification in terms of efficiency for network activities to continue being natural monopolies:
It would be both prohibitive and wasteful for two or more companies to build power lines
across the same region to supply the same community of consumers. Therefore in order avoid
these monopolist suppliers from exploiting their market power, there must be some form of
regulation and control mechanisms. Chapter 2 will focus on the different regulatory schemes
that are available for the distribution business and how they affect the design and planning of
the distribution network.
Distribution companies obtain their revenues from the tariffs they charge to their clients, so
regulators must find the equilibrium between the economic viability of the company and at
the same time the maintenance of reduced tariffs for the users. The question that now arises
is: Which method is the most appropriate?
The two most common types of regulation are: the traditional one, known as cost of service
regulation, which was used in the electric industry for many years and a “new” mechanism,
known as incentive-based regulation which is becoming more and more popular in many
countries since the unbundling.
2.1 Cost of service regulation
In cost of service regulation, also known as rate of return regulation, the tariffs
charged by the distributors to the clients are set and established by the regulators and are
periodically negotiated, once a year for instance. Normally this process includes the following:
- Regulators or distributors decide to go over the tariffs either because the previous
period has ended or because tariffs are considered too high or too low.

4
- Distributors submit all the accounting information to the regulators, so that these
last ones can identify the company’s costs and investments and can fix the
appropriate rate of return.
- Finally, the tariff structure is determined for each different type of customer.
Therefore, the cost of service is determined in a way that allows the company to recover from
the costs incurred plus a reasonable rate of return according to the investments made:
Where:
AR: Allowed Revenues
C: Costs, which include operating and maintenance costs (fuel, material, replacement of parts
and supervision), depreciation expenses on the company’s gross assets and taxes
s: Allowed rate of return
RB: Rate Base, which measures the company’s investments (net fixed assets plus net current
assets)
2.1.1 Advantages and disadvantages of cost of service regulation
On the one hand, this method makes sure that the tariffs follow a stable evolution
which is controlled year after year by the regulators. This provides financial security to the
companies as they are able to cover all their costs. In addition, if there are measures to avoid
over-investment, in case of the rate of return being too high, this regulatory scheme gives a
good balance between optimal investments and quality service.
However, on the other hand, if this type of regulation is not correctly implemented it can lead
to over-investment in non efficient facilities and therefore to higher prices for consumers. One
of the main drawbacks of this system is that it does not provide enough incentives to reduce
costs. Tariffs are revised frequently and hence, year after year the company can recover from
all the duly justified expenses. Finally, another weak point is that regulators need as much
accounting information as possible, whereas distributors might be reticent to do so, not only
because they do not want others to know about their financial situation but also because of all
the work involved in presenting the information correctly.

5
2.2 Incentive-based regulation
The basic principle of the incentive-based regulation is to extend the time period
between regulator and distributor negotiations. Costs and revenues are decoupled for a period
of time (typically four or five years) and with this there is an incentive to reduce costs and
thereby increase profits. There are two different types within this incentive-based regulation:
Price cap and revenue cap.
2.2.1 Price cap
In the price cap approach, the regulator fixes a maximum yearly price for the service
provided for a period of four to five years. Each year this price is adjusted to reflect the
variation of prices (i.e. inflation index) and the increases in productivity:
Where:
: Maximum price that the company can charge for service m in year t
: Annual price variation (retail price index or inflation rate) per unit in year t
: Productivity factor per unit
: Adjustments due to unexpected events such as natural disasters or tax rises
Cost of service regulation, with tariffs frozen over a period of time, can be viewed as price cap
regulation with no corrections for the growth of productivity.
Figure 1 shows the price evolution under a price cap scheme for a certain period.
Figure 1. Price evolution under a price cap regulation

6
It is observed that as X adopts a positive value prices decrease, representing a benefit to
customers. If the company manages to decrease costs below the amount fixed by the
regulator, the distributor will also obtain a profit. There might be situations, however, where
the evolution of the prices could increase instead of decrease. This would happen if high
investments for a certain regulatory period were recognised by the regulator.
2.2.2 Revenue cap
In this case what is fixed is the maximum revenue allowed per period. It is adjusted
with the inflation index, the correction factor associated with the expected improvements in
productivity and also with the market’s variation (i.e. number of customers, KW or KWh). It is
again necessary to consider some external factors that are out of control such as increase in
taxes or natural disasters.
Where:
: Authorised remuneration or revenues in year t
: Consumer growth adjustment factor (unit/consumer)
: Variation in the number of consumers in year t
This method is commonly used in Australia, Norway and Spain.
2.2.3 Advantages and disadvantages of incentive-based regulation
The main strong point of the incentive-based regulation is how it provides clear and
simple incentives for efficiency and cost reduction. Furthermore, the information required
from the companies and the cost of regulation itself are much lower than in the traditional
cost of service.
However this method may lead to discrimination between distribution companies when the
initial base remuneration is established and finally but most importantly is the fact that
reducing costs might mean supplying a much worse quality to the users.

7
2.3 Quality supplied by the distributors
As explained above, the regulator’s job is to find the optimal balance between
investment, operation and maintenance costs and the quality provided to the customers. It is
obvious that the higher investments and costs are, the higher will be quality and vice versa.
Under the incentive-based regulation, companies tend to reduce costs to increase their benefit
and one of the easiest way to do so it is to decrease the investments, leading to a progressive
spoilage of the supply quality.
Consumers’ costs can be significantly affected by of the lack of quality on site, especially if a
firm’s manufacturing process has to be stopped because there is not enough electric supply.
Under the traditional regulatory method, the distribution company was in charge of keeping
the quality according to the right limits, incurring the necessary costs and investments. In case
there was a major failure it was not common to give a financial compensation to those
affected. However, with the new regulation scheme, the idea is that each distribution
company is responsible for the lack of quality of its users and responds somehow for the
service interruption. The regulator must ensure that the quality limits are achieved. If not, the
company must pay some type of penalty. On the contrary, if the distribution company provides
quality levels that are above the standard, an economic compensation will be recognised.
Accordingly, what must be done is minimize the social net cost (SNC) for both distributing
companies and customers. This means regulators must find the point where distributors do
not have to spend large quantities of money in investments but at the same time the required
quality level is maintained and therefore users do not suffer enormous costs corresponding to
interruptions. Figure 2 presents both cost curves (clients’ cost curve associated with lack of
quality and distributors’ cost curve associated with the investments made) and the resultant
added one (SNC).
Moving along the x-axis (quality one) in Figure 2 results in a reduction of the costs for the
clients (the higher the quality, the less likely the production process will get affected) but an
increase for the distributors (good quality implies investments). The point where the optimal
quality is found is known as OQL and the intention nowadays is that distribution companies
evolve from their actual quality levels to these optimal ones. This is done by measuring
reliability indices and by a penalty/incentive mechanism indicated by the slope of the cost
curves at point OQL that reflects the revenues for the distributors.

8
Figure 2. Minimization of the Social Net Cost according to the quality supplied
There are two possible reliability indices (system and individual ones) that can be used to
ensure optimal quality.
System indices are linked to the different geographical areas. Depending on the distributors’
energy supply to urban, semi-urban or rural areas the cost curves on Figure 2 will vary.
Normally in rural areas, in order to improve the reliability indices, there will be a major
investment cost in the network and its maintenance, and even so, the indices will always be
worse than in urban areas, where distribution is done underground and with insulated wires.
In Spain the two main reliability system indices that are used are: TIEPI (interruption time
equivalent to power installed) and NIEPI (number of interruptions equivalent to power
installed).
Where:
n is the number of interruptions in the area in the considered period
is the duration of interruption i

9
is the rated power of the facilities whose supply has been stopped with interruption i
P is the rated power of the facilities in the considered area
The regulator’s job then is to fix for each type of distribution area (rural, semi-urban and
urban) standard TIEPI and NIEPI indices. When the quality supplied is above the standard,
distributors receive a bonus, whereas if it is below then they must pay economic penalties.
Regulators have a second objective, related with the previous one, which is to make sure that
every consumer receives minimum levels of individual quality. To do so, individual indices and
individual penalty mechanisms are established. The compensation the user obtains, when the
quality supplied is below the standard, should be enough to make up for the possible damages
caused by the lack of quality and at the same time be a stimulus for the distributors in order
for them to solve the problems and invest more money in facilities and equipment. This
compensation is calculated in terms of the energy not supplied (ENS) due to the interruption
and is then multiplied by the price assigned, for instance 1€/KWh not supplied.
Figure 3 shows how the penalty-incentive mechanisms mentioned are related with the quality
provided.
Figure 3. Remuneration as a function of the quality supplied
Figure 3 points out a base remuneration associated with a base quality. Distribution companies
tend to pivot along this point. If they move to the left they have to pay penalties. If, on the

10
contrary, they move to the right, they receive incentives but that also implies major
investments.
With both mechanisms (system and individual indices) regulators can set the appropriate
revenues for the distributors according to the investments and costs made and make sure, at
the same time, that minimum quality levels are achieved.
Figures 4a and 4b represent the effect of both indices on the probability distribution curve.
The objective is to get rid of bad quality areas and assure a product with minimum
characteristics for every consumer.
Figure 4. Distributor with average value a) equal to OQL or b) smaller than OQL
This chapter describes how depending on the regulatory scheme applied, the quality
provided to the users can get affected and the obvious need, therefore, to plan the
distribution network correctly, with the adequate investments in facilities and equipment in
order to reduce the failure rates. So after studying how the regulator must find a compromise
between the tariffs charged to the clients and the adequate remuneration for the distributors,
making always sure that the supplied quality is appropriate, chapter 3 we will focus on how
this distribution network is planned.

11
3. Planning of the distribution network
The highest complexity feature that the electric system presents is that electric energy
cannot be stored in great quantities and so there is an obvious need to have an instant balance
between generation and demand. Electricity starts its way in the generation stations. Here, the
primary energies (renewable or based on fossil and nuclear combustion) are converted to
electricity. Once the electric energy is produced, it is transported to the big consumptions
centres, which are normally hundreds of kilometres away from the power stations. In order to
access the million of final consumers geographically distributed across the country, branched
networks, known as distribution networks, are used. This chapter will focus on how these
distribution grids are designed and planned. Figure 5 shows the structure of the electric
system.
Figure 5. Structure of the electric system. High voltage transmission lines carry
electricity from power plants to distribution systems that feed the industrial, commercial and
domestic consumers.
The distribution grid contains great number of clients. Thus its objective is to provide service to
this huge number of clients with the highest possible quality. Distributors have the
responsibility of guaranteeing the electric supply and serving new customers, so their main
functions involve planning and maintenance of the grid, as well as developing new
investments. If we focus our attention on Spain, there are more than 300 distribution
companies being 80% of the market already shared between 4 main ones (Unión Fenosa
Distribución, Iberdrola, Endesa and Hidrocantábrico).

12
The structure of the distribution grid is typically hierarchical and is further divided into three
different networks (Figure 6) according to voltage levels: High, medium and low voltage
distribution networks.
Figure 6. Parts of the distribution grid
The three networks differ in structure, operation, number of clients connected, number of
facilities, operation flexibility and degree of monitoring as shown in Table 1. All these
characteristics will be analyzed deeply for each of the networks throughout the chapter.
Table 1: Structure and operation of the distribution network
Type of
network
(typical values)
Structure Operation Number of
clients
Number of
facilities
Operation
flexibility
Degree of
monitoring
High voltage
network
(132, 66, 45kV)
Mesh Mesh/
Radial
Few Several Medium High
Medium
voltage
network
(20, 15kV)
Mesh/
Radial
Radial Several Many Low Medium
Low voltage
network
(400,380V)
Mesh/
Radial
Radial Many Many Very low Low

13
3.1. High voltage (HV) distribution network
This HV distribution network comprises values between 132 kV and 36 kV and has very
few clients connected, typically industry, trains and special regime generators. Another
characteristic is the high degree of monitoring it has. This is achieved through a system, known
as System Control Supervisory And Data Acquisition (SCADA) used by distributors to gather
data remotely and monitor all the facilities in order to detect real-time failures and incidences.
HV distribution networks are quite robust and they typically have a mesh structure with the
configurations shown in Figures 7-9:
Figure 7. HV Loop structure
Figure 8. HV Bridge structure

14
Figure 9. HV Mesh structure
However, and even though the topology of an HV network is mesh, its exploitation can vary
depending on the level of demand and can either be operated in a mesh or radial way.
Under low demand circumstances the network is slightly overloaded and covers the n-1
criterion. This means that if one of the lines that make up the grid is lost, for example due to a
breakdown, the electric supply is not interrupted because automatically loads are fed by an
alternative way that is not affected by the failure. Therefore, power is not lost and the best
operating configuration is the mesh one.
Nevertheless, if the demand starts to increase sometimes the n-1 criterion may not be covered
and it will lead to a loss of power. Under this situation, the network is split to minimize the
energy not supplied to customers and thereby the optimal operating procedure is the radial
one. The objective here is to narrow the possible power loss and have the lines back again to
their normal functioning conditions.
If the demand continues to increase, this could lead to overloading or low voltage problems. In
this last situation and to avoid further problems, the grid should again be operated under a
mesh configuration. However, there is a difference between this mesh exploitation and the

15
one discussed in the low demand case, it being that in the high demand state, criterion n-1 is
not covered and a failure may imply overloading or loss of market power.
Figure 10 summarizes the different HV operation schemes that the network experiences as the
demand increases. Table 2 indicates the predominant operation mode according to voltage
levels of the HV distribution network.
Figure 10. Exploitation criteria in the HV distribution network
Table 2. Operation mode according to voltage levels in the HV distribution network
Voltage Function Topology or
structure
Operationa
132 kV HV network Mesh
M/R
66 kV HV network Mesh M/R
45 kV HV network Mesh
M/R
a
R represents a radial running whereas M a mesh one. The size of the letters denotes which type of
exploitation is the predominant one. Big M compared to little R shows that the mesh operation is
predominant over the radial one and vice versa.

16
3.2. Medium voltage (MV) distribution network
The MV distribution network links the end of the HV distribution network to the
transformation centers, which are in charge of converting MV into LV. MV distribution
networks have a moderate degree of monitoring, but unlike the HV networks they are not able
to operate in real time.
MV networks are always exploited in a radial way so that whenever a failure occurs, power
loss is limited and it can be repaired as soon as possible. Furthermore, these networks are
totally dependent on the geographical areas where the power is distributed and so, linked to
the level of quality supplied to the customers. On the one hand, urban areas usually have
underground and insulated cables to ensure the maximum supply reliability. Therefore, they
typically present structures such as spindle (Figure 11), supported spindle (Figure 12), spike
(Figure 13) and supported spike (Figure 14). On the other hand, rural areas are made up of
bare, overhead cables because their reliability requirements are lower and so the predominant
structures are petal (Figure 15), supported petal (Figure 16) and bunch (Figure 17).
Figure 11. MV Spindle structure
Figure 12. MV Supported spindle structure

17
Figure 13. MV Spike structure
Figure 14. MV Supported spike structure
Figure 15. MV Petal structure
Figure 16. MV Supported petal structure

18
Figure 17. MV Bunch structure
3.3. Low voltage distribution network (LV distribution network)
LV distribution networks, which are normally triphasic and of about 400V, connect MV
networks to the final consumer. This type of network has a very low degree of monitoring,
almost none, and cannot operate in real time. In fact, the information is received lately and
generally the first notice that the service has been interrupted is through customer complaints.
Due to this low monitoring and to help restrict the loss of power, LV networks are exploited in
a radial way.
3.4. Planning of the distribution grid
This section will deal with how the networks, studied above, affect the planning
process of the distribution grid. This planning has to be integral and hierarchical and must start
with reinforcements in the HV network, followed by the MV and end up with the design of the
LV. The process, which consists of several steps, always starts by estimating the demand
growth that the distribution company will have to supply in the future. This forecast is
essential to assure the energy is supplied to the clients in a secure and reliable way. The
second step is to build different scenarios with a horizon of typically 15 to 20 years to
determine the optimum network arrangements that would fulfil the demand needs. The
scenarios are studied under constraint and sensitiveness analysis and always try to leave a
wide load margin in the substations for possible future use. The third step is to determine the
investments associated with each scenario and study which one is the most profitable. Finally,
the construction of the grid takes place.

19
Within these four steps, when analyzing the different scenarios it is essential to look at the
reliability criteria, as they have a significant influence on the planning of the grid, for instance
on deciding whether the structure should be mesh or radial. These scenarios must cover the n-
1 criterion and therefore the distribution network should be exploited according to the
following guidelines:
-Voltage levels within established margins (±7%)
-Overloads within established limits (±20%)
-Maximization of the supply continuity
-Minimization of technical losses in the grid
Whenever one of these aspects is not achieved new investments are needed. These
investments should maximize the quality and security of the energy supplied to the clients but
at the same time minimize the company’s costs. This may be done by using reference models
(from scratch or incremental ones) that analyze how far away the grid is from the optimal case.
Provided that the optimal investments take into account the regulatory framework explained
in Chapter 2, as well as all the service quality standards, then the future grid is constructed.
The construction is always done under standardization procedures because of the great variety
of facilities, equipment, clients and number of suppliers the distribution network has. Figure 18
represents all the steps of the planning process of the distribution grid.
Figure 18. Steps of the planning process of the distribution grid

20
3.5 Drawbacks of the actual system. Needs for change.
Throughout the chapter it has been explained how energy flows from the large
distribution stations to the transmission networks, which then pour the energy into the
distribution networks (HV, MV and LV) and these last ones into the final consumers. Under this
scheme, the electric system is centralized and operates in a unidirectional way (Figure 19)
playing a passive role. However, with the liberalization of the electric market, together with
the new regulatory framework (Chapter 2) and the actual environmental criteria, there is a
need to revise, update and renew part of the infrastructures; especially those related with the
management and operation of the distribution grid.
Figure 19. Unidirectional flow in the electric system
It is now necessary to explain the concept of active networks, understood as the vehicles that
will help integrate distributed energy resources (demand and distributed generation) into the
grid, in order to obtain a sustainable system that improves the supply security, increases
energetic efficiency and leads to an intelligent consumption. The main problem though, is that
to achieve this efficient integration of the demand (able to modify its own consumption) and
of the distributed generation, the actual design and exploitation of the electric networks may
be not valid.
Nowadays, distributed energy resources are displacing conventional technologies in terms of
power but since the distribution grids are designed for power and not for energy, they have to
be oversized to guarantee supply coverage. As a result there is a significant spare capacity for

21
many hours during the year. Therefore, and in order to avoid this inefficient mechanism,
distribution grids must adopt a higher degree of control, monitoring and operation flexibility;
in other words they must leave behind their passive, centralized role and develop an active,
decentralized one. The question that now arises is: how to achieve this?
Chapter 4 will carry out an in-depth study of these distributed energy resources mentioned
and will focus on their characterization, their firmness and how their introduction affects the
planning of the distribution network.

22
4. Firmness and characterization of the Distributed Energy Resources (DER)
One of the main challenges that the electric system now faces, as explained at the end
of Chapter 3, is to achieve an effective integration of the DER (global name given to both
Distributed Generation and Demand-Side Management) in the distribution grids. Up to now,
whenever distribution grids have experienced a demand higher than the actual installed
capacity, distributors have invested in facilities such as new lines or transformers. However,
since these distribution facilities are designed for power and not for energy most
infrastructures are oversized, leading to an important excess of unused capacity for many
hours during the year. Therefore, and in order to avoid this over-sizing there is an immediate
need nowadays to consider the DER as an alternative to investments in new facilities. Thus, the
first step is to give a brief definition of these two resources.
On the one hand, Distributed Generation (DG) is the name given to the group of generators
connected to the distribution grid, which normally have a small size (in Spain smaller than
50MW) and are closely located to the consumption points. As a consequence, and provided
that their penetration level is not very high, they reduce the losses in the network. In addition,
several studies have shown that the DG can allow distributors to delay or even avoid new
investments in the distribution grid, with the consequent economic savings this would bring.
On the other hand, Demand-Side Management (DSM) is known as the planning and
implementation of the measures needed to influence the way of consuming energy so that the
demand curve experiences the necessary changes. In the case of electricity, consuming more
efficiently does not only mean reducing consumption, but also distributing it over time. The
idea is that clients shift part of their consumption, without reducing their comfort, from the
most expensive hours (busy/peak hours) to the cheapest ones (off-peak hours), leading to a
slight flattening of the demand curve. As the integration level of DSM increases in the grid, the
required power/capacity is reduced and so the efficiency of the facilities improves. The
objective of the DSM, therefore, is to reduce and get rid of the demand peaks and together
with the DG delay investments in the distribution grid.
However, until the moment, distribution companies have not usually considered DER in the
planning of the grid. The reason behind is that the generators connected to the distribution
grid are not obliged to produce during hours of peak demand and nor are the consumers to
manage consumption efficiently with time, so the security and firmness of the electric system
are not guaranteed. Since distribution companies are the ones ultimately responsible for

23
supplying the customers, these first ones are not willing to look upon any framework that
might endanger the quality of the service. Nevertheless, distributors must leave behind their
passive role and become active agents able to incorporate the DER into the grid in order to
bring as much efficiency as possible to the system.
Therefore, it is extremely important to look at the concept of firmness, understood as one of
the four requirements that the distribution of electric energy must verify in addition to
reliability, security and sufficiency and analyze how it is achieved by the energy resources
above mentioned. Firmness refers to the assurance of energy production even in times when a
very high demand can overload the distribution grids. Taking this into account, chapter 4 will
focus on the characterization of the Distributed Generation and Demand-Side Management
and on how these can help manage potential overloads efficiently. The method proposed in
this project for such characterization consists on 2 main steps:
1) Identify hours in which there is an excess of demand
2) Calculate the MWs that can be offered to the distribution companies
4.1. Identify hours in which there is an excess of demand
This first step is common for both DG and DSM. The idea is to analyze a typical annual
demand curve for the region under study, similar to the one shown in Figure 20 (green line)
together with the grid’s installed capacity (red line) in order to identify the areas (those above
the red line) where the demand exceeds the grid’s power. These regions will, therefore,
represent the extra capacity that must be supplied by the DER so that customer needs are
satisfied.
Figure 20. Annual demand curve (in green) with grid’s installed capacity (in red)

24
Normally the demand peaks correspond either to the winter months due to the use of heating
and electricity or to the hot summer months due to the use of air conditioning. Thereby, as it is
most likely that the demand will exceed the installed power under these conditions it is on
these two seasons where we will specially focus our attention. In Figure 20, however, only the
months from November to February experience a higher demand than the actual installed
capacity, so for this particular example we would only need to study these four months.
Now that we have identified the months where the extra capacity is required, we need to carry
out a similar study for all the hours throughout these months in which the grid’s power is not
enough to supply the client’s needs. For instance, assuming that for the example shown in
Figure 20 between November and February the demand is higher than the grid’s maximum
limit, our objective is to study for these 120 days all the hours per day in which the installed
capacity is in fact exceeded. Therefore, following the same approach as before, we analyze a
typical daily curve (belonging to a day chosen randomly from the months under study) as the
one shown in Figure 21 (green line) together with the grid’s installed capacity (red line). In this
case, the areas above the red line correspond to the number of hours in a day (from 18.00 to
23.00 for this example) in which distributors must rely on the DER to supply the energy to the
clients with the appropriate quality standards.
Figure 21. Daily demand curve (in green) with grid’s installed capacity (in red)
Once we have identified the hours in which extra power is needed we move on to step 2.

25
4.2 Calculate the MWs that can be offered to the distribution companies
This second phase is different for both resources. In order to calculate the MWs that
can be offered to the distribution companies we have used in the case of the DG a scheme
based on a normal probability distribution and in the case of the DSM a scheme based on
percentage decomposition.
4.2.1 MWs that can be offered to the distribution companies by the DG
The project’s approach to determine the MWs that the DG can offer to the distributors
is based on estimating the power’s production of the different generators using a normal
probability distribution (based on the central limit theorem). Therefore, it is critical to
understand the basics of how a normal distribution works.
The normal distribution (denoted by ) is a continuous probability distribution,
defined by the formula:
Where:
µ represents the mean of the normal distribution
σ is the standard deviation of the normal distribution
Figure 22 shows different normal distribution curves depending on the values for the mean
and standard deviation given.
Figure 22. Normal distribution curves according to different and σ values

26
If =0 and σ=1 (red line), the distribution is called standard normal distribution and is
described by the following expression:
It is important to remark that any normal distribution is a version of the standard normal
distribution (normally denoted as )) whose domain has been stretched by a factor σ
and then translated by µ, as shown below:
This property is very useful because the standard normal distribution values are tabulated and
just by using the simple transformation shown above, other normal distributions and
parameters can be obtained. With this idea in mind, it is possible to calculate for any normal
distribution a confidence interval which will indicate the reliability of an estimate and which
will then help set the basis for our project. Confidence intervals are defined as a range of
numbers which contain, with an associated success probability, a certain unknown value.
Normally these intervals are obtained from sample data and the unknown values correspond
to population parameters. Therefore, the underlying idea is to determine what probability will
hold the true population parameters inside the confidence intervals. This probability is
expressed as:
σ
Where:
1- is the success probability and is known as level of confidence
represents the failure probability and is known as level of significance
is the sample mean
N is the sample size
and are the values of the x axis that leave on their right and left respectively
an area equal to . They are referred to as critical values, are tabulated according to the
level of confidence, and they delimit the probability for the intervals as shown in Figure 23.

27
Figure 23. Limits of the confidence interval
If we operate the probability equation from the previous page we can solve for µ
and obtain the confidence intervals that we are looking for:
Therefore, according to this, confidence intervals are achieved by adding/subtracting the
sample mean ( ) to the product of the critical value ) times the standard error ( ). As it is
observed in Figure 23, wider confidence intervals imply higher success probabilities (1- ),
whereas smaller intervals, on the other hand, imply higher failure probabilities ( ). The reason
behind is obvious: It is more likely (higher success probability) to find the true population
parameter inside a bigger confidence interval than inside a narrower one or explained in other
words, it is not the same to affirm that the true population parameter is contained in the
interval with a 99% security than just with a 60% possibility.
Once that this theoretical background has been established, we will explain how to calculate
the power that can be offered to the distribution companies by the DG using normal
probability distributions and confidence intervals.
This process starts by obtaining the MWs produced by the different available DG technologies
in the hours previously identified in step 1. Hence, for every hour in which extra capacity is
required we need to estimate the MWs that the different generators can produce, obtaining a

28
similar table to the one shown below (Table 3). For this example, we have used the data from
the annual and daily curves represented in step 1, where the months and hours under study
were November to February from 18.00 to 23.00 respectively.
Table 3. Production associated with hours of peak demand
Now that we have a certain production associated with every hour of peak demand we need
to approximate our data using a normal probability distribution and calculate the mean value,
standard deviation and confidence intervals to determine the MWs that the different DG
technologies can offer to the distribution companies. Table 4 and the equations below show,
for the example previously mentioned, how to calculate these parameters for a period of time
comprising from 18.00 to 19.00 from the 1st November until 28th February.
Month Day Hour Production
Generator 1
Production
Generator 2 …
Production
Generator n
November 1 18:00 P1 G1 P1 G2 … P1 Gn
…
…
…
…
…
…
…
February 28 18:00 P715 G1 P715 G2 … P715 Gn

29
Table 4. Production for a period of time comprising from 18.00 to 19.00 from the 1st
November until 28th February.
It is very important to notice that the MWs offered by the generators are not just calculated
with the average mean value, but in fact using confidence intervals. The rational for this is that
by using the mean value we are not taking into account the risk of not supplying energy to the
clients. On the contrary, if we use confidence intervals, we are able to determine a generator’s
power production with a certain success/failure probability. It is not the same to estimate that
Month Day Hour Production
Generator 1
Production
Generator 2 …
Production
Generator n
November
…
…
…
…
…
…
December 1 18:00 P181 G1 P181 G2 … P181 Gn
December
…
…
…
…
…
…
January 1 18:00 P367 G1 P367 G2 … P367 Gn
January 2 18:00 P373 G1 P373 G2 … P373 Gn
January
…
…
…
…
…
…
January 31 18:00 P547 G1 P547 G2 … P547 Gn
February
…
…
…
…
…
…

30
a co-generator, for instance, is able to produce 18 MW on average without knowing how often
these 18 MW will exactly take place than to ensure a production of 17 MW with a 95%
probability, being this last option much more reliable. Therefore, this project will estimate the
MWs offered by the different DG generators as the lower limit of the confidence interval of a
normal probability distribution, calculated for the particular case of Generator 1 as:
The same procedure has to be done for all the other hours in which extra capacity is required
(i.e. from 19.00 to 23.00) and for all the other available generators. The objective is to obtain a
set of data similar to Table 5 which contains for every hour of needed firm capacity the
average, standard deviation and lower limits of the confidence intervals for the production
data associated.
Table 5. Summary table with average, standard deviation and lower limits of the confidence
intervals for the production data associated
18:00 19:00 20:00 21:00 22:00 23:00
Generator
1
Generator
2
... ... ... ... ... ... ...
Generator
n
Considering that the lower limits of the confidence intervals correspond, as mentioned above,
to the MWs that can be offered to the distribution companies by the different generators, it is
possible to estimate whether or not the DG will be able to cope with the needed production

31
for every hour in which the demand exceeds the grid’s installed capacity and can, as a
consequence, be seen as an alternative to traditional investments.
4.2.2 MWs that can be offered to the distribution companies by the DSM
The project’s approach to determine the MWs that the DSM can offer to the
distributors is based on a percentage decomposition method, which basically consists on
estimating the possible reduction and displacement percentages that customers can achieve.
This is done by studying the nature of the electric loads, which will be sorted out according to
consumer and technical preferences. This means that it is necessary to determine which
equipment is susceptible of admitting changes and only carry out the actions that are not
inadmissible for the user (the freezer, for example, must work all day long).Taking into account
this dependence of the technical equipment feasibility and of the clients’ acceptance on the
potential reduction and displacement percentages it is necessary to do a breakdown of the
demand according to the different activity sectors (residential, service and industrial) and
analyze the consumption patterns for each one of them (Figures 24-26).
Figure 24. Demand curve for the residential sector

32
Figure 25. Demand curve for the service sector
Figure 26. Demand curve for the industrial sector
The most remarkable fact observed in these figures is that the industrial sector has a flat/plain
profile, due to the lack of flexibility in its production processes and as a result, it is very difficult

33
to determine a reduction in the electricity consumption. Indeed, the highest consumption
percentage in the industrial sector is due to the use of specific machinery needed for each
activity. Therefore, the option of shifting the loads to off-peaks is not feasible and distributors
cannot rely on this sector to achieve the aimed potential demand reduction. Nevertheless,
both the residential and service sectors can experience significant displacement and reduction
percentages and can thereby bring with them benefits for both: Distribution companies
(higher efficiency in the system and delayed investments in the grid) and the users (reduction
of the electricity bill).
The idea proposed in the project is to consider that each hourly consumption in the daily
demand curve is made up of smaller consumptions, or in other words that the sum of several
smaller intakes adds up to 100% of the daily demand (Table 6). This is the same as saying that
if the total demand for a certain hour in a day is equal to 100 MW, then these 100 MW, for
instance, are made up of 30 MW light, 50 MW heating and the remaining 20 MW kitchen
equipment.

34
Table 6. Decomposition of the daily demand curve into n consumptions
Following the same approach as in the case of the offered MWs by the DG we must associate
for every hour in which the demand exceeds the grid’s installed capacity (calculated in step 1)
what percentage of the demand can be shifted or partially reduced in such a way that is
favourable for the system. Considering that we have divided the total demand into several
consumptions, we can apply such percentage reductions and displacements to each of these
different consumptions.
Therefore, we have to establish for every hour identified in step 1 the potential MWs from
each consumption (C1, C2...Cn-1, Cn) that can be reduced and shifted, as shown in Table 7. We
will again assume that the demand exceeds the installed firm capacity for a period of time
comprising from 18.00 to 23.00 from the 1st November until 28th February, being the total
daily demand curve for such a period the one represented in Figure 21.
Total
demand
Consumption
1
Consumption
2
…
Consumption
n-1
Consumption n
0:00 TD 0 C1 = %TD 0 C2 = %TD 0 … Cn-1 = %TD 0 Cn = %TD 0 = TD 0 -(C1+C2+…+Cn-1)

35
Table 7. Reduction and displacement percentages associated to peak demand hours
According to Table 7, the new daily demand curve for the hours between 18.00 and 23.00 is
calculated by adding all the resulting MWs associated to from C1 to Cn. Therefore the MWs
that the DSM can offer to the distribution companies, represented by the corresponding
reduction and displacement percentages, are calculated as the initial daily demand (TD in
Table 6) curve minus the new daily demand curve (NTD). Both of these curves are represented
in green and blue respectively in Figure 27:
Figure 27. Initial (in green) and resulting demand curves after % reduction and displacement
(in blue)
Where:
(1) Represents the initial demand. For the particular hour chosen (21.00 h):
(2) Represents the new resulting demand. For the particular hour chosen (21.00 h):
Hours C1
Reduction &
displacement %
associated to C1
{%r&d (C1)}
Resulting MWs
associated to C1
… Cn
Reduction &
displacement %
associated to Cn
{%r&d (Cn)}
Resulting MWs
associated to Cn
18:00 C1,18 {%r&d (C1),18} C1,18 -{%r&d (C1),18} … Cn,18 {%r&d (Cn),18} Cn,18 -{%r&d (Cn),18}
70
75
80
85
90
95
100
105
110
18:00 19:00 20:00 21:00 22:00 23:00
MWs
Hours
(2)
(3)
(1)

36
(3) Represents the MWs offered to the distributors by the DSM. For the particular
hour chosen (21.00 h):
Taking into account that these equations are also applied to all the other hours in which the
demand exceeds the installed firm capacity, it is possible to estimate whether or not the DSM
will be able to cope with the needed production and can, as a consequence, be seen as an
alternative to traditional investments.
This chapter has looked at how the distributed resources contribute to the firmness of
the grid and at the possibility distributors have to consider them as an alternative to network
investments. Therefore, the next step , carried out in Chapter 5, is to analyze which of the
options (investing in new facilities, investing in DG or in DSM or even not investing at all and
paying the corresponding penalty) provides the widest benefits and is the most profitable
solution.

37
5. Methodology. Possible investments
As we have seen in the previous chapters whenever the demand exceeds the installed
capacity, distributors must act. We will analyze three possible options: Invest in system
facilities, invest in DER or not invest at all and pay the consequent penalty. Hence, this chapter
will analyze deeply all of these options and theoretically study which one of them is the most
economically viable for the distribution companies.
5,1 Investment in system facilities
This first option, which is the one that has been done up to the moment, consists on
carrying out investments in new facilities such as transformers, positions or lines. On the one
hand, it assures that the demand needs are well satisfied but on the other hand, it requires a
long and expensive outlay.
The costs associated to such investment are calculated by identifying all the necessary items
that must be built in order to increase the grid’s capacity. Normally these new network
elements correspond to transformers, positions and lines, as aforementioned. In this project
we will calculate these costs by using the following equation below:
Where:
Costs 2000LF refer to the costs published in the legal framework in Spain in year 2000
for the different items considered
is the variation of the consumer price index for year under study
is the variation of the industrial price index for year under study
is the variation of the aluminium price for year under study. This term is only
applied when calculating lines and not for transformers or positions.
All of these terms are multiplied together to obtain the real and updated values for the year
under study.

38
Throughout chapter 4 we have modelled how the different DER technologies can contribute to
provide firm power to the system and have seen the way to calculate whether or not they can
be considered by the distribution companies as an alternative to traditional investments. The
main problem, as mentioned along the project, is that neither generators connected to the
grid are obliged to produce during hours of peak demand nor consumers to manage their
consumption efficiently with time, so the security of the system is endangered and distributors
(being the ones responsible for the quality of the supply) do not want to count on these
resources. In order to solve this conundrum, we propose a market mechanism based on
annual auctions, called reliability options for DER (RODER).
This procedure starts by identifying possible overload problems (detailed in step 1 chapter 4)
one year in advance. This overloading problem, as mentioned throughout chapter 4 takes
place when the gross demand exceeds the installed firm capacity in the system. Therefore, the
energy that cannot be supplied to the customers by the distributors (ENS) is calculated as the
difference between the gross demand curve and the installed power. Hence, it represents the
additional capacity (C) that is required (Figure 28).
Figure 28. Representation of a generic load duration curve together with the installed power
Once the overloaded areas and the amount of firm power needed are identified, distribution
companies shall convene an auction in year n for year n+1 in each of the areas which present
capacity shortage problems towards next year (n+1). The firm capacity required for each
auction, is then published. This firm capacity is not just calculated to offset the energy not
supplied (ENS) but also including a security margin/overloading value (Ov) as shown in Figure
29, that reflects possible failures in the system:

39
Figure 29. Periods in which firm capacity is required
The idea is that due to the nature of the DER technologies (not having a controllable primary
source or a production profile similar to the local demand in the area analysed), both DG and
DSM take part voluntarily in the auctions, receiving a premium whose value is determined by
the market. However, once they voluntarily accept to join in, they assume the obligation to
produce and offer the necessary MWs during the periods in which distributors foresee that
such additional capacity is required. If they fail to achieve this, they must pay a penalty linked
to the cost of the ENS incurred by the distributing companies as a result of the DER not
providing the established MWs. The objective of this RODER method is to achieve a
compromise which will, on the one hand guarantee that companies are able to provide firm
service to the clients with the adequate quality standards and, on the other hand, that the two
DER through economic incentives are willing to offer MWs to cover the demand peaks. Both
DG and DSM would be partially responsible for the interruptions and the benefits would be
shared between these two and the distributors.
Therefore, according to this model we have determined the price at which DER can offer their
MWs to the distribution companies as a function of the penalty above mentioned and of their
own risk (taking into account failure probabilities and unavailability of primary source), as
shown in the following equation:
Where:
is the price at which each generator and consumer offer MWs to the distributors in
the bid [€/MW]
represents the availability rate of each generator and consumer

40
is the rate between the hours in a year in which firm capacity is required and the
total number of hours in a year (8760)
PEN is the penalty applied to the different generators and consumers for not fulfilling
their power commitment. It is indexed as the cost that distributors incur by not supplying the
adequate service as a result of the DER not providing the established MWs during the required
periods
If we now multiply this price by the MWs offered (described in step 2 chapter 4) by each of the
DER technologies we obtain the following expression in €:
As it is observed in the equation above, less reliable consumers and generators or those with
an intermittent nature (lower and therefore higher ) bid at a higher price, whereas
more reliable resources associated with a more constant profile (higher and therefore lower
)) bid at lower prices. The result is a set of power blocks sorted out from the lowest to
the highest price according to their merit order (Figure 30).
Figure 30. Power blocks in increasing price order
Distribution companies will count on all the necessary consumers and generators until the
required firm capacity (vertical dotted line in Figure 30) is fulfilled. The price of the last firm
MW that satisfies the required capacity is known as the Premium Fee (PF). Payment of the
resulting PF to the different DER is performed by the distributors and can have a maximum

41
established value or cap. A closer analysis of Figure 30, indicates how, in this example, the
power offered by DER1 and part of the one offered by DER2 is enough to satisfy the required
firm capacity and thereby receive a premium. It is important to remark however, that DER1
will not get paid the amount at which it initially bet, but instead at PF, receiving therefore
more money than what was originally expected for such an offer.
Below we will illustrate this proposed distribution network planning mechanism with some
numbers. We will consider 4 different DER technologies and that there are for instance 6 hours
every day from 18.00 to 23.00 (inclusive) from November to February in which firm capacity is
required (being 4 MWs the maximum for this period). This makes up a total of 720 hours per
year giving therefore a value of . The capacity that is auctioned is
calculated as explained in step 2 of chapter 4, although for this particular example, as the
objective here is to show how the bids work, we have chosen random numbers. The value for
depends on the different technologies and varies according to the firmness and reliability of
each DER. It is possible that a same DER can offer power blocks at different prices, depending
on its generation availability in hours of peak demand. Thus, generators and consumers can
either offer their whole rated power or just a part of it. Finally, for PEN we will adopt the value
of 1€/KWh set by the Spanish Regulation. With this in mind, we obtain the results shown in the
following table:
Table 8. DER bids for the period comprising from November to February from 18.00 to 23.00
As it observed in Table 8 those DERs with the highest bid at a lower price and are therefore
the first ones to be considered by the distribution companies (1st: 1MW from DER 3 with 99%
availability at a price of 7200€; 2nd: 2,5 MWs from DER 2with 98% availability and finally just
0,5 MWs from DER 1 with 97% availability to make up the total 4MWs of firm capacity
required). It is also important to notice that since the last firm MW that satisfies this capacity
has a price of 21.600€ then all the others included in the auction are paid this same price as
shown in Figure 31:

42
Figure 31. Annual auction (DER1, DER2 and DER3) for the period comprising from November
to February from 18.00 to 23.00
The only difference, however, that we will make when applying this RODER method to the real
case in the next chapter is that instead of convening just a unique auction with the total
number of hours throughout the year in which extra capacity is required we will, in fact,
convene an auction for every hour in which the demand exceeds the grid’s power. Therefore
for the example being used (18.00-23.00 from November to February) we would have 6
different auctions with the corresponding: F irm capacity required for each hour and not
just the maximum for the period considered; MWs that DG and DSM offer for each needed
hour (step 2 chapter 4) and a new value of . Table 9 and Table 10
represent the possible results for two of these hours (18.00 and 22.00). We will consider that
the capacities required are 2 MWs and 3,7 MWs for 18.00 and 22.00 respectively. We will also
assume, in order to make the example easier, that the different DERs have a constant
production profile from 18.00 to 23.00 and therefore the capacity auctioned will remain the
same.

43
Table 9. DER auction for 18.00
Table 10. DER auction for 22.00
As it is observed in both tables, again those DERs with the highest bid at a lower price and
are therefore the first ones to be considered by the distribution companies. In addition the last
firm MW that satisfies the required hourly capacity determines the price at which all the other
DERs included in the bid are paid, as shown in Figures 32 and 33:
Figure 32. 18.00 auction (DER2 and DER3)

44
Figure 33. 22.00 auction (DER1, DER2 and DER3
Just to finish with, there are several aspects that can influence the proposed market
mechanism that must be highlighted. From the distributors’ viewpoint, the decision to
consider firm power offered by DER as an alternative to traditional investments depends on
the potential benefit obtained when comparing the cost of both options. Taking into account
what was explained in chapter 2 about the possible regulatory mechanisms, the perspective of
the distribution companies can vary. Contrary to a cost of service approach, incentive
regulation fosters distributors to reduce costs. Hence, distributors would be more willing to
implement a RODER mechanism under this type of regulation. From the DER’s viewpoint and
assuming that the mechanism is voluntary the price of the RODER should represent a
reasonable amount compared to the rest of the income obtained. Regarding the computation
of penalties, ENS is deemed as a suitable index for the cases in which DG and DSM do not fulfill
their firmness commitment. However, there can be a situation in which a certain DER has not
fulfilled its commitment but there is no ENS. This situation is possible if there are other
technologies that have not taken part in the RODER auction, but are providing MWs during
critical periods. In this case, DER units that have not fulfilled the set up requirements would
still have to pay for the unsupplied power.

45
5.3 No investment
The last possible option distributors have whenever there is an overloading of the system is to
not satisfy the demand needs. The idea behind is to remain with the actual grid power and
installed DG technologies and not invest at all. As a consequence these companies will have to
pay a penalty for the power that remains unsupplied. Therefore, the cost incurred is calculated
as the product of the expected non-served energy (ENSE) times a penalty factor (PEN)
established by law:
The PEN value is obtained from the Spanish regulation, whereas the ENSE is calculated using
the Probabilistic Production Cost (PPC) method, which has been traditionally used as a support
tool to assess the reliability of electric power systems. Hence, this method will be analyzed
below in detail.
5.3.1 PPC input variables
The objective of the PPC method is to evaluate the ENSE by means of a probability distribution
function, calculated as the difference between two random input variables: i) The
complementary distribution function of the demand and ii) the unavailability of the different
generation plants present in the electric system. Considering that the variables are statistically
independent, then the computation of the former difference can be simplified and calculated
as the convolution of their probability distribution functions. Therefore, we must study how
the demand and the generating units are modeled and what is the order they follow for such
convolution operation.
5.3.1.1 Complementary distribution function of the demand
In order to calculate the complementary distribution function of the demand we must first
study the theoretical concept that lies behind. It is first necessary to define what a distribution
function is. This is understood as the probability that a real-valued random variable X will be
found at a value less than or equal to x, as shown in the following equation:

PLANNING OF THE DISTRIBUTION GRIDS WITH DISTRIBUTED GENERATION AND DEMAND SIDE MANAGEMENT

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