A Hierarchical Framework for Day-Ahead Optimal Operation Planning of Active Distribution Networks with Multi-Microgrids

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Vol.66: e23220379, 2023
https://doi.org/10.1590/1678-4324-2023220379
ISSN 1678-4324 Online Edition
Brazilian Archives of Biology and Technology. Vol.66: e23220379, 2023 www.scielo.br/babt
Article - Engineering, Technology and Techniques
A Hierarchical Framework for Day-Ahead Optimal
Operation Planning of Active Distribution Networks
with Multi-Microgrids
Cyntia Cristinne Corrêa Baia de Aquino1*
https://orcid.org/0000-0002-5085-8086
Thaís Marzalek Blasi1
https://orcid.org/0000-0002-8933-1521
Clodomiro Unsihuay-Vila1
https://orcid.org/0000-0002-1639-7765
Thelma Solange Piazza Fernandes1
https://orcid.org/0000-0002-5167-1547
Rafael Silva Pinto1
https://orcid.org/0000-0002-0574-1444
Mauro Obladen de Lara Filho1
https://orcid.org/0000-0002-7306-4369
Alexandre Rasi Aoki1
https://orcid.org/0000-0001-9863-6610
Fabricio Henrique Tabarro2
https://orcid.org/0000-0002-0689-459X
Rodrigo Braun dos Santos2
https://orcid.org/0000-0001-6163-4558
1Universidade Federal do Paraná, Departamento de Engenharia Elétrica, Curitiba, Paraná, Brasil; 2Companhia
Paranaense de Energia – COPEL Distribuição, Curitiba, Paraná, Brasil.
Editor-in-Chief: Bill Jorge Costa
Associate Editor: Daniel Navarro Gevers
Received: 19-May-2022; Accepted: 10-Jan-2023.
*Correspondence: cyntiacristinne@ufpr.br; Tel.: +55-96-988030303 (C.C.C.B.A).
Abstract: The insertion of new distributed energy resources, such as distributed generation (DG), energy
storage systems (ESS), demand response (DR), and microgrids (MG), is emerging, bringing new challenges
to the current distribution network. In this regard, the active distribution networks (ADN) with multi-microgrids
concept appears. The present paper proposes a hierarchical (master-slave problem) computational model to
achieve optimal coordinated operation of multi-microgrids connected to an ADN. Day-ahead operation
planning of an ADN was formulated as a multiperiod non-linear optimal power flow model, resulting in a non-
linear optimization problem, additionally, the day-ahead operation planning of MGs was formulated as a
multiperiod linearized optimal power flow resulting in a mixed-integer linear optimization problem. Numerical
results on four different test-system microgrids connected to a 359-nodes ADNs test-system belonging to a
Brazilian distribution company show the effectiveness of the proposed model and solution strategy. Three
cases have been tested: with a maximum load-shedding restriction, without this restriction, and considering
insertion of DG. Besides, the hierarchical model can evaluate how much losses and load shedding take effect
without integrated operation and expansion planning of emerging distributed networks. This study showed
HIGHLIGHTS
• Multi-microgrids and distributed energy resources in active distribution networks (ADNs).
• A coordinated hierarchical optimization model.
• Optimal day-ahead operation planning for ADNs with Multi-Microgrids.

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the importance of analyzing the systemic impact of integrating multi-MGs and ADN synergistic operation
interactions, resulting in improvements in the voltage quality levels, operation costs, and power losses. The
results showed that, including DG in the system, the costs were reduced by 13,48% compared to the case
base.
Keywords: microgrids; active distribution network; multiperiod optimal power flow; hierarchical optimization
framework.
INTRODUCTION
In the last years, distribution grids are facing transformations guided by the digitalization of the process,
as well as the introduction of new elements as distributed energy resources (DER). Driven by concern about
climate change and energy transition, the increase of renewable energy solutions is being encouraged
worldwide, with new equipment, markets, and solutions, that can push for a more sustainable energy system.
Part of this process is known as the 3Ds of energy transformation, corresponding to Decarbonization,
Digitalization, and Decentralization. Moreover, some authors consider a fourth D, that corresponds to system
Democratization, which means, changes in energy systems with consumers actuating more actively on it.
The Brazilian Energy Research Office (EPE) considers that DERs contemplate distributed generation;
energy storage; electric vehicles and recharging infrastructure; and, demand-side management such as
energy efficiency, demand response, etc. As reported in the EPE discussion note, DERs can pose several
challenges for electric power distribution systems operation and planning, at the same time they can provide
many benefits, such as reducing network costs, improving grid reliability, and others [1].
Another possibility is the development of microgrids or energy communities, based on the existence of
energy generation systems simultaneous to storage systems and management devices. Microgrids can be
defined as part of the power grid that can be disconnected from the main grid and operate autonomously.
Thus, for a microgrid to be possible, it is necessary to have distributed energy resources such as distributed
generation and storage systems that allow the load to be supplied in periods when it is disconnected from
the main grid [2].
In this context, new concepts were defined, such as active distribution networks, distributed energy
resources, and microgrids, creating a new scenario for a grid in a constant transformation. In the Technical
Brochure 457 – Development and Operation of Active Distribution Networks, from [2], there are multiple ways
to define an Active Distribution Network (ADN). However, in general, it is possible to define an ADN as a grid
that enables the distribution system operator (DSO) to interact with the consumers, manage the power flow,
coordinate, and control the distributed energy resources, and multi-microgrids integration and operation.
Microgrids have brought new paradigms, since several applications can be realized, e.g.:
residential/commercial microgrids, with customers acting actively in the energy market; microgrids providing
ancillary services to the distribution grid, acting together with the distributor, for example, for voltage support
and load shifting; or the microgrids can be constituted to serve isolated localities, in places where there is no
electrical grid.
Currently, in Brazil, there are already several microgrids for isolated systems, as is the case of the island
of Fernando de Noronha, served by diesel and solar photovoltaic generation systems, with the recent
installation of a storage system with lithium batteries. In addition, there are microgrid applications to serve
communities in remote locations such as the islands of Lençóis and Ilha Grande, both in the state of
Maranhão, as well as to serve the populations living in the Pantanal Sul-Matogrossense region.
For large scale implementations of multi-microgrids connected to a Brazilian distribution network, in
September 2021, the Brazilian regulatory agency (ANEEL) approved the implementation of a pilot project for
the Public Call of the Companhia Paranaense de Energia (Copel) for the acquisition of energy from distributed
generation through the formation of a microgrid. The pilot project will last five years, since ANEEL's
authorization is configured as a “regulatory sandbox” in which some rules can be relaxed and/or changed,
with duration and conditions previously delimited so that the agents in the sector can carry out innovations
[3,4].
With the integration of DERs and microgrids, the distribution system operator (DSO) starts to face new
challenges and in this way, studies should be developed to allow the evaluation of grid integration and their
main impacts on emerging distribution networks operations.
Among the main challenges faced by utilities are the voltage control, aiming to avoid the voltage limits;
the reverse power flow at some points and equipment of the power grid that are not prepared for such
behavior; the power factor control in the power system boundaries; as well as new technical configurations,
new business models and system digitalization [5,6].

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In this way multiple papers had proposed the usage of optimization techniques looking for new planning
and operational systems, in the context of large DG penetration and an ADN behavior. The Optimum Power
flow implementation is proposed by [7–11] in a similar approach considering multiple optimizations in the
objective function, such as the minimization of costs, power losses, load shedding and voltage deviations,
considering the behavior and the operational limits of the equipment modeled. In these cases, the authors
considered the integration of DG, such as photovoltaic and wind generation, as well as storage systems, and
the power grid itself is not modeled in detail.
In this context, a large-scale and complex distribution system increase the computational efforts of the
day-ahead operation planning process of ADNs. Similarly, many microgrids connected to a traditional or an
active distribution network increases the complexity of the day-ahead operation planning of an ADN with
multi-MGs. The computational dimension and complexity can be reduced by decomposition or a hierarchical
optimization model. Works, such as [12–16],have already analyzed the operation planning of single or
multiple microgrids, in terms of cost, energy storage systems capacity, flexibility, stability and inclusion of
distributed energy resources (DERs), which contributes to the MGs performance in many aspects that were
also analyzed. The work developed by [17] consider the integration of a microgrid in a completed modeled
distribution grid, with distribution transformers, capacitor banks and voltage regulators, as well consider the
integration of DG, storage systems and a microgrid. In this case the authors also proposed a hierarchical
approach between the optimization of the microgrid itself, consisting of optimization of its equipment, and the
optimization of the entire ADN. It is important to highlight that [17] do not consider the integration of multiple
microgrids simultaneously in the optimization problem, not even considering multiple and independent
optimizations for each microgrid interacting with the power grid optimization, as proposed in the current paper.
In this way, the main objective of this paper is to develop a hierarchical optimization model considering
as master problem the day-ahead optimal operation planning of ADN formulation and as slave problem the
day-ahead optimal operation planning of each microgrid in a multi-microgrid system, resulting in a non-linear
programming and mixed-integer linear programming. The day-ahead optimal operation planning of ADN
formulation considers the completed ADN’s network system with the connection of distributed energy
resources, such as distributed solar generation, battery energy storage systems, and demand response
corresponding to the DSO point of view and it is solved using the interior-point algorithm. Similarly, the
formulation of the day-ahead optimal operation planning of an MG considers the MG´s network connected to
its distributed energy resources, such as distributed solar generation, battery energy storage systems, and
demand response, the optimization of each microgrid was done using the Gurobi Optimizer solver, which
optimizes the dispatch of DERs and its injection/consumption from the main grid.
Considering this approach, the proposed model was tested for different scenarios, considering the
simultaneous connection of four different test-system microgrids to a 359-nodes DN test-system belonging
to a Brazilian distribution company located in Curitiba, Brazil, and later is simulated in a scenario where it DN
is considered as an active distribution grid. The challenge of the scenarios proposed consists in optimizing
each microgrid connected independently, but at the same time optimizing the entire ADN and multi-MGs
operation planning, considering their operational network and power quality constraints.
Thus, the main contribution of this paper is the proposes of a coordinated hierarchical optimization model
for day-ahead optimal operation planning of ADNs with multi-microgrids, considering the ADN formulation
as a large-scale full non-linear programming and the each MGs as a large scale mixed-integer linear
programming. It is important to highlight that this paper is an extension from [17] in order to include multi-
microgrids simultaneously instead of a single microgrid operation.
This paper is organized as follows: the material and methods section present the main mathematical
formulation and data used in the proposed model, followed by the results section. The paper ends with the
conclusion section.
MATERIAL AND METHODS
In this section, the concepts and data of the proposed hierarchical model are discussed. The model is
formulated by the coordinated day-ahead optimal operation planning of active distribution networks (ADN)
and multiple microgrids operating connected to an ADN. The final architecture considers a master-slave
model, to find the optimal global performance of the full system. The master level corresponds to day-ahead
operation planning optimization of an ADN, in this paper, it is named multiperiod optimal power flow (MOPF),
and the slave level model contemplates to the day-ahead operation planning optimization of each microgrid,
which is named as multiperiod optimization of a microgrid (MOuG).
The methodologies proposed in this section were chosen based on the literature review and the
implementation of this methodology in previous researches developed by the authors, where parts of the

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problem were previous implemented and published in [17-19]. At this point is also important to highlight that
the chosen methodology were based on several papers that already exists in the literature, proving the
efficiency of these methods for the application on power grids and microgrids optimization. Additionally, this
paper consists in a different approach where multiple microgrids were optimized independently and
simultaneously, interacting with the main grid optimization in a master-slave approach.
Hierarchical Model
Multiperiod Optimal Power Flow to Active Distribution Networks Methodology (MOPF)
For the master level, it is necessary to optimize the day-ahead or daily operation of the active distribution
network. The planning horizon for both master and slave levels is 24 hours, respectively. The detailed
formulation of the master optimization problem (MOPF) is based on [17,18] and comprises the minimization
of electrical losses (󰇜, cost operation (󰇜, cost operation of the batteries () and load
shed of the microgrids (FPd), :
          󰇛
 󰇜



 ,
(1)
Where nb is the number of buses, np is the number of periods, the factor 󰇛
󰇜 is applied at the load
bus of microgrids 󰇛
󰇜.
From the power grid point of view, it is necessary to consider the integration of multiple microgrids. In this
case it will receive the results of the optimizations of each microgrid as inputs to be inserted in the optimization
problem, as proposed in [17].
Each microgrid behavior should be provided to the master in the same number of periods of the power
grid optimization. The MGs will be considered as flexible loads, so that if any constraints are violated, the
master optimization will propose changes in the operation of the microgrids, sending this information to the
slave.
The corresponding values of the ideal percentage of 
 of the power injection/consumption of
microgrids (
) are sent to the slave problem, suggesting a new dispatch of the microgrids, when gamma
is a value smaller than 1, it means that the power injection of microgrids must be reduced. If the gamma is
equivalent to 1, it means that the injected power does not need to be changed, as it does not affect any
technical operational aspect of the network.
Microgrids Optimization Model for Day-ahead Operation Planning (MOuG)
The slave problem considers the day-ahead operation planning problem for microgrids to perform the
optimal microgrid elements dispatch. Notice that the microgrids could be connected to the ADN in different
nodes, which are usually called points of common coupling (PCCs). In each iteration process of MOuG model,
the power injection/consumption gamma values provided by the master problem are used as known input
data. As the hierarchical model is solved iteratively, at each iteration, it is sought to recover the power required
by the microgrids in the penultimate iteration and how much of this power needs to be adjusted for the new
dispatch, as shown in (2):

 

,
(2)
where the power injected from the main grid 
 in iteration i for microgrid mg during period t,

is the power injected in the penultimate iteration i-1 for microgrid mg during period t, and

 sent by MOPF to MOuG is identified for each microgrid mg during period t for iteration i.
The day-ahead operation planning of a microgrid was modeled according to [19], that is, considering
demand response, battery storage systems, photovoltaic generation, and thermal generation. However, due
to the lack of space, the scope and contribution of this work are to present a hierarchical model for day-ahead
operation planning of ADNs and microgrids, not considering the uncertainties related to parts of the energy
resources used. Therefore, the formulation corresponds to the first level of the formulation of [19], and for the
injected/consumption power deviations suggested by the master problem to be respected, then a penalty
formulation was inserted in the objective function between what was requested by the network and what was
carried out by microgrids:
 󰇡  󰇡󰇻
 
󰇻󰇢 󰇢,
(3)

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where Hpen is the penalty value for the non-adjustment of the ideal power injection in the hierarchical model
and Tcost is the total cost, which depends on the cost of energy exchange with the main grid for each
microgrid in each bus, the cost of batteries energy storage systems (BESS), the cost of thermal generation,
and load shedding costs. The authors recommend checking [13] for more information about the cost terms
and other details of the formulation. Differently than in [13], the demand response can only happen for
controllable loads. However, the demand response program adopted in this work considers that part of the
total load (maximum 15%) can be managed. So, if it is necessary to cut more loads than that percentage,
there would be infeasibility problems caused by this restriction. That is why an adaptation from the original
formulation is made, where the controllable load can be allocated along the 24-hours horizon, as in (4):




  󰇛  󰇜,
(4)
where 
 is the controllable load for bus b during period t, DR is an auxiliary variable that varies from 0 to 1
to represent the percentage of 
that will be allocated during the planning horizon, and TL is the total amount
of loads, controllable and non-controllable. Besides, (5) presents that the maximum amount of controllable
load that can be allocated in a period t is equal to the total amount of controllable load for the entire time
horizon. The sum of the controllable load must be equal to 1, as seen in (6),
  
 ,
(5)



  
(6)
guaranteeing that all loads will be allocated during the time horizon. However, the load shedding is available
for non-controllable loads and must respect this limit, as shown in (7),
  

,
(7)
where 
 is the load shedding and

 is the non-controllable load for bus b during period t. With the
adaptations made, the hierarchical model can be implemented. As the power grid and the microgrid
equipment are modeled the first step it load all the grid model and the equipment behavior. At this point the
microgrid optimization is realized individually for all the microgrids, considering only the internal restrictions
of the microgrid itself (MOUG). The result of this first optimization is sent to the MFOP, for the power grid
optimization considering all the equipment of the ADN. If no constraints are violated, the network optimization
converges and you have optimal operation of the network and the microgrids. If at least one of the network's
operational constraints is violated, the network optimization proposes a new dispatch for the micro-grids, so
the MOUG optimization is redone considering the constraint imposed by the network. This new microgrid
dispatch is then sent to the master optimization. This process is repeated until the optimization is able to
converge without any constraints being violated, presenting as a result the joint optimization of the network
and the microgrids. A detailed scheme can be seen in [17].
Data of Test-System
In this paper is used a 359-nodes ADN test system located in Curitiba city, Brazil. This distribution
network test-system has an operating voltage of 1 pu, with 411 medium voltage (nominal 13.8 kV) lines and
489 low voltage (nominal 220/110 V) lines. It has 22 medium voltage consumer units and 1236 low voltage
consumer units. As mentioned above, the proposed framework also considers photovoltaic distributed
generation systems, batteries, and demand response considering that these systems can be added in the
future. In this context, it is considered a scenario that of the 359 nodes in the system, 58 of these would have
the installation of a photovoltaic system with different installed capacities. So, in this scenario, the total
installed photovoltaic power distributed generation is 451.36 kWp. The microgrids test-system data used in
this paper is adapted from [20], by replacing wind turbines for PV generation.
RESULTS
Intending to evaluate the behavior of the distribution network concerning the insertion of multiple
microgrids connected to it at different points in the system, as well as evaluate the impacts of the insertion of
PV distributed generation in the distribution network using the hierarchical model, this section presents the
results of the computational model proposed.

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To simulate cases with feedback from the hierarchical model, the results presented here refer to the
insertion of four microgrids considering a substantial increase in the load presented in the materials and
methods section for the cases:
• Case I: The four microgrids operating simultaneously located at different points of the feeder. In this
case, there is a maximum load shedding constraint limited to 5%;
• Case II: Case I without constraints of the maximum load shedding;
• Case III: Case II with the insertion of photovoltaic distributed generation in several points of the feeder,
that is, the network functioning as an active distribution network.
The solar generation was inserted in several nodes of the distribution network that present load. For the
calculation of the insertion of DG, a penetration percentage of 30% was considered, which was calculated
from the total installed power at the point, for example, if the bus has 10 kW of installed capacity, the input of
3 kW of distributed photovoltaic generation is considered. Therefore, in this case, this represents 30% of the
451,36 kWp which results in 135,41 kWp.
It is important to note that there were purposeful modifications to the test cases presented in the previous
step:
• The load increases are 65 times greater for microgrids, since, through exhaustive computational tests,
it was observed that for smaller values, it would not imply undervoltage, not bringing to light the computational
capacity of the proposed model.
• Increase of 10 times greater for the other loads connected to the main network, because for smaller
values there was also no undervoltage;
For a microgrid to act on or impact the ADN, it must be strategically placed on the feeder, because of
that, the microgrids 1, 2, 3, and 4 were allocated in nodes 51, 319, 339, and 347, respectively. In the following
subsections, the main results obtained from the simulations performed are presented.
Case I
Pre-processing
This process step is necessary for the initialization of the hierarchical model, informing what would be
the ideal injected/consumed power from the point of view of the microgrid if no adjustment was necessary,
such as load reallocation or even load shedding. With this, the dispatches of the microgrids are shown in
Figure 1.

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(a)
(b)
(c)
(d)
Figure 1. MOuG optimization dispatch during pre-processing for microgrids (a) 1, (b) 2, (c) 3, and (d) 4. NC-load in blue;
C-load in purble, battery charge in green; battery discharge in red; PV-gen in red.
The results of pre-processing dispatches show that non-controllable loads (in blue), battery charging (in
green), and controllable loads (in purple) are not allocated during peak hours, seeking to take advantage of
PV generation (in orange) to reduce operating costs. In contrast, battery discharging (in red) is used during
peak periods (from 5 pm to 9 pm), to reduce the use of energy from the distribution network, help in voltage
levels, and supply loads from the point of view of microgrids. For this pre-processing, the resulting costs of
microgrids are shown in Table 1.
Table 1. Pre-processing Operational Costs of the Microgrids.
Microgrid
Operational Costs
MG1
3,593.14 BRL
MG2
2,959.78 BRL
MG3
2,471.10 BRL
MG4
5,338.31 BRL
Total Cost
14,362.33 BRL
First Feedback
In this step, the master-level is run for the distribution network but considering the amount of
injection/power consumption of the microgrids as a result of the pre-processing step. The MOPF results
considering the original dispatch of the microgrid imply violations of minimum voltage magnitude constraint
for the main grid. So then, there is a request from the master program so that there is a readjustment of this
dispatch by the microgrids, being necessary to cut part of their original load. The convergence process takes
53 iterations. The numerical results related to the variation in the original load, losses, and operating costs
are presented in Table 2:

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Table 2. Numerical Results for case I in first feedback.
Total Costs
Losses
Total Consumed Energy
Readequation from Pdideal
148,763.98 BRL
9.43 MWh/day
269 MWh/day
-19.99% (MG1)
-18.8% (MG2)
-15.97% (MG3)
-31.36% (MG4)
Table 2 shows that the ideal for the distribution network would be a reduction (in %) of consumption by
microgrid loads, precisely because of violations of restrictions related to minimum voltages at the feeder
nodes. Thus, the MOPF model indicates that undervoltage can be remedied from these suggested cuts.
However, as can be seen in Table 3, the master level requires the slave level to cut percentages of its total
load to eliminate undervoltage. Following these cut requirements, MOuG is executed, but it sends a new load
shedding proposal to the master program, informing the impossibility of meeting the totality of the required
cut since the microgrids can cut a maximum of 5% of their loads. Thus, at the end of the feedback, the new
power suggestion demanded by the microgrids is sent to the master problem. In this case, even if the entire
load change is not tolerated, the dispatch of the microgrids seeks to achieve part of the required change,
suggesting a load shedding during peak hours, from 5 pm to 9 pm, mainly for microgrid 4.
In addition, the load shedding required by the master level is absorbed by the slave level so that it can
perform a new dispatch that reallocates controllable loads and reduces battery charging so that the smallest
amount of load is shed but seeking to adjust to the dispatch suggested by the main network. Therefore, it is
possible to observe that, for microgrid 4, for example, a large part of the controllable load is allocated to the
last period of the planning horizon, and that for this microgrid there is no dispatch of the batteries taking place
because its financial benefit would not compensate for the load shedding required. The costs of microgrids
for this case are shown in Table 3.
Table 3. Microgrids costs for case I in first feedback.
Microgrid
Load Shedding Costs
Hierarquical Penalty Costs
Total Costs
MG1
814.20 BRL
3,075.15 BRL
7,291.56 BRL
MG2
779.93 BRL
2,257.67 BRL
5,808.53 BRL
MG3
553.11 BRL
1,651.02 BRL
4,540.48 BRL
MG4
4,524.13 BRL
4,556.26 BRL
13,337.73 BRL
The costs are higher than those of the pre-processing because in this feedback process there is an
increase in the load shedding of the microgrids due to the operational restrictions imposed by the distribution
network as discussed above, in addition to the penalties for non-compliance with the proposed dispatch
suggestion by the MOPF. These penalties result in the need of performing new feedback in the hierarchical
model. This information exchange happens till the third feedback, which the results will be shown in the next
subsection.
Third Feedback
In the hierarchical model, one of the input parameters is that the maximum number of the feedback
process is up to three. Thus, this was the last feedback process performed, in which the MOPF algorithm
was able to converge in 14 iterations. The numerical results of this feedback process are shown in Table 4:
Table 4. Numerical Results for case I in third feedback.
It is possible to verify through the data inferred from Table 4 that the total cost of the main grid was
reduced compared to the cases of the first feedback, as well as the losses and the total energy consumed
since the dispatches presented from the microgrids were able to contribute with an improvement of the
technical characteristics of the main grid.
The load readaptation shown in Table 4 is necessary for the voltage profile to operate within the pre-
established limits, which have some minimum voltage restrictions being activated. Therefore, it was still
necessary for the microgrids to have part of their load shed so that these restrictions were not violated.
Total Costs
Losses
Total Consumed Energy
Readequation from Pdideal
147,397.88 BRL
9.253 MWh/day
267 MWh/day
-18.54% (MG1)
-17.22% (MG2)
-14.6% (MG3)
-23.94% (MG4)

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As it is the last feedback process, it is possible to observe that for the maximum number of iterations,
the microgrids could not adapt to the dispatch suggested by the main grid. Therefore, the hierarchical model
has a resource in the situation of non-adaptation between the two systems, which is the reduction of the
minimum voltage. In this case, the minimum voltage was reset to 0.9 pu. The results of this feature will be
presented in the next subsection.
Minimum Voltage Limit Reduction for 0.9 pu
As it was not possible to find a dispatch from the microgrids that would not violate the minimum voltage
limit on the feeder buses and that the power injected by the distribution network was enough to supply the
microgrid loads, the minimum voltage was reduced, and the pre-processing information is resumed to check
the network with the new minimum voltage threshold.
By allowing it to operate with a minimum voltage below 0.93 pu, load shedding on microgrids is no longer
necessary. Figure 2 presents the new voltage profile. It is observed that in some hours of the day, the network
operates with voltage below 0.93 pu (ie, with undervoltage).
Thus, the network was able to accept all the power suggested by the microgrids already in the pre-
processing, which was the first dispatch devised by the microgrids. However, this first dispatch, without any
load shedding, implies a violation of the minimum voltage limits required by PRODIST, as they were relaxed.
Table 5 brings the numerical results for this case, demonstrating that there is an increase in costs, losses,
and energy consumed since the network can meet all the necessary load power of the microgrids, not
requiring any type of variation in its dispatch.
Table 5. Numerical results for case I after reducing the minimum voltage limit.
Total Costs
Losses
Total Consumed Energy
Readequation from Pdideal
152,559.06 BRL
9.987 MWh/day
276 MWh/day
0% (MG1)
0% (MG2)
0% (MG3)
0% (MG4)
The costs of the microgrids are the same as those of pre-processing, totaling 14,362.33 BRL. However,
the total operating costs of the main grid (152,559.06 BRL) plus the costs of the microgrids result in
166,921.39 BRL. In this case, as there is no load shedding by the microgrids, some buses of the main grid
showed undesirable undervoltage (<0.93), but higher than the newly established limit of 0.9).
Thus, the hierarchical model shows that for this case, a minimum voltage of 0.93, it would be necessary
to make other investments, such as installing voltage regulators and capacitor banks, so that the voltage
profile on the feeder bars could be adjusted without cut a large part of the loads from microgrids.
Thus, it is evident the importance of properly designing and sizing the loads, generation, and storage of
microgrids aiming at the minimum impact on the active distribution networks where they will be connected.
This is of great importance for the development of computational models for the integrated planning of the
expansion of microgrids and active distribution networks, considering the optimal operation of distributed
energy resources in both active and multi-microgrids.
(a)
(b)
Figure 2. (a) Voltage for all buses; (b) Voltage for GLD buses.

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Case II
As the results of Case I showed that the load shedding required by the network makes the convergence
process of the hierarchical model impossible, it was decided to remove the maximum load shedding
constraint from the MOUG model (which was around 5%), to re-evaluate the procedure of the hierarchical
model.
In this case, after carrying out the ideal dispatch of the microgrids obtained by the pre-processing, which
is identical to the one found for Case I, the main grid sends the suggestion of load shedding to MOuG. And,
as in this case there is no restriction for load shedding in the microgrids, they adapt to the shed proposed by
the first feedback of case I, and there are no penalty costs for not adjusting to the dispatch suggested by the
main grid, as shown in Table 6.
Table 6. Microgrids costs for case II.
Microgrid
Load Shedding Costs
Hierarquical Penalty Costs
Operational Costs
Total Costs
MG1
4,504.38 BRL
0 BRL
2,835.11 BRL
7,339.52 BRL
MG2
3,489.14 BRL
0 BRL
2,348.07 BRL
5,837.21 BRL
MG3
2,534.33 BRL
0 BRL
2,029.30 BRL
4,563.63 BRL
MG4
9,991.64 BRL
0 BRL
3,458.76 BRL
13,450.40 BRL
However, it can be observed that the highest cost for the microgrids is the cost of load shedding, mainly
for microgrid 4, in which the load shedding cost represents 74.29% of its total cost, with the biggest shedding
occurring for all microgrids, 3,330.55 kW, that is, 24.53% of the total load shedding, plus adjustments to
controllable loads and batteries, reaching a variation of 31.36% of the ideal dispatch presented in the first
feedback section for Case I.
Figure 3 shows the behavior of microgrids when accepting the first dispatch suggestion given by the
main grid. In this case, it is possible to observe that there is a greater load shedding for all cases (in pink)
and that only microgrids 2 and 3 can dispatch a small part of the batteries, so that less energy is used for
charging, mainly microgrid 3, since the amount of load shedding is the smallest of all microgrids, with an
average of 844.77 kW, which represents 10.72% of load shedding for microgrid 3.
(a)
(b)
(c)
(d)
Figure 3. MOuG optimization dispatch in case II for microgrids (a) 1, (b) 2, (c) 3, and (d) 4. NC-load in blue; C-load in
purble, battery charge in green; battery discharge in red; PV-gen in red.

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The total costs of the microgrids for this case were 31,190.76 BRL. However, the total operating costs of
the main grid (148,763.98 BRL) plus the costs of the microgrids result in 179,954.74 BRL. This cost is 8%
higher than that presented in case I. This cost increase is due to the load shedding costs that occurred in the
microgrids. It can be concluded that this 8% is the cost of having a better quality of voltage levels, that is,
appropriate voltage levels in the main network, which is the cost to ensure the quality of energy referring to
the voltage level of the network. main. This additional cost that is incurred by the microgrids could be paid to
them through the appropriate allocation among all the agents of the distribution system and the microgrids.
So then, these costs could be paid via regulatory mechanisms for ancillary services. Thus, it is possible to
prove that the hierarchical model shows that with the correct adequacy and a refined parameterization, the
results can both help in the dispatch of microgrids and the main grid.
Case III
The third and final scenario analyzed in this work considers the insertion of distributed photovoltaic
generation systems. That is, considering a future scenario in which the distributions network-test system
considered in this paper starts to present a massive insertion of distributed energy resources, the analysis
was carried out considering the penetration of 30% of distributed generation in this feeder. The allocation of
this penetration was carried out proportionally in the load bars, considering that part of the consumer units
allocated in the equivalent low voltage may present the photovoltaic solar generation systems, as well as for
the case referring to medium voltage consumers.
For this case, the results of the pre-processing of the microgrids are the same as presented in case I.
And, as in case II, here it is considered that the modeling of the microgrids does not contemplate a maximum
limit for load shedding, which implies say that, if no other microgrid constraint is violated from the main grid's
dispatch suggestion, the microgrid is capable of accepting any load shedding level. Thus, as shown in Figure
4, the voltage profile shows that in the first period of the planning horizon, the feeder operates with minimum
voltage limits activated for some buses, such as in one of the buses where there is a microgrid allocation, as
observed in Figure 4-(b):
(a)
(b)
Figure 4. (a) Voltage for all buses; (b) Voltage for GLD buses.
The numerical results of the main grid are presented in Table 7, showing that the insertion of distributed
generation reduces the feeder operating costs:
Table 7. Numerical Results for case III.
Total Costs
Losses
Total Consumed Energy
Readequation from Pdideal
133,742.08 BRL
7,778 MWh/day
273 MWh/day
-9,09% (MG1)
-8,77% (MG2)
-7,27% (MG3)
-14,23% (MG4)
The results presented in Table 7 compared to case II show that the insertion of PV generation reduces
the amount of load shedding suggested for microgrids to less than half. For case II, the readjustment
(reduction or load shedding and re-dispatch of batteries of the microgrids, etc) for all the microgrids was
86.12%, while for this case, with the insertion of DG, this readjustment was reduced only to 39.36%. In case

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III, there is greater total energy consumed when compared to the previous cases, since the PV generation
contributes to supply part of the loads that were previously cut.
Figure 5 shows the total power injected by the substation into the main grid (in green) as well as the
liquid power injection performed by the microgrids (in black), in addition to the total insertion of PV generation
(in red). In this figure, the contribution of DG to the total supply of the feeder load is evident. It should be
noted that in Figure 5, the portion of microgrids corresponds to the total net value, obtained from the algebraic
sum of all of them for each period, that is, it reflects the behavior of all microgrids connected to the feeder
from the grid point of view.
Figure 5. Power balance indexes of the feeder for the planning horizon with the distributed energy resources used.
In addition, the behavior of the normalized curve of the PV generation can be seen in Figure 6, verifying
the typical behavior for injection of active power and a small injection of reactive power in the period of
photovoltaic generation, since the inverters of the generation systems solar panels have a power factor of
0.92 pu.
Figure 6. Active and reactive power for case III.
From the main grid point of view, the ideal power injection for microgrids is presented in Figure 7:

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(a)
(b)
(c)
(d)
Figure 7. Ideal power injection from the main grid point of view for microgrids (a) 1; (b) 2; (c) 3; and (d) 4.
From Figure 7, it can be seen that the load shedding is greater for microgrid 4 in this case, as it is the
microgrid with the highest installed power, both in terms of loads and energy resources. It is also observed
that the required cuts are much smaller when compared to cases I and II. As there is no maximum load
shedding restriction, this new dispatch suggested by the MOPF is accepted by the microgrids and the
algorithm is finished. The new operating costs of microgrids are shown in Table 8, and their dispatches are
shown in Figure 8.
Table 8. Microgrids costs for case III.
Microgrid
Load Shedding Costs
Hierarquical Penalty Costs
Operational Costs
Total Costs
MG1
2,048.29 BRL
0 BRL
3,239.89 BRL
5,288.29 BRL
MG2
1,628.09 BRL
0 BRL
2,670.32 BRL
4,298.41 BRL
MG3
1,153.03 BRL
0 BRL
2,268.56 BRL
3,421.59 BRL
MG4
4,533.38 BRL
0 BRL
4,409.53 BRL
8,942.91 BRL
(a)
(b)

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(c)
(d)
Figure 8. MOuG optimization dispatch in case III for microgrids (a) 1, (b) 2, (c) 3, and (d) 4. NC-load in blue; C-load in
purple, battery charge in green; battery discharge in red; PV-gen in red.
Like what happens in other cases, the microgrid seeks to optimize the dispatch of all its resources to
both reduce operating costs and meet the dispatch suggested by the grid, having the lowest possible load
shedding, which is mainly during peak periods. In this case, it is possible to observe that there is a greater
load shedding, as there is no restriction of maximum load shedding, and for microgrid 4, there is no dispatch
of batteries taking place, as the aim is to reduce the use of energy from the feeder, which results in the
batteries not charging, and consequently, not discharging.
In Table 9, a comparison of the costs and losses for each case is presented.
Table 9. Costs and losses comparison for each case.
MGs Costs
Main grid Costs
Total Costs
Losses (MWh)
Case I
14,362.33 BRL
152,559.06 BRL
166,921.39 BRL
9.987
Case II
31,190.76 BRL
148,763.98 BRL
179,954,74 BRL
9.43
Case III
21,951.20 BRL
133,742.08 BRL
155,693,28 BRL
7.778
From Table 9, it can be seen that case I has an intermediate cost, but in this case, the quality of the
voltage levels is compromised. While case II has a higher cost (179,954.74 BRL), however, the quality of the
voltage levels is satisfactory. Finally, case III has the lowest cost (155,693.28 BRL) among all cases, due to
the insertion of distributed generation in the distribution network, and the readjustment of the microgrids
dispatch is smaller (when compared to the case II) in order to maintain adequate network voltage levels.
From the same Table 9, it is also possible to observe that the losses were considerably reduced
compared to case I and case II. For example, comparing case III to case I, there was a reduction of 22.12%.
These reductions in both cases are due to the insertion of DG in the network, which reduces the flows through
the feeders. The losses in case I are greater than in case II because in case I it is observed that there is
undervoltage, as discussed above.
In addition to the results presented in this technical report, other computational tests were carried out,
such as the insertion of battery storage systems, which did not impact the reduction of load shedding, and
therefore, were not presented in this work. In addition, the gradual insertion of microgrids was also evaluated,
but as the objective was to show the behavior of the network given the insertion of multiple microgrids, the
authors chose not to bring this theme, since the greater the number of microgrids, the more technical issues
must be resolved and investigated, such as those evaluated here.
CONCLUSION
This paper aimed to develop a computational model with a coordinated operation of active distribution
networks and multiple microgrids through a hierarchical framework. Three study cases were used,
considering a maximum load shedding level, without it and adding PV distributed generation. The analyzes
were carried out by observing the iterative feedback processes of the proposed model, verifying how the
operation changes according to the suggested load cuts.
Case I was the scenario in which a maximum load shedding restriction is activated for the microgrids
since load cuts do not bring financial advantages to the consumer. Therefore, a maximum load shedding rate
of 5% has been inserted into the MOUG model. In this case, in three feedback processes, it was not possible
to find a solution that would not violate the constraints of the grid and the microgrids simultaneously, since
the ideal would be a load shedding greater than 14.6%. However, by relaxing the minimum voltage limit to

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0.9 pu, it was not necessary to perform load cuts on the microgrids, and a dispatch was obtained for both
systems (undervoltage being admitted). This result shows that an integrated planning of the expansion of
active networks and microgrids would be necessary, however, considering the expansion and optimal
operation of distributed energy resources and including other resources, such as voltage regulators or
capacitor banks, present both in the active network and in the microgrids.
In case II, the results were presented with the four microgrids operating on the feeder without the load
shedding restriction, which led to the convergence of the hierarchical process in the first feedback, requiring
the adjustment and reduction of 19.99%, 18.8%, 15.97%, and 31.36% of loads of microgrids 1, 2, 3 and 4,
respectively, compared to the initial proposition. This factor significantly increases the costs related to
microgrids, with the largest increase occurring for microgrid 4. Initially, its operating cost, which was 5,338.31
BRL, became 13,450.40 BRL, that is, an increase of 251 .96%.
Finally, at several points of the feeder, distributed photovoltaic generation sources were inserted (case
III), so that the network started to operate as an active distribution network. DG helps to reduce the variation
of the ideal dispatch for microgrids to 9.09%, 8.77%, 7.27%, and 14.23% for microgrids 1, 2, 3, and 4,
respectively, reducing operating costs that were previously from R$ 148,763.98 to R$ 133,742.08, as well as
the electrical losses that went from 9.43 MWh per day to 7,778 MWh per day.
Thus, the great importance of optimal operation planning and integrated expansion of emerging
distribution networks is highlighted. There is a need for new computational developments to carry out
planning studies of the optimal expansion integrated into the optimal operation of microgrids and active
distribution networks, aiming at the economy, energy quality, and reliability.
Funding: This research was funded by the Companhia Paranaense de Energia - COPEL research and technological
development (RTD) program, through the PD-02866-0511/2019 project, regulated by ANEEL.
Conflicts of Interest: The authors declare no conflict of interest
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(https://creativecommons.org/licenses/by-nc/4.0/).