Optimal Fuzzy-Based Energy Management Strategy to Maximize Self-Consumption of PV Systems in the Residential Sector in Ecuador

Abstract

This paper proposes a fuzzy-based energy management strategy (EMS) to maximize the self-consumption from a PV installation with an energy storage system (ESS) for the residential sector adapted to the Ecuadorian electricity market. The EMS includes two control levels: Energy management at the end-user level (Fuzzy-based EMS and optimized by genetic Algorithm) and Energy management at the distribution grid level (Fuzzy-based EMS). Both strategies aim to maximize the use of the energy generated at home (taking into account the local solar generation profile), fulfilling the loads’ demand and injecting the energy surplus into the main grid to be economically compensated. Additionally, this paper presents economical modeling according to the electricity market in Ecuador. The main results showed a cost reduction in the electricity bill up to 83.64% from the base case (residential consumption without a PV system). In the scenario of a community electricity market (still not contemplated under the Ecuadorian electricity law), the potential economic savings may be more than double compared to the exact case but only with a self-consumption system.

1. Introduction

Recently, the requirement for more accessible and eco-friendly energy has been considered a primary problem for many countries, which are trying to reduce the greenhouse effect due to CO₂ emissions of thermal electricity generators, as well as contamination issues related to nuclear power plants [1]. Consequently, the adoption of renewable energy sources for electricity generation is more frequently implemented, taking advantage mainly of solar and wind energy [2] and the installation of these kinds of generation systems into the electrical systems [3]. The main adopted solutions, from renewable energy sources, include solar generation derived from rooftop installations in residential and commercial sectors [4] and big solar power plants that provide MWh of energy to the national electrical system [5]. Focal implementation of these technologies near energy demand groups has introduced the microgrid (MG) electricity concept, which is conformed to decentralized energy sources and loads [6]. Therefore, an MG can generate and consume its energy when it is disconnected from the central grid, working in an isolated mode, but it can also operate in an interconnected mode with the synchronous grid to interchange electricity depending on pricing, generation, consumption rates, and schedules, etc.

There are large, medium, and small renewable generators within distributed generation units. The promotion of small-scale generators is vital since these technologies can be applied in the household sector and contribute to the decarburization of the residential sector, reducing greenhouse gas emissions (11.3% of total emissions in 2019 [7]). The EU promotes several strategies to favor the development of these generation technologies: MGs, self-consumption (individual or collective) [8], and energy communities (ECs) [9].

Due to the high investments required for energy storage systems (ESS) implementations, ESS would be inaccessible for each user in an MG. Therefore, a community or shared ESS could also be implemented to temporarily store a user’s surplus energy until it can decide to use it or sell it in the MG [9]. The efficiency of MG and energy transactions between users considering two scenarios, an MG with and without community ESS, was evaluated in [10], concluding that energy transaction efficiency is increased when a community energy storage system is introduced.

A brief literature review denotes the existence of various research works on MG studies and implementations, and economic-energetic transactions in energy markets. On the one hand, regarding MG, a hybrid renewable energy system (HRES) to supply a small remote locality in Saudi Arabia is reported in [11]. The MG is composed of photovoltaic and wind turbine energy plants, and a pumped hydro energy system (PHES) is used as an energy storage system (ESS) instead of alternatives such as expensive battery storage systems (BSS) or green hydrogen storage systems (GHSS). In [12], a direct current (DC) MG for a small island in Belize was designed and simulated, highlighting the importance of DC MGs in reducing power losses due to DC-AC module conversion. Alternatively, in [13], a hybrid AC-DC MG is proposed with an optimization model for planning the optimal placement of DC feeders since DC loads can be randomly distributed in the MG. Regarding the Latin America region, a review of several projects, laboratories, and test systems related to MG implementations developed from academy and industry sectors is presented in [14]. Further, the study presented in [15] deals with an optimal design for an electrical hybrid MG composed of a diesel generator, photovoltaic panels, wind turbine, and batteries. The scenario is dedicated to isolated communities in Colombia, and the regulation of production rates is performed under fuel price variation. Otherwise, [16] describes the potential renewable energy resources available in Ecuador for MG implementations, compiles a couple of design and modeling studies on MG solutions as part of Ecuador’s Interconnected National Electricity System, as well as describes country policies and laws in force for implementing MGs in Ecuador.

The latest advances in ECs have been presented in different studies as presented in [17,18], or projects as in [19,20]. Additionally, the development of policies and framework laws for the introduction of ECs in the worldwide energy system is critical to accelerating the energy transition to cleaner sources [21], and even to reaching community energy sovereignty [22]. On the one side, ECs have been defined in the EU directives in 2019 [23], although each member state was given the authority to transpose the definition to their law resulting in some countries considering ECs in their regulation, and others not [24]. For instance, one country that recognizes it is Spain, where the recent Royal Decree 23/2020 defines the concept of ECs [25]. Similar situations were reported for Italy [26], Austria [27], and Germany [28] among others [29]. By contrast, in Romania’s current legislation in force, Order 165 16/09/2020, ECs have not been transposed [30]. On the other side, non-EU countries in different latitudes have made efforts to boost ECs, self-consumption energy [31], and energy transition as presented in [32,33]. Regarding the interest of this work, in 2019 the country of Ecuador promoted the self-consumption operation under the ARCONEL-042/18 regulation, which released the opportunity for householders to install PV generation up to 100 kWp for residential and commercial users [34]. Despite such regulation, end-users are not allowed to sell surplus energy produced, but they are granted an energy credit by the distribution and commercialization company, which can be redeemed within two years. Thus, such operations open the possibility of a kind of energy market with the main grid, but not to energy communities at all.

Different small-scale distributed generation units can be employed for self-consumption energy solutions: photovoltaic (PV), mini—wind, etc. Among the technologies, PV energy is the leading one for the residential sector [9]. The location of solar panels is a crucial factor because the solar penetration is different depending on the climate and latitude. Another crucial element for self-consumption is the electricity tariff associated with the country where the PV installation is placed and their self-support policies. This distinct quantity of PV generation, electricity tariffs, and support policies generate different self-consumption benefits. However, the high investment cost of the necessary equipment and installation is still a big challenge in facilitating the integration, at a big scale, of this kind of energy generation solution [35]. Thus, it can be said that ECs are still in their infancy, as some EU and non-EU member states did not transpose the definition to their law yet or implemented clear aids to facilitate a wide implementation of self-consumption systems at the end-user level. Hence, the initial step to integrating ECs into the current scenario is the different modalities of self-consumption, individual or collective, as reported in [36].

According to [37,38], PV energy participation in the world energy market is 56% (168 GW) of total renewable power generation (302 GW) until 2021. However, such production represents only 3.7% of total energy production worldwide. Best solar energy generation sceneries in 2021 were formed by countries with the highest PV power generation as China (54.9 GW), the United States (27.3 GW), and India (14.2 GW), followed by Japan, Australia, Germany, and Spain, who produced between 4.8 and 6.4 GW of solar energy. It is important to highlight that in such countries, a rooftop residential segment for PV micro-generation systems is significantly high, to leading self-consumption and ECs opportunities. Contrary to this, Latin America has low penetration of PV generation; Brazil is seen as the principal producer with 3.43% (5.5 GW) of renewable energy production (REP). Notably, in Ecuador, the REP is 60.82% (5.3 GW) of the demand, whereas the PV production represents barely 0.53% (0.28 GW), which is one of the lowest participation rates in the region only over Venezuela and Paraguay, which nearly does not have PV power initiatives [39]. Even more discouraging for the region is no real grids integration and lack of appropriate energy policies, the flexibility of tariffs, and private participation in the energy markets, in addition to little knowledge in the implementation and management of renewable electricity generation technology together with high investments required, which prevents a more significant penetration of PV generation systems for self-consumption and ECs.

A detailed review of characteristics, models, and controllers for prosumers as active market participants is presented in [40]. For instance, [41] displays a controller for pricing in prosumer aggregations using a reinforcement learning algorithm based on the use of soft actor-critic architecture that tries to maximize the entropy of its actions to explore the search space; however, prosumers require a large number of interactions and computational costs. Additionally, ref. [42] proposes a predictive control architecture to optimize prosumer’s resources in a demand response framework. The controller demonstrates optimal preservation of resources, even in the case of significant previsions errors or poorly resolved system representation. In [43], the implementation of an adaptive neuro-fuzzy inference system as a forecasting module inside prosumers is presented. In [44], a fuzzy logic energy management system (EMS) of on-grid electrical system for residential prosumers is presented proposing a climate-independent fuzzy logic EMS that integrates solar and wind generators, battery energy systems, electric vehicle (EV) load, dynamic electricity pricing, and tariffs, aiming to reduce the prosumer’s electricity bill. The fuzzy controller strategy was compared with a simple rule-based system and a linear optimization approach, obtaining the lowest consumption cost, with the possibility of improving the control strategy based on the expert knowledge by adjusting the controller for more energy/cost savings, even more.

Table A1. References Classified by Content.

Energy Status	[1], [7], [23], [33], [34], [37], [38]
Self-Consumption	[4], [5], [11], [24], [40], [41], [42], [43], [44]
Microgrids	[2], [3], [4], [5], [6], [11], [12], [13], [14], [15], [16], [40], [41], [42], [43], [44], [45]
Policies and Regulation	[8], [21], [22], [25], [27], [28], [30], [31], [32], [33], [34], [37], [39], [41], [45]
Energy Communities	[4], [9], [10], [17], [18], [19], [20], [26], [28], [29],[31], [32], [33], [35], [36]

suggests a classification for the aforementioned references in order to group them according to the scope of their study.

As established through several studies reviewed in this work, the ECs and self-consumption systems will be the trend in the electrical grids of the future. This kind will allow the end-users to be more involved in their energetic behavior and reach their energetic independence. This improvement can be higher depending on the size of the installation and flexibility of the main grid operation to negotiate the end-users’ energy surplus with the main grid or the members of an energy community. This topic is under research and development in the named first-world countries. However, the development and installation of self-consumption systems based on solar energy are relatively new in Latin American countries, including Ecuador. This way, on the one hand, it is necessary to promote the massive installation of this kind of energy solution by the legal legislation (at the user and EC levels) as well as with evident reductions in taxes to import the required technology. On the other hand, this kind of system needs the development of energy management strategies that maximize the exploitation of the local renewable resources and respond according to the local legislation and user consumption behavior.

Therefore, this paper proposes a fuzzy-based energy management strategy (EMS) to maximize the self-consumption from a PV installation with an energy storage system for the residential sector adapted to the Ecuadorian electricity market. The EMS includes two control levels: Energy management at the end-user level (Fuzzy-based EMS and optimized by genetic Algorithm) and Energy management at the distribution grid level (Fuzzy-based EMS). Both strategies aim to maximize the use of the energy generated at home (taking into account the local solar generation profile), fulfilling the loads demand and injecting the energy surplus into the main grid to be economically compensated. The paper includes the modeling of the end-user (PV plant, energy storage system, power electronics, and EMS) as part of an EC and considers different ranges of solar generation for three cities in Ecuador. Additionally, this paper presents the economical modeling according to the electricity market in Ecuador to identify the economic saving in the electricity bill for a home with a self-consumption PV installation and the potential saving in case of having a community electricity market (CEM) contemplated in the Ecuadorian electricity regulation.

2. Materials and Methods

2.1. Grid Modeling

This section provides a general description of the electrical models of each element included in the self-consumption system and the main components to interact with the main grid. The electrical model allows for simulating the behavior of both the end-user generation and consumption profiles, energy storage system, and energy exchange with the main grid. This information is the one analyzed by the EMS to determine the optimal operation (energy flows) to maximize the use of the energy resources (generated and stored) and guarantee a reduction in the electricity bill.

Figure 1 illustrates the arrangement of each element from the end-user point of view. These elements are described in the following subsections.

2.1.1. Irradiance and Temperature Data

For the present study, 15 different generation profiles corresponding to 15 end-users are available in a collaborative database of the Universities in the affiliation of this paper. This data includes the irradiance and temperature information generated for three cities in Ecuador. For the study proposed in this paper, from the database, three user profiles have been selected, which correspond to User 2 (5561 [Wh/m²-day]), User 13 (3594 [Wh/m²-day]), and User 6 (1870 [Wh/m²-day]).

Figure 2a,b illustrates the reference values of temperature and irradiance considered as case studies. The data is represented as a vector with a length of 96 samples, taking as reference a sampling period of 15 min for 24 h as a daily profile.

2.1.2. PV System

The model of solar panel available in Matlab/Simulink was considered for this study and configured with the characteristics presented in

Table 1. Solar panel main technical characteristics.

Element	Characteristics	Value
Solar panel	Maximum Power	410 [W]
	$\mathrm{Open} \mathrm{circuit} \mathrm{voltage} (Voc$)	41 [V]
	$\mathrm{Voltage} \mathrm{at} \mathrm{maximum} \mathrm{power} \mathrm{point} (Vmp$)	33.93 [V]
	$\mathrm{Temperature} \mathrm{coefficient} \mathrm{of} Voc$	−0.29 [%/°C]
	$\mathrm{Cells} \mathrm{per} \mathrm{module} (Ncell$)	120
	$\mathrm{Short}-\mathrm{circuit} \mathrm{current} (Isc$)	10.82 [A]
	$\mathrm{Current} \mathrm{at} \mathrm{maximum} \mathrm{power} \mathrm{point} (Imp$)	10.02 [A]
	$\mathrm{Temperature} \mathrm{coefficient} \mathrm{of} Isc$	0.048 [%/°C]
	$\mathrm{Shunt} \mathrm{resistance} (Rsh$)	102.209 [Ω]
	$\mathrm{Series} \mathrm{resistance} (Rs$)	0.23233 [Ω]
	Diode ideality factor	0.49595
PV systems	Solar panels in series	2
	Branches of solar panels in parallel	3
	Rated voltage	81 [V]
	Rated power	2.46 [kWp]

corresponding to the JINKO JKM340M-60H product. Each self-consumption installation consists of a PV system composed of an array of 2 solar panels in series and 3 branches of solar panels in parallel with a current/power performance per branch shown in Figure 3. The PV system sizing was done by considering the criteria proposed for the ARCONEL (Agencia de Regulación y Control de Electricidad) regulation which is explained in Section 2.2.

2.1.3. Buck DC-DC Converter and MPPT Charge Controller

The DC-DC model includes both the electrical model of the buck power converter and the MPPT controller with characteristics defined in

Table 2. DC-DC system main characteristics.

Element	Characteristics	Value
MPPT	Incremental Conductance Algorithm	-
Buck DC-DC converter	Input-Voltage	41 [V]
	Switching frequency	50 [kHz]
	Lmin	5.1875 [µH]
	Voltage ripple	5%
	Capacitor	826 [µF]
	Output-Voltage	24 [V]

. The MPPT algorithm of incremental conductance type, which has been selected based on the criteria stated in [33], provides a percentage pulse width to generate a pulse width modulation (PWM), corresponding to the switching signal for the converter denoted as s_buck. The topology of the buck DC-DC converter is depicted in Figure 4. Due to the PV system supplying a voltage of 41 [V], a buck converter is applied to reduce the voltage [33].

2.1.4. Energy Storage System

The ESS used in the self-consumption installation is illustrated in Figure 5, which presents the characteristics detailed in

Table 3. Battery system characteristics.

Element	Characteristics	Value
Battery cell	Rated voltage	12 [V]
	Rated capacity	100 [Ah]
	Technology	AGM VRLA
Battery pack (ESS)	Rated voltage	24 [V]
	Rated capacity	300 [Ah]
	Batteries in series	2
	Branches of batteries in parallel	3
	Rated ESS energy	2.4 [kWh]

, corresponding to the Greensun product under the model JFM100-12, which was selected based on the quality report presented by the organization of consumers and users, and the availability of the product in Ecuador.

As illustrated in Figure 5, the ESS has two operation modes (charging and discharging) which are controlled by the switches with a binary signal as outputs determined by the fuzzy-based control. The electrical model also includes an inductor L = 0.5 [mH] and a capacitor C = 635 [µF] that allows for filtering the current peaks injected into the ESS. The model outputs are the state of charge (SOC), current, and voltage of the ESS. The arrangement configured for the ESS considers the installation of 2 batteries in series and 3 branches of batteries in parallel, as detailed in Table 3.

2.1.5. End-User Load Profile

This section describes the ranges of the maximum and minimum power consumption profile per hour corresponding to each selected end-user, working under the following conditions:

-

The base maximum and minimum power consumption were considered taking into account the information presented in the report presented by the ARCONEL [34] with a value of 116 [W] and 21 [W], respectively. These values were upscaled by a factor of 12 to reach the average consumption levels of the residential sector for a middle-class family in Ecuador.

The operation profile and base power consumption ranges were extracted from Figure 6, which represents a consumption characteristic curve of the Ecuadorian residential sector [34]. This profile presents different ranges: a low consumption (R1) from 00:00 to 05:00, a low-medium consumption (R2) from 05:00 to 07:00, medium consumption from 07:00 to 18:00, medium-high consumption from 18:00 to 19:00, and high consumption from 19:00 to 22:00 [34].

Table 4. Base consumption profile for end-user.

Time Interval	Power Range	Demand Level
01h00–04h00	21 W–30 W	LOW (R1)
05h00–06h00	23 W–39 W	LOW/MEDIUM (R2)
07h00–17h00	39 W–49 W	MEDIUM (R3)
18h00–19h00	51 W–92 W	MEDIUM/HIGH (R4)
20h00–22h00	82 W–116 W	HIGH (R5)
23h00–24h00	51 W–92 W	MEDIUM/HIGH (R4)

summarizes the base power ranges for each consumption region.

2.1.6. Microgrid Scenario

The microgrid has been modeled following a bidirectional energy exchange approach between the end-user and the distribution grid. It is worth mentioning that the current Ecuadorian electricity law only contemplates the possibility of injecting energy into the distribution grid to be compensated by a monthly energy balance by considering the total energy consumed. The main grid acts as an energy buffer, virtually storing the energy injected by the users for up to 2 years. Currently, the law does not contemplate the structure of a CEM that allows exchanging the energy among end-users for economical compensation purposes. However, in this paper, a preliminary analysis of this potential energy exchange has been considered to quantify the energy that could be considered in this pool of energy and the economic benefits for the end-users.

As depicted in Figure 7, the proposed scenario considers three end-users connected to the distribution grid, evaluating the performance of the EMS when multiple users access the microgrid, consuming or injecting energy into it.

2.2. Self-Consumption Regulation in Ecuador

The regulation for energy self-consumption installations in Ecuador is relatively new, with its first version regulated by ARCONEL in 2018 [34]. The regulation applies to distribution companies and to those regulated users who decide to install a photovoltaic micro-generation system with a nominal capacity of up to 100 [kW] in medium and/or low voltage, which operates in synchronism with the main grid (on-grid). The objective of these installations must be energy self-consumption and the possibility of pouring surpluses into the distribution grid.

It is important to point out that the electricity supplying the architecture in Ecuador, at the level of distribution grids, contemplates the zoning of the territory. The geographical areas covered by the distribution companies normally cover a province or a group of provinces. The electricity supply service in the country is carried out through 10 distribution and marketing companies. This way, the regulations for energy self-consumption installations are of national application; however, the rate calculation will depend on the geographical region where the installation is located and the distribution and marketing company to which the end-users are connected.

At the moment, the aspect of economic compensation for the surpluses injected into the electricity grid is not fully regulated. Currently, the user who injects energy into the distribution network cannot negotiate the volume of energy injected, neither economically nor energetically, with other users (CEM).

The compensation mechanism is based on a balance calculation between the energy consumed from the grid and that injected. If the result of the monthly balance is positive (greater energy consumption from the distribution grid), the total energy is quantified with the reference price per kWh (according to the distribution and commercialization company to which it is geographically connected), and the corresponding value is billed. On the other hand, if the result of the balance is negative (greater injection of energy into the distribution grid), the total energy becomes an energy credit that can be deducted from future bills for up to 2 years. This energy balance is considered in (1).

$$\Delta E_{grid}=E_{consumed\_grid}-E_{inyected\_grid} \left[\mathrm{kWh}\right]$$

(1)

where:

• $\Delta E_{grid}$: End-user energy balance (monthly).
• $E_{consumed\_grid}:$ Energy consumed from the network [kWh].
• $E_{inyected\_grid}:$ Energy injected into the network [kWh].
• $\Delta E<0$ negative remaining
• $\Delta E>0$ positive remaining

This way, the connected user who has registered a self-consumption installation must have a bidirectional meter approved by the distribution and marketing company. If the end-user operates in off-grid mode, they are not subject to national self-consumption regulations.

The following subsections describe the main technical characteristics of a self-consumption installation at a residential and commercial level and the rate calculation mechanisms that will later be applied in the economic model.

2.2.1. PV Installation Sizing

The maximum nominal capacity installed in the solar micro-generation system is defined by (2).

$$NIC=\frac{{{\displaystyle \sum }}_{i=month 1}^{month 12}{E}_{monthly\_i}\left[kWh\right]}{F_{plant\_design}·8760\left[h\right]} \left[kW\right]$$

(2)

being:

• $NIC:$Nominal Installed Capacity
• $E_{monthly\_i}$: Monthly energy billed to the user
• $F_{plant\_design}:$ Plant design factor, determined by the technical study carried out by the distribution and marketing company (or a consulting company) taking into account the user’s average power consumption.

In this study, the PV installed power will be defined by (2) where the $F_{plant\_design}$ value is usually between 0.2 and 0.4. In this analysis, a $F_{plant\_design}$= 0.4 has been considered where a PV installed power of 2.4 [kWp] was calculated.

2.2.2. Calculation of Energy Flows from the Point of View of the End-User and Main Grid

At the level of the energy system of the end-user, the energy generated is also considered within the energy balance. From the point of connection to the main grid into the end user’s installation, the corresponding equation is as follows:

$$\Delta E_{end-user}=\left(E_{consumed-loads}-E_{PVgeneration}\right) \left[\mathrm{kWh}\right]$$

(3)

being:

• $\Delta E_{end-user}$: End-user energy balance (from the end-user point of view)
• $E_{consumed-loads}:$ Energy consumed by the loads that the end-user has
• $E_{PVgeneration}:$ Power generated by the PV system

If the energy balance $\Delta E_{end-user}$is positive, it implies that the user has an energy deficit that must be covered by the main grid ($E_{consumed-grid}$) or, in the case of having a local storage system using batteries, from said system. On the other hand, if the energy balance is negative, it implies that the user has a surplus of energy that can be injected into the main grid and/or stored in the ESS. Therefore, $E_{consumed-grid}$ and $E_{inyected-grid }$ can be defined by (4) and (5), respectively.

$$E_{consumed-grid}=E_{consumed-loads}-E_{PVgeneration}+K_{ESS}·E_{ESS} \left[\mathrm{kWh}\right]$$

(4)

$$E_{inyected-grid}=E_{consumed-loads}-E_{PVgeneration}-K_{ESS}·E_{ESS} \left[\mathrm{kWh}\right]$$

(5)

being:

• $K_{ESS}$: A constant from the ESS model and commanded by the EMS wich can be +1 or −1 depending on the energy flow to-from the ESS
• $E_{ESS}$: energy injected or absorbed from/to the battery (depending of $K_{ESS}$).

2.2.3. General Low Voltage Rate with Hourly Demand Recorder

This rate is applied to users who contracted up to 10 [kW] and who have an hourly demand recorder that makes it possible to identify peak, average, and base periods for power demand and energy consumption.

The consumer within this rate, in addition to the general charges, must pay:

-

A charge [USD/kW-month] for each kW of monthly demand independent of energy consumption, multiplied by a demand management factor (DMF).

-

An energy charge [USD/kWh-month] based on the energy consumed in period 1 (08:00 to 22:00) and period 2 (22:00 to 08:00).

2.2.4. Billable Demand

The billable demand (BD) is the result of comparing the maximum power demand recorded by the metering equipment and the contracted power.

-

Meter that registers maximum demand

The BD corresponds to the maximum demand (MD) registered in the corresponding month and may not be less than 60% of the value of the MD in the last 12 months ($M{D}_{max12}$) applying the following criteria:

$$BD=\left\{\begin{array}{c}0.6·M{D}_{max12} if MD<0.6·M{D}_{max12}\\ MD if MD\ge 0.6·M{D}_{max12}\end{array}\right\}$$

(6)

-

Demand management factor

The maximum monthly demand (MPD) of the consumer during peak hours (18:00–22:00) and the maximum monthly demand of the consumer (MD) must be established. The calculation is done using the following equation:

$$DMF=\left\{\begin{array}{c}0.6 if \frac{MPD}{MD}<0.6\\ \frac{MPD}{MD} if 0.6\le \frac{MPD}{MD}\le 1\end{array}\right\}$$

(7)

2.2.5. Economic Cost Calculation

The billing of the electrical energy consumed (or, in a potential case, the energy balance for the energy injected into the grid) is carried out over a monthly period. In the residential case, they are those users who use energy exclusively for domestic use, independent of the connected load and with a low-voltage supply (less than 600 V). In Ecuador, this category includes consumers with low economic resources and/or who have a small commercial or craft activity at home. All the users must pay:

-

A sales charge [USD/consume-month] independent of energy consumption.

-

Incremental charges for energy [USD/kWh] based on consumed energy.

The bill of the public electricity supply service is the sum of the economic items of the components: energy, power, commercialization, loss in transformers, and penalty for low power factor (mainly in industrial and commercial environments). The general equation is as follows:

$$Total\_Cos{t}_{EE}=E_{consumed-grid}·Uni{t}_{cost-kWh}+BD·DMF+C+TL+P_{power-factor} [\mathrm{USD}-\mathrm{month}]$$

(8)

where:

• $Total\_Cos{t}_{EE}:$ Economic cost per month [USD/month]
• $Uni{t}_{cost-kWh}$: Referential cost of the kWh defined by the public distribution company [USD/kWh]
• $C:$ Economic cost for commercialization defined by the public distribution company [USD]
• $TL:$ Economic for transformer losses defined by the public distribution company [USD]
• $P_{power-factor}:$ Penalty for low power factor defined by the distribution company [USD]

For the analysis proposed in this paper the factors $C, TL$ and $P_{power-factor}$have not been considered due to the case study being focused on the residential sector. The referential costs were obtained from the document published by the Electric Company Quito S.A. which is the distribution and marketing company operating in the capital of Ecuador. The referential costs for $C$ and $Uni{t}_{cost-kWh}$ are 1.414 [USD] and 0.083 [USD/kWh], respectively. The current electricity legislation does not consider an economic remuneration for the end-user that injects energy into the main grid. The compensation is from the energetic point of view, it means, considering an energy balance of the energy consumed and injected into the main grid (a kWh consumed by a kWh injected).

It is important to highlight that, in the case of a traditional end-user (consumer without a PV system installation), the electricity bill is calculated by Equation (8). However, the energy balance of the energy consumed and injected into the main grid is not considered. The traditional end-user has a unidirectional grid-metering device (the electromagnetic or digital one) while the prosumer end-user has a bidirectional grid metering device.

2.3. Energy Management Strategy (EMS)

For the scenario proposed in this paper, the energy management architecture is divided according to the following strategies:

-

Energy management at the end-user level: Fuzzy-based EMS and optimized by Genetic Algorithm

-

Energy management at distribution grid level: Fuzzy-based EMS

The implemented fuzzy strategy is based on the Mamdani fuzzy inference system. The scheme depicted in Figure 8 and Figure 9 represents the input and output variables of the fuzzy system, where the block “Battery” activates a local battery connection and disconnection signal to operate the ESS according to the power demand resulting from the balance between the load’s power demand and PV power generated. This output signal allows controlling the second fuzzy block named “Main Grid”.

The proposed strategy allows the user to manage the energy (surplus or deficit) appropriately and prioritize energy consumption from PV system and ESS in ranges of greater power demand by the user. The fuzzy strategy has an instantaneous response since the input data corresponds to the instantaneous information of the system. The system tries to make the best energy management decision to guarantee the best energy distribution for given conditions.

Figure 10 details the different inputs/outputs for the fuzzy-based strategies. It is worth mentioning that the ranges have been defined by considering the base end-user power profile provided in Figure 6, which can be scaled up for different rates of consumers depending on their consumption behavior. The linguistic terms for the membership functions (MF) have been defined as follows:

• State of charge variable (SOC):
  (B) low state-of-charge; (M) medium state-of-charge; (A) high state-of-charge.
• Error of power variable (EP):
  (N) negative power error; (P) positive power error.
• Prosumer user power variable (PUP):
  (B) low end-user power (A) high end-user power.
• Battery status variable (EB):
  (D) battery discharge status; (C) battery charge status.
• MG status variable (ER):
  (D) Disconnected MG status; (C) connected MG status

The ranges for the MF depicted in Figure 10 are detailed in

Table 5. Input/Output parameters of the fuzzy systems.

Type	Variable	Linguistic Representation	Range
Input	SOC	Low	[0, 0, 25, 55]
		Medium	[25, 55, 85]
		High	[55, 85, 100, 100]
	EP	Positive	[−20, 200]
		Negative	[−200, 20]
Output	EB	Discharge	[0, 0, 40, 60]
		Charge	[40, 60, 100, 100]
Input	PUP	High	[40, 60,1 50, 150]
		Low	[0, 0, 40, 60]
	EP	Positive	[−20, 200]
		Negative	[−200, 20]
	EB_r	Connected	[0, 0, 40, 60]
		Disconnected	[40, 60, 100, 100]
Output	ER	Connected	[0, 0, 40, 60]
		Disconnected	[40, 60, 100, 100]

and have the following characteristics:

-

SOC [input]: In the ESS, the SOC is controlled in the range of 55–85% covered by the MF: SOC_M and SOC_A. The objective is to maintain enough stored energy for the power peak demand response and prevent deep discharge at SOC_B <25%.

-

EP [input]: This variable relates the power generated by the PV system minus the power demanded by the user’s loads. The input EP has the purpose of triggering the surplus or deficit of power from the balance to be managed by the ESS and/or main grid.

-

PUP [input]: Two membership functions have been considered to cover the power demand range: a range with a higher demand PUP > 60 W and another with a lower demand PUP < 60 W. Based on the behavior of the fuzzy rules, the local ESS is prioritized to supply the maximum power demand, and the main grid compensates the positive or negative surplus.

-

EB_r [input]: The battery status variable provides information about the loads’ behavior and whether the ESS injects energy to the DC bus to feed the loads with EB_r >60; otherwise, if the loads need to be fed from the main grid.

-

EB and ER [outputs]: These outputs control the ESS operation, enabling or disabling the ESS operation (ER) and determining the power rate to charge or discharge the ESS (EB).

2.4. Optimization Process Using Genetic Algorithms

In this section, the behavior of the prosumer user power demand (PUP) is analyzed to maximize the self-consumption operation and the exploitation of the energy generated by the PV system. For this purpose, an optimization process based on genetic algorithms (GA) has been proposed. The optimization aims to provide a forecasting profile of end-user consumption to the fuzzy-based EMS. Thus, this data helps to determine properly and more accurately the energetic behavior of the system taking into account the energy sources (PV system, main grid), energy storage (ESS), and user demand.

The genetic algorithm generates an initial population depending on the Power vs. Demand Time Ranges. In each iteration, the GA selects individuals (parents) by applying the roulette method to reproduce them to obtain children with improved characteristics in each generation. The parameters to configure the GA are shown in

Table 6. Genetic algorithm configuration parameters.

Parameter	Value
Type of population	string of 7 bits
Population size	100
Number of generations	50
Initial population	power range PUP
Mutation	0.07

, and they have been determined based on empirical analysis to get the best-fitted values to improve the system operation. The optimization process allows maximizing the PUP from the end-user power demand ranges presented in

Table 7. Demand-side power ranges.

Power Range [W]	R1	R2	R3	R4	R5
	[21–30]	[23–39]	[39–49]	[51–92]	[82–116]
Time [h]	[0–5]	[5–7]	[7–18]	[18–20]	[20–23]

. The implemented GA optimization provides data in a quarter-hour system for 24 h according to the consumption profile.

The behavior of the GA fitting optimization under the end-user power demand profile is illustrated, for example, in Figure 11. This optimization presents a maximum deviation of around 5% from the base profile (Figure 3).

3. Results and Discussion

3.1. System Operation Results

Three end-user types with different irradiance and temperature profiles corresponding to the geographic environment of three different cities in Ecuador have been selected (

Table 8. Main characteristic parameters of the users.

Parameter	User 2	User 13	User 6
Irradiance [Wh/m2-day]	5561	3594	1870
Initial battery state-of-charge [%]	40	55	75

). Three initial states of charge (SOC) for the ESS have been defined for these end-users, with values corresponding to 40%, 55%, and 75%.

The data of irradiance and temperature for the 3 selected users (Table 8), based on the PV system model described in Section 2.1.2, presents the power generation profiles depicted in Figure 12.

The end-user power demand profile considered for this study is depicted in Figure 13. It is worth clarifying that, the power demand profile presented in Figure 13 has been applied to the three end-users selected as case studies for the scenario proposed in this paper. The power demand profile was built taking as a basis the profile depicted in Figure 3 and the optimization based on GA described in Section 2.4 to fit the consumption according to the information provided by the ARCONEL regarding the average consumption levels of the residential sector for a middle-class family in Ecuador. This consumption profile acts as a forecasting input to the fuzzy-based control.

The dynamic power error profile as a function of time is illustrated in Figure 14. In the case of a high generation profile, during the daily operation, the system has a total of 8.8 [kWh] of energy surplus and 10.38 [kWh] of energy deficit with an energy balance of −1.58 [kWh] (which must be compensated from the ESS and/or main grid). On the other side, in the case of a medium generation profile, the energy surplus is around 5.7 [kWh] and a deficit of 10.7 [kWh] with an energy balance of about −5 [kWh]. Finally, in the case of a low generation profile, the energy balance is around 8.8 [kWh].

The variable power error (EP) analyzes the surplus or deficit of energy based on the energy generated from the PV system and the end-user load demand. Figure 15 illustrates the energy balance analysis for each case study (the end-user type with different irradiance characteristics). Therefore, with irradiance values of 5561 [Wh/m²-day], the energy generated is fully consumed by the loads and around 5% is compensated by the ESS and main grid. In the case of irradiance of 3594 [Wh/m²-day], around 33% of the energy demand has to be compensated by the ESS and main grid. Finally, in the case of low irradiance of 1870 [Wh/m²-day], close to 70% of energy demand must be compensated.

Figure 16 presents the behavior of the state of charge of the battery for three different case studies presented in

Table 9. Economic analysis for User 2.

Total Bill Cost [USD/Month] for a Single End-User				Potential Energy [kWh] and Total Bill Cost [USD/month] for a Single End-User in Case of a CEM in the Current Legislation
SOC	Base Cost (without PV System) [USD/Month]	Case Cost (with PV System) [USD/Month]	Reduction in the Electricity Bill [%] (from Base Cost)	Energy Surplus at End of Day (Potential Amount of Energy for Negotiation in the CEM) [kWh]-[USD/Month]		Potential Reduction in the Electricity Bill [%] (from Base Cost)
40%	42.92	22.83	46.81%	7.02	17.48	87.54%
55%	42.92	16.77	60.93%	4.59	11.43	87.55%
75%	42.92	7.02	83.64%	0.67	1.67	85.23%

. These case studies consider different values for the initial SOC to analyze the system behavior depending on the energetic conditions imposed by the previous day. The study has been replicated for the three end-user types.

For an initial SOC of 40%, the behavior for the three end-user types disables consuming energy from the ESS to avoid operating below the minimum SOC level. Therefore, during the period from 0 to around 9 [h] the energy deficit is supplied by the main grid.

However, for the cases with initial SOC of 55% and 75%, the ESS provides energy to supply the end-user demand during all the periods both when the ESS is the only energy source as well as when the PV system is in low generation mode due to the low climate conditions.

The fuzzy-based EMS activates the charging and discharging process to control the ESS, as shown in Figure 17. As illustrated in Figure 17, the charging behavior mostly begins during the presence of PV generation and the discharging process mainly during periods of lack of irradiance. Additionally, both in charging and discharging periods, the fuzzy-based EMS decides the proper operation for:

-

ESS (charging/discharging process and power rate)

-

Main grid (absorbing energy to compensate for the end-user demand)

-

Main grid (absorbing energy to charge the ESS to use it in a different time frame)

-

Main grid (injecting the energy surplus when the ESS is close to fully charge and to be compensated by the energy credit contemplated in the Ecuadorian legislation as explained in Section 2.2)

Figure 18 shows the power profiles regarding the main grid once the EMS is applied and depending on the end-user type. $P_{surplus}$ represents the power surplus after the power demand (from end-user loads, Figure 12) and power generation (from the PV system, Figure 11) are compared. Then, the fuzzy-based EMS, considering the SOC level, power generated, and system operation determines the power needed to be absorbed or injected from/to the main grid. Later, this data is computed and allows for calculating the monthly electricity bill as described in Section 2.2 and summarized in the next section.

3.2. Economical Assessment by End-User Type

This section aims to describe the main results regarding the application of the economic model presented in Section 2.2. For this purpose, it can be considered that the three end-users generation profiles correspond to the different solar irradiance levels. Additionally, the three different SOC levels considered by end-user were established as a baseline for the study presented in this section and the system performance corresponds to the ones presented in the previous section, respectively.

3.2.1. Electricity Bill Cost Assessment

This section presents the assessment of the monthly electricity bill from the economic point of view and identifies the potential benefits in case of installing PV systems at home and the added value for the end-user in case of the current law contemplates the figure of the CEM for energy exchange among end-users and the main grid. Figure 19 shows the energy performance for each end-user type. The results presented in the previous figures correspond to an average day. The energy consumption from the home loads ($E_{consumed}$) and the energy generated by the PV system ($E_{generated}$) have been maintained constant in all the case studies and correspond to the power profiles depicted in Figure 12 and Figure 11, respectively.

Figure 19,$E_{bt-injected}$ is the total daily energy that battery-based ESS has injected throughout the day to the DC bus and which can be consumed by the home loads and/or injected into the main grid (depending on the performance determined by the EMS). On the other hand, $E_{bt-absorbed}$ is the total daily energy that has been stored in the ESS throughout the day. The unbalance between $E_{bt-injected}$ and $E_{bt-absorbed}$ represents the final SOC of the ESS and the end of the day which in most case studies is higher than the initial one. This behavior shows that, at the end of an average day, we can have an energy surplus that can be negotiated with a CEM and sold to the main grid (or other end-users throughout the distribution grid).

Additionally, in Figure 19, $E_{grid-absorbed}$ and $E_{grid-injected}$ are the total daily energy that is absorbed and injected into the main grid throughout the day, respectively.

Based on the energy results presented in Figure 19 and using the economic model described in Section 2.2, the electricity bill costs for each end user considered in this study have been calculated. The economic results have been summarized in Table 9,

Table 10. Economic analysis for User 13.

Total Bill Cost [USD/Month] for a Single End-User				Potential Energy [kWh] and Total Bill Cost [USD/month] for a Single End-User in Case of a CEM in the Current Legislation
SOC	Base Cost (without PV System) [USD/Month]	Case Cost (with PV System) [USD/Month]	Reduction in the Electricity Bill [%] (from Base Cost)	Energy Surplus at End of Day (Potential Amount of Energy for Negotiation in the CEM) [kWh]-[USD/Month]		Potential Reduction in the Electricity Bill [%] (from Base Cost)
40%	42.92	29.58	31.08%	6.22	15.49	67.29%
55%	42.92	23.50	45.25%	3.88	9.66	67.75%
75%	42.92	13.53	68.48%	0	13.53	68.48%

and

Table 11. Economic analysis for User 6.

Total Bill Cost [USD/Month] for a Single End-User				Potential Energy [kWh] and Total Bill Cost [USD/Month] for a Single End-User in Case of a CEM in the Current Legislation
SOC	Base Cost (without PV System) [USD/Month]	Case Cost (with PV System) [USD/Month]	Reduction in the Electricity Bill [%] (from Base Cost)	Energy Surplus at End of Day (Potential Amount of Energy for Negotiation in the CEM) [kWh]-[USD/Month]		Potential Reduction in the Electricity Bill [%] (from Base Cost)
40%	42.92	34.77	18.99%	4.56	10.94	44.48%
55%	42.92	30.21	29.61%	4.43	10.63	54.38%
75%	42.92	15.92	62.91%	−0.82	17.97	58.15%

, and can be interpreted as follows:

-

SOC represents the different levels of battery state of charge considered.

-

The base cost was calculated with the total energy consumed from the main grid ($E_{consumed}$) presented in Figure 19 and using the economic model from Section 2.2 considering a traditional end-user (consumer without a PV system installed at home).

-

The case cost corresponds to the scenario of an end-user with a PV system installed at home and recognized as a prosumer (current contract) by the local distribution and marketing company. The economic model of Section 2.2 is applied and, as a result of the energy saving, the economic cost is calculated.

-

The percentage reduction represents the reduction in the electricity bill cost of the scenario with a PV system from the one without a PV system (traditional end-user).

As stated in Section 2.2, the current electricity law in Ecuador does not consider an economic compensation (only an energetic one) for the energy injected into the main grid. However, an analysis under the consideration that a potential CEM was included in the current legislation has been developed. The main results of this analysis are included in Table 9, Table 10 and Table 11, and can be interpreted as follows:

-

The energy surplus at the end of the day was calculated taking into account the energy balance of the battery ($E_{bt-absorbed}-E_{bt-injected}$) [kWh] with the data presented in Figure 19. To this energy surplus was applied the economic model described in Section 2.2 with the referential costs of 1.414 [USD] and 0.083 [USD/kWh] for $\mathrm{C}$ and ${\mathrm{Unit}}_{\cos \mathrm{t}-\mathrm{kWh}}$, respectively. The resulting economic cost [USD/month] represents the potential electricity bill cost in the case of a CEM is considered where:

• The energy balance (and economic model of Section 2.2) is considered for the energetic compensation (current law) of a kWh consumed by a kWh injected.
• The energy surplus available in the battery at the end of the day (as calculated from data presented in Figure 19 and depicted in Figure 16 with the difference between the initial and final SOC values) can be negotiated with the main grid to be used by itself or other end-users (during the next day). This energy surplus will represent the amount of energy that can be compensated economically by the main grid (or by an intermediary) to the end-user who offers it. It is worth clarifying that this assumption is an expected scenario in the case of including the figure of CEM in the current law.

-

The potential reduction represents the reduction in the electricity bill cost of the scenario with a PV system (considering the two points previously described) from the one without a PV system (traditional end-user).

The scenario proposed in this paper considers the behavior of generation and consumption of the three end-users described throughout the paper as case studies. The total surplus of energy that could be available to be used by the community will depend on the number of end-users who enroll as prosumers (current contract) with the local distribution and marketing company. Other relevant factors which can impact the total available energy for community use are the sizing both of the PV system and ESS installed by the end-users. As comparative data, the Electric Company Quito S.A. currently has a total of 392.14 [kW] of installed capacity divided by 37 end-users of PV systems considered for self-consumption use and, at a country level, a total of 771.11 [kW] of installed capacity divided in 50 end-users [39].

In all the cases summarized in Table 9, Table 10 and Table 11, there is an apparent cost reduction from 18.99% up to 83.64%. The economic saving may be higher if the energy surplus and the end of the day ($E_{bt-absorbed}-E_{bt-injected}$ from Figure 19) could be negotiated in a potential CEM which is not already considered in the Ecuadorian electricity law.

Under this potential scenario, the monthly energy balance could be even negative with an economic compensation for the end-user. The amount of energy surplus at the end of the day is also included in Table 9, Table 10 and Table 11. For economic representation purposes, this amount of energy has been quantified by considering a referential cost of 0.083 [USD/kWh]. Therefore, in this scenario of a CEM, the potential economic benefit may increase up to 87.54% and in some cases, the saving is more than double compared to the same case but with only the self-consumption considerations under the current Ecuadorian electricity regulation.

The reduction in economic cost in the electricity bill for each end-user and SOC case is a result of combining, on the one hand, a self-consumption system including an ESS which allows a degree of freedom to manage the energy surplus from the PV system and store it to be used when the end-user consumption increase. On the other hand, the fuzzy-based EMS allows for management in an optimal way of the power and energy flow in the self-consumption system. This intelligent EMS allows the exploitation of the installed systems and guarantees the minimum economic cost in the monthly bill. Additionally, it is important to highlight the benefits contemplated in the current Ecuadorian law for self-consumption installations, which allows the use of the main grid as an energy buffer and virtually maintains the energy injected for a period of up to 2 years. However, improvements can be included to contemplate the figure of the CEM, thus enabling the users to interact in a techno-economic way both with the main grid as well as with other end-users in order to establish energetic transactions among them.

3.2.2. Lifecycle Cost Assessment

This section aims to evaluate the return of investment (ROI) regarding the PV installations considered in the scenario proposed in this paper: 2.46 [kW] of solar panels installed (together with the power electronics devices required for proper operation) and 2.4 [kWh] of ESS (batteries of AGM VRLA technology). For this purpose, referential costs of solar products in Ecuador [45] have been considered as summarized in

Table 12. Referential costs for PV installations in Ecuador.

Referential Cost for PV Installation	Referential Cost for a Battery-Based ESS	Estimated Total Cost of the System (Investment Cost)
1000 [USD/kW]	300 [USD/kWh]	3180 [USD]

. The analysis has been carried out by considering the three end-users and SOC scenarios proposed in the previous section and the results are depicted in

Table 13. Lifecycle analysis by end-user.

SOC	User 2				User 13				User 6
	Estimated Monthly Saving [USD/Month]		ROI [Years]		Estimated Monthly Saving [USD/Month]		ROI [Years]		Estimated Monthly Saving [USD/Month]		ROI [Years]
	PV	PV + CEM	PV	PV + CEM	PV	PV + CEM	PV	PV + CEM	PV	PV + CEM	PV	PV + CEM
40%	20.09	25.44	13.2	10.4	13.34	27.43	19.8	9.7	8.15	31.98	32.5	8.3
55%	26.15	31.49	10.1	8.4	19.42	33.26	13.6	7.9	12.71	32.29	20.8	8.2
75%	35.90	41.25	7.4	6.4	29.39	29.39	9.0	9.0	27.00	24.95	9.8	10.6

.

4. Conclusions

This paper proposed a fuzzy-based energy management strategy (EMS) to maximize the self-consumption from a PV installation with ESS for the residential sector adapted to the Ecuadorian electricity market. The paper presented the modeling of the end-user (PV plant, energy storage system, power electronics, and EMS) as part of an EC and considered different ranges of solar generation for three cities in Ecuador. Additionally, this paper described the economical modeling according to the electricity market in Ecuador in order to identify the potential saving in the electricity bill for a home with a self-consumption PV installation.

The main results showed a cost reduction in the electricity bill up to 83.64% from the base case (residential consumption without a PV system). In addition, in the scenario of a CEM, the potential economic saving may increase up to 87.54% and in some cases, the saving is more than double compared with the same case but only with the self-consumption considerations under the current Ecuadorian electricity regulation.

The reduction in economic cost is a result of combining, on the one hand, a self-consumption system including an ESS which allows a degree of freedom to manage the energy surplus from the PV system and store it to be used when the end-user consumption increase. On the other hand, the fuzzy-based EMS allows exploitation of the installed systems and guarantees the minimum economic cost in the monthly bill.

Finally, the Ecuadorian electricity legislation for self-consumption installations presents different benefits; the most important is the possibility to consider the main grid as an energy buffer and virtually maintain the energy injected for a period of up to 2 years. However, improvements can be included to contemplate the figure of the CEM, thus enabling the users to interact in a techno-economic way both with the main grid as well as with other end-users in order to establish energetic transactions among them with higher economic benefits to the end-users.

Future work will be focused on two main aspects, on the one hand, improving the performance of the fuzzy control by considering predictive models from the generation and end-user consumption behavior learning. On the other hand, to design a techno-economical energy management strategy to manage the multiple users’ energetic transactions by smart contracts, maximizing the profitability of the end-user’s PV installation and guaranteeing the energy balance from the main-grid side. However, the main limitations for realistic calculations about costs and potential benefits are limited by the assumptions done regarding the energy cost and accurate economic and/or energetic compensation by the main grid to the end-user and the legal framework for the energy exchange in a CEM.