Engineering Applications of Artificial Intelligence 85 (2019) 284–294
Contents lists available atScienceDirect
Engineering Applications of Artificial Intelligence
journal homepage:www.elsevier.com/locate/engappaiWavelet-fuzzy power quality diagnosis system with inference method based
on overlap functions: Case study in an AC microgrid
✩
Diego H.S. Nolasco
a,b,∗, Flavio B. Costa
b, Eduardo S. Palmeira
c, Denis K. Alves
b, Benjamín
R.C. Bedregal
b, Thiago O.A. Rocha
b, Ricardo L.A. Ribeiro
b, Juliano C.L. Silva
baFederal Institute of Bahia, Vitória da Conquista 45030-220, Brazil bFederal University of Rio Grande do Norte, Natal 59072-970, Brazil cState University of Santa Cruz, Ilhéus 45662-900, Brazil
A R T I C L E
I N F O
Keywords:Power quality Microgrid Wavelet packet Hierarchical fuzzy system Extended overlap function
A B S T R A C T
This work proposes a wavelet-fuzzy power quality (PQ) diagnosis method able to evaluate the PQ impact of steady-state (stationary) PQ events in alternating current (AC) microgrids considering the influence of the power level penetration. The proposed method is composed by a wavelet packet-based signal processing to compute the root mean square (RMS) and steady-state PQ indices of measured voltages and currents, providing accurate results even if transient disturbances take place. Thereafter, a cascade-type hierarchical fuzzy system receives the PQ indices and performs the power quality diagnosis to evaluate the impacts of disturbances on electrical system power quality. The proposed method considers subjectivities of several PQ standards simultaneously and applies an adaptive algorithm that allows the evaluation of the PQ diagnosis from the total harmonic distortion of currents considering different levels of power penetration of microgrids. Experimental results obtained from an ac microgrid laboratory setup evaluates the proposed PQ diagnosis method. In addition, the fuzzy system uses a new inference concept based on an extended n-dimensional overlap function.
1. Introduction
According to the World Bank, there are 1.06 billions of people without access to electricity in the world, and without improvements, this frame will remain the same in the near decade (World Bank, 2017). As a solution to this problem, the electricity access report published by the World Bank indicates the importance of the expansion of conventional national electrical grids, the increase of renewable energy sources (RES), and the microgrid insertions in the electrical power system.
Microgrids are small scale electrical grids composed of a diver-sification of generation systems, energy storage systems (ESSs), and electrical loads (Olivares et al.,2014). Generation systems can employ RES, such as photovoltaic (PV) plants, wind (WT) plants, biomass, and small hydroelectric plants (SHPs), or carbon-based sources like diesel or gas. A microgrid can operate in both grid-connected and stand-alone modes (Karimi et al.,2008). Currently, the main challenges lie in: control systems (Pulcherio et al.,2018), protection systems (Bukhari
✩ No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer tohttps://doi.org/10.1016/j.engappai.2019.05.016.
∗ Corresponding author at: Federal Institute of Bahia, Vitória da Conquista 45030-220, Brazil.
E-mail addresses: diegonolasco@ifba.edu.br(D.H.S. Nolasco),flaviocosta@ect.ufrn.br(F.B. Costa),espalmeira@uesc.br(E.S. Palmeira),
alvesk3@hotmail.com(D.K. Alves),bedregal@dimap.ufrn.br(B.R.C. Bedregal),thiago.rocha@ct.ufrn.br(T.O.A. Rocha),rlucio@ct.ufrn.br(R.L.A. Ribeiro), julianoleal86@gmail.com(J.C.L. Silva).
et al.,2018), power management strategies (Arcos-Aviles et al.,2018), stability (Li et al.,2018), and power quality (de Araujo Ribeiro et al., 2012).
The impacts due to the insertion of distributed generations (DGs) in power systems have challenged several areas because power quality problems have appeared (Ferraro et al., 2017; Liang, 2017). Based onLineweber and McNulty(2013), PQ problems cost billions of dollars to companies. In this fashion, it is necessary to invest in research to minimize these problems.
Two categories classify the power quality problems: transient dis-turbances, which are short-time non-occasional events, and steady-state disturbances, which are long-time waveform distortions in the current and/or voltage signals (Alves et al., 2017). In steady-state, the eval-uation of the single-phase systems employ the following PQ indices: total harmonic distortions (THD) of current and voltage, power factor (PF), and steady-state voltage variations (SSVV). PQ indices out of established standards can damage the power systems, especially in low-voltage level, such as failures in equipment and productive process
https://doi.org/10.1016/j.engappai.2019.05.016
Received 28 February 2019; Received in revised form 28 May 2019; Accepted 30 May 2019 Available online xxxx
interruptions.Montoya et al.(2016) presents a study about publications related to power quality between 1970–2013, and indicates that PQ publications have decreased since 2011 as well as investments in this area, which is on the contrary of the aforementioned needs.
The power quality diagnosis (PQD) in low-voltage electrical net-works usually is accomplished as follows: (1) PQ indices estimated in the voltage/current monitoring point; (2) comparison of PQ indices with levels defined in a specific standard or set of standards; (3) a decision to define the power quality condition in the power system (e.g., suitable or critical). However, there is no conventional method-ology which provides the total PQD and evaluates the influence of each PQ index in the total PQD. Another concern is the existence of several PQ standards (IEEE519,2014;IEC61000-3-6,2008;IEC61727, 2004;IEC61000-2-2,2002;EN50160,2010;AS/NZS61000-3-6,2012; GB/T14549, 1993; GB/T12325, 2008; NRS048-2, 2003; PRODIST, 2012; Preferred Voltage Levels for AC Systems, 2015; Aprueban la Norma,1997;ANEEL,2012). However, there is no consensus about the limits imposed by each standard for a specific PQ index be considered suitable. For example, depending on the selected standards the SSVV is considered suitable if it presents variation lower than ±5% (Preferred Voltage Levels for AC Systems, 2015), ±7.5% (Aprueban la Norma, 1997), ±10% (EN50160, 2010), −10/+7% (GB/T12325, 2008) or ±15% (NRS048-2,2003) from the nominal voltage reference, whereas the voltage THD is suitable if it presents distortion levels lower than 3% (IEEE519,2014), 5% (IEEE519,2014), 6.5% (AS/NZS61000-3-6, 2012), 8% (IEC61000-3-6,2008;EN50160,2010;NRS048-2,2003), or 10% (IEEE519,2014; PRODIST, 2012). A possible solution for these concerns can be obtained from the fuzzy logic since it is a technique that allows the development of an intelligent decision-making system based on the analysis of various worldwide PQ standards, includ-ing their uncertainties, as well as linclud-inguistic conditions (e.g., suitable, precarious, and critical).
The PQ indices must be estimated as the first step of a PQD as aforementioned, andMontoya et al.(2016) pointed out that the wavelet transform (WT) has been a method of signal processing to properly treat signals with PQ problems. The WT has been widely used to estimate PQ indices because it presents better performance, especially in the case of nonstationary waveforms, than the Fourier transform. For instance, Alves et al. (2017), Morsi and El-Hawary (2009) and Urbina-Salas et al.(2017) proposed methods for estimating PQ indices based on the WT and highlighted advantages. However, althoughAlves et al. (2017), Morsi and El-Hawary (2009) and Urbina-Salas et al. (2017) have demonstrated good results to estimate PQ indices, it is still necessary the human intervention for accomplishing the PQ diagnosis based on the estimated PQ indices and the analysis of PQ standards.
The linguistic subjectivities in the PQ diagnosis, as well as uncer-tainties due to difficulties to follow more than one PQ standards, are issues inherent to human reasoning which can be overcome adequately by a fuzzy system. Indeed, the fuzzy theory has been a technique widely used in the development of intelligent decision-making methods from subjectivities and uncertainties inherent to human reasoning ( Mahapa-tra et al.,2011). However, it is necessary an inference system capable of analyzing the nuances of the considered problem for the development of an accurate, and robust system. In this framework, Yager (2001) states that uninorms are good logical operators for building fuzzy infer-ence systems since they are generalizations of t-norms and t-conorms that can be used for defining fuzzy implications.
There are various trends of research in PQ (Kappagantu et al.,2015; Aqueveque et al.,2016;Meher and Pradhan,2010;Faisal et al.,2011; Wang et al., 2017; Nolasco et al., 2019). Kappagantu et al. (2015) andAqueveque et al.(2016) published two case studies of PQ analysis based on IEEE, EN50160 and IEC standards. However, neither ( Kap-pagantu et al., 2015) nor (Aqueveque et al., 2016) performed the PQD without human intervention. Conversely, the logic fuzzy has been used to overcome this drawback. For instance, Meher and Pradhan (2010) proposed a method based on fuzzy rule classification to iden-tify transient disturbances in voltages, whereas (Faisal et al., 2011)
proposed a method based on the WT and rules of fuzzy knowledge to classify transient disturbances. In addition, Wang et al. (2017) proposed a parameter standardization from voltage and frequency PQ indices computed through subjective and objective weights based on China standards. However, Meher and Pradhan(2010), Faisal et al. (2011) andWang et al.(2017) did not propose PQD methods able to analyze PQ problems in steady-state, and they did not propose methods that consider uncertainties existing in several PQ standards as well. Nevertheless,Nolasco et al.(2019) proposed a fuzzy-based method to accomplish the PQD of steady-state events and considered uncertainties existing in several PQ standards. However, it did not propose an adaptive fuzzy system able to perform the PQ diagnosis considering the power penetration level in the electrical system. Therefore, it could not be properly applied for microgrids with a high insertion of RES. Besides,Nolasco et al.(2019) proposed the fuzzy method to be used only in offline mode where a commercial device must collect and provide the PQ indices. Therefore, its dependence of an external device for estimating PQ indices is another drawback, which provides errors in the time spot when transient disturbances take place.
Based on the wavelet-packet transform (Alves et al.,2017), cascade-type hierarchical fuzzy system with additional defuzzification of lay-ers (Nolasco et al.,2019), and overlap functions (Gómez et al.,2016), this paper proposes a wavelet-fuzzy power quality diagnosis (WF-PQD) method to define an intelligent diagnosis system able to accomplish a complete PQD of an AC microgrid with different generation systems (PV, WT, SHP), an ESS, and different loads (linear and non-linear). The PQ indices are computed in the real-time through a wavelet-based system embedded in hardware considering a median statistical scheme in a sliding window, providing accurate steady-state PQ indices even if fast transient PQ disturbances take place. The membership functions of the fuzzy method were constructed from comparisons of uncertain-ties existing among several worldwide PQ standards (IEEE519,2014; IEC61000-3-6,2008;IEC61727,2004;IEC61000-2-2,2002;EN50160, 2010;AS/NZS61000-3-6,2012;GB/T14549,1993;GB/T12325,2008; NRS048-2, 2003; PRODIST, 2012; Preferred Voltage Levels for AC Systems, 2015; Aprueban la Norma, 1997). The proposed WF-PQD selects the best membership functions for the current THD based on the power penetration to attend the standards (IEEE519,2014; IEC61000-3-6, 2008; IEC61727, 2004). In this fashion, the proposed WF-PQD presents a sensitive and robust fuzzy system that was evaluated in an experimental microgrid, attesting its efficiency and capacity in practical applications. Also, as a theoretical contribution, it is presented a new fuzzy inference system based on extended overlap functions able to treat uncertainties existing among the different PQ standards in a simple, fast, and efficient form.
The paper is organized as follows: Section2presents the prelim-inary concepts of the Mamdani inference system. Section3presents the proposed inference method based on overlap functions. Section4 presents the proposed Wavelet-fuzzy PQ diagnosis method. Section5 presents the case studies implemented in the experimental AC micro-grid. Section6presents the performance evaluation of the proposed WF-PQD applied to an experimental microgrid. Section7presents the conclusions.
2. Mamdani fuzzy inference system modelling
Mamdani-type fuzzy inference system (FIS) is widely used for pro-cessing imprecise information in different issues (Perera et al.,2014; Chiu and Chang,2012;Sun et al.,2018;Rezaei,2018). However, most users do not bother adjusting the inference machine. Hence, they only make use of the classical Mamdani inference based on the max–min fuzzy relation which does not allow a fine tuning with the problem in question since only the maximum activation value is considered to rules.
Generally, a FIS design is split into three main parts:
(S1) Fuzzifier: where the crisp inputs 𝑥1, 𝑥2,… , 𝑥𝑛are converted into
fuzzy values 𝐴𝑖𝑗 (previously designed by an expert) with 𝑖 ∈
{1, 2, … , 𝑛} and 𝑗 ∈ {1, 2, … , 𝑘}. For each 𝑖 = 1, 2, … , 𝑛 sets
𝐴𝑖1,… , 𝐴𝑖𝑘are designed in order to interpret the fuzziness of each
input 𝑥𝑖;
(S2) Inference Machine: where the information obtained in the pro-cess (S1) is interpreted and aggregated to provide a unique fuzzy subset 𝑅 as a result of the inference. First, for each 𝑖 ∈ {1, 2, … , 𝑛} degree 𝐴𝑖𝑗(𝑥𝑖)is used to choose which rules in the base should be
activate:
𝑅𝑗∶ 𝐴1𝑗(𝑥1) ∧⋯ ∧ 𝐴𝑛𝑗(𝑥𝑛) ⇒ 𝐵𝑗(𝑦), (1) where 𝑗 = 1, 2, … , 𝑘. If the result of each rule on the base is denoted by:
𝑅𝑗(𝑥, 𝑦) = 𝐴1𝑗(𝑥1) ∧⋯ ∧ 𝐴𝑛𝑗(𝑥𝑛) ∧ 𝐵𝑗(𝑦), (2)
wherein, for each 𝑗 = 1, 2, … , 𝑘, 𝑥 = (𝑥1, 𝑥2,… , 𝑥𝑛)is the input and 𝑦is the output. The next step is to use an aggregation operator
𝐴𝑔𝑔to provide a final fuzzy result of the inference process, i.e.:
𝐴𝑔𝑔(𝑅1(𝑥, 𝑦), … , 𝑅𝑘(𝑥, 𝑦)) = 𝑎 ∈ [0, 1]. (3)
(S3) Defuzzifier: where the fuzzy subset output obtained in step (S2) is converted in a crisp value (output) (Leekwijck and Kerre, 1999).
From the theoretical point-of-view, some researchers tried to study which aggregation operators, and its properties, can suitably per-form an adjustment in the FIS considering characteristics of the prob-lem (Pham and Castellani,2002;Yager,2001;Duu et al.,2018;Ding et al.,2000;Wu and Mendel,2004;Aceves-Lopez and Aguilar-Martin, 2006).Pham and Castellani (2002) states that in a FIS the else con-nective must be an associative and commutative operator because the ordination of the set in the base of knowledge does not matter.
For aggregating information (input–output) in the FIS general mod-eling, the aggregation operator must satisfy the following proper-ties (Yager,2001):
(P1) Commutativity - the indexing of rules is not important;
(P2) Monotonicity - in order to provide a positive association between effective rule output and total system output;
(P3) Must contain an identity - since the non-relevant rules play no role in the process;
which are natural properties of uninorms.
The property (P3) is necessary when 𝑅1, 𝑅2,… , 𝑅𝑘are the
knowl-edge rules of the system, and if the rule R1 (without loss of generality) has relevance zero, it must not affect the whole aggregation process, i.e., in case R1 assigns the same value 𝑔 ∈ [0, 1] for all inputs, it should not be considered in the output of the system, mathematically described as follows:
𝐴𝑔𝑔(𝑔, 𝑅(𝑥, 𝑦)) = 𝐴𝑔𝑔(𝑅(𝑥, 𝑦)), (4)
where 𝑅(𝑥, 𝑦) = 𝑅2(𝑥, 𝑦), … , 𝑅𝑘(𝑥, 𝑦). However, it is not the case in
general when one considers Mamdani-type FIS since the selection of relevant rules is well-designed. But if all rules 𝐹𝑖(𝑖 = 1, 2, … , 𝑛) assign the same value 𝑥 for a given input 𝑦 then the aggregation operator must returns 𝑥, i.e.:
𝐴𝑔𝑔(𝑅1(𝑥, 𝑦), 𝑅2(𝑥, 𝑦), … , 𝑅𝑘(𝑥, 𝑦)) = 𝐴𝑔𝑔(𝑥, … , 𝑥) = 𝑥. (5)
Another desirable property is that the aggregation result of rules
𝐹𝑖(where 𝑖 = 1, 2, … , 𝑛) only returns the value 1 if there is a kind of consensus of that value, i.e., if all rules 𝐹𝑖have value 1, which can be
expressed as follows: 𝐴𝑔𝑔(𝑥1, 𝑥2,… , 𝑥𝑛) = 1 ⇔ 𝑛 ∏ 𝑖=1 𝑥𝑖= 1. (6)
Similarly, aggregation function should assign to zero only the n-uplas having at least one of its coordinates zero, i.e.:
𝐴𝑔𝑔(𝑥1, 𝑥2,… , 𝑥𝑛) = 0 ⇔ 𝑛
∏
𝑖=1
𝑥𝑖= 0, (7)
which means that none of the rules that are irrelevant to a given system entry should influence the final processing result.
Stability and robustness must also be considered because they are factors linked to the continuity of the aggregation operator so that for the small domain, the return value must have small variations of the range (Reiser and Bedregal,2014).
3. The proposed FIS based on overlap functions
According to the discussion above, the n-dimensional overlap func-tions are natural candidates to be used as aggregation operators in the FIS because they satisfy all properties described as follows:
Definition 1. A function 𝑂𝑛∶ [0, 1]𝑛→[0, 1]is called an n-dimensional
overlap function if and only if (Gómez et al.,2016): (O1) 𝑂𝑛is symmetric;
(O2) 𝑂𝑛(𝑥1, 𝑥2,… , 𝑥𝑛) = 0if and only if∏𝑛𝑖=1𝑥𝑖= 0;
(O3) 𝑂𝑛(𝑥1, 𝑥2,… , 𝑥𝑛) = 1if and only if 𝑥𝑖= 1for all 𝑖 = 1, 2, … , 𝑛;
(O4) 𝑂𝑛is increasing; (O5) 𝑂𝑛is continuous.
Example 3.1. Based on Gómez et al. (2016), the 2-dimensional overlap function 𝑂𝑝 𝐷𝐵∶ [0, 1] 2→[0, 1]is obtained as follows: 𝑂𝑝 𝐷𝐵(𝑥, 𝑦) = ⎧ ⎪ ⎨ ⎪ ⎩ ( 2𝑥𝑝𝑦𝑝 𝑥𝑝+ 𝑦𝑝 )1 𝑝 , 𝑖𝑓 𝑥𝑝+ 𝑦𝑝≠ 0 0, 𝑖𝑓 𝑥𝑝+ 𝑦𝑝= 0, (8)
where 𝑂𝐷𝐵𝑝 is an idempotent1overlap function.
The dual operator of n-dimensional overlap is given in the following definition.
Definition 2. A function 𝐺𝑛∶ [0, 1]𝑛→[0, 1]is called an n-dimensional
grouping function if and only if (Gómez et al.,2016): (G1) 𝐺𝑛is symmetric;
(G2) 𝐺𝑛(𝑥1, 𝑥2,… , 𝑥𝑛) = 0if and only if 𝑥𝑖= 0for all 𝑖 = 1, 2, … , 𝑛;
(G3) 𝐺𝑛(𝑥1, 𝑥2,… , 𝑥𝑛) = 1if and only if there exists 𝑖 ∈ {1, 2, … , 𝑛} such
that 𝑥𝑖= 1;
(G4) 𝐺𝑛is non-decreasing;
(G5) 𝐺𝑛is continuous.
Example 3.2. Function 𝐺𝐷𝐵𝑝 ∶ [0, 1]2→[0, 1]given by:
𝐺𝑝 𝐷𝐵(𝑥, 𝑦) = ⎧ ⎪ ⎨ ⎪ ⎩ 1 − (2(1 − 𝑥)𝑝(1 − 𝑦)𝑝 (1 − 𝑥)𝑝+ (1 − 𝑦)𝑝 )1 𝑝 , 𝑖𝑓 𝑛𝑜𝑡𝑒1 1, 𝑖𝑓 𝑛𝑜𝑡𝑒2, (9)
𝑛𝑜𝑡𝑒1∶ 𝑥≠ 1 ∧ 𝑦 ≠ 1, 𝑛𝑜𝑡𝑒2∶ 𝑥 = 𝑦 = 1. Is a 𝑁-dual grouping function of overlap 𝑂𝑝𝐷𝐵where 𝑁 is the fuzzy negation2defined by 𝑁(𝑥) = 1 − 𝑥 for all 𝑥 ∈ [0, 1].
An interesting way to define a multi-dimensional overlap (grouping) function is given below.
1 A function 𝐻 ∶ [0, 1]𝑛
→[0, 1]satisfies the idempotency property if and only if 𝐻(𝑥, … , 𝑥) = 𝑥 for all 𝑥 ∈ [0, 1].
2 A function 𝑁 ∶ [0, 1] → [0, 1] is a fuzzy negation if it satisfies: (1) 𝑁(0) = 1
Fig. 1. Block diagram of the proposed WF-PQD method.
Definition 3. A function 𝐹 ∶ ⋃𝑘∈N∗[0, 1]𝑘 → [0, 1] is called an
extended overlap (grouping) function if and only if for each given
𝑘∈ N∗restriction of 𝐹 to [0, 1]𝑘is a n-dimensional overlap (grouping)
function, i.e., 𝐹|
[0,1]𝑘 = 𝑂𝑘(𝐹|[0,1]𝑘 = 𝐺𝑘) for each 𝑘 ∈ N
∗. By convention
𝐹(𝑥) = 𝑥for every 𝑥 ∈ [0, 1].
According to theDefinition 3, a dynamic operator that can aggre-gate a different number of inputs is formulated. In this fashion, the fuzzy system has an adaptive way to handle the number of entries at different stages of processing.
Example 3.3. Given 𝐹 ∶ [0, 1]2→[0, 1]. The function ̃𝐹 ∶⋃
𝑛∈N∗[0, 1]𝑛
→[0, 1]is defined as follows:
̃
𝐹(𝑥1,… , 𝑥𝑛) = 𝐹 (𝑥(1), 𝐹(𝑥(2),… ., 𝐹 (𝑥(𝑛−1), 𝑥(𝑛)))), (10) where (𝑥(1),… , 𝑥(𝑛)) is the increasing permutation of (𝑥1,… , 𝑥𝑛) ∈
[0, 1]𝑛.
If 𝐹 is a 2-dimensional overlap (grouping), then ̃𝐹 is an extended overlap (grouping). Therefore, given Example 3.1, 𝑂𝑝̃
𝐷𝐵 ≠ 𝐸𝑂 𝑝 𝐷𝐵
whereas𝑂̃𝑝
𝐷𝐵(𝑥1,… , 𝑥𝑛) = 𝐸𝑂𝑝𝐷𝐵(𝑥(1),… , 𝑥(𝑛)).Hence, the proposed FIS based on the extended overlap function and 𝑁-dual extended grouping function is given as follows.
Definition 4. Given a FIS as described in (S1), (S2) and (S3) for inputs
⃗
𝑥= (𝑥1,… , 𝑥𝑛)and output 𝑦, the relation:
𝜇𝐺𝑂(⃗𝑥, 𝑦) = 𝐺(𝑅1(⃗𝑥, 𝑦), … , 𝑅𝑘(⃗𝑥, 𝑦)), (11)
is a Mamdani-type inference machine, where 𝑅𝑗(⃗𝑥, 𝑦) = 𝑂(𝐴1𝑗(𝑥1), … ,
𝐴𝑛𝑗(𝑥𝑛), 𝐵𝑗(𝑦))for each 𝑗 = 1, 2, … , 𝑘, 𝑂 is an extended overlap function and 𝐺 is its 𝑁-dual extended grouping function both satisfying the idempotency property.
4. The proposed wavelet-fuzzy power quality diagnosis system
Fig. 1depicts the proposed WF-PQD system. Firstly, the voltages (𝑣𝐴) and currents (𝑖𝐴) are measured with sensors in the point common coupling (PCC) of the grid, and the stationary wavelet packet transform (SWPT) accomplishes the digital processing of these electrical signals for estimating the desired power quality indices. Then, the median values of these indices are provided to the cascade-type HFS with FIS based on a new extended overlap function for performing the power quality diagnosis. Further details of the proposed system are discussed as follows.
4.1. The proposed wavelet packet-based PQ index estimation method
According to Alves et al. (2017), the SWPT coefficients at the decomposition level 𝑗 is computed as follows:
𝑠2𝑧𝑗 (𝑘) =√1 2 𝐿∑−1 𝑙=0 ℎ𝜑(𝑙)𝑠𝑧𝑗−1(𝑘 + 𝑙 − 𝐿 + 1), (12) 𝑠2𝑧+1 𝑗 (𝑘) = 1 √ 2 𝐿∑−1 𝑙=0 ℎ𝜓(𝑙)𝑠𝑧 𝑗−1(𝑘 + 𝑙 − 𝐿 + 1), (13) where 𝑠0
0 = 𝑥 is the input signal; 𝑧 is the node number; 𝑠
𝑧 𝑗 are
decomposition packet coefficients at scale 𝑗; 𝐿 is the length of the wavelet filter; 𝑘 is the current sampling; ℎ𝜑 and ℎ𝜓 are low- and
high-pass filters, respectively.
The root mean square (RMS) voltage is given byAlves et al.(2017):
𝑉(𝑘) = √ √ √ √(𝑉0 𝑗(𝑘))2+ 2𝑗−1 ∑ 𝑧=1 (𝑉𝑧 𝑗(𝑘))2, (14) where 𝑉𝑗0(𝑘) = √ √ √ √ 1 2𝑁 𝑘 ∑ 𝑛=𝑘−𝑁+1 𝐿−1 ∑ 𝑙=0 [ 𝑠0𝑗,𝑣(𝑘 − 𝑙)] 2 , (15) 𝑉𝑗𝑧(𝑘) = √ √ √ √ 1 2𝑁 𝑘 ∑ 𝑛=𝑘−𝑁+1 𝐿−1 ∑ 𝑙=0 [ 𝑠𝑧 𝑗,𝑣(𝑘 − 𝑙) ]2 . (16)
Similarly, the RMS current is computed in the same way by
𝐼(𝑘) = √ √ √ √(𝐼0 𝑗(𝑘))2+ 2𝑗−1 ∑ 𝑧=1 (𝐼𝑧 𝑗(𝑘))2, (17)
where 𝑉𝑗0and 𝐼𝑗0are RMS voltages and currents of the lowest frequency band at the node zero and level 𝑗, whereas 𝑉𝑧
𝑗 and 𝐼𝑗𝑧are RMS voltages
and currents at the node 𝑧≠ 0.
The voltage total harmonic distortion (𝑇 𝐻𝐷𝑉) and current total harmonic distortion (𝑇 𝐻𝐷𝐼) using the SWPT-based method are defined
as follows: 𝑇 𝐻 𝐷𝑉(𝑘) = √ √ √ √2∑𝑗−1 𝑧=1 (𝑉𝑗𝑧(𝑘))2 𝑉0 𝑗(𝑘) , (18) 𝑇 𝐻 𝐷𝐼(𝑘) = √ √ √ √2∑𝑗−1 𝑧=1 (𝐼𝑗𝑧(𝑘))2 𝐼𝑗0(𝑘) . (19)
The active power 𝑃 can be computed as follows (Alves et al.,2017):
𝑃(𝑘) = 𝑃𝑗0(𝑘) + 2𝑗−1 ∑ 𝑧=1 𝑃𝑗𝑧(𝑘), (20) where, 𝑃𝑗0(𝑘) = 1 2𝑁 𝑘 ∑ 𝑛=𝑘−𝑁+1 [𝐿∑−1 𝑙=0 𝑠0𝑗,𝑖,(𝑘 − 𝑙)𝑠0𝑗,𝑣(𝑘 − 𝑙) ] , (21) 𝑃𝑗𝑧(𝑘) = 1 2𝑁 𝑘 ∑ 𝑛=𝑘−𝑁+1 [𝐿∑−1 𝑙=0 𝑠𝑧𝑗,𝑖(𝑘 − 𝑙)𝑠𝑧 𝑗,𝑣(𝑘 − 𝑙) ] , (22)
where 𝑃𝑗0is the active power of the lowest frequency band at node zero and level 𝑗, and 𝑃𝑧
𝑗 are the set of power of the higher frequency band
at the node 𝑧≠ 0.
The apparent power (𝑆) and power factor (𝑃 𝐹 ) are given by:
𝑆(𝑘) = 𝑉 (𝑘)𝐼(𝑘), (23)
𝑃 𝐹(𝑘) =𝑃(𝑘)
𝑆(𝑘). (24)
The RMS voltages and currents as well as the PQ indices (𝑉𝑟𝑚𝑠, 𝐼𝑟𝑚𝑠, 𝑇 𝐻𝐷𝑉, 𝑇 𝐻𝐷𝐼, and 𝑃 𝐹 ) are respectively computed through of
the Eqs.(14),(17),(18),(19), and(24)in accordance withAlves et al. (2017). However,Alves et al.(2017) did not provide a PQ diagnosis as proposed in this paper. Therefore, additional improvements were accomplished in this paper in order to make feasible the stationary PQ diagnosis as follows:
Fig. 2. Cascade-type hierarchical fuzzy PQD method.
1. the RMS voltages and currents as well as the PQ indices (𝑉𝑟𝑚𝑠,
𝐼𝑟𝑚𝑠, 𝑇 𝐻𝐷𝑉, 𝑇 𝐻𝐷𝐼, and 𝑃 𝐹 ) are computed with a sampling frequency in the order of few kHz to be sensible to transient PQ disturbances;
2. the proposed method computes the medians of PQ indices ( ̃𝐼𝑟𝑚𝑠,
̃
𝑉𝑠𝑠,𝑇 𝐻 𝐷̃ 𝑉,𝑇 𝐻 𝐷̃ 𝐼, and ̃𝑃 𝐹) in time intervals in the order of few cycles of the fundamental frequency. In this way, the stationary PQ analysis is scarcely affected by fast transient PQ events which take place in the power system frequently.
4.2. The proposed fuzzy system-based method for PQD
Based on Nolasco et al.(2019),Fig. 2depicts the proposed PQD method which is based on the cascade-type hierarchical fuzzy system with additional defuzzification of layers. The analysis of PQ standards is defined following linguistic terms modeled as: suitable (S), precarious (P), critical (C), and extremely critical (EC) in accordance with No-lasco et al. (2019). Three layers divide the hierarchical system with one sequential fuzzy subsystem (SFS𝑞) in each layer where 𝑞 is a
se-quence number. The subsystems comprise the fuzzification system (FS), decision-making system (DMS), fuzzy aggregation (FA), and defuzzifi-cation system (DS). The decision-making systems are composed of the knowledge bases according toNolasco et al.(2019), and the overlap function-based inference method proposed in this paper (Section3). The proposed FIS of the fuzzy PQ diagnosis method employs the Mam-dani inference model. However, it is used the aggregations of extended overlap ( ̃𝑂𝑝
𝐷𝐵) given by Eq.(8)and N-dual extended grouping ( ̃𝐺 𝑝 𝐷𝐵)
given by Eq.(9)considering the factor 𝑝 = 2. The used defuzzification method is the center of gravity (Leekwijck and Kerre,1999).
In the first layer, the diagnosis is accomplished from THD median values of voltages and currents (𝑇 𝐻 𝐷̃ 𝑉, and 𝑇 𝐻 𝐷̃ 𝐼 in Fig. 2). The knowledge base has 20 rules of linguistic diagnosis, and after of the decision-making process, the aggregated fuzzy information (𝐴𝑔𝑔) is
provided to both the defuzzification system and the second layer. The 𝐴𝑔𝑔 defuzzified in the DS provides the diagnosis of the quality
index THD (𝐼𝑄𝑇 𝐻 𝐷), whereas the 𝐴𝑔𝑔transferred to the SFS2provides information to compose the next diagnosis.
In contrast toNolasco et al.(2019), the𝑇 𝐻 𝐷̃ 𝐼 membership func-tions (MFs) are adaptive and change with the power penetration level in the PCC in this paper. Therefore, the proposed diagnosis method becomes more robust to iterant changes occasioned by the connec-tion of different RES in microgrids. Fig. 3presents the flowchart of the algorithm that adapts for four different MFs considering various penetration levels to meet the standards (IEEE519,2014; IEC61000-3-6,2008;IEC61727,2004). The power penetration level in the PCC is defined through the ratio of the calculated short-circuit current (𝐼𝑐𝑐)
and the median load current ( ̃𝐼𝐿) measured in the PCC, i.e., 𝐼𝑐𝑐∕ ̃𝐼𝐿,
whereas, the short-circuit current is obtained from the ratio of the grid rated voltage (𝑉𝑛𝑜𝑚) and grid impedance (𝑍𝑛), i.e., 𝐼𝑐𝑐= 𝑉𝑛𝑜𝑚∕𝑍𝑛.
Fig. 3. Fluxogram of the adaptive 𝑇 𝐻 𝐷̃ 𝐼 membership function based on power penetration.
Fig. 4. Membership functions: (a) THD of voltage; (b)–(e) Adaptive current THD with power penetration levels; (f) Power factor; (g) Steady-state voltage; (h) PQ diagnosis.
According toFig. 3, the𝑇 𝐻 𝐷̃ 𝐼is associated to one of four MF types in accordance with the power penetration level, where thresholds 20, 50, 100, and 1000 were selected because the standards (IEEE519,2014; IEC61000-3-6, 2008; IEC61727, 2004) refer to these thresholds to determinate the relation between the allowed reference for current THD level with the power penetration in an electrical system. The𝑇 𝐻 𝐷̃ 𝐼
adaptive algorithm can be used in power systems with or without RES integration.
In the second layer inFig. 2, a new diagnosis is accomplished from the estimated median power factor𝑃 𝐹̃ . The FSF2 has two decision-making processes, the first one (DMS = 1) has a knowledge base with 16 linguistic rules and provides the power factor contribution to the total PQD which is transferred to next layer from the 𝐴1
𝑔𝑔. The second one
power factor index (𝐼𝑄𝑃 𝐹) which is obtained from the defuzzification of the fuzzy information aggregated 𝐴2
𝑔𝑔.
In the third layer, a new diagnosis is accomplished from the es-timated median steady-steady voltage ( ̃𝑉𝑠𝑠). The FSF3 also has two decision-making processes, the first process (DMS = 1) has knowledge base with 16 linguistic rules and provides the contribution of the SSVV in total PQ diagnosis (𝑃 𝑄𝐷), which is obtained from of the defuzzification of the 𝐴1
𝑔𝑔in the HFS exit. The second decision-making
(DMS = 2) has additional 16 linguistic rules to provide the diagnosis of the quality index ̃𝑉𝑠𝑠(𝐼𝑄𝑉𝑠𝑠) obtained with the defuzzification of the fuzzy information aggregated 𝐴2
𝑔𝑔.
Fig. 4depicts the membership functions 𝑇 𝐻 𝐷̃ 𝑉, 𝑇 𝐻 𝐷̃ 𝐼, 𝑃 𝐹̃ , ̃𝑉𝑠𝑠
constructed from the comparative analysis of worldwide PQ standards (IEEE519, 2014; IEC61000-3-6, 2008; IEC61727, 2004; IEC61000-2-2,2002;EN50160,2010;AS/NZS61000-3-6,2012;GB/T14549,1993; GB/T12325,2008;NRS048-2,2003;PRODIST,2012;Preferred Voltage Levels for AC Systems,2015;Aprueban la Norma,1997;ANEEL,2012) as follows:
•𝑇 𝐻 𝐷̃
𝑉 in Fig. 4a: the voltage THD is suitable if it presents
distortion levels lower than 3% (IEEE519,2014), 5% (IEEE519, 2014), 6.5% (AS/NZS61000-3-6,2012), 8% (IEC61000-3-6,2008; EN50160, 2010; NRS048-2, 2003), or 10% (IEEE519,2014;PRODIST,2012).
•𝑇 𝐻 𝐷̃
𝐼 inFig. 4b–e: the current THD has different suitable,
pre-carious and critical functions in accordance with the power pen-etration level to attend the standards (IEEE519,2014; IEC61000-3-6,2008;IEC61727,2004). However, the extremely critical MF is not modified since it models the diagnosis to a high distortion level that must be considered as extremely critical independently of the power penetration. In addition, one of the membership functions in Fig. 4b–e is selected from the adaptive algorithm described inFig. 3.
• ̃𝑃 𝐹 in Fig. 4f: power factor limits applied in some countries: Venezuela (0.90); Chile (0.93); Colombia (0.90); Uruguay (0.92); Argentina (0.85); Spain (0.95, 0.90, 0.80); Ecuador (0.92); Brazil (0.92); United States (0.928); France (0.928) (ANEEL,2012). • ̃𝑉𝑠𝑠inFig. 4g: the SSVV is considered suitable if it presents
varia-tion lower than ±5% (Preferred Voltage Levels for AC Systems, 2015), ±7.5% (Aprueban la Norma, 1997), ±10% (EN50160, 2010), −10/+7% (GB/T12325,2008) or ±15% (NRS048-2,2003) from the nominal voltage (which is 127 V in the used experimen-tal microgrid).
The membership functions shown Fig. 4were modeled as triangular and quadrangular fuzzy sets due to their simplicity.
The diagnosis defuzzification (Fig. 4h) is according toNolasco et al. (2019) in a way that the MF of the defuzzification shown inFig. 4h con-templates both the total PQ diagnosis and indices of the PQ diagnosis (outputs 𝑃 𝑄𝐷 and 𝐼𝑄).
5. Case studies in an experimental AC microgrid
Fig. 5 depicts the laboratory setup of a three-phase AC microgrid composed by three distributed generation systems (PV of 8 kW, SHP of 5 kVA, WT of 1.67 kW), and an ESS of 3 kW (Ribeiro et al.,2015; Nunes et al.,2017). The PCC employed in the laboratory setup has the rated phase voltage of 127 V with the internal impedance comprised of
𝑟𝑔 = 0.4 Ω and 𝑙𝑔= 400 μH, respectively.
The evaluation of the proposed wavelet-fuzzy system considers the stationary PQ disturbances produced from linear (L) and nonlinear (NL) loads connected in the PCC. The controlled switch K2 interconnects the linear load composed by a three-phase RL load (𝑟𝑙 = 20 Ω and
𝑙𝑙= 60mH), and the switch K3 interlinks a nonlinear load comprised by a three-phase rectifier feeding an RL load (𝑟𝑛𝑙 = 30 Ω and 𝑙𝑛𝑙=
30 mH). The laboratory setup also has a fault (short-circuit) emulator
Fig. 5. Experimental microgrid.
Table 1
Case studies evaluated in this work for the experimental microgrid.
Microgrid topology Loads Fault sim. Case study
L NL L+NL √ – – – Grid – √ – – 1 – – √ – √ – – √ SHP + Grid – √ – – 2 – – √ √ √ – – – PV + Grid – √ – – 3 – – √ √ √ – – √ SHP + PV + Grid – √ – √ 4 – – √ – √ – – – PV + WT + ESS + Grid – √ – – 5 – – √ √ √ – – –
All sources + Grid – √ – √ 6
– – √ √
L: Linear load; NL: Non-linear load; Sim.: Simulation. SHP: Small hydropower plant; PV: Photovoltaic power plant. WT: wind plant; ESS: Energy storage system.
implemented by controlled switch K1 that interconnects the three-phase resistive load (𝑟𝑓 = 5 Ω) in parallel to the interlinked linear
and/or nonlinear loads at the PCC. The wavelet-based PQ estimation was embedded in the fast prototyping system dSPACE 1104 in order to provide the real-time measurement of PQ indices.
Table 1presents six case studies evaluated in this paper: (1) mi-crogrid without DG, (2) only the SHP interconnected, (3) only PV interconnected (4) SHP and PV interconnected, (5) the WT, ESS, and PV interconnected, and (6) all DGs and ESS interconnected. All case studies consider three different types of load connection: (i) linear load, (ii) non-linear, and (iii) both linear and non-linear, termed here as L, NL, and L+NL, respectively. Besides, the experiments also employ fault emulation in case studies 2, 3, 4, 5, and 6. The combination of these different experimental system configurations comprises a wide variety of complex operational scenarios, which lie in relevant data for PQ evaluation in microgrids.
Table 2
Individual analysis of the estimated PQ indices.
Case study PQ indices Information obtained to connected loads
L L+NL NL
𝐼𝐿 Low High Low
𝑉𝑠𝑠 Ideal Ideal Ideal
1 𝑃 𝐹 Low Ideal Ideal
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Ideal Ideal Ideal
𝐼𝐿 Low High Low
𝑉𝑠𝑠 Ideal Ideal Ideal
2 𝑃 𝐹 Ideal Ideal Low
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Ideal Ideal Ideal
𝐼𝐿 Low Slightly high Slightly high
𝑉𝑠𝑠 High Ideal high
3 𝑃 𝐹 Ideal Ideal Ideal
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Slightly high Slightly high Slightly high
𝐼𝐿 Slightly high Low Low
𝑉𝑠𝑠 High Ideal high
4 𝑃 𝐹 Ideal Low Ideal
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Slightly high Slightly high Slightly high
𝐼𝐿 High Slightly high Low
𝑉𝑠𝑠 Slightly high Slightly high Ideal
5 𝑃 𝐹 Ideal Ideal very Low
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Slightly high Slightly high Slightly high
𝐼𝐿 High Slightly high Slightly high
𝑉𝑠𝑠 High High Ideal
6 𝑃 𝐹 Ideal Ideal Ideal
𝑇 𝐻 𝐷𝐼 – – –
𝑇 𝐻 𝐷𝑉 Slightly high Slightly high Slightly high
For all the case studies inTable 1, PQ indices (𝐼𝐿, 𝑉𝑠𝑠, 𝑃 𝐹 , 𝑇 𝐻𝐷𝐼,
and 𝑇 𝐻𝐷𝑉) were estimated in the real-time through phase-A voltage
and current measurements in the PCC. For instance,Fig. 6depicts the PQ indices calculated in the case study 2. The PQ indices were ob-tained in five-minutes intervals with a sampling frequency of 1920 Hz (576.000 samples in five minutes for each index), and in each every 10 s median values (𝑇 𝐻 𝐷̃
𝑉,𝑇 𝐻 𝐷̃ 𝐼, ̃𝑉𝑠𝑠, and𝑃 𝐹̃ ) are provided to be
evaluated by the fuzzy-diagnosis method, i.e., during this five-minute interval, the fuzzy system evaluates 30 samples of each PQ index. Information such as that shown in Fig. 6was also obtained for each microgrid topology inTable 1.
5.1. Conventional analysis of the power quality
Considering a simple visual inspection of Fig. 6, i.e., a non-fuzzy diagnosis, and following just one PQ standard a subjective PQ analysis is possible per individual PQ index. For instance, following just the PQ standard (PRODIST, 2012), the ideal PQ index values are: 116 V ≤ 𝑉𝑠𝑠 ≤ 133 V, 𝑃 𝐹 ≤ 0.92, and 𝑇 𝐻𝐷𝑉 ≤ 10%. Since 𝑇 𝐻𝐷𝐼 is
not mentioned in PRODIST (2012), no PQ diagnosis was issued for this index. As highlighted inFig. 6, there were faults when the linear and non linear were connected. These faults are fast events and its effects disregarded since the diagnosis to be provided is for stationary PQ events. Therefore, following these reference values the individual analysis of the PQ indices shown inFig. 6(case study 2) would be as summarized inTable 2, where a specialist quantifies if a specific PQ index is ideal (within normal limits), low/high, slight low/high, very low/high, etc., which is very subjective.Table 2also summarizes the individual analysis for the other case studies which were not plotted as inFig. 6for the sake of space limitation.
The following drawbacks are highlighted by considering a simple visual inspection of PQ indices in accordance with just one PQ standard:
Fig. 6. Quality indices signals obtained to SPH considering the case study 2.
• The subjectivity is high, and the individual diagnosis as presented in Table 2 can change according to the interpretation of the analyzer. For instance, slightly high can be interpreted as high by another specialist.
• Just an individual PQ diagnosis is possible, i.e., a total PQD considering the combination of several PQ indices is not indicated in PQ standards. Therefore, besides the subjectivity, it is difficult to state if the total PQ in the scenarios 2 with load NL is good or not for instance, since two indices are low (𝑃 𝐹 and 𝑇 𝐻𝐷𝐼 not specified).
• It is necessary to follow just one PQ standard. In this case, the index 𝑇 𝐻𝐷𝐼 could not be assessed. If another PQ standard is
select, the content ofTable 2will change.
However, all these drawbacks can be overcome through the proposed fuzzy system as addressed in the remainder of this paper.
6. Performance evaluation
The performance assessment of the proposed wavelet-fuzzy ap-proach was accomplished considering all case studies inTable 1. As expected, via the examination of several PQ standards (IEEE519,2014; IEC61000-3-6,2008;IEC61727,2004;IEC61000-2-2,2002;EN50160, 2010;AS/NZS61000-3-6,2012;GB/T14549,1993;GB/T12325,2008; NRS048-2, 2003; PRODIST, 2012; Preferred Voltage Levels for AC Systems,2015;Aprueban la Norma,1997), the proposed method could issue a total PQD, indicating the PQ as extremely critical, critical, precarious, and suitable. Besides, a PQ diagnosis for an individual PQ index such as power factor was also issued as addressed as follows.
Fig. 7. PQD in the case study 1.
6.1. Microgrid topology: Grid
Fig. 7depicts the fuzzy diagnoses considering the PQ indices in the conventional grid without distributed generation (case study 1), i.e., the PCC interconnects just the loads, summarized follows as:
• Linear load: the total PQ diagnosis was critical mainly because the diagnosis of the power factor index 𝐼𝑄𝑃 𝐹 was critical (low 𝑃 𝐹 ),
even with proper diagnoses of total harmonic distortions 𝐼𝑄𝑇 𝐻 𝐷 and steady-state voltage 𝐼𝑄𝑉𝑠𝑠.
• Linear + non-linear loads: the 𝑃 𝑄𝐷 was precarious, indicating a small improvement in the power quality compared to the linear load case. The 𝐼𝑄𝑃 𝐹 improved from critical to suitable
(improve-ment of 𝑃 𝐹 ); however, the 𝐼𝑄𝑇 𝐻 𝐷 changed from suitable to
precarious (due to the increase of the 𝑇 𝐻𝐷𝐼). 𝐼𝑄𝑉
𝑠𝑠 did not change.
• Non-linear load: the 𝑃 𝑄𝐷 was critical; however, the quantita-tive value was the worst. The 𝐼𝑄𝑃 𝐹 and 𝐼𝑄𝑉𝑠𝑠 stayed suitable; however, the diagnosis to the 𝐼𝑄𝑇 𝐻 𝐷 was the worst due to the significant increase of 𝑇 𝐻𝐷𝐼.
6.2. Microgrid topology: SHP + Grid
Fig. 8depicts the fuzzy diagnoses considering the PQ indices in the conventional grid with distributed generation (case study 2 -Fig. 6) in which the PCC interlinks the SHP and loads, summarized follows as:
• Linear load: the total PQ diagnosis was suitable because diagnoses of all quality indices were suitable. As aforementioned, this case presents a short-duration fault, which can confuse the stationary PQ diagnosis. Since this fault is a transient event, it must be disregarded. In fact, as expected the fault did not affect the obtained diagnosis since the computed median values are not affected by fast transient disturbances.
• Linear + non-linear load: adding the non-linear load the 𝑃 𝑄𝐷 was precarious, indicating a deterioration in power quality. The 𝐼𝑄𝑃 𝐹 and 𝐼𝑄𝑉𝑠𝑠stayed suitable, whereas the 𝐼𝑄𝑇 𝐻 𝐷was precarious.
Fig. 8. PQD obtained to SPH considering the case study 2.
• Non-linear load: the 𝑃 𝑄𝐷 was critical because the 𝐼𝑄𝑇 𝐻 𝐷 was
critical and the 𝐼𝑄𝑃 𝐹 was precarious. The 𝐼𝑄𝑉𝑠𝑠was suitable due to the improvement of the voltage level. Again, the fault did not affect the obtained diagnosis.
6.3. Microgrid topology: PV + Grid
Regarding the interconnection of grid with the photovoltaic power plant and loads in the PCC (case study 3), the total PQ diagnosis was critical to all loads because the 𝐼𝑄𝑇 𝐻 𝐷 also was critical to all loads; the 𝐼𝑄𝑃 𝐹 was suitable to all loads; the 𝐼𝑄𝑉
𝑠𝑠was precarious to linear and non-linear loads and suitable to linear + non-linear loads.
6.4. Microgrid topology: SHP + PV + Grid
Regarding the interconnection of the grid with the small hydroelec-tric plant, the photovoltaic power plant, and loads in the PCC (case study 4), the total PQ diagnosis was critical to the linear load and extremely critical to non-linear loads. The diagnoses were: (1) 𝐼𝑄𝑇 𝐻 𝐷
critical, 𝐼𝑄𝑃 𝐹suitable, and 𝐼𝑄𝑉𝑠𝑠precarious to linear load; (2) 𝐼𝑄𝑇 𝐻 𝐷 extremely critical, 𝐼𝑄𝑃 𝐹critical, and 𝐼𝑄𝑉𝑠𝑠suitable to the linear + non-linear; and (3) 𝐼𝑄𝑇 𝐻 𝐷extremely critical, 𝐼𝑄𝑃 𝐹 precarious, and 𝐼𝑄𝑉𝑠𝑠 between suitable and precarious to the non-linear load.
6.5. Microgrid topology: PV + WT + ESS + Grid
Fig. 9depicts the fuzzy diagnoses considering the PQ indices in the conventional grid connected with the photovoltaic power plant, wind turbine, energy storage source, and the loads in the PCC (case study 5). In the case where the linear + non-linear loads were connected, a significant external disturbance of approximately 2 min occurred in the begin of the measurement of PQ indices. After this event, the electrical system came back to the normal behavior. The diagnosis is summarized follows as:
Fig. 9. PQD obtained to PV, WT and ESS considering the case study 5.
• Linear load: the 𝑃 𝑄𝐷 was precarious decaying to critical at the end of measurements mainly because 𝐼𝑄𝑇 𝐻 𝐷 and 𝐼𝑄𝑉
𝑠𝑠 were
between suitable and precarious, whereas 𝐼𝑄𝑃 𝐹 was always
suit-able.
• Linear + non-linear load: 𝑃 𝑄𝐷 was extremely critical because the
𝐼 𝑄𝑇 𝐻 𝐷was extremely critical due to the high level of distortion in the current; the 𝐼𝑄𝑃 𝐹 was highly affected by the external
dis-turbance, changing from suitable to extremely critical diagnosis during the disturbance; the 𝐼𝑄𝑉𝑠𝑠oscillated between suitable and precarious.
• Non-linear load: the 𝑃 𝑄𝐷 was extremely critical because both the
𝐼 𝑄𝑇 𝐻 𝐷 (high level of distortion of current) and 𝐼𝑄𝑃 𝐹 (low PF) were extremely critical, even if a suitable 𝐼𝑄𝑉
𝑠𝑠.
6.6. Microgrid topology: SHP + PV + WT + ESS + Grid
Regarding the interconnection of the grid with all DGs and the loads (case study 6), the 𝑃 𝑄𝐷 diagnosis was between critical and extremely critical to the load NL and precarious to the loads L and L+NL. The diagnoses of the quality indices were: (1) 𝐼𝑄𝑇 𝐻 𝐷suitable, 𝐼 𝑄𝑃 𝐹suitable, and 𝐼𝑄𝑉
𝑠𝑠between suitable and precarious to the loads L; (2) 𝐼𝑄𝑇 𝐻 𝐷precarious, 𝐼𝑄𝑃 𝐹 suitable, and 𝐼𝑄𝑉
𝑠𝑠 between suitable and precarious to the loads L and L+NL; (3) 𝐼𝑄𝑇 𝐻 𝐷 between critical
and extremely critical, 𝐼𝑄𝑃 𝐹 between critical and extremely critical,
and 𝐼𝑄𝑉
𝑠𝑠suitable to the load NL.
6.7. Evaluation of the PQ impacts of the microgrid
Power quality mitigation in a microgrid is a challenge because of the different RES and non-linear loads with power electronics interfaces, which usually degrade the power quality. The power quality can be verified through various PQ indices, and there are several PQ standards to follow as aforementioned, which difficult the achievement of a total PQD. However, the proposed method could identify the impact in the power quality due to different RES and loads connected to the microgrid as depicted inFig. 10.
Fig. 10. PQ impact in the microgrid with different topologies.
According to the results obtained from the proposed method (Fig. 10), the power quality of the microgrid was not good. The total PQD was suitable only in one case (SHP+G with the linear load in Fig. 10c). The worst PQD were obtained when non-linear loads were connected to the microgrid, where high harmonic distortions and low power factor were identified through 𝐼𝑄𝑇 𝐻 𝐷and 𝐼𝑄𝑃 𝐹. The voltage level variation represented by 𝐼𝑄𝑉𝑠𝑠presented no relevant influence in the total PQD.
Each RES component of the used microgrid employed conventional control systems, which cannot properly deal with power quality prob-lems. Thereafter, the proposed method could identify power quality problems indicating the need for improvement in the microgrid control system. For instance, active filters can be used to mitigate harmonic distortions (Illindala and Venkataramanan, 2012). Also, the control system setting adjusting of PV and wind energy systems can be used to improve both the harmonic distortion and power factor (Ribeiro et al., 2015). The control system of the ESS can also mitigate PQ problems in a microgrid (Tabart et al.,2018). Additional devices can also be inserted to minimize problems in the voltage, such as temporary voltage sags (Zheng et al.,2018).
7. Conclusion
This paper proposes a hybrid WF-PQD able to provide the automatic power quality diagnosis considering several PQ indices as well as un-certainties and subjectivity existing in several worldwide PQ standards. In addition, the proposed inference method considers a new extended overlap function also proposed in this paper able to treat the logical attributes of fast and efficient form. As discussed in Section 3, the overlap provides all the necessary features for a FIS with the advantage of forming a much more comprehensive class of operators and a more robust system design.
The proposed WF-PQD was evaluated with data of an experimental microgrid considering different energy sources (e.g., photovoltaic and wind energy systems), an ESS, and various load types. Under con-sideration of 18 combinations of common microgrid components, the proposed WF-PQD method provided the PQD successfully. Besides the PQD as a whole, the valuable information related to specific PQ indices (harmonic distortion, power factor, and voltage variation) provided by the proposed method that consists of essential information to allows a
precise identification which PQ indices must be corrected in order to improve the power quality. Besides, the degrees of the PQ, identified as suitable, precarious, critical, and extremely critical, is also essential to determine the post-analyses actions recommended to follow by power grid management.
From 18 microgrid combinations, the obtained power quality di-agnosis results demonstrated that five combinations were extremely critical, six combinations were critical, six combinations were precari-ous, and only one was suitable. The power quality was mainly affected by high rates of harmonic distortions and the reduced power factor. The steady-state voltage variation did not affect the power quality sig-nificantly. The poor power quality in most of the results was expected since the microgrid presented no specific control system or additional devices to mitigate power quality problems. Nevertheless, based on the obtained diagnosis solutions such as active filters or improvements in the microgrid control systems could be recommended.
Acknowledgment
This study was financed in part by the Coordination for the Im-provement of Higher Education Personnel (CAPES) – Brazil – Finance Code 001, and the National Council for Scientific and Technological Development (CNPq) — Brazil.
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