Harmonic Distorted Load Control in a Microgrid
A. Khaledian, B. Vahidi, M. Abedi
Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran
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The local tangent frame is used as the navigation frame (lower). For navigation in a local tangent frame, the origin of the <span class="elsevierStyleItalic">ned</span> coordinate axes would be at some convenient point near the area of operation.</p>" ] ] ] "autores" => array:1 [ 0 => array:2 [ "autoresLista" => "R. Munguía" "autores" => array:1 [ 0 => array:2 [ "nombre" => "R." "apellidos" => "Munguía" ] ] ] ] ] "idiomaDefecto" => "en" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S1665642314700963?idApp=UINPBA00004N" "url" => "/16656423/0000001200000004/v2_201501220327/S1665642314700963/v2_201501220327/en/main.assets" ] "itemAnterior" => array:18 [ "pii" => "S166564231470094X" "issn" => "16656423" "doi" => "10.1016/S1665-6423(14)70094-X" "estado" => "S300" "fechaPublicacion" => "2014-08-01" "aid" => "70094" "copyright" => "Universidad Nacional Autónoma de México" "documento" => "article" "licencia" => "http://creativecommons.org/licenses/by-nc-nd/4.0/" "subdocumento" => "fla" "cita" => "Journal of Applied Research and Technology. 2014;12:782-91" "abierto" => array:3 [ "ES" => true "ES2" => true "LATM" => true ] "gratuito" => true "lecturas" => array:2 [ "total" => 1490 "formatos" => array:3 [ "EPUB" => 29 "HTML" => 1088 "PDF" => 373 ] ] "en" => array:11 [ "idiomaDefecto" => true "titulo" => "Synchronization of Irregular Complex Networks with Chaotic Oscillators: Hamiltonian Systems Approach" "tienePdf" => "en" "tieneTextoCompleto" => "en" "tieneResumen" => array:2 [ 0 => "en" 1 => "es" ] "paginas" => array:1 [ 0 => array:2 [ "paginaInicial" => "782" "paginaFinal" => "791" ] ] "contieneResumen" => array:2 [ "en" => true "es" => true ] "contieneTextoCompleto" => array:1 [ "en" => true ] "contienePdf" => array:1 [ "en" => true ] "resumenGrafico" => array:2 [ "original" => 0 "multimedia" => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 616 "Ancho" => 740 "Tamanyo" => 101927 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0020" class="elsevierStyleSimplePara elsevierViewall">Phase space of the chaotic attractor generated by Rössler oscillator <a class="elsevierStyleCrossRef" href="#eq0085">(13)</a>, projected onto (<span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf">1</span>, <span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf">2</span>, <span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf">3</span>).</p>" ] ] ] "autores" => array:1 [ 0 => array:2 [ "autoresLista" => "C. Posadas-Castillo, E. Garza-González, D.A. Diaz-Romero, E. Alcorta-Garcia, C. Cruz-Hernández" "autores" => array:5 [ 0 => array:2 [ "nombre" => "C." "apellidos" => "Posadas-Castillo" ] 1 => array:2 [ "nombre" => "E." "apellidos" => "Garza-González" ] 2 => array:2 [ "nombre" => "D.A." "apellidos" => "Diaz-Romero" ] 3 => array:2 [ "nombre" => "E." "apellidos" => "Alcorta-Garcia" ] 4 => array:2 [ "nombre" => "C." "apellidos" => "Cruz-Hernández" ] ] ] ] ] "idiomaDefecto" => "en" "EPUB" => "https://multimedia.elsevier.es/PublicationsMultimediaV1/item/epub/S166564231470094X?idApp=UINPBA00004N" "url" => "/16656423/0000001200000004/v2_201501220327/S166564231470094X/v2_201501220327/en/main.assets" ] "en" => array:15 [ "idiomaDefecto" => true "titulo" => "Harmonic Distorted Load Control in a Microgrid" "tieneTextoCompleto" => true "paginas" => array:1 [ 0 => array:2 [ "paginaInicial" => "792" "paginaFinal" => "802" ] ] "autores" => array:1 [ 0 => array:3 [ "autoresLista" => "A. Khaledian, B. Vahidi, M. Abedi" "autores" => array:3 [ 0 => array:2 [ "nombre" => "A." "apellidos" => "Khaledian" ] 1 => array:3 [ "nombre" => "B." "apellidos" => "Vahidi" "email" => array:1 [ 0 => "vahidi@aut.ac.ir" ] ] 2 => array:2 [ "nombre" => "M." "apellidos" => "Abedi" ] ] "afiliaciones" => array:1 [ 0 => array:2 [ "entidad" => "Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran" "identificador" => "aff0005" ] ] ] ] "resumenGrafico" => array:2 [ "original" => 0 "multimedia" => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 484 "Ancho" => 839 "Tamanyo" => 39816 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0020" class="elsevierStyleSimplePara elsevierViewall">A microgrid with harmonic distorted load.</p>" ] ] ] "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">1</span><span class="elsevierStyleSectionTitle" id="sect0015">Introduction</span><p id="par0005" class="elsevierStylePara elsevierViewall">Power electronic devices have been widely used with different operations in power system. As the aspect of loads these nonlinear structures provide high efficiency and controllability, while decreasing overall power quality by distorting source voltages and/or currents. This causes pollution in power system that is harmful for sensitive loads, such as computers and processor controlled based devices.</p><p id="par0010" class="elsevierStylePara elsevierViewall">In 1976, Gyugyi presented active filters and the concept of harmonic distortion mitigation, consisting of PWM inverters using active power switches <a class="elsevierStyleCrossRef" href="#bib0005">[1]</a>.</p><p id="par0015" class="elsevierStylePara elsevierViewall">In the past, the performance of active filters was considered with the battery as a dc source <a class="elsevierStyleCrossRef" href="#bib0010">[2]</a> but recently using distributed generator as an active filter is considered. Many literatures have already proposed new techniques to alleviate the harmonics produced by nonlinear loads <a class="elsevierStyleCrossRef" href="#bib0015">[3]</a> and many researches have been done on this control scheme. In <a class="elsevierStyleCrossRef" href="#bib0020">[4]</a> the use of automatic gain control in the shunt active power filter for harmonic reduction in a distorted power system is presented. In <a class="elsevierStyleCrossRef" href="#bib0025">[5]</a> digital-controlled active filter, based on voltage recognition to decrease harmonic distortion is proposed. The application of neural networks as a smart control scheme for a shunt active filter has been described. Other intelligent control algorithms such as artificial intelligence and genetic as controllers for active filters can also be used <a class="elsevierStyleCrossRef" href="#bib0030">[6]</a>.</p><p id="par0020" class="elsevierStylePara elsevierViewall">The instantaneous reactive power (IRP) theory (p–q theory) that is presented by Akagi and developed by others, provides mathematical methods for the control of PWM inverter based switching active power filters <a class="elsevierStyleCrossRefs" href="#bib0035">[7–9]</a>. Although there is still no exact information with respect to the definition of power concept in power system with non-sinusoidal and unbalanced conditions, the p–q theory seems to be well established in power system compensation <a class="elsevierStyleCrossRefs" href="#bib0050">[10–12]</a>.</p><p id="par0025" class="elsevierStylePara elsevierViewall">Since the p–q theory was proposed, many control methods based on instantaneous reactive power theory have been presented for the harmonic compensation strategies of the active filters and power quality enhancement <a class="elsevierStyleCrossRefs" href="#bib0065">[13–17]</a>; “constant source power” and “sinusoidal source current” are <a name="p793"></a>effective control schemes used in different applications. Development of IRP theory in recent studies is also remarkable <a class="elsevierStyleCrossRefs" href="#bib0090">[18–21]</a>.</p><p id="par0030" class="elsevierStylePara elsevierViewall">Recently the growing integration of renewable energy resources into power networks has had a significant impact on power system <a class="elsevierStyleCrossRef" href="#bib0110">[22]</a>. Distributed generation and microgrid are new concepts in power system studies and inverter interfaced DGs can play an important role in harmonic distortion mitigation <a class="elsevierStyleCrossRef" href="#bib0115">[23]</a>.</p><p id="par0035" class="elsevierStylePara elsevierViewall">In this paper, in order to evaluate the effectiveness of IRP theory control strategy, an experimental microgrid is studied and simulated in PSCAD based on sinusoidal source current strategy. DG operates as a shunt active filter. Different harmonic distortions are applied to the aforementioned load; Source and load currents THD and third harmonic percent before and after the DG location are observed. In order to reduce THD in the source and other load sides, a new control strategy for DGs in a microgrid is presented and the results are compared with the IRP control theory.</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">2</span><span class="elsevierStyleSectionTitle" id="sect0020">P-Q Control Strategy</span><p id="par0040" class="elsevierStylePara elsevierViewall">Conventional control strategy for active power filters is based on p-q theory which is called IRP (instantaneous reactive power) theory. This control scheme is used to detect and compensate undesirable powers. To achieve this goal active and reactive powers are calculated in time domain and presented in a coordinate frame in which power components are obvious. Clarke Transform of voltages and currents specified in phase a, b and c coordinates, as shown in <a class="elsevierStyleCrossRef" href="#fig0005">figure 1</a>, into quantities in orthogonal <span class="elsevierStyleItalic">¿</span>, <span class="elsevierStyleItalic">¿</span> and 0 coordinates can help us to achieve this goal.</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0045" class="elsevierStylePara elsevierViewall">Clarke Transformation of three-phase voltages and currents has the form below.<elsevierMultimedia ident="eq0005"></elsevierMultimedia><elsevierMultimedia ident="eq0010"></elsevierMultimedia>and consequently, instantaneous active and reactive power of such a system are equal to:<elsevierMultimedia ident="eq0015"></elsevierMultimedia></p><p id="par0050" class="elsevierStylePara elsevierViewall">Active power is presented in two separate zero and summation of positive and negative consequence modes. If the voltage and current of such a load has the form <a class="elsevierStyleCrossRef" href="#eq0020">(4)</a> and <a class="elsevierStyleCrossRef" href="#eq0025">(5)</a> respectively:<elsevierMultimedia ident="eq0020"></elsevierMultimedia><elsevierMultimedia ident="eq0025"></elsevierMultimedia></p><p id="par0055" class="elsevierStylePara elsevierViewall">According to the previous equations we can represent the active and reactive powers as:<elsevierMultimedia ident="eq0030"></elsevierMultimedia><elsevierMultimedia ident="eq0035"></elsevierMultimedia><elsevierMultimedia ident="eq0040"></elsevierMultimedia><elsevierMultimedia ident="eq0045"></elsevierMultimedia><a name="p794"></a><elsevierMultimedia ident="eq0050"></elsevierMultimedia><elsevierMultimedia ident="eq0055"></elsevierMultimedia><elsevierMultimedia ident="eq0060"></elsevierMultimedia><elsevierMultimedia ident="eq0065"></elsevierMultimedia></p><p id="par0060" class="elsevierStylePara elsevierViewall">When we have harmonic distorted or imbalanced loads in the grid, alternative component of active and reactive powers appear.<elsevierMultimedia ident="eq0070"></elsevierMultimedia></p><p id="par0065" class="elsevierStylePara elsevierViewall">Undesirable powers shown in <a class="elsevierStyleCrossRef" href="#eq0040">equations (8)</a> to <a class="elsevierStyleCrossRef" href="#eq0070">(14)</a> should be compensated.</p><p id="par0070" class="elsevierStylePara elsevierViewall">To identify the positive sequence of fundamental component of voltage and current, PLL (phase locked loop) and PSD (positive sequence detector) tools are used to obtain the fundamental frequency and amplitude of the main signal.</p><p id="par0075" class="elsevierStylePara elsevierViewall">For active filters there are two different compensation strategies; “Constant supply power” and “sinusoidal supply current”. Second one can help us to achieve our purpose to reduce the load and supply current THD; Block diagram of this control method is shown in <a class="elsevierStyleCrossRef" href="#fig0010">figure 2</a>.</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><p id="par0080" class="elsevierStylePara elsevierViewall">As it can be seen from <a class="elsevierStyleCrossRef" href="#fig0010">figure 2</a>, power components that are candidates to be compensated are negative and alternative components of Pa¿¿ and the whole amount of reactive power. After operation of the control process, the outputs of system are reference currents that should be applied as a signal to the inverter switches.</p><p id="par0085" class="elsevierStylePara elsevierViewall">After calculation of reference currents by sinusoidal current strategy, we should control DG's current in the reference current range. The hysteresis control method can help us to achieve this goal. We determine an appropriate hysteresis band for the current tolerance in this control method. As it can be seen from <a class="elsevierStyleCrossRef" href="#fig0015">figure 3</a>, if DG's current passes the determined band, control system send the gate signal to the inverter switches to increase or decrease the current.</p><elsevierMultimedia ident="fig0015"></elsevierMultimedia><p id="par0090" class="elsevierStylePara elsevierViewall">Switching frequency depends on current changing rate from the lower side to the upper side band or viceversa. By adjusting the hysteresis band as a small value the output current of DG will have close shape to the reference signal but it increases switching frequency and losses and causes EMI effect.<a name="p795"></a></p><p id="par0095" class="elsevierStylePara elsevierViewall">When the load is unbalanced, active and reactive powers are time variant and do not provide exact information on power properties of the grid. An additional analysis is required to determine active, reactive and unbalanced powers.</p><p id="par0100" class="elsevierStylePara elsevierViewall">Time-domain based IRP theory has no advantages over the frequency-domain approach with respect to the time period needed for identification the exact value of power properties of the grid loads.</p><p id="par0105" class="elsevierStylePara elsevierViewall">DG designation as an active power filter, based on p-q control strategy can be extended to compensate unbalanced nonlinear load currents, even when the source voltage and current are unbalanced and distorted, like the microgrid that is shown in <a class="elsevierStyleCrossRef" href="#fig0020">figure 4</a>.</p><elsevierMultimedia ident="fig0020"></elsevierMultimedia><p id="par0110" class="elsevierStylePara elsevierViewall">There are three harmonic detection methods which play an important role in control strategy of the active filter <a class="elsevierStyleCrossRef" href="#bib0120">[24]</a>:<ul class="elsevierStyleList" id="lis0005"><li class="elsevierStyleListItem" id="lsti0005"><span class="elsevierStyleLabel">1)</span><p id="par0115" class="elsevierStylePara elsevierViewall">Load current detection: This method detects load current, which flows downstream of the point of location and extracts harmonic current from load current.</p></li><li class="elsevierStyleListItem" id="lsti0010"><span class="elsevierStyleLabel">2)</span><p id="par0120" class="elsevierStylePara elsevierViewall">Source current detection: This method detects supply current, which flows upstream of the point of location and extracts harmonic current from source current.</p></li><li class="elsevierStyleListItem" id="lsti0015"><span class="elsevierStyleLabel">3)</span><p id="par0125" class="elsevierStylePara elsevierViewall">Voltage detection: This method detects bus voltage at the point of location and then extracts harmonic voltage.</p></li></ul></p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3</span><span class="elsevierStyleSectionTitle" id="sect0025">Microgrid Harmonic Control Scheme</span><p id="par0130" class="elsevierStylePara elsevierViewall">Droop control has been widely used in microgrids in order to share the demand power. This control method mimics the governer and exciter of a synchronous generator and regulates output frequency and voltage of the generator according to the active and reactive power derived from it's terminal.</p><p id="par0135" class="elsevierStylePara elsevierViewall">Droop control method considered in this paper contains inner voltage and current controllers rejecting disturbances.</p><p id="par0140" class="elsevierStylePara elsevierViewall">Proposed control strategy is conducted in dq0 frame which facilitates control process by transforming the voltage and current variables in three phase (abc) frame which are time variant quantities to the proposed frame. In dq0 frame control variable are time invariant (dc) quantities. <a class="elsevierStyleCrossRef" href="#fig0025">Figure 5</a> shows dq0 and abc frames. Transformation equation and reverse equation are shown in <a class="elsevierStyleCrossRef" href="#eq0075">(15)</a> and <a class="elsevierStyleCrossRef" href="#eq0080">(16)</a> and <span class="elsevierStyleItalic">¿</span> is defined in <a class="elsevierStyleCrossRef" href="#eq0085">(17)</a>. In <a class="elsevierStyleCrossRef" href="#eq0085">(17)</a>, <span class="elsevierStyleItalic">¿</span> is time variant angular velocity and ¿<span class="elsevierStyleInf">0</span> is initial phase angle.<a name="p796"></a><elsevierMultimedia ident="eq0075"></elsevierMultimedia><elsevierMultimedia ident="eq0080"></elsevierMultimedia><elsevierMultimedia ident="eq0085"></elsevierMultimedia></p><elsevierMultimedia ident="fig0025"></elsevierMultimedia><p id="par0145" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#fig0030">Figure 6</a> shows power, voltage and current controllers, output LC filter and coupling inductance of a DG unit in a microgrid, by this assumption that the input of DG inverter is ideal dc link <a class="elsevierStyleCrossRefs" href="#bib0125">[25–27]</a>.</p><elsevierMultimedia ident="fig0030"></elsevierMultimedia><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3.1</span><span class="elsevierStyleSectionTitle" id="sect0030">Power controller</span><p id="par0150" class="elsevierStylePara elsevierViewall">According to the voltage and current quantities in dq0 frame, instantaneous amount of powers can be calculated as follows:<elsevierMultimedia ident="eq0090"></elsevierMultimedia><elsevierMultimedia ident="eq0095"></elsevierMultimedia></p><p id="par0155" class="elsevierStylePara elsevierViewall">To derive active and reactive powers, the above quantities should be passed through the low pass filters with <span class="elsevierStyleItalic">¿</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> as cut-out frequency.<elsevierMultimedia ident="eq0100"></elsevierMultimedia><elsevierMultimedia ident="eq0105"></elsevierMultimedia></p><p id="par0160" class="elsevierStylePara elsevierViewall">Considering the droop characteristic, reference voltage and frequency of power controller can be obtained as follows:<elsevierMultimedia ident="eq0110"></elsevierMultimedia><elsevierMultimedia ident="eq0115"></elsevierMultimedia></p><p id="par0165" class="elsevierStylePara elsevierViewall">In the above equations <span class="elsevierStyleItalic">¿</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">n</span></span> and <span class="elsevierStyleItalic">V</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">n</span></span> are nominal amounts of frequency and voltage of microgrid and <span class="elsevierStyleItalic">m</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> and <span class="elsevierStyleItalic">n</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">q</span></span> are droop gains. These gains relates to some economic and technical features of a generator but are assumed same for all the generators in this paper for simplicity. <a class="elsevierStyleCrossRef" href="#fig0035">Figure 7</a> summarize power controller.</p><elsevierMultimedia ident="fig0035"></elsevierMultimedia></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">3.2</span><span class="elsevierStyleSectionTitle" id="sect0035">Voltage and current controller</span><p id="par0170" class="elsevierStylePara elsevierViewall">Reference voltage and frequency produced by power controller are sent to the voltage controller and outputs of this controller are sent to the current controller. Both controllers are shown below (<a class="elsevierStyleCrossRef" href="#fig0040">figure 8</a> and <a class="elsevierStyleCrossRef" href="#fig0045">9</a>).<a name="p797"></a></p><elsevierMultimedia ident="fig0040"></elsevierMultimedia><elsevierMultimedia ident="fig0045"></elsevierMultimedia><p id="par0175" class="elsevierStylePara elsevierViewall">Inner PI controller guarantees zero difference signal of real and reference quantities steady state error and improve system transient response. Also feed-forward loops isolate generators from load disturbances and enhance system power quality in presence of harmonic distorted loads.</p></span></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">4</span><span class="elsevierStyleSectionTitle" id="sect0040">Simulation Results</span><p id="par0180" class="elsevierStylePara elsevierViewall">Performance of discussed control strategies is examined in this section. First IRP theory control is considered for a DG near the harmonic distorted load, operating as a shunt active filter. The analysed circuit schema is shown in the <a class="elsevierStyleCrossRef" href="#fig0020">Figure 4</a>. Nonlinear load is a resistor connected to the output of a three phase full bridge rectifier. There is an LC filter in the output of the generator to eliminate switching high order frequencies.</p><p id="par0185" class="elsevierStylePara elsevierViewall">Parameters of the simulated system in PSCAD are shown in <a class="elsevierStyleCrossRef" href="#tbl0005">table 1</a>. To create different harmonic distortion levels in the load, rectifier thyristor firing angle is tunable. Six harmonic levels are tested and the results are shown.</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia><p id="par0190" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#fig0050">Figure 10</a> and <a class="elsevierStyleCrossRef" href="#fig0055">11</a> show source, load and DG currents for 10 and 60 degrees rectifier firing angles respectively.</p><elsevierMultimedia ident="fig0050"></elsevierMultimedia><elsevierMultimedia ident="fig0055"></elsevierMultimedia><p id="par0195" class="elsevierStylePara elsevierViewall">As it can be seen, harmonic distortion in the load and source current in the 60 degrees mode is higher than 10 degrees mode.</p><p id="par0200" class="elsevierStylePara elsevierViewall">Third harmonic percent is chosen among the harmonic components spectrum of the source and<a name="p798"></a> load current. The exact amount of six harmonic distortion levels applied to the load with the system response is also shown in <a class="elsevierStyleCrossRef" href="#tbl0010">table 2</a>.</p><elsevierMultimedia ident="tbl0010"></elsevierMultimedia><p id="par0205" class="elsevierStylePara elsevierViewall">Second simulation is made in MATLAB Simulink to evaluate the proposed droop control in the presence of nonlinear load.</p><p id="par0210" class="elsevierStylePara elsevierViewall">One phase schematic of microgrid and system parameters are shown in <a class="elsevierStyleCrossRef" href="#fig0060">figure 12</a> and <a class="elsevierStyleCrossRef" href="#tbl0015">table 3</a> respectively.</p><elsevierMultimedia ident="fig0060"></elsevierMultimedia><elsevierMultimedia ident="tbl0015"></elsevierMultimedia><p id="par0215" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#fig0065">Figure 13</a> shows the load current and it's THD and 3<span class="elsevierStyleSup">rd</span> harmonic and <a class="elsevierStyleCrossRef" href="#fig0070">figure 14</a> and <a class="elsevierStyleCrossRef" href="#fig0075">15</a> show the effect of harmonic distorted load in the source (DG1) and other load (load 2) side. It can be seen that in presence of the proposed controller, harmonic distortion is reduced obviously in comparison with the traditional p-q control.</p><elsevierMultimedia ident="fig0065"></elsevierMultimedia><elsevierMultimedia ident="fig0070"></elsevierMultimedia><elsevierMultimedia ident="fig0075"></elsevierMultimedia><p id="par0220" class="elsevierStylePara elsevierViewall">In detail important drawback of the IRP theory is the inability of this control method to reduce the amount of THD with respect to the proposed droop control and also to maintain the source current THD and third harmonic percent in constant¬ value when increasing the load harmonic distortion.<a name="p799"></a></p><p id="par0225" class="elsevierStylePara elsevierViewall">The main causes of this drawback for IRP control strategy are:<ul class="elsevierStyleList" id="lis0010"><li class="elsevierStyleListItem" id="lsti0020"><span class="elsevierStyleLabel">1)</span><p id="par0230" class="elsevierStylePara elsevierViewall">The high pass filter separating alternative value of the active power P<span class="elsevierStyleInf">¿¿</span> has a fixed crossing frequency. By increasing load harmonic distortion, the amplitude of the all harmonic components in the active power increases including sub-harmonics. By deleting all high frequency components (for example higher than 20<span class="elsevierStyleHsp" style=""></span>Hz in <a class="elsevierStyleCrossRef" href="#fig0010">figure 2</a>), remained sub-harmonics can generate voltage and/or current internal or main harmonic components considering active power formula in <a class="elsevierStyleCrossRef" href="#eq0035">(7)</a> and <a class="elsevierStyleCrossRef" href="#eq0040">(8)</a>.</p></li><li class="elsevierStyleListItem" id="lsti0025"><span class="elsevierStyleLabel">2)</span><p id="par0235" class="elsevierStylePara elsevierViewall">In p-q control strategy load imbalance that affects source current asymmetry and associated unbalanced power (D) is missed:<elsevierMultimedia ident="eq0120"></elsevierMultimedia></p></li></ul></p><p id="par0240" class="elsevierStylePara elsevierViewall">Compensating the unbalanced power reduces harmonic components (especially 3rd harmonic) that are influenced by asymmetry and load imbalance. By ignoring this power component in compensation as we can see in IRP theory, we have higher THD in currents of the grid. As a result, DGs operating as an active filter controlled by IRP theory does not eliminate all harmonics and cause high THD.<a name="p800"></a></p><p id="par0245" class="elsevierStylePara elsevierViewall">By demonstrating the traditional sinusoidal source current control strategy based on IRP theory, it was concluded that ignoring the distortion power (D) in compensating process and also sub-harmonics of Pep crossing from the controller interior high pass filter cause the presence of some harmonic components and high THD.</p><p id="par0250" class="elsevierStylePara elsevierViewall">Proposed control scheme have the capability of sharing load active and reactive powers among all the generators in a microgrid as well as compensating harmonic distortion generated by nonlinear loads.</p><p id="par0255" class="elsevierStylePara elsevierViewall">In order to conclude the generality of the proposed method, two different loads are also concluded in the case study. Resistive load with step change and induction motor in fault condition are two sample of loads added to the simulation of the microgrid.</p><p id="par0260" class="elsevierStylePara elsevierViewall">First, step change in active power is considered as it can be shown in <a class="elsevierStyleCrossRef" href="#fig0080">Figure 16</a>. All the active power requested by network and loads is 12<span class="elsevierStyleHsp" style=""></span>kW before the demand change. After 1 second 9<span class="elsevierStyleHsp" style=""></span>kW of total P is increased by controlled current source.</p><elsevierMultimedia ident="fig0080"></elsevierMultimedia><p id="par0265" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#fig0085">Figure 17</a> shows active powers generated by DGs in each three buses. DGs produce equal P in steady state time because droop gains of w-P characteristics have the same value. This figure shows that the proposed controller maintains grid stability after step change in demand power.</p><elsevierMultimedia ident="fig0085"></elsevierMultimedia><p id="par0270" class="elsevierStylePara elsevierViewall">In order to study dynamic loads in the microgrid with proposed droop controller, induction motor as the most common industrial load is tested in fault condition. Two 7.5<span class="elsevierStyleHsp" style=""></span>kW motors are in buses 1 and 3.</p><p id="par0275" class="elsevierStylePara elsevierViewall">Single phase schematic of the circuit is shown in <a class="elsevierStyleCrossRef" href="#fig0090">Figure 18</a>.</p><elsevierMultimedia ident="fig0090"></elsevierMultimedia><p id="par0280" class="elsevierStylePara elsevierViewall">After 0.6 seconds of motor starting a two phases to ground fault is occurred in bus1. After 3 cycles the fault is cleared. <a class="elsevierStyleCrossRef" href="#fig0095">Figure 19</a> shows stator current of the motor in bus 1. It can be seen that the<a name="p801"></a> controller has the capability of maintaining system stability during and after fault clearance.</p><elsevierMultimedia ident="fig0095"></elsevierMultimedia><p id="par0285" class="elsevierStylePara elsevierViewall">It is concluded that in different types of load, proposed controller has the satisfying performance.</p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleLabel">5</span><span class="elsevierStyleSectionTitle" id="sect0045">Conclusion</span><p id="par0290" class="elsevierStylePara elsevierViewall">In this paper the response of a microgrid to the interfaced harmonic distorted load was analysed. A new control algorithm to mitigate harmonic distortion was considered for distributed generators (DGs) and the effect of this control scheme was shown in the currents of DGs and other loads.</p><p id="par0295" class="elsevierStylePara elsevierViewall">The proposed control algorithm was compared with the conventional control strategy for harmonic distorted loads that is sinusoidal source current strategy based on the instantaneous reactive power theory. PSCAD simulation results for IRP theory control had high total harmonic distortion (THD) and 3rd harmonic percent. In comparison inner voltage and current controllers of the proposed control scheme with their disturbance rejection capability, mitigated THD and 3rd harmonic percent and MATLAB simulation results confirmed this.</p><p id="par0300" class="elsevierStylePara elsevierViewall">The generality of the proposed method was also examined in presence of different loads such as step change of demand power and induction motor in fault condition.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:8 [ 0 => array:2 [ "identificador" => "xres413285" "titulo" => "Abstract" ] 1 => array:2 [ "identificador" => "xpalclavsec388973" "titulo" => "Keywords" ] 2 => array:2 [ "identificador" => "sec0005" "titulo" => "Introduction" ] 3 => array:2 [ "identificador" => "sec0010" "titulo" => "P-Q Control Strategy" ] 4 => array:3 [ "identificador" => "sec0015" "titulo" => "Microgrid Harmonic Control Scheme" "secciones" => array:2 [ 0 => array:2 [ "identificador" => "sec0020" "titulo" => "Power controller" ] 1 => array:2 [ "identificador" => "sec0025" "titulo" => "Voltage and current controller" ] ] ] 5 => array:2 [ "identificador" => "sec0030" "titulo" => "Simulation Results" ] 6 => array:2 [ "identificador" => "sec0035" "titulo" => "Conclusion" ] 7 => array:1 [ "titulo" => "References" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "PalabrasClave" => array:1 [ "en" => array:1 [ 0 => array:4 [ "clase" => "keyword" "titulo" => "Keywords" "identificador" => "xpalclavsec388973" "palabras" => array:4 [ 0 => "distributed generation" 1 => "instantaneous reactive power theory" 2 => "harmonic distortion" 3 => "microgrid" ] ] ] ] "tieneResumen" => true "resumen" => array:1 [ "en" => array:2 [ "titulo" => "Abstract" "resumen" => "<p id="spar0115" class="elsevierStyleSimplePara elsevierViewall">In this paper the response of a microgrid to the interfaced harmonic distorted load is analyzed. A new control algorithm to mitigate harmonic distortion is considered for distributed generators (DGs) and the effect of this control scheme is shown in the currents of DGs and other loads.</p><p id="spar0120" class="elsevierStyleSimplePara elsevierViewall">The proposed control algorithm is compared with the conventional control strategy for harmonic distorted loads that is sinusoidal source current strategy based on the instantaneous reactive power (IRP) theory. PSCAD simulation results for IRP theory control show high total harmonic distortion (THD) and 3rd harmonic percent. In comparison inner voltage and current controllers of the proposed control scheme with their disturbance rejection capability, mitigate THD and 3rd harmonic percent. For this control system MATLAB simulation results are shown.</p><p id="spar0125" class="elsevierStyleSimplePara elsevierViewall">By demonstrating the traditional sinusoidal source current control strategy based on IRP theory, it is concluded that ignoring the distortion power (D) in compensating process and also sub-harmonics of P¿¿ crossing from the controller interior high pass filter cause the presence of some harmonic components and high THD.</p>" ] ] "multimedia" => array:46 [ 0 => array:7 [ "identificador" => "fig0005" "etiqueta" => "Figure 1" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr1.jpeg" "Alto" => 455 "Ancho" => 891 "Tamanyo" => 26676 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">coordinate frame transform.</p>" ] ] 1 => array:7 [ "identificador" => "fig0010" "etiqueta" => "Figure 2" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr2.jpeg" "Alto" => 569 "Ancho" => 1519 "Tamanyo" => 63917 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">sinusoidal current strategy of active filter.</p>" ] ] 2 => array:7 [ "identificador" => "fig0015" "etiqueta" => "Figure 3" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr3.jpeg" "Alto" => 596 "Ancho" => 753 "Tamanyo" => 41267 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0015" class="elsevierStyleSimplePara elsevierViewall">Hysteresis current control.</p>" ] ] 3 => array:7 [ "identificador" => "fig0020" "etiqueta" => "Figure 4" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr4.jpeg" "Alto" => 484 "Ancho" => 839 "Tamanyo" => 39816 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0020" class="elsevierStyleSimplePara elsevierViewall">A microgrid with harmonic distorted load.</p>" ] ] 4 => array:7 [ "identificador" => "fig0025" "etiqueta" => "Figure 5" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr5.jpeg" "Alto" => 552 "Ancho" => 474 "Tamanyo" => 29951 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0025" class="elsevierStyleSimplePara elsevierViewall">dq0 and abc frames.</p>" ] ] 5 => array:7 [ "identificador" => "fig0030" "etiqueta" => "Figure 6" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr6.jpeg" "Alto" => 352 "Ancho" => 883 "Tamanyo" => 50164 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0030" class="elsevierStyleSimplePara elsevierViewall">DG components and controllers.</p>" ] ] 6 => array:7 [ "identificador" => "fig0035" "etiqueta" => "Figure 7" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr7.jpeg" "Alto" => 221 "Ancho" => 917 "Tamanyo" => 37975 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0035" class="elsevierStyleSimplePara elsevierViewall">Power controller.</p>" ] ] 7 => array:7 [ "identificador" => "fig0040" "etiqueta" => "Figure 8" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr8.jpeg" "Alto" => 613 "Ancho" => 783 "Tamanyo" => 51736 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0040" class="elsevierStyleSimplePara elsevierViewall">voltage controller.</p>" ] ] 8 => array:7 [ "identificador" => "fig0045" "etiqueta" => "Figure 9" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr9.jpeg" "Alto" => 370 "Ancho" => 678 "Tamanyo" => 39908 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0045" class="elsevierStyleSimplePara elsevierViewall">current controller.</p>" ] ] 9 => array:7 [ "identificador" => "fig0050" "etiqueta" => "Figure 10" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr10.jpeg" "Alto" => 2029 "Ancho" => 765 "Tamanyo" => 150012 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0050" class="elsevierStyleSimplePara elsevierViewall">10 degrees firing angle applied to the rectifier: a)source b)load c)DG currents.</p>" ] ] 10 => array:7 [ "identificador" => "fig0055" "etiqueta" => "Figure 11" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:2 [ 0 => array:1 [ "imagen" => "gr11a.jpeg" ] 1 => array:1 [ "imagen" => "gr11b.jpeg" ] ] "descripcion" => array:1 [ "en" => "<p id="spar0055" class="elsevierStyleSimplePara elsevierViewall">60 degrees firing angle applied to the rectifier: a)source b)load c)DG currents.</p>" ] ] 11 => array:7 [ "identificador" => "fig0060" "etiqueta" => "Figure 12" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr12.jpeg" "Alto" => 336 "Ancho" => 921 "Tamanyo" => 34169 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0060" class="elsevierStyleSimplePara elsevierViewall">Microgrid with droop control.</p>" ] ] 12 => array:7 [ "identificador" => "fig0065" "etiqueta" => "Figure 13" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr13.jpeg" "Alto" => 1121 "Ancho" => 929 "Tamanyo" => 128966 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0065" class="elsevierStyleSimplePara elsevierViewall">Nonlinear load current and it's THD and 3rd harmonic.</p>" ] ] 13 => array:7 [ "identificador" => "fig0070" "etiqueta" => "Figure 14" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr14.jpeg" "Alto" => 941 "Ancho" => 905 "Tamanyo" => 92882 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0070" class="elsevierStyleSimplePara elsevierViewall">DG1 current THD and 3rd harmonic.</p>" ] ] 14 => array:7 [ "identificador" => "fig0075" "etiqueta" => "Figure 15" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr15.jpeg" "Alto" => 952 "Ancho" => 930 "Tamanyo" => 92732 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0075" class="elsevierStyleSimplePara elsevierViewall">Load 2 current THD and 3rd harmonic.</p>" ] ] 15 => array:7 [ "identificador" => "fig0080" "etiqueta" => "Figure 16" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr16.jpeg" "Alto" => 317 "Ancho" => 910 "Tamanyo" => 36596 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0080" class="elsevierStyleSimplePara elsevierViewall">Simulation of step change in active power.</p>" ] ] 16 => array:7 [ "identificador" => "fig0085" "etiqueta" => "Figure 17" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr17.jpeg" "Alto" => 341 "Ancho" => 929 "Tamanyo" => 45677 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0085" class="elsevierStyleSimplePara elsevierViewall">Active powers generated by DGs.</p>" ] ] 17 => array:7 [ "identificador" => "fig0090" "etiqueta" => "Figure 18" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr18.jpeg" "Alto" => 288 "Ancho" => 843 "Tamanyo" => 31869 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0090" class="elsevierStyleSimplePara elsevierViewall">Simulation of fault in the microgrid with induction motors.</p>" ] ] 18 => array:7 [ "identificador" => "fig0095" "etiqueta" => "Figure 19" "tipo" => "MULTIMEDIAFIGURA" "mostrarFloat" => true "mostrarDisplay" => false "figura" => array:1 [ 0 => array:4 [ "imagen" => "gr19.jpeg" "Alto" => 341 "Ancho" => 944 "Tamanyo" => 68931 ] ] "descripcion" => array:1 [ "en" => "<p id="spar0095" class="elsevierStyleSimplePara elsevierViewall">Stator current in two phases to ground fault.</p>" ] ] 19 => array:7 [ "identificador" => "tbl0005" "etiqueta" => "Table 1" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " rowspan="2" align="center" valign="middle">Source</td><td class="td" title="table-entry " align="center" valign="middle">Voltagerms (V) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">200 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Inductance (mH) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Load \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">Resistor (ohm) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">2.5 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " rowspan="3" align="center" valign="middle">DG</td><td class="td" title="table-entry " align="center" valign="middle">Low pass filterInductance (mH) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Low pass filterCapacitor (¿F) \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">Hysteresis band \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.002 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab643224.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0100" class="elsevierStyleSimplePara elsevierViewall">System with p-q control Parameters.</p>" ] ] 20 => array:7 [ "identificador" => "tbl0010" "etiqueta" => "Table 2" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><thead title="thead"><tr title="table-row"><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Rectifier Firing Angle \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Source THD(%) \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Load THD (%) \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Source 3<span class="elsevierStyleSup">rd</span> Harmonic (%) \t\t\t\t\t\t\n \t\t\t\t</th><th class="td" title="table-head " align="center" valign="middle" scope="col" style="border-bottom: 2px solid black">Load 3<span class="elsevierStyleSup">rd</span> Harmonic (%) \t\t\t\t\t\t\n \t\t\t\t</th></tr></thead><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">0 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">33 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">12.1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">11.8 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">10 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.4 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">34.1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">11.8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">11.9 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">20 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">35.7 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">11.7 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">12 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">30 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">37.3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">12.1 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">12.1 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">40 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">39.5 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">11.9 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">12.4 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">50 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.4 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">41.3 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">12.6 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">13.1 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">60 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">28.7 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">44.8 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="char" valign="middle">13.6 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">13.7 \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab643225.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0105" class="elsevierStyleSimplePara elsevierViewall">Grid with p-q control Response To Load Harmonic Distortion.</p>" ] ] 21 => array:7 [ "identificador" => "tbl0015" "etiqueta" => "Table 3" "tipo" => "MULTIMEDIATABLA" "mostrarFloat" => true "mostrarDisplay" => false "tabla" => array:1 [ "tablatextoimagen" => array:1 [ 0 => array:2 [ "tabla" => array:1 [ 0 => """ <table border="0" frame="\n \t\t\t\t\tvoid\n \t\t\t\t" class=""><tbody title="tbody"><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">L</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">f</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1.35<span class="elsevierStyleHsp" style=""></span>mH \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">f</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">s</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">8<span class="elsevierStyleHsp" style=""></span>kHz \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">r</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">Lf</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">C</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">f</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">50<span class="elsevierStyleHsp" style=""></span>¿F \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle">rLc \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.03<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">L</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.35<span class="elsevierStyleHsp" style=""></span>mH \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">F</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.75 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">¿</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">c</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">31.41 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">n</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">q</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">1.3<span class="elsevierStyleHsp" style=""></span>×<span class="elsevierStyleHsp" style=""></span>10<span class="elsevierStyleSup">−3</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">m</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">p</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">9.4<span class="elsevierStyleHsp" style=""></span>×<span class="elsevierStyleHsp" style=""></span>10<span class="elsevierStyleSup">−5</span> \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">iv</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">390 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">pv</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.05 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">ic</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">16000 \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">K</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">pc</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">10.5 \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">line1</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.1<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">r</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">line1</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.23<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td></tr><tr title="table-row"><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">x</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">line2</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.58<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle"><span class="elsevierStyleItalic">r</span><span class="elsevierStyleInf"><span class="elsevierStyleItalic">line2</span></span> \t\t\t\t\t\t\n \t\t\t\t</td><td class="td" title="table-entry " align="center" valign="middle">0.35<span class="elsevierStyleHsp" style=""></span><span class="elsevierStyleBold">¿</span> \t\t\t\t\t\t\n \t\t\t\t</td></tr></tbody></table> """ ] "imagenFichero" => array:1 [ 0 => "xTab643223.png" ] ] ] ] "descripcion" => array:1 [ "en" => "<p id="spar0110" class="elsevierStyleSimplePara elsevierViewall">Microgrid with droop control Parameters.</p>" ] ] 22 => array:6 [ "identificador" => "eq0005" "etiqueta" => "(1)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "v0v¿v¿=231/21/21/21−1/2−1/203/2−3/2vavbvc" "Fichero" => "si2.jpeg" "Tamanyo" => 5879 "Alto" => 69 "Ancho" => 321 ] ] 23 => array:6 [ "identificador" => "eq0010" "etiqueta" => "(2)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "i0i¿i¿=231/21/21/21−1/2−1/203/2−3/2iaibic" "Fichero" => "si3.jpeg" "Tamanyo" => 5887 "Alto" => 69 "Ancho" => 315 ] ] 24 => array:6 [ "identificador" => "eq0015" "etiqueta" => "(3)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p0p¿¿q=v0000v¿v¿0−v¿v¿i0i¿i¿" "Fichero" => "si4.jpeg" "Tamanyo" => 3797 "Alto" => 68 "Ancho" => 233 ] ] 25 => array:6 [ "identificador" => "eq0020" "etiqueta" => "(4)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "v(t)=∑n=1∞2vnsin(n ¿t+¿n)" "Fichero" => "si5.jpeg" "Tamanyo" => 2505 "Alto" => 46 "Ancho" => 207 ] ] 26 => array:6 [ "identificador" => "eq0025" "etiqueta" => "(5)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "i(t)=∑n=1∞2insin(n ¿t+¿n)" "Fichero" => "si6.jpeg" "Tamanyo" => 2410 "Alto" => 46 "Ancho" => 199 ] ] 27 => array:6 [ "identificador" => "eq0030" "etiqueta" => "(6)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p¿¿=p¯¿¿+p¿;¿¿" "Fichero" => "si7.jpeg" "Tamanyo" => 1019 "Alto" => 16 "Ancho" => 113 ] ] 28 => array:6 [ "identificador" => "eq0035" "etiqueta" => "(7)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p¯¿¿=∑n=13v+ni+ncos(¿+n−¿+n)+∑n=1∞3v−ni−ncos(¿−n−¿−n)p¿;¿¿  =∑m≠nm=1∞∑n=1∞3v+mi+ncos((m−n)¿t+¿+m−¿+n)" "Fichero" => "si8.jpeg" "Tamanyo" => 8951 "Alto" => 131 "Ancho" => 432 ] ] 29 => array:6 [ "identificador" => "eq0040" "etiqueta" => "(8)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "+∑m≠nm=1∞∑n=1∞3v−mi−ncos((m−n)¿t+¿−m−¿−n)−∑m=1∞∑n=1∞3v−mi+ncos((n+m)¿t+¿−m+¿+n)" "Fichero" => "si9.jpeg" "Tamanyo" => 7509 "Alto" => 136 "Ancho" => 338 ] ] 30 => array:6 [ "identificador" => "eq0045" "etiqueta" => "(9)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p0=p¯0+p¿;0" "Fichero" => "si10.jpeg" "Tamanyo" => 878 "Alto" => 14 "Ancho" => 92 ] ] 31 => array:6 [ "identificador" => "eq0050" "etiqueta" => "(10)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p¯0∑n=1∞3v0ni0ncos(¿0n−¿0n)" "Fichero" => "si11.jpeg" "Tamanyo" => 2309 "Alto" => 46 "Ancho" => 187 ] ] 32 => array:6 [ "identificador" => "eq0055" "etiqueta" => "(11)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p¿;0=∑n=1∞∑m=1m≠n∞3v0mi0mcos((n−m)¿t+¿0n−¿0m)" "Fichero" => "si12.jpeg" "Tamanyo" => 4419 "Alto" => 79 "Ancho" => 353 ] ] 33 => array:6 [ "identificador" => "eq0060" "etiqueta" => "(12)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "q=q¯+q¿;" "Fichero" => "si13.jpeg" "Tamanyo" => 682 "Alto" => 14 "Ancho" => 68 ] ] 34 => array:6 [ "identificador" => "eq0065" "etiqueta" => "(13)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "q¯=∑n=1∞−3v+ni+nsin(¿+n−¿+n)+∑n=1∞3v−ni−nsin(¿−n−¿−n)" "Fichero" => "si14.jpeg" "Tamanyo" => 4444 "Alto" => 46 "Ancho" => 432 ] ] 35 => array:6 [ "identificador" => "eq0070" "etiqueta" => "(14)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "q¿;=∑m=1m≠n∞∑n=1∞−3v+mi+nsin((m−n)¿t+¿+m−¿+n)+∑m=1m≠n∞∑n=1∞3v−mi−nsin((m−n)¿t+¿−m−¿−n)+∑m=1∞∑n=1∞3v+mi−nsin((m+n)¿t+¿+m−¿−n)−∑m=1∞∑n=1∞3v−mi+nsin((m+n)¿t+¿−m−¿+n)" "Fichero" => "si15.jpeg" "Tamanyo" => 15139 "Alto" => 281 "Ancho" => 373 ] ] 36 => array:6 [ "identificador" => "eq0075" "etiqueta" => "(15)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "xdxqx0=23cos(¿)cos(¿−2¿3)cos(¿+2¿3)−sin(¿)−sin(¿−2¿3)−sin(¿+2¿3)121212xaxbxc" "Fichero" => "si16.jpeg" "Tamanyo" => 8535 "Alto" => 111 "Ancho" => 423 ] ] 37 => array:6 [ "identificador" => "eq0080" "etiqueta" => "(16)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "xaxbxc=cos(¿)−sin(¿)1cos(¿−2¿3)−sin(¿−2¿3)1cos(¿+2¿3)−sin(¿+2¿3)1xdxqx0" "Fichero" => "si17.jpeg" "Tamanyo" => 7845 "Alto" => 97 "Ancho" => 351 ] ] 38 => array:6 [ "identificador" => "eq0085" "etiqueta" => "(17)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "¿=¿0+∫0t¿(¿) d¿" "Fichero" => "si18.jpeg" "Tamanyo" => 1491 "Alto" => 57 "Ancho" => 133 ] ] 39 => array:6 [ "identificador" => "eq0090" "etiqueta" => "(18)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "p=vodiod+voqioq" "Fichero" => "si19.jpeg" "Tamanyo" => 1132 "Alto" => 16 "Ancho" => 131 ] ] 40 => array:6 [ "identificador" => "eq0095" "etiqueta" => "(19)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "q=vodioq−voqiod" "Fichero" => "si20.jpeg" "Tamanyo" => 1087 "Alto" => 16 "Ancho" => 130 ] ] 41 => array:6 [ "identificador" => "eq0100" "etiqueta" => "(20)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "P=¿cs+¿cp" "Fichero" => "si21.jpeg" "Tamanyo" => 856 "Alto" => 20 "Ancho" => 75 ] ] 42 => array:6 [ "identificador" => "eq0105" "etiqueta" => "(21)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "Q=¿cs+¿cq" "Fichero" => "si22.jpeg" "Tamanyo" => 916 "Alto" => 20 "Ancho" => 75 ] ] 43 => array:6 [ "identificador" => "eq0110" "etiqueta" => "(22)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "¿=¿n−mpP" "Fichero" => "si23.jpeg" "Tamanyo" => 932 "Alto" => 16 "Ancho" => 104 ] ] 44 => array:6 [ "identificador" => "eq0115" "etiqueta" => "(23)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "vod*=Vn−nqQ voq*=0" "Fichero" => "si24.jpeg" "Tamanyo" => 1556 "Alto" => 19 "Ancho" => 178 ] ] 45 => array:6 [ "identificador" => "eq0120" "etiqueta" => "(24)" "tipo" => "MULTIMEDIAFORMULA" "mostrarFloat" => false "mostrarDisplay" => true "Formula" => array:5 [ "Matematica" => "D=S2−P2−Q2" "Fichero" => "si25.jpeg" "Tamanyo" => 1387 "Alto" => 20 "Ancho" => 145 ] ] ] "bibliografia" => array:2 [ "titulo" => "References" "seccion" => array:1 [ 0 => array:2 [ "identificador" => "bibs0005" "bibliografiaReferencia" => array:27 [ 0 => array:3 [ "identificador" => "bib0005" "etiqueta" => "[1]" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:1 [ "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "L. 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|---|---|---|---|
| 2024 October | 22 | 4 | 26 |
| 2024 September | 38 | 6 | 44 |
| 2024 August | 27 | 2 | 29 |
| 2024 July | 38 | 4 | 42 |
| 2024 June | 46 | 4 | 50 |
| 2024 May | 56 | 5 | 61 |
| 2024 April | 45 | 8 | 53 |
| 2024 March | 51 | 10 | 61 |
| 2024 February | 55 | 10 | 65 |
| 2024 January | 52 | 12 | 64 |
| 2023 December | 46 | 13 | 59 |
| 2023 November | 51 | 13 | 64 |
| 2023 October | 61 | 29 | 90 |
| 2023 September | 34 | 6 | 40 |
| 2023 August | 25 | 11 | 36 |
| 2023 July | 38 | 8 | 46 |
| 2023 June | 37 | 10 | 47 |
| 2023 May | 80 | 24 | 104 |
| 2023 April | 50 | 5 | 55 |
| 2023 March | 71 | 7 | 78 |
| 2023 February | 49 | 14 | 63 |
| 2023 January | 48 | 4 | 52 |
| 2022 December | 46 | 15 | 61 |
| 2022 November | 33 | 8 | 41 |
| 2022 October | 34 | 14 | 48 |
| 2022 September | 31 | 5 | 36 |
| 2022 August | 48 | 12 | 60 |
| 2022 July | 46 | 15 | 61 |
| 2022 June | 30 | 11 | 41 |
| 2022 May | 44 | 13 | 57 |
| 2022 April | 39 | 12 | 51 |
| 2022 March | 54 | 12 | 66 |
| 2022 February | 52 | 7 | 59 |
| 2022 January | 81 | 10 | 91 |
| 2021 December | 53 | 11 | 64 |
| 2021 November | 61 | 11 | 72 |
| 2021 October | 54 | 17 | 71 |
| 2021 September | 39 | 16 | 55 |
| 2021 August | 42 | 14 | 56 |
| 2021 July | 26 | 12 | 38 |
| 2021 June | 25 | 17 | 42 |
| 2021 May | 45 | 13 | 58 |
| 2021 April | 108 | 15 | 123 |
| 2021 March | 40 | 15 | 55 |
| 2021 February | 41 | 18 | 59 |
| 2021 January | 43 | 7 | 50 |
| 2020 December | 62 | 16 | 78 |
| 2020 November | 58 | 17 | 75 |
| 2020 October | 32 | 8 | 40 |
| 2020 September | 28 | 12 | 40 |
| 2020 August | 56 | 13 | 69 |
| 2020 July | 43 | 17 | 60 |
| 2020 June | 32 | 10 | 42 |
| 2020 May | 43 | 14 | 57 |
| 2020 April | 38 | 21 | 59 |
| 2020 March | 51 | 13 | 64 |
| 2020 February | 52 | 11 | 63 |
| 2020 January | 37 | 5 | 42 |
| 2019 December | 51 | 6 | 57 |
| 2019 November | 42 | 17 | 59 |
| 2019 October | 50 | 9 | 59 |
| 2019 September | 50 | 27 | 77 |
| 2019 August | 42 | 16 | 58 |
| 2019 July | 60 | 16 | 76 |
| 2019 June | 67 | 36 | 103 |
| 2019 May | 152 | 73 | 225 |
| 2019 April | 104 | 17 | 121 |
| 2019 March | 30 | 10 | 40 |
| 2019 February | 15 | 10 | 25 |
| 2019 January | 28 | 4 | 32 |
| 2018 December | 22 | 10 | 32 |
| 2018 November | 37 | 6 | 43 |
| 2018 October | 36 | 5 | 41 |
| 2018 September | 30 | 8 | 38 |
| 2018 August | 20 | 9 | 29 |
| 2018 July | 18 | 7 | 25 |
| 2018 June | 12 | 15 | 27 |
| 2018 May | 20 | 18 | 38 |
| 2018 April | 16 | 7 | 23 |
| 2018 March | 16 | 0 | 16 |
| 2018 February | 17 | 9 | 26 |
| 2018 January | 20 | 4 | 24 |
| 2017 December | 19 | 7 | 26 |
| 2017 November | 11 | 4 | 15 |
| 2017 October | 28 | 6 | 34 |
| 2017 September | 20 | 6 | 26 |
| 2017 August | 33 | 10 | 43 |
| 2017 July | 25 | 10 | 35 |
| 2017 June | 39 | 14 | 53 |
| 2017 May | 42 | 13 | 55 |
| 2017 April | 41 | 5 | 46 |
| 2017 March | 37 | 11 | 48 |
| 2017 February | 31 | 9 | 40 |
| 2017 January | 31 | 4 | 35 |
| 2016 December | 31 | 12 | 43 |
| 2016 November | 52 | 16 | 68 |
| 2016 October | 34 | 16 | 50 |
| 2016 September | 57 | 16 | 73 |
| 2016 August | 45 | 23 | 68 |
| 2016 July | 41 | 9 | 50 |
| 2016 June | 44 | 27 | 71 |
| 2016 May | 51 | 29 | 80 |
| 2016 April | 64 | 38 | 102 |
| 2016 March | 55 | 29 | 84 |
| 2016 February | 54 | 47 | 101 |
| 2016 January | 66 | 23 | 89 |
| 2015 December | 47 | 27 | 74 |
| 2015 November | 58 | 25 | 83 |
| 2015 October | 53 | 27 | 80 |
| 2015 September | 50 | 24 | 74 |
| 2015 August | 73 | 22 | 95 |
| 2015 July | 98 | 21 | 119 |
| 2015 June | 65 | 19 | 84 |
| 2015 May | 62 | 19 | 81 |
| 2015 April | 80 | 27 | 107 |
| 2015 March | 125 | 25 | 150 |
| 2015 February | 120 | 19 | 139 |
| 2015 January | 8 | 7 | 15 |
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