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 = Previsão de Potência Solar Utilizando Métodos de Simulação de Monte Carlo, K-= Means= e SVM: Um Estudo de Caso na Região Metropolitana de Vitória/ES

 

Solar Power Forecasting Usin= g Monte Carlo Simulation, K-Means, and SVM Methods: A Case Study in the Metropolitan Region of Vitória/ES

 

 =

Caroline Tedesco Santos<= /span>

            http://orcid.org/0000-0002-1= 453-2847<= /o:p>

Mestre em Energia. Universidade Federal do Espírito Santo (UFES) – Brasil. tedescocarol@hotmail.com =

            Ivaniel Fôro Maia

            http://orcid.org/0000-0002-1508-9074

Especialista em Gestão de Emergências em Saúde Pública. Instituto Capixaba de Pesquisa, Assistência Técnica e Exte= nsão Rural (INCAPER) – Brasil. ivanielforo@gmail.com

Augusto César Rueda Medina

            http://orcid.org/0000-0002-4= 291-3153

Doutor em Engenharia Elétrica. Universi= dade Federal do Espírito Santo (UFES) – Brasil. augusto.rueda@ufes.br

Jussara Farias Far= din

            http://orcid.org/0000-0003-4= 785-556X

Doutora em Engenharia Elétrica. Univers= idade Federal do Espírito Santo (UFES) – Brasil. jussara@ele.ufes.br

 

 

 

RESUMO

O estu= do apresenta uma abordagem para prever a potência gerada por sistemas fotovoltaicos considerando a variabilidade da cobertura de nuvens. A partir= da combinação da Simulação de Monte Carlo, do método de agrupamento K-Means e de previsões com a ferramenta SVM, foram analisados dados de radiação solar da região metropolitana de Vitória/ES. Os modelos mostraram-se eficazes, produzindo previsões precisas com baixos índ= ices de erro, mesmo sob diferentes condições climáticas. Os resultados indicam q= ue o uso de dados reais e a segmentação adequada dos cenários meteorológicos permitem compreender como a variação da radiação solar afeta a geração de energia. Essa abordagem contribui para o planejamento e a otimização da ene= rgia solar e evidencia a importância de estudos futuros que integrem novas técni= cas de aprendizado de máquina para aperfeiçoar as previsões.

Palavras-chave: radiação solar; cenários meteorológicos; cobertura de nuvens.  

 

ABSTRACT

This study presents an appro= ach to forecasting the power generated by photovoltaic systems while considering c= loud cover variability. By combining Monte Carlo Simulation, the K-Means clustering method, and predictions using the SVM tool, solar radiation data from the metropolitan region of Vitória-ES were analyzed. The models proved= to be effective, delivering accurate forecasts with low error rates even under varying weather conditions. The results indicate that using real data and appropriately segmenting weather scenarios allows for a better understandin= g of how solar radiation variation affects power generation. This approach suppo= rts solar energy planning and optimization and highlights the need for future studies that integrate new machine learning techniques to further enhance forecasting accuracy.

Keywords: solar radiation; weather scenarios; cloud cover.=

 

Recebido em 16/04/2025.  Aprovado em 02/09/2= 025. Avaliado pelo sistema double blind peer review. Publicado conforme normas da ABNT.

https://doi.org/10.22279/navus.v16.2116


 

1 INTRODUÇÃO

 

Nos últimos = anos, os sistemas de distribuição de energia elétrica têm registrado um aumento expressivo na adoção de fontes de energia distribuída (DERs). Esse avanço é impulsionado pela busca por alternativas energéticas mais sustentáveis e menos poluentes, diante da comprovada insustentabilidade do modelo tradicional baseado em combustíveis fósseis. As DERs, especialmente aquelas provenientes de fontes renováveis, têm se mostrado eficientes na redução das emissões de dióxido de carbono (CO) e na mitigaComo alterna= tiva promissora aos combustíveis fósseis, a energia solar vem se destacando em pesquisas e no mercado por suas inúmeras vantagens. A geração fotovoltaica = não emite poluentes, exige pouco espaço e apresenta baixos custos de manutenção, configurando-se como uma das opções mais viáveis e sustentáveis para o futu= ro energético (Ferraz; Ferraz & Rueda, 2024). O elevado potencial de irradiação solar no Brasil torna essa fonte uma alternativa estratégica na busca por um desenvolvimento nacional mais limpo e sustentável.

Para que a e= nergia solar assuma o papel de principal fonte de gera= ção elétrica no país e substitua gradualmente as fontes não renováveis, é imprescindível compreender o comportamento da irradiação solar ao longo do tempo. Isso inclui analisar fatores externos ao controle humano, como a presença de nuvens e as variações climáticas, que afetam diretamente a capt= ação de energia solar. Esse conhecimento é essencial para o planejamento eficien= te do uso da fonte renovável e para assegurar a confiabilidade do fornecimento= de energia elétrica em escala nacional.

A radiação proveniente do Sol é responsável por abastecer a atmosfera da Terra e suste= ntar os processos vitais, sendo a principal fonte de energia do planeta (Paralič, 2020). As nuvens exercem papel determin= ante no sistema climático, pois interferem no balanço de radiação solar (Yuan et al., 2016). Suas propriedades ópticas e o grau de cobertura (Zhang; Zha= ng, 2017) fazem com que a radiação varie rapidamente ao longo do dia, influenci= ando diretamente a geração de energia fotovoltaica. A presença e a densidade das nuvens afetam a quantidade de radiação disponível, impactando a eficiência = e a previsibilidade da geração elétrica.

Este artigo = tem como objetivo analisar a correlação entre a formação de diferentes tipos de nuve= ns e as variações na radiação solar, a fim de compreender o impacto dessas variá= veis na geração de energia elétrica a partir da fonte solar. A investigação conc= entra-se na previsão da irradiação solar, considerando os efeitos da presença e da densidade das nuvens. Para isso, propõe-se o desenvolvimento de um método de previsão baseado em técnicas de deep learning, visando obter estimativas mais precisas e representativas da realidade. Essa abordagem é viável porque o banco de dados utilizado é comp= osto por medições reais da região metropolitana de Vitória, no Espírito Santo, um local relevante tanto por seu contexto climático quanto por seu elevado potencial para geração de energia solar.

 <= /o:p>

2 ESTADO DA ART= E

 <= /o:p>

A crescente integração de fontes renováveis de energia, especialmente a solar, aos sist= emas de distribuição elétrica tem impulsionado o desenvolvimento de métodos para previsão precisa da irradiância solar. Essa previsão é fundamental para assegurar a confiabilidade e a eficiência da geração de energia, uma vez qu= e a radiação solar é naturalmente variável e influenciada por fatores meteorológicos, como a cobertura de nuvens.

De acordo co= m Reikard (2009), métodos tradicionais de séries tempor= ais já apresentavam bom desempenho na previsão da radiação solar em horizontes de curto prazo, sobretudo quando aplicados a dados com alta resolução temporal. Entretanto, o advento de técnicas baseadas em inteligência artificial, como= as redes neurais artificiais (ANNs), trouxe avanços expressivos em termos de acurácia. Nesse contexto, Di Piazza et al. (2019) demonstraram que modelos de redes neurais profundas superam os métod= os estatísticos clássicos, especialmente em aplicações que envolvem séries temporais de demanda e geração de energia solar, evidenciando o potencial dessas abordagens para o setor energético.

Nos últimos = anos, modelos baseados em deep learning= têm se destacado na previsão da irradiância solar, devido à sua capacidade de l= idar com dados intermitentes, instáveis e não estacionários. Conforme revisado p= or Kumari e Toshniwal (2021), técnicas como redes neurais convolucionais (CNN), redes neurais recorrentes do tipo LSTM, redes= de crença profunda (DBN) e redes de estado de eco (ESN) apresentam desempenho superior aos métodos estatísticos e de machine learning tradicionais. Além disso, modelos híbridos têm se mostrado particularmente promissores. Um exemplo é o modelo CEEMDAN–CNN–LSTM, proposto por Gao et al. (2020),= que integra a decomposição empírica adaptativa em modo completo (CEEMDAN) à arquitetura CNN-LSTM para melhorar a extração de características dos dados históricos e prever a irradiância solar horária. Os experimentos realizados= com diferentes bases de dados reais, representando variados tipos climáticos, mostraram que esse modelo não apenas supera de forma significativa técnicas isoladas, mas também mantém desempenho estável, alcançando um erro quadráti= co médio (RMSE) de 38,49 W/m². Esses avanços confirmam a eficácia dos modelos híbridos de deep learning e refor= çam sua importância para o planejamento e a operação eficiente de sistemas fotovoltaicos em redes inteligentes.

No que se re= fere à influência das nuvens na radiação solar, Wang et al. (2021) conduzir= am uma investigação abrangente utilizando dados do satélite CloudSat para analisar a contribuição radiativa de diferentes fases de nuvens (gelo, mista e água super-resfriada) na região do Planalto Tibetano. Os resultados indicaram que, além de apresentarem variações sazonais, essas fases impacta= m de maneira distinta a radiação incidente. As nuvens de gelo foram predominante= s no inverno, enquanto nuvens mistas e super-resfriadas se destacaram no verão, afetando de forma significativa o balanço energético atmosférico. De forma complementar, Zhang et al. (2022) analisaram a interação entre aerossóis, nuvens e radiação solar por meio de simulações com o modelo WRF-= Chem, evidenciando que propriedades radiativas das nu= vens — como fração de cobertura e tipo — desempenham papel central na variabilidad= e da energia solar em diferentes regiões da China. Dentre os efeitos observados,= o efeito radiativo das nuvens (CRE) mostrou-se dominante em várias localidade= s, especialmente no Delta do Rio das Pérolas, onde contribuiu com até 78,4% pa= ra o aumento da energia solar disponível. Esses achados reforçam que propriedades ópticas das nuvens, como espessura, fase e distribuição espacial, são determinantes para a precisão na previsão da irradiância solar e, consequentemente, para o desempenho de sistemas fotovoltaicos.

No contexto nacional, estudos também têm avançado no uso de dados reais para previsão da potência solar. Um exemplo relevante é apresentado por Ramos et al. (2022), que avaliaram o desempenho do modelo WRF-Solar na previsão da irradiância global horizontal (GHI) com até 48 horas de antecedência. O est= udo foi realizado no Centro de Referência em Energia Solar da Eletrobras Chesf (CRESP), em Petrolina/PE, durante os meses de julho e outubro de 2020, representando períodos de menor e maior incidência solar. Os resultados mostraram que o WRF-Solar superou o modelo de controle (WRF-CTL) em termos = de precisão, sobretudo em condições de céu claro e nublado, resultado atribuíd= o à parametrização mais avançada de nuvens. Contudo, ambos os modelos apresenta= ram limitações na representação do ciclo diurno da GHI, com maiores erros concentrados no período da manhã. Esses achados reforçam o potencial do WRF-Solar para previsões de curto prazo, ao mesmo tempo em que destacam a necessidade de calibrações adicionais e validações em diferentes contextos climáticos para ampliar sua aplicabilidade.

Dessa forma, evidencia-se a necessidade de abordagens que integrem dados reais de cobert= ura de nuvens, com maior granularidade e qualidade, a modelos de previsão basea= dos em deep learning. Além disso, há = espaço para pesquisas que considerem as especificidades regionais do clima tropica= l, como as da região Sudeste do Brasil, cujo regime de nuvens influencia diretamente a geração solar fotovoltaica.

 <= /o:p>

3 METODOLOGIA

 =

3.1 Característ= icas gerais do clima local

 <= /o:p>

O Estado do = Espírito Santo está localizado entre as coordenadas 17º52' e 21º17' de latitude Sul e 41º54' e 39º38' de longitude Oeste. Seu território, com aproximadamente 46.= 184 km², situa-se na costa sudeste do Brasil e faz divisa com Minas Gerais a oe= ste, Bahia ao norte, Rio de Janeiro ao sul e o Oceano Atlântico a leste. O estado apresenta, predominantemente, dois padrões climáticos: o tropical chuvoso e= o tropical de altitude (Seki et al., 2021)= .

O clima trop= ical caracteriza-se por temperaturas elevadas e pela alternância entre uma estaç= ão seca e outra chuvosa, sendo típico de áreas de média e baixa latitude (Mede= iros et al., 2020). Nessa configuração, o verão apresenta altos índices pluviométricos, enquanto o inverno é marcadamente seco, resultando em uma distribuição não uniforme das chuvas ao longo do ano (INPE, 2023). Essa condição varia de acordo com a latitude: quanto maior a distância em relaçã= o à linha do Equador, maior é a duração da estação seca, que pode se estender p= or mais de oito meses sem registros de chuva (Mastella et al., 2019).

Na faixa lit= orânea do Espírito Santo, a estação chuvosa ocorre, em média, entre outubro e abri= l, enquanto os meses mais secos vão de junho a agosto — sendo agosto o menos chuvoso do ano. Maio e setembro são considerados meses de transição (Incape= r, 2023).

 <= /o:p>

Para compor = o banco de dados referente às condições de nebulosidade no local de estudo, delimitou-se o período chuvoso e o período seco dos últimos seis anos (2019-2023). Como o período seco se restringe a apenas três meses, o período chuvoso foi padronizado para os três meses de maior índice pluviométrico: outubro, novembro e dezembro (Incaper, 2023). Assim, o período de análise considerou os dados de outubro a dezembro de 2013 e de junho a agosto de 20= 23, organizados conforme apresentado no Quadro 1.

 <= /o:p>

Quadro 1 – Divisão entre meses secos e chuvosos na região de estudo

        Mês

Período

Jan

Fev=

Mar

Abr=

Mai

Jun=

Jul

Ago=

Set

Out

Nov=

Dez

Seco

 

 

 

 

 

X

X

X

 

 

 

 

Chuvoso

 

 

 

 

 

 

 

 

 

X

X

X

Fonte: Autores (2025).

 <= /o:p>

3.2 Coleta de d= ados

 <= /o:p>

A disponibil= idade dos dados de nebulosidade é fornecida pelo METAR (M= ETeorological Aerodrome Report), boletim meteorológico re= gular emitido por aeródromos brasileiros. Esse relatório descreve de forma comple= ta as condições meteorológicas observadas em um aeródromo específico. Cada MET= AR é gerado a cada 60 minutos, com base na observação meteorológica dos últimos = 10 minutos (DECEA, 2019). Para este estudo, os dados foram obtidos na REDEMET (2023), referentes ao Aeroporto de Vitória (SBVT), e decodificados por meio= do software Metar Reader and = Decoder v3.1, da Flight = Utilities (2023). A estação de medição do METAR está localizada nas coordenadas 20°15'9.61" S e 40°17'11.87" O, com um raio de abrangência de 10 = km.

Como os dado= s de nebulosidade seriam correlacionados com os de irradiação solar, foram selecionadas apenas as observações realizadas durante o período de insolaçã= o. Dessa forma, o intervalo considerado foi das 07h às 17h no período seco e d= as 06h às 18h no período chuvoso. Os dados de radiação solar referentes aos me= smos intervalos foram cedidos pelo Incaper, provenientes de sua estação meteorológica de superfície localizada nas coordenadas 20°16'15.89" S e 40°18'21.77" O. Os registros são expressos em kJ/m² e possuem raio de abrangência de 25 km.

A distância = entre a estação METAR e a estação meteorológica é de 2.877 m em linha reta, conforme ilustrado na Figura 1. Essa proximidade não compromete a correlação dos dad= os, uma vez que o raio de abrangência de ambas as estações cobre integralmente = a área de estudo.

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

Figura 1 – Distância entre a estação meteorológica e estação METAR

= Fonte: Autores (2025).

 <= /o:p>

3.3 Análise de tendência

 

3.3.1 Simulação de Monte Carlo

 <= /o:p>

A Simulação = de Monte Carlo é uma técnica que utiliza simulações aleatórias repetidas para modela= r o comportamento de sistemas complexos. Quando se pretende prever um cenário futuro com várias incertezas, a Simulação de Monte Carlo gera cenários variados, baseando-se em distribuições de probabilidade para essas incertez= as, o que resulta em muitos resultados possíveis (Garg; Yadav & Aswal, 2019).=

A fórmula bá= sica utilizada pela Simulação de Monte Carlo é expressa conforme Equação 1.

                                                   (1)

 <= /o:p>

Onde:=

 representa a estimativa esperada de X;

 é o número de simulações realizadas;

 é um = valor amostrado a partir da distribuição de probabilidade especificada;

 é a função de interesse aplicada aos val= ores amostrados .

 <= /o:p>

Essa fórmula= calcula a média dos resultados obtidos a partir de cada simulação, aproximando assi= m o valor esperado para a variável de interesse.

Neste estudo= , a técnica de Monte Carlo foi utilizada para criar diferentes cenários de comportamento da variável de interesse ao longo do tempo. Por exemplo, ao analisar a radiação solar, a Simulação de Monte Carlo permite a geração de cenários variados com base em padrões climáticos distintos, a fim de proporcionar uma visão mais ampla dos possíveis comportamentos futuros dos dados.

Combinada a = ela, utilizou-se o K-Means, isso se deu devid= o à necessidade de segmentar grandes volumes de dados em grupos com característ= icas semelhantes, permitindo identificar padrões distintos e facilitando a análi= se detalhada. A aplicação do K-Means possib= ilitou agrupar dados históricos em diferentes cenários, como condições climáticas = ou operacionais, que apresentam comportamento homogêneo. A partir desses clust= ers, a simulação de Monte Carlo foi implementada para modelar a variabilidade das variáveis de entrada em cada grupo, gerando múltiplas simulações que result= aram em distribuições probabilísticas específicas para cada cenário.

 

3.3.2 Agrupamento K-Means

 

O K-Means é uma técnica de agrupamento que organiza d= ados em diferentes grupos (ou clusters) com base nas semelhanças entre eles. Sua operação é bastante direta: ele busca padrões nos dados e agrupa os pontos = que são mais semelhantes entre si em um mesmo grupo (Huang et al., 2021)= .

A fórmula bá= sica utilizada pelo K-Means é a minimização d= a soma das distâncias quadradas entre cada ponto e o centro do cluster ao qual ele pertence. O objetivo é encontrar 𝑘 clusters, minimizando a variabilidade interna dos clusters. A fórmula matemática do K-Means é expressa como na= Equação 2.

                                              (2)

 

Onde:

 é a função objetivo que representa a som= a das distâncias quadradas entre os pontos e os centroides dos clusters;

 é o número de clusters;

 é o número de pontos no cluste= r .

 representa o ponto  pertencente ao cluster .

 é o centroide do cluster <= span style=3D'mso-bookmark:_Hlk4746433'> .

 representa a distância euclidiana entre o ponto  e o centroide  elevado ao quadrado.

 

Neste contexto, o método K-Means é aplicado pa= ra identificar padrões e tendências ocultas nos dados. Ao analisar as variaçõe= s de irradiação solar ao longo do ano, essa técnica auxilia na categorização de diferentes condições, como dias ensolarados, parcialmente nublados ou chuvo= sos. Tal segmentação é fundamental para que os dados possam ser analisados com m= aior nível de detalhe, possibilitando uma compreensão mais precisa das características de cada grupo identificado.

A definição do número de clusters foi realizada por meio da técnica do cotovelo, amplamente utilizada para determinar o ponto ótimo em que a adiçã= o de novos grupos deixa de trazer ganhos significativos na redução da variabilid= ade interna. Essa técnica consiste em calcular a soma dos erros quadráticos méd= ios (ou variabilidade interna) para diferentes quantidades de clusters e= , em seguida, representar esses valores em um gráfico. O ponto de inflexão da cu= rva, que se assemelha a um "cotovelo", é adotado como o número ideal d= e clusters a ser utilizado (Fajar; Adi & Widodo, 2018), equilibrando a complexidade do modelo e a precisão da segmentação.

A técnica do cotovelo utiliza a fórmula da Soma das Distâncias Quadradas Intra-Clusters (Within-Cluster Sum of Squares, ou WCSS) para avaliar a variabilidade interna dos clusters. A fórmula do WCSS é dada pela Equação 3= .

 

 

 

                                                 =                                                            (3)

 <= /o:p>

Onde:

 é o número de clusters;

 representa um ponto de dado pertencente = ao cluster ;

 é o centroide do cluster <= span style=3D'mso-bookmark:_Hlk4746433'> ;

 é a distância euclidiana quadrada entre o ponto  e o centroide .

 

3.3.3 Máquina de Vetores de Suporte (SVM)

 

A Máquina de Vetores de Suporte (SVM, Support Vec= tor Machine) é uma técnica de aprendizado de máquina amplamente utilizada para tarefas de classificação e regressão. Seu objetivo principal é identificar = uma linha — ou um hiperplano, no caso de dados em dimensões superiores — que se= pare de forma ótima as diferentes classes ou permita prever uma variável alvo (Cervantes et al., 2020).

Nos problemas de classificação, o SVM procura encontrar o hiperplano que maximi= ze a margem entre as classes de dados. Essa margem corresponde à distância entre= o hiperplano e os pontos mais próximos de cada classe, denominados vetores de suporte. Dessa forma, o algoritmo seleciona o hiperplano que oferece a maior margem possível, garantindo uma separação mais robusta entre as classes (Tharwat, 2019).

Em situações envolvendo duas classes, o objetivo é determinar um hiperplano que satisfaça a condição de maximização da margem, conforme expresso na Euqação 4.

                                               =        (4)

 

Onde:

 é o vetor de pesos que define a orientaç= ão do hiperplano.

 é o vetor de características de um ponto= de dado.

 é o viés do hiperplano.

 

Em problemas de regressão, a SVM é adaptada para prever valores contínuos (Deo et al., 2016). Nesse caso, a técnica tenta encontrar uma função que minimize o erro dentro de uma margem de tolerância= (ϵ). Isso é feito de forma similar à classificação, mas o objetivo é ajustar uma linha (ou hiperplano) que passe pela maioria dos dados, mantendo os desvios dentro de uma faixa específica.

Para avaliar a eficácia de cada uma das ferramentas utilizadas, será calculado o Erro Médio Absoluto (MAE) de cada abordagem. O MAE é uma métrica que mede a média das diferenças absolutas entre os valores previstos e os valores reai= s, proporcionando uma visão clara da precisão de cada modelo, ele é dado pela Equação 5.

   =                                                                                                          (5)

 

Onde:

 é o número total de observações;

 representa o valor real na observação ;

 representa o valor previsto pelo modelo = na observação i ;

 é o valor absoluto da diferença entre o = valor real e o valor previsto.

 

A ferramenta que apresentar o menor MAE foi considerada a mais eficaz, indica= ndo sua capacidade superior de previsão e modelagem dos dados analisados.<= /o:p>

 

4 RESULTADOS E DISCUSSÃO

 

Os dados de irradiação solar utilizados neste estudo foram obtidos na estação meteorológica do Incaper, enquanto as informações sobre cobertura de nuvens foram extraídas dos relatórios METAR, que fornecem observações detalhadas e= em tempo real das condições meteorológicas em aeródromos. Essas duas bases de dados foram fundamentais para assegurar a precisão das análises e previsões realizadas. Para o tratamento dos dados, todas as informações foram reunida= s em uma planilha do Excel e organizadas linha a linha, de acordo com o dia e a = hora de cada medição, garantindo o alinhamento entre os registros de irradiação = e de cobertura de nuvens.

Nas medições de cobertura de nuvens, o céu é dividido em oitavos, denominados <= span class=3DSpellE>octas, que representam diferentes frações de ocupação= do céu. Cada octa corresponde a um grau específico= de cobertura de nuvens, afetando diretamente a quantidade de radiação solar que atinge a superfície. Por exemplo, um céu com 0 octas (céu limpo) permite a máxima incidência de radiação solar, enquanto o aumen= to do número de octas reduz progressivamente a rad= iação que atravessa a atmosfera. No entanto, essa redução não é linear, o que exi= ge a utilização do Fator de Modificação de Nuvens (CMF, Cloud Modification Factor) para estimar a irradiação correspondente a cada condição de cobertu= ra.

O CMF é uma métrica que quantifica o efeito das nuvens na atenuação da radiaç= ão solar incidente na superfície terrestre (Jesus, 2023). O cálculo da irradia= ção solar acima das nuvens possibilita estimar a quantidade de radiação que che= ga ao topo da camada de nuvens e, a partir disso, determinar o valor efetivo de irradiação em cada octa para cada medição.=

A relação básica é expressa de acordo com a Equação 6.

                                                        (6)

 

Onde:

 é a irradiação solar no topo das nuvens = (ou irradiação sem a influência das nuvens);

 é a irradiação solar medida na superfíci= e;

 é o Fator de Modificação de Nuvens, que = varia entre 0 e 1 e representa a fração da radiação que passa através das nuvens e atinge a superfície. Valores de CMF mais próximos de 1 indicam poucas nuven= s ou céu claro, enquanto valores menores indicam maior cobertura de nuvens.=

 

Em geral, o CMF é calculado da seguinte forma:

                                                           (7)

O índice  pode ser observado no Quadro 1.

 

Quadro 1 - Transmissão de UV-B para Tipos de Nuvens

Estágio

Tipo de nuvem

k

Alto (Acima de 8 km)

Cirrus (Ci)

≈ 0.2 0.3

Cirrocumulus (Cc)

≈ 0.2 0.3

Cirrostratus (Cs)

≈ 0.3 0.4

Médio (2 – 8 km)

Altocumulus (Ac)

≈ 0.5 0.6

Altostratus (As)

≈ 0.6 0.7

Nimbostratus (Ns)

≈0.8 0.9

Baixo (Até 2 km)

Stratocumulus (Sc)

≈ 0.6 0.7

Stratus (St)

≈ 0.7 0.8

Cumulus (Cu)

≈ 0.5 0.6

Cumulonimbus (Cb)

≈ 0.7 0.8

Fonte: Adaptado de Iqbal (1983), Kuchinke e = Nunez (1999) e Jesus (2015).=

Após o cálculo do CMF para cada octa ao longo de seis anos, tanto para o período chuvoso quanto para o período seco, foi possível calcular a radiação solar e a potência disponível para cada octa, com base nos dados da radiação medida.

Com os dados de potência e radiação, iniciaram-se as previsões, utilizando como variáveis preditoras a Radiação e o CMF, e como variável alvo a Potência, q= ue é o parâmetro a ser previsto. Essa abordagem permitiu modelar a influência di= reta da radiação solar e da cobertura de nuvens sobre a geração de energia, possibilitando uma estimativa mais precisa do desempenho do sistema em diferentes cenários climáticos.

 

4.1 Simulação de Monte Carlo e agrupamento K-Means

 <= /o:p>

Os resultados gerados foram divididos por octa, ou seja, fora= m 8 previsões realizadas no período chuvoso e 8 previsões no período seco. O resultado da técnica do cotovelo pode ser visto na Figura 2 (2a à 2h) para o período chuvoso e Figura 3 (3a à 3h) para o período seco, o que resulta a escolha dos clusters.

 

 

 

 

Figura 2 – Escolha dos clusters pela téc= nica do cotovelo período chuvoso=

= Fonte: Autores (2025).

 <= /o:p>

 

Figura 3 – Escolha dos clusters pela téc= nica do cotovelo período seco

= Fonte: Autores (2025).

=  

Para o período chuvoso, definiu-se o núme= ro de clusters como cinco, enquanto para o período seco foram utilizados seis clusters<= /i>. Essas quantidades foram determinadas a partir da identificação do ponto de inflexão (“cotovelo”) nos respectivos gráficos, que indicam o número ideal = de clusters para cada regime climático.

Assim, os agrupamentos foram realizados utilizando o método K-Means, e as previs= ões subsequentes foram conduzidas por meio da Simulação de Monte Carlo. Os resultados do MAE obtidos para cada octa= são apresentados na Tabela 1.

 

Tabela 1 – Resultado do MAE das simulações de Monte Carlo para o período chuvoso

Octa

Média de Potência: 418,41

Mediana de Potência: 342,12

MAE

Proporção do MAE em relação à Média

Proporção do MAE em relação à Mediana<= /span>

1

1,5951219512195123

0,38%

0,47%

2

1,5863414634146342

0,38%

0,46%

3

1,6018118466898954

0,38%

0,47%

4

1,5887108013937283

0,38%

0,46%

5

1,5974912891986062

0,38%

0,47%

6

1,5689198606271777

0,37%

0,46%

7

1,5662717770034844

0,37%

0,46%

8

1,566829268292683

0,37%

0,46%

Fonte: Autores (2025).

 

A proporção = do MAE em relação à média de potência manteve-se bastante baixa, variando entre 0,= 37% e 0,38%. Esse resultado indica que o erro absoluto médio representa menos de meio por cento da potência média durante o período chuvoso, evidenciando qu= e o modelo apresenta alta precisão mesmo sob a influência da cobertura de nuvens em ca= da octa.

Quando compa= rado à mediana de potência, o MAE também se mostrou baixo, variando entre 0,46% e 0,47%. Essa proporção ligeiramente superior à da média sugere que o MAE exe= rce maior impacto relativo sobre a mediana, o que pode ser explicado pelo fato = de a mediana ser um valor central inferior, aumentando a representatividade percentual do erro.

Observa-se a= inda que os valores de MAE se mantiveram muito próximos entre os oito octas, variando em uma faixa estreita de 1,566= a 1,601. Essa consistência indica que o modelo não foi significativamente influenciado pela cobertura de nuvens em diferentes oitavos, sugerindo robu= stez e capacidade de capturar as variações de potência de forma consistente.

Os resultados referentes ao período seco são apresentados na Tabela 2.

 

Tabela 2 – Resultado do MAE das simulações de Monte Carlo para o período seco

Octa

Média de Potência: 340,06

Mediana de Potência: 319,07

MAE

Proporção do MAE em relação à Média

Proporção do MAE em relação à Mediana<= /span>

1

1,81782243452479

0,54%

0,57%

2

1,8252347224509966

0,54%

0,57%

3

1,819799044638445

0,54%

0,57%

4

1,802997858672377

0,53%

0,57%

5

1,7692307692307692

0,52%

0,55%

6

1,8188107395816175

0,54%

0,57%

7

1,8059627738428594

0,53%

0,57%

8

1,8150222368637787

0,53%

0,57%

Fonte: Autores (2025).

 

Os valores d= e MAE para cada octa variaram entre 1,769 e 1,= 825, indicando apenas uma ligeira variação dos erros entre os diferentes oitavos. Esse resultado confirma que o modelo é consistente ao lidar com distintos padrões de cobertura de nuvens durante o período seco.

A proporção = do MAE em relação à média de potência permaneceu baixa, entre 0,52% e 0,54%, enqua= nto em relação à mediana variou de 0,55% a 0,57%. Esses valores demonstram que o erro absoluto médio corresponde a pouco mais de meio por cento da potência = média nesse período. Apesar de serem levemente superiores aos do período chuvoso, esses resultados ainda evidenciam elevada precisão do modelo.

A pequena di= ferença observada entre os períodos chuvoso e seco reforça que o modelo é robusto e capaz de lidar adequadamente com diferentes condições de cobertura de nuven= s e variações na irradiação solar. Dessa forma, confirma-se sua versatilidade p= ara oferecer previsões confiáveis ao longo de diferentes cenários climáticos.

 

4.2 Máquina de Vetores de Suporte (SVM)

 <= /o:p>

A Figura 4 (= 4a à 4h) expõe os resultados das previsões dos oito oitavos no período chuvoso e a distribuição dos resíduos dos erros.

 <= /o:p>

Figura 4 – Resultado SVM do período chuv= oso

= Fonte: Autores (2025).

=  

Figura 5 – Resultado SVM do período seco=

= Fonte: Autores (2025).

 <= /o:p>

Os valores d= e MAE variaram de 10,72 no primeiro octa até 1= 5,36 no oitavo, apresentando uma progressão crescente. Esse comportamento sugere= que os erros absolutos se tornam maiores à medida que a cobertura de nuvens aum= enta ou as condições climáticas se tornam mais complexas ao longo dos oitavos.

Nos três pri= meiros octas, os MAEs permaneceram na faixa de 9,96 a 10,72, indicando maior precisão nessas condições. Já nos oitavos subsequentes, os erros se elevaram, evidenciando desafios adicionais na previsão em cenários de maior variabilidade climátic= a.

A análise dos resíduos revelou uma distribuição com desvio positivo, indicando que o mode= lo tende a subestimar os valores reais em determinadas situações. Entretanto, a presença de picos próximos a zero na maioria dos gráficos é um indicativo favorável, pois demonstra que, na maior parte das previsões, os erros são reduzidos ou muito próximos de zero.

 

3 CONSIDERAÇÕES= FINAIS

 <= /o:p>

Conclui-se que a modelagem preditiva da potência disponível, desenvolvida a partir dos dados de radiação solar e utilizando as técnicas de Simulação de Monte Carlo e agrupamento K-Means, mostrou-se eficaz para a análise das variá= veis de radiação solar e cobertura de nuvens. A abordagem proposta permitiu identificar padrões de variabilidade nos dados e gerar previsões precisas de potência, mesmo em cenários meteorológicos distintos. A aplicação da SVM evidenciou maior sensibilidade à variabilidade de potência quando considera= da a cobertura de nuvens.

O uso de dados reais da região metropo= litana de Vitória-ES, aliado à incorporação do CMF, contribuiu de forma significativa para o aumento da precisão das previsões, reforçando o potencial do modelo para apoiar a gestão eficiente da geração = de energia solar. Contudo, persistem desafios relacionados à detecção de padrõ= es mais complexos de cobertura de nuvens e às variações climáticas específicas= da região. Nesse sentido, recomendam-se estudos futuros voltados à integração = de novas técnicas de aprendizado de máquina, a fim de aprimorar ainda mais a qualidade das previsões.

 

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Previsão de Potência Solar Utilizando Métodos de Simulação de Monte Carlo, K-Mean= s e SVM: Um Estudo de

Caso na Região Metropolitana de Vitória/ES

Caroline Tedesco Santos; Ivaniel Fôro Maia; Augusto César Rueda Medina; Jussara Farias Fardin                                                 =               

IS= SN 2237-4558    Navus    <= /span>Florianópolis    SC    <= /span>v. 16 • p. 01-7jan./dez. 2025

7

 

 

 

                  =                                                                            =        

 

ISSN 2237-4558    Navus  • &n= bsp;Florianópolis  •  SC    v.9    n.2    <= /span>p. XX-XX    abr./jun. 2019

 

 

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