光伏阵列的平面太阳能辐照度和辐射计算-王斯成-国家发改委能源研究所

Model of In-Plane Solar Irradiance for Front and Rear Side of PV Arrays光伏方阵正反面辐照度的计算模型Wang Sicheng ERI, NDRCDec. 4-5, 2018, Weihai, China11th PV Performance and Modeling Workshop PVPMC PV-Inverter Capacity Ratio 光伏-逆变器容配比Battery Capacity Sizing蓄电池容量设计Balancing of Load Profile发电与负荷的平衡In-plane solar irradiance is the basic data to estimate PV power generation and useful in PV system designes In-plane solar irradiance can not be got from weather stations, they only have horizontal solar data. 气象局没有方阵面辐射量和辐照度的数据，只能提供水平面辐照度和辐射量的数据。 PV Arrays in Ground Horizontal CoordinatesThe solar trackers are tracking the solar altitude and the solar azimuth by regulating the array tilted angle and array azimuth. Ground Horizontal PV ArraysFixed PV ArraySolar Azimuth Trackers Manual Regulated ArraysDouble Axis Trackers PV Arrays in Equatorial CoordinatesThe solar trackers are tracking the solar declination and the solar hour angle by regulating the array tilted angle and rotating angle of main axis. 6Tilted E-W Tracking Horizontal E-W Tracking Pole-Axis TrackingDouble Axis TrackingEquatorial Tracking Systems 3 Basic Rules and Concept1. Cosine Rule of Arc in Spherical Tringles[5]The tringle at celestial sphere球面三角边的余弦定律 球面三角中的“边”是角度（弧），不是长度。 2. Cosine Rule of Direct Incidence（直接辐射的余弦定律）ST’ SD’cos SH ’ SD’cosθZ SD’sin S D’ SH ’ /sinα So ST’ SH ’cos / sinα 3. Formula of Solar Altitude α [3,11]太阳高度角的公式能够在很多教科书上找到。Can be found from any text book [3,11] Solar Declination太阳赤纬角28423.5sin 360 365N     Cooper’s Formula How to get the Irradiance on PV front surfaceDT DH 1 cos Z’/2 RT ρQH 1-cos Z’/2QT ST DT RT5 variables are required for the calculation of in-plane total irradiance Q’T 1 Q’ H Total irradiance on horizontal surface kW/m22 S’H Direct irradiance on horizontal surface kW/m23 D’H Diffuse irradiance on horizontal surface kW/m24 cos θ cosine of solar incident angle5 cos Z’ the instantaneous tilted angle of PV arrayST SH x cosθ/sinα S’H x Rb Rb cosθ/sinα is the ratio of tilted irradiance to the horizontal irradiance Diffuse Irradiance can be either Isotropic or AnisotropicIsotropic model [1][ 2] is for low irradiation and cloudy days DT DH 1 cos Z’/2 by RetScreenFor clear and sunny day, anisotropic model should be used [6][8][9]DT’ DH ’（Kcosθ/sinα 1/21 cos Z’1 – K） anisotropic diffuse from circumsolar isotropic sky diffuse K S H /Q0 K the share of circumsolar diffuse which has the same characteristic of direct irradiance. How to get Horizontal Irradiance DataQ’H global irradiance at each hour kW/m2 D’H diffuse irradiance at each hour kW/m2S’H direct irradiance at each hour kW/m2QH DH SH 1. Multi-Year average real-tested hourly data can be found at Weather station or the database of NASA , PVSyst or Meteonorm database or NREL database. 多年平均实测数据（小时量）2. The horizontal hourly data can be got from Daily global and diffuse irradiation data by the distribution models Klein distribution [2,9,10] or Bouguer-Lambert distribution[4]. 从日总辐射量和日散射辐射量，通过日辐射分布模型得到。3. Daily Irradiation data can be got from Monthly Irradiation Data by the way of interpolation [4]. 日辐射量可以通过插值从月辐射量得到。 cosθ forGround Horizontal Coordinates [3,11] By J.E. Braun and J.C. Mitchell and used by RetScreen [3,10,11]. Derived from the rule of spherical tringle cosθ cosZ’sinαsinZ’cosα cos β-γ cosθ forEquatorial H-E-W Tracking [Wang Sicheng]Referenced by the formula of solar altitude α , we can get cosθ sinφsinδcosφcosδ cos ω-Ω General formula of cosθ can be derived for Equatorial Coordinates [Wang Sicheng] Instantaneous Tilted Angle of Array Z’ [3,11]a Fixed Array Z’ Z；it is the same with manual regulated arraysb Azimuth Tracking Z’ Z； c Double Axis TrackingZ’ 90- α。Ground Horizontal Coordinates Instantaneous Tilted Angle of Array Z’ for Equatorial Coordinates can be derived from the rule of spherical tringle. [4, Wang Sicheng] a H-E-W Tracking Z 0, z 0, cosZ’ cosΩ Z’ Ω；b Tilted E-W Tracking Z 0, z z, cosZ’ coszcosΩ；c Pole-Axis Tracking Z φ, z 0, cosZ’ cosφcosΩ；d Double Axis Tracking Z φ, z -δ, Ω ω cosZ’ sin-δsinφ cos-δcosφcosωFor double-axis tracking in ground horizontal coordinates, we have Z’ 90 - αIf we set z δ and b 90- zWe will havecosZ’ sinα Then Z’ 90 - α Now we have all required formulas for θ and Z’For θ Ground Horizontal Coordinates cosθ cosZ’sinαsinZ’cosα cos β-γEquatorial Coordinatescosθ sin90-φZz）sinδcos 90-φZzcosδcosω-ΩFor Z’ Ground Horizontal Coordinates Z’ is always known.Equatorial Coordinates cosZ’ sinz sinZ cosz cosZcosΩ QT’ST’DT’RT’ S’T S’Dcos S’H Rb Rb cosθ/sinα D’TD’H 1cosZ’/2 take diffuse irradiance as isotropicR’TQ’H 1-cosZ’/2 The In-plane Solar Irradiance for Front-sideThe in-plane solar daily irradiation by integrating the irradiance from sunrise ωr to sunset ωs The monthly and yearly irradiation on PV array can be got simply sum-up the daily solar irradiations on PV array. If we use anisotropic model for diffuse irradianceAnd the in-plane daily irradiation by integrating the irradiance from sunrise ωr to sunset ωs How about Bifacial PV ModulesHow to calculate the irradiance on the rear side surface The Main Differences between Front side and Rear side 1、All irradiance received by front side and rear side direct irradiance, diffuse irradiance anisotropic circumsolar and isotropic sky diffuse, and reflected irradiance by the ground; 2、The models for direct and circumsolar diffuse on backside, and the sky diffuse irradiance on backside are the same as that for front side；3、The main difference is the reflected irradiance. Reference [1] Direct Irradiation and circumsolar diffuseSum of Sky Diffuse Irradiance and the Reflected Irradiance by Ground Segment German PaperModel for Rear side Ground Reflection Key Points1. The beam and diffuse sky irradiance components received on the backside may be modeled with the same model used for the front side. This paper only study on reflected irradiance；2. Assuming that the shadowing is caused only by the direct irradiance, and the reflected direct part of irradiance to the backside only from area outside of the shading. 3. The principle of View Factor Fv can be applied for the calculation of ground reflected irradiance at the module rear side. 4. The View Factor denotes the ratio of the irradiance reaching the back surface to the available irradiance on the ground. Reference [2] German Referencethe Backside Reflected IrradianceThe Reflected Irradiance to the backside Diffuse Part Direct Part View Factor Fv Assuming the reflected direct part of irradiance to the rear side only from area outside of the shading. Fraunhofer Developed a Ray Tracing Model The Main Factors to Affect the Irradiance on Rear Side Assumptions for the model on rear side irradiance 1 the direct and isotropic sky diffuse irradiation on backside will follow the same models as that of front side; 2 the Direct and Circumsolar Diffuse part can only be reflected by the area without shading; 3 the installation height above the ground is high enough, so the non-uniformity on backside can be neglected, otherwise we need calculate the backside irradiance column by column （string by string from bottom to top. ; 4 the installation height above the ground is high enough, so the transparent ratio does not further affect the backside irradiance. Or, we add a percentage of transparent ratio to the formulas; 5 The affect from the incident angle will be ignored, if calculating the power generation from backside, we can add a coefficient; 6 the reflected Direct part of irradiance will relay on the Shading Ratio or Shining Ratio, and not relevant to GCR.