## 物理代写|光电技术代写Photovoltaic Technology代考|The Probability Algorithm

According to the viewpoint of probability, the two-stage method and CVT actually belong to probability algorithms. For an input/output system, $X$ and $Y$ are the input and output sets, respectively. Set the input variable $x \in X$, output variable $y \in Y$ and $\Omega={(x, y) \mid x \in \mathrm{X}, y \in \mathrm{Y}}$, where $X=\left{x \mid x=f_{\mathrm{R}}\right}, Y=\left{u_{\mathrm{MPP}}, \bar{u}{\mathrm{MPP}}\right}$. The function Prob could be defined as the probability function for output $y$ is equal to $u{\mathrm{MPP}}$ if the input $x$ is equal to $f_{\mathrm{R}}[32-36]$.
$$\operatorname{Prob}\left(f_{\mathrm{R}}, u_{\mathrm{MPP}}\right)=f_{Y \mid X}\left(u_{\mathrm{MPP}} \mid f_{\mathrm{R}}\right)=\frac{f\left(f_{\mathrm{R}}, u_{\mathrm{MPP}}\right)}{\int_{\alpha \in Y} f\left(f_{\mathrm{R}}, \alpha\right) \mathrm{d} \alpha}$$
where $f$ is the distribution function of $\Omega$. As discussed above, there are three different types of probahility finctions about $u_{\mathrm{MI}}$, , i.c., $\operatorname{Proh}\left(f_{\mathrm{B}}(u), u_{\mathrm{M}}\right)$, Prok $\left(f_{\mathrm{R}}(p), u_{\mathrm{MPP}}\right), \operatorname{Prob}\left(f_{\mathrm{R}}(u, p), u_{\mathrm{MPP}}\right)$, can be proposed based on the statistical regularities in $P-U$ coordinate system. From the previous studying, the two functions, $\operatorname{Prob}\left(f_{\mathrm{R}}(u), u_{\mathrm{MPP}}\right)$, and $\operatorname{Prob}\left(f_{\mathrm{R}}(u, p), u_{\mathrm{MPP}}\right)$ in this probability theory, can be illustrated with the example of CVT method and two-stage tracing method. The CVT method is derived from the observation that, usually, the MPP voltage is located at a fraction of open-circuit voltage $\left(U_{\mathrm{OC}}\right)$. Then, the probability function of this method can be expressed by $\operatorname{Prob}\left(f_{\mathrm{R}}(u), u_{\mathrm{MPP}}\right)$, where $f_{\mathrm{R}}(u)=k U_{\mathrm{OC}}, k=0.8$.

## 物理代写|光电技术代写Photovoltaic Technology代考|Maximum Power Point Estimation

Maximum power point estimation (MPPE) techniques represent the simplest form of conventional technique for controlling the power captured from a PV system. These techniques utilise a measured value and predefined relationships to identify a likely MPP location. The predefined relationship is usually defined between known quantities for uniform environmental conditions.

The simplest MPPE methods rely on relating either the short-circuit current or the open-circuit voltage to the MPP current and voltage, respectively via a linear relationship. These techniques are called the fractional short-circuit current and fractional open-circuit voltage methods. A constant of proportionality is used in each case to relate the measured quantity to the desired quantity as shown in (1) and (2). Here the constant $k_1$ typically takes a value between $0.71$ and $0.78$, and $k_2$ between $0.78$ and $0.92$ [4].
$$\begin{gathered} V_{\mathrm{mpp}}=k_1 V_{\mathrm{oc}} \ I_{\mathrm{mpp}}=k_2 I_{\mathrm{sc}} \end{gathered}$$
These techniques provide a very simple approximation of the MPP location based on a linear relationship that will degrade with time. Under non-uniform environmental conditions, these techniques will also have poor performance as the linear relationship will be unable to capture the complexities of shading [5].

The next class of MPPE methods utilise more than one measurement to improve the estimation of the MPP location. Six current-voltage (I, V) pairs can be sampled to provide an approximation of the $I-V$ curve and therefore predict a likely MPP location [6]

Other MPPE approaches take a model-based approach by utilising either empirical relationships [7] or analytical relationships $[8,9]$ to provide an estimation of the MPP location under particular environmental conditions. These techniques provide a good estimation of the MPP location under uniform environmental conditions; however, the analytical and empirical relationships cannot capture information relating to non-uniform shading of the system.

## 物理代写|光电技术代写光伏技术代考|概率算法

$$\operatorname{Prob}\left(f_{\mathrm{R}}, u_{\mathrm{MPP}}\right)=f_{Y \mid X}\left(u_{\mathrm{MPP}} \mid f_{\mathrm{R}}\right)=\frac{f\left(f_{\mathrm{R}}, u_{\mathrm{MPP}}\right)}{\int_{\alpha \in Y} f\left(f_{\mathrm{R}}, \alpha\right) \mathrm{d} \alpha}$$

## 物理代写|光电技术代写光伏技术代考|最大功率点估计

$$\begin{gathered} V_{\mathrm{mpp}}=k_1 V_{\mathrm{oc}} \ I_{\mathrm{mpp}}=k_2 I_{\mathrm{sc}} \end{gathered}$$这些技术提供了基于线性关系的MPP位置的非常简单的近似，该线性关系将随着时间的推移而降低。在非均匀的环境条件下，这些技术也会有较差的性能，因为线性关系将无法捕捉阴影[5]的复杂性

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