A method of short-term risk and economic dispatch of the hydro-thermal-wind-PV hybrid system considering spinning reserve requirements

Optimal allocation of photovoltaic generations in buildings‐to‐distribution‐network integration system using improved backtracking search optimization algorithm

“…By choosing $$s_{\mathrm{pv}, n_{\mathrm{pv}}}^{\max }=A_{\mathrm{pv},n_{\mathrm{pv}}}^{\mathrm{amp}} \cdot p_{\mathrm{pv}, n_{\mathrm{pv}}}^{\max }$$, the reactive power supported by the inverter of PVG n pv ($$n_{\mathrm{pv}} \in \mathcal {N_{\rm {pv}}}$$) can be relaxed as [12] $$$$\begin{eqnarray} \hspace*{-12pt}-\sqrt {{\big(A_{\mathrm{pv},n_{\mathrm{pv}}}^{\mathrm{amp}}\big)}^{2}-1} \cdot {p}_{\mathrm{pv}, n_{\mathrm{pv}}}^{\max } \le q_{\mathrm{pv}, n_{\mathrm{pv}}}^{t} \le \sqrt {{\big(A_{\mathrm{pv},n_{\mathrm{pv}}}^{\mathrm{amp}}\big)}^{2}-1} \cdot {p}_{\mathrm{pv}, n_{\mathrm{pv}}}^{\max } \end{eqnarray}$$$$where $$A_{\mathrm{pv},n_{\mathrm{pv}}}^{\mathrm{amp}}$$ is the amplification factor of $$p_{\mathrm{pv}, n_{\mathrm{pv}}}^{\max }$$. In addition, to limit the change rate of a PVG's output power at adjacent time, ($$p_{\mathrm{pv}, n_{\mathrm{pv}}}^{t+1}-p_{\mathrm{pv}, n_{\mathrm{pv}}}^{t}$$) satisfies [41] …”

“…For the active and the reactive power of BESS n bess ($$\forall n_{\rm {bess}} \in \mathcal {N}_{\rm {bess}}$$), the following constraints should be satisfied [12, 41]. $$$$\begin{equation} p_{\text{bess},n_{\rm {bess}}}^{\min } \le p_{\text{bess}, n_{\mathrm{bess}}}^t \le p_{\text{bess},n_{\rm {bess}}}^{\max } \end{equation}$$$$ $$$$\begin{equation} -10\% \times p_{\text{bess},n_{\rm {bess}}}^{\max } \le p_{\text{bess}, n_{\mathrm{bess}}}^{t+1}-p_{\text{bess}, n_{\mathrm{bess}}}^t \le 10\% \times p_{\text{bess},n_{\rm {bess}}}^{\max } \end{equation}$$$$ …”

“…By choosing s max pv,n pv = A amp pv,n pv ⋅ p max pv,n pv , the reactive power supported by the inverter of PVG n pv (n pv ∈ 𝒩 pv ) can be relaxed as [12] (25) where A amp pv,n pv is the amplification factor of p max pv,n pv . In addition, to limit the change rate of a PVG's output power at adjacent time, (p t +1 pv,n pv − p t pv,n pv ) satisfies [41] −10% × p max pv,n pv ≤ p t +1 pv,n pv − p t pv,n pv ≤ 10% × p max pv,n pv (26)…”

“…For the active and the reactive power of BESS n bess (∀n bess ∈ 𝒩 bess ), the following constraints should be satisfied [12,41].…”

Capacity evaluation of hydropower for accommodating wind‐photovoltaic power generation in the dry season

“…Generally, the difference between predicted output and actual output can be used to illustrate this uncertainty [10,11]. To extract and fit uncertain factors, one can utilize specific models such as the time sequence model, probability distribution model, and deep learning model [12]. Then, random wind-PV output can be obtained using random sampling and multi-scenario generation technology [13].…”