Coordinated Planning Method for Renewable Energy Plant Multi-Pathway Retrofitting and Multi-Type Generation Considering Frequency Security

LI Pengzhan, LIU Lu, SUN Chao, CHENG Haozhong

Electric Power Construction ›› 2026, Vol. 47 ›› Issue (10) : 45-61.

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Electric Power Construction
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Electric Power Construction ›› 2026, Vol. 47 ›› Issue (10) : 45-61. DOI: 10.12204/j.issn.1000-7229.2026.10.004
Planning & Construction

Coordinated Planning Method for Renewable Energy Plant Multi-Pathway Retrofitting and Multi-Type Generation Considering Frequency Security

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Abstract

[Objective] To address the decline in primary frequency response capability and the resulting threats to frequency security caused by the high-proportion integration of renewable energy，a coordinated planning method for multi-path retrofitting of renewable energy plants and multi-type generation considering frequency security is proposed. [Methods] First，a multi-path retrofit model for renewable energy plants was constructed，including the installation of primary frequency response controllers （PFRCs），grid-following （GFL） energy storage，and grid-forming （GFM） energy storage，so as to characterize the differences among various retrofitting pathways in terms of primary frequency regulation，inertia response，and investment costs. Second，a coordinated planning model was established with the objective of minimizing the total sum of generation investment cost，renewable energy plant retrofit cost，and operational cost. To overcome the difficulty of embedding highly nonlinear frequency deviation constraints into the planning model，an iterative master-subproblem solution framework was developed. The master problem solved the multi-scenario-based generation expansion and renewable energy retrofit decisions，while the subproblem used a system frequency response model to evaluate frequency security indicators. The master and subproblems were linked through physics-informed strengthening cuts derived from three dimensions： regulation power，frequency regulation reserve capacity，and system inertia. [Results] The verification results on the modified IEEE 24-bus system and an actual regional power system demonstrate that the proposed method can obtain the optimal construction scheme while fully exploiting the complementary advantages of diversified renewable energy retrofit pathways. Compared with the conventional planning method，the total cost was reduced by 1.2%，and the renewable energy accommodation rate was increased by 0.4%. Furthermore，as the penetration rate of renewable energy capacity further increases，the system rotational inertia decreases，leading to a significant increase in the configured capacity of GFM energy storage. [Conclusions] The proposed method can effectively coordinate system frequency support performance and overall economic cost，avoid over-investment in conventional coal-fired thermal power plants，and provide a practical and feasible solution to the decline in primary frequency response capability caused by the high-proportion integration of renewable energy.

Key words

renewable energy retrofitting / power source planning / frequency security / inertia / primary frequency regulation

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LI Pengzhan , LIU Lu , SUN Chao , et al. Coordinated Planning Method for Renewable Energy Plant Multi-Pathway Retrofitting and Multi-Type Generation Considering Frequency Security[J]. Electric Power Construction. 2026, 47(10): 45-61 https://doi.org/10.12204/j.issn.1000-7229.2026.10.004

附录A

系统等效惯性时间常数和各类电源增益系数计算如式（A1）所示。

$\left\{\begin{array}{l}{\mathit{K}}_{\mathit{g},\mathit{m}}={\mathit{P}}_{\mathit{g}}^{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathit{u}}_{\mathit{g}}^{\mathrm{o}\mathrm{n}}/{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}},\mathrm{ }\mathit{g}\in {\mathit{G}}_{\mathrm{t}\mathrm{h}}\\ {\mathit{K}}_{\mathit{h},\mathit{m}}={\mathit{P}}_{\mathit{h}}^{\mathrm{m}\mathrm{a}\mathrm{x}}({\mathit{u}}_{\mathit{h}}^{\mathrm{d}\mathrm{i}\mathrm{s}}+{\mathit{u}}_{\mathit{h}}^{\mathrm{c}\mathrm{h}})/{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}},\mathrm{ }\mathit{h}\in {\mathit{G}}_{\mathrm{p}\mathrm{h}}\\ {\mathit{K}}_{\mathit{w},\mathit{m}}={\mathit{P}}_{\mathit{w}}{\mathit{x}}_{\mathit{w}}^{\mathrm{d}\mathrm{e}\mathrm{v}}/{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}},\mathrm{ }\mathit{w}\in {\mathit{G}}_{\mathrm{r}\mathrm{e}\mathrm{s}}\\ {\mathit{K}}_{\mathrm{g}\mathrm{f}\mathrm{l},\mathit{m}}={\mathit{P}}_{\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}{\mathit{n}}_{\mathit{w}}^{\mathrm{g}\mathrm{f}\mathrm{l}}/{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}},\mathrm{ }\mathit{w}\in {\mathit{G}}_{\mathrm{r}\mathrm{e}\mathrm{s}}\\ {\mathit{K}}_{\mathrm{g}\mathrm{f}\mathrm{m},\mathit{m}}={\mathit{P}}_{\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}{\mathit{n}}_{\mathit{w}}^{\mathrm{g}\mathrm{f}\mathrm{m}}/{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}},\mathrm{ }\mathit{w}\in {\mathit{G}}_{\mathrm{r}\mathrm{e}\mathrm{s}}\end{array}\right.$

式中：Pw为新能源场站w的最大可用出力。

$\begin{array}{l}\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }{\mathit{S}}_{\mathrm{B},\mathrm{s}\mathrm{y}\mathrm{s}}=\sum _{\mathit{g}\in {\mathit{G}}_{\mathrm{t}\mathrm{h}}}{\mathit{P}}_{\mathit{g}}^{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathit{u}}_{\mathit{g}}^{\mathrm{o}\mathrm{n}}+\sum _{\mathit{h}\in {\mathit{G}}_{\mathit{p}\mathit{h}}}{\mathit{P}}_{\mathit{h}}^{\mathit{m}\mathit{a}\mathit{x}}({\mathit{u}}_{\mathit{h}}^{\mathit{d}\mathit{i}\mathit{s}}+{\mathit{u}}_{\mathit{h}}^{\mathit{c}\mathit{h}})+\\ \mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\sum _{\mathit{w}\in {\mathit{G}}_{\mathrm{r}\mathrm{e}\mathrm{s}}}{\mathit{P}}_{\mathit{w}}+\sum _{\mathit{e}\in {\mathit{G}}_{\mathrm{e}\mathrm{s}\mathrm{s}}}{\mathit{P}}_{\mathit{e}}^{\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}$

式中： ${\mathit{u}}_{\mathit{h}}^{\mathrm{c}\mathrm{h}}$为抽蓄抽水指示变量。

火电、抽蓄、新能源和储能的调频备用计算如式（A3）—（A6）所示。

${\mathit{r}}_{\mathit{g},\mathit{s},\mathit{t}}={\mathit{\gamma }}_{\mathit{g}}{\mathit{P}}_{\mathit{g}}^{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathit{u}}_{\mathit{g},\mathit{s},\mathit{t}},\mathrm{ }\mathit{g}\in {\mathit{G}}_{\mathrm{t}\mathrm{h}}$
$\left\{\begin{array}{l}{\mathit{r}}_{\mathit{h},\mathit{s},\mathit{t}}\le {\mathit{u}}_{\mathit{h},\mathit{s},\mathit{t}}^{\mathrm{d}\mathrm{i}\mathrm{s}}{\mathit{P}}_{\mathit{h}}^{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathit{P}}_{\mathit{h},\mathit{s},\mathit{t}}\\ {\mathit{r}}_{\mathit{h},\mathit{s},\mathit{t}}\le {\mathit{\gamma }}_{\mathit{h}}{\mathit{u}}_{\mathit{h},\mathit{s},\mathit{t}}^{\mathrm{d}\mathrm{i}\mathrm{s}}{\mathit{P}}_{\mathit{h}}^{\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}\right.,\mathrm{ }\mathit{h}\in {\mathit{G}}_{\mathrm{p}\mathrm{h}}$
$0\le {\mathit{r}}_{\mathit{w},\mathit{s},\mathit{t}}\le {\mathit{P}}_{\mathit{w},\mathit{s},\mathit{t}}^{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{t}},\mathrm{ }\mathit{w}\in {\mathit{G}}_{\mathrm{r}\mathrm{e}\mathrm{s}}$
$\left\{\begin{array}{l}{\mathit{r}}_{\mathit{e},\mathit{s},\mathit{t}}\le {\mathit{P}}_{\mathit{e}}^{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathit{P}}_{\mathit{e},\mathit{s},\mathit{t}}\\ {\mathit{r}}_{\mathit{e},\mathit{s},\mathit{t}}\le {\mathit{\gamma }}_{\mathrm{e}}{\mathit{P}}_{\mathit{e}}^{\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}\right.,\mathrm{ }\mathit{e}\in {\mathit{G}}_{\mathrm{e}\mathrm{s}\mathrm{s}}$

式中：γg、γh和γe分别为火电、抽蓄和储能的调频限幅，其中火电在额定功率运行状态下仍然可以短暂增加有功功率进行一次调频。

表A1 SFR模型参数物理意义

Table A1 Physical meaning of SFR model parameters

参数 物理意义 参数 物理意义
${\mathit{T}}_{\mathrm{R}}$ 火电再热时间常数 ${\mathit{T}}_{\mathit{e}1}$ GFL储能响应时间
${\mathit{F}}_{\mathrm{h}}$ 高压缸做功比例 ${\mathit{T}}_{\mathit{e}2}$ GFM储能响应时间
${\mathit{T}}_{\mathrm{C}}$ 原动机时间常数 $\mathrm{\Delta }{\mathit{P}}_{\mathit{T}}$ 火电频率响应功率
${\mathit{T}}_{\mathrm{G}}$ 调速器时间常数 $\mathrm{\Delta }{\mathit{P}}_{\mathit{h}}$ 抽蓄频率响应功率
$\mathit{R}$ 火电机组调差系数 $\mathrm{\Delta }{\mathit{P}}_{\mathit{w}}$ 新能源频率响应功率
${\mathit{T}}_{\mathrm{d}}$ 抽蓄响应时间 $\mathrm{\Delta }{\mathit{P}}_{\mathit{e}1}$ GFL储能频率响应功率
${\mathit{R}}_{\mathrm{d}}$ 抽蓄永久下降率 $\mathrm{\Delta }{\mathit{P}}_{\mathit{e}2}$ GFM储能频率响应功率
${\mathit{R}}_{\mathrm{C}}$ 抽蓄综合下降率 ${\mathit{K}}_{\mathit{g}}$ 火电增益系数
${\mathit{R}}_{\mathit{w}}$ 新能源调差系数 ${\mathit{K}}_{\mathit{h}}$ 抽蓄增益系数
${\mathit{R}}_{\mathit{e}1}$ GFL储能调差系数 ${\mathit{K}}_{\mathit{w}}$ 新能源增益系数
${\mathit{R}}_{\mathit{e}2}$ GFM储能调差系数 ${\mathit{K}}_{\mathrm{g}\mathrm{f}\mathrm{l}}$ GFL储能增益系数
${\mathit{T}}_{\mathit{w}}$ 新能源响应时间 ${\mathit{K}}_{\mathrm{g}\mathrm{f}\mathrm{m}}$ GFM增益系数

附录B

表B1 待改造新能源场站详情

Table B1 Details of new energy stations to be retrofitted

场站名称 装机容量/MW 接入节点 场站名称 装机容量/MW 接入节点
光伏场站1 100 5 光伏场站18 400 17
光伏场站2 100 6 光伏场站19 300 23
光伏场站3 100 7 光伏场站20 300 14
光伏场站4 100 8 风电场站1 100 22
光伏场站5 100 18 风电场站2 100 23
光伏场站6 100 21 风电场站3 100 11
光伏场站7 200 1 风电场站4 100 12
光伏场站8 200 2 风电场站5 200 9
光伏场站9 200 3 风电场站6 200 10
光伏场站10 200 4 风电场站7 200 15
光伏场站11 300 11 风电场站8 200 16
光伏场站12 300 24 风电场站9 300 19
光伏场站13 400 16 风电场站10 300 20
光伏场站14 400 15 风电场站11 400 21
光伏场站15 500 12 风电场站12 400 22
光伏场站16 500 13 风电场站13 500 18
光伏场站17 600 11
表B2 改进的IEEE 24节点系统机组详情

Table B2 Details of generation units in the modified IEEE 24-bus system

机组名称 装机容量/MW 接入节点 机组名称 装机容量/MW 接入节点
火电机组1 20 1 火电机组18 12 15
火电机组2 20 1 火电机组19 12 15
火电机组3 76 1 火电机组20 155 15
火电机组4 76 1 火电机组21 155 16
火电机组5 20 2 火电机组22 400 18
火电机组6 20 2 火电机组23 400 21
火电机组7 76 2 火电机组24 50 22
火电机组8 76 2 火电机组25 50 22
火电机组9 100 7 火电机组26 50 22
火电机组10 100 7 火电机组27 50 22
火电机组11 100 7 火电机组28 50 22
火电机组12 197 13 火电机组29 50 22
火电机组13 197 13 火电机组30 155 23
火电机组14 197 13 火电机组31 155 23
火电机组15 12 15 火电机组32 350 23
火电机组16 12 15 GFL储能电站1 60 24
火电机组17 12 15 GFM储能电站1 10 12
图B1 不同聚类数下误差平方和曲线

Fig. B1 Sum of squared errors curve under different cluster numbers

图B2 各场景风电功率曲线

Fig. B2 Each scenario wind power curve

图B3 各场景光伏功率曲线

Fig. B3 Each scenario photovoltaic power curve

图B4 各场景负荷功率曲线

Fig. B4 Each scenario load power curve

图B5 改进的IEEE 24节点系统拓扑图

Fig. B5 Topology diagram of the modified IEEE-24 bus system

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Abstract
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To address the challenges posed by the increasing penetration of wind power on grid frequency regulation, this paper establishes a life-cycle cost-benefit calculation model for wind farms equipped with energy storage systems participating in primary frequency regulation services. The model considers energy storage costs, real-time electricity revenue, and primary frequency regulation revenue, with energy storage capacity and power as decision variables. To tackle the difficulty of accurately evaluating primary frequency regulation actions, a frequency regulation model for the combined wind-storage system is developed using an open-loop processing method based on the closed-loop dynamic process of the power system frequency. This model incorporates wind turbine control and energy storage system state-of-charge (SOC) constraints, and proposes an open-loop calculation method for primary frequency regulation actions using annual frequency curves as inputs. By combining the wind-storage system frequency regulation simulation model with annual operational frequency and power data of the wind farm, the change rule of the annual energy storage costs and primary frequency regulation revenue are obtained. The results show that for a wind farm with an installed capacity of 30 600 kW, the optimal primary frequency regulation revenue is achieved when the energy storage power is 4 553.6 kW and the energy storage capacity is 9 822.6 kWh.
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Footnotes

利益冲突声明（Conflict of Interests）： 所有作者声明不存在利益冲突。

作者贡献声明（Authors' Contributions）： 李鹏展负责模型构建、程序设计、实验验证、论文撰写；柳璐提出研究思路和研究方向，设计论文总体框架，参与论文修订、审核；孙超参与了方案可行性研究和论文修订；程浩忠负责论文最终版修订。所有作者均阅读并同意了论文终稿内容。

Funding

National Key R&D Program of China(2022YFB2403200)
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