Optimized scheduling of the power grid with participation of distributed microgrids considering their uncertainties

doi:10.3969/j.issn.2097-0706.2024.01.005

Abstract

Abstract:

Connecting distributed microgrids characterized by high-proportion renewable energy to the grid system can effectively reduce the carbon emissions from the whole system， but seriously impact the stable operation for the system as well. A wind-solar-power-battery integrated system is constructed in pursuit of the optimal economy，highest quality of power，lowest carbon emissions and highest level of customer satisfaction. The negative effects of grid-connection of distributed sources， such as wind power and solar power， on the operation of power grid are summarized. Then， the uncertain parametric model for the microgrid is constructed using probabilistic model， fuzzy affiliation model， robust uncertainty set and interval-censored data set as reference. Different solutions for the optimization scheduling plans for the microgrid considering the uncertainties of renewable energy are proposed and compared. Finally， the development outlook of the power sources with uncertainties is proposed to guide the optimization scheduling of the distributed microgrids.

Key words: renewable energy, microgrid, carbon emissions, stochastic optimization scheduling model, robust optimization scheduling model, distributionaly robust optimization model, fuzzy optimization model

CLC Number:

TK019：TM727

TAN Jiuding, LI Shuaibing, LI Mingche, MA Xiping, KANG Yongqiang, DONG Haiying. Optimized scheduling of the power grid with participation of distributed microgrids considering their uncertainties[J]. Integrated Intelligent Energy, 2024, 46(1): 38-48.

Figures/Tables 11

Fig.1

Table 1

Table 2

Fig.2

Table 3

Typical membership functions and their representations

函数	函数图像	函数表达式
高斯函数		$f x, k, c = e x p - x - P 2 σ 2$
矩形函数		$μ (P) = 0 P < P 1 P 1 ≤ P ≤ P 2 0 P 2 < P$
三角函数		$μ (P) = 0 P < P 1 P 2 - P P 2 - P 1 P 1 ≤ P < P 2 1 P = P 2 P 3 - P P 3 - P 2 P 2 < P ≤ P 3 0 P > P 3$
梯形函数		$μ (P) = 0 P < P 1 P 2 - P P 2 - P 1 P 1 ≤ P < P 2 1 P 2 ≤ P ≤ P 3 P 4 - P P 4 - P 3 P 3 < P ≤ P 4 0 P > P 4$

Table 3

Fig.3

Fig.4

Table 4

Optimization scheduling model and its derivatives

模型	数学表达式
随机规划模型	$m i n / m a x F [c T y (x j)] s . t . A x j n + B x j n - 1 + ⋯ + C = 0 x j m i n ≤ x j ≤ x j m a x j = 1,2, ⋯, m$
期望值随机规划模型	$m i n / m a x F [c T y (x)] s . t . x = ∑ t = 1 n P j ω j P j ∈ P 1, P 2, ⋯, P n j = 1,2, ⋯, n$
机会约束随机规划模型	$m i n / m a x P r {F [c T y (x j)]} ≤ α s . t . A x j n ± B x j n - 1 ± ⋯ ± C = 0 x j m i n ≤ x j ≤ x j m a x j = 1,2, ⋯, m$
多阶随机规划模型	$m i n / m a x P r {F [c T y (x j)]} ≤ α s . t . A x j n ± B x j n - 1 ± ⋯ ± C = 0 x j m i n ≤ x j ≤ x j m a x j = 1,2, ⋯, m$
鲁棒规划模型	$m i n / m a x F [c T y (x, ω)] s . t . x j ∈ x j m i n, x j m a x y (x, ω) ≠ ∅ ∀ ω = (ω i), ω i ∈ ω$
多阶鲁棒规划模型	$m i n / m a x F i ⋯ m i n / m a x F 1 (c T x j) s . t . x j ∈ x j m i n, x j m a x ∀ ω = (ω i), ω i ∈ ω$
分布式鲁棒规划模型	$m i n / m a x ∑ s y s n u m = 1 n λ F n [c T y (x, ω)] s . t . x j ∈ x j m i n, x j m a x y (x, ω) ≠ ∅ ∑ λ = 1, ∀ ω = (ω i), ω i ∈ ω$
多阶分布式鲁棒规划模型	$m i n / m a x ∑ λ F i ⋯ m i n / m a x λ F 1 (c T x j) s . t . x j ∈ x j m i n, x j m a x y (x, ω) ≠ ∅ ∑ λ = 1, ∀ ω = (ω i), ω i ∈ ω$
模糊规划模型	$m i n / m a x F [g (x j)] s . t . 0 ≤ g (x j) ≤ 1 x j ∈ x j m i n, x j m a x$

Table 4

Fig.5

Table 5

Table 6

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优化目标	研究内容	研究特点
经济最优	经济性最优调度^[3]	改进粒子群算法求解
	经济优化子问题与经济优化主问题多重优化^[4]	不确定场景集概率模型、粒子群算法求解
	考虑高比例绿电并网的系统鲁棒性提升消纳率^[5]	对偶分解为多子系统，利用本地搜寻求解
	结合碳减排目标结合多目标调度^[6]	同时考虑电源侧与负荷侧两端数据变化开展多能互补
电能质量最优	综合经济性规划兼顾电网安全性优化^[7]	多种群遗传算法求解
碳排放最优	阶梯碳交易机制、分时电价结合优化微电网成本与系统碳排放^[8]	粒子群算法求解
碳排放最优	添加碳捕集设备并联合调度实现成本、碳排放最优化^[9]	随机规划模型、多目标求解
用户满意度最优	考虑用户功率需求不确定性开展调度^[10]	区间线性规划
多目标协同优化	潮流计算、多目标嵌套、储能灵活优化^[11]	不确定场景集合、鲁棒优化、复合差分进化算法求解
	能量损耗最小、最优经济性、调峰调度^[12]	双层优化调度、线性规划求解
	最小化节点电压降、最小化碳排放、最小化网损^[13]	二代非支配排序遗传算法（NSGA-II）求解

随机采样方法	结合原理	应用优势
蒙特卡洛	随机采样	生成随机场景，利用特殊场景表示数据总体数据特征
序列蒙特卡洛	递推逼近	利用递推逼近，可使模型具有自适应能力
重要性采样	加权分配	引入权重系数，可全局考虑历史数据特征
拉丁超立方	均匀、分层采样原理	分段采样确保样本不重叠，场景均匀分布
拟蒙特卡洛	低差异率列采样	尽量多地填充单位超立方利用数量提升精度
马尔科夫链蒙特卡洛	马尔科夫链、场景树	可实现动态场景随机模拟

算法	初值选取	计算速度	结果
常规算法	除非线性算法外其他算法均严格要求参数保持线性	线性规划算法速度较快，非线性规划、混合整数规划法速度较慢，动态规划计算速度慢	动态规划通过分段求解可得到全局最优解，其他算法均不同程度陷入次优解
启发式算法	除遗传算法、禁忌算法外其他算法对参数有不同程度的线性要求	禁忌搜索算法、粒子群优化算法减速度快；退火算法、遗传算法求解速度较慢且计算过程随机化程度高,难以控制	退火算法、粒子群算法逼近全局最优解能力较好；禁忌算法、遗传算法结果优劣取决于预先设置的参数，否则易陷入次优解
组合式算法	需要根据算法选取数据	计算精度、计算速度均具优势	均能得到全局最优解，其中改进粒子群算法全局性最优

算法	实施方法	特点
线性规划	Lamda迭代法^[43]	迭代至误差小于人工设定参数λ
线性规划	内点法^[44]	向目标函数最快下降方向搜寻收敛最优解
非线性规划	牛顿法^[45]	一阶雅可比与二阶海森矩阵实现梯度下降
	拉格朗日算法^[46]	分解多约束主问题为子问题依次优化计算
	二次规划法^[47]	泰勒级数重构目标函数形成二次函数
混合整数规划	Benders算法^[48]	主次问题逐次迭代并修正参数逼近最优解
混合整数规划	C&CG算法^[49]	结合对偶理论转化主、子问题简化计算
动态规划		基于时序或空间分解主问题为子问题求解