## 5 Complementarity Evaluation Indexes  
MECSs can make full use of the complementarity of different power sources and the peaking capacity of TPP and HS to improve the grid connection of clean energy. In this section, the complementarity evaluation indexes of the MECS are constructed. Moreover, complementation scenarios with different power combinations are considered so that the comprehensive operation benefits of MECSs can be comparatively analyzed. In a previous study [26], the load tracking degree, HS secondary peaking capacity, and TPP unit coal consumption were used as evaluation indexes. (1) The load tracking degree (LTD)  
To fully utilize the complementarity of different power sources, the load tracking degree (LTD) is used to evaluate whether the complementary ratio of power sources is optimal. LTD shows the degree of dispersion of the revised load curve compared with the average value, which can reflect the smoothing effect of the complementary functions of different power sources on the load demand. When the LTD is closer to 1, the capacity of the bundled power output to track the load change is higher and the load curve is smoother [26]. The LTD is defined as  
\[\vartheta=\frac{\sum\limits_{t=1}^{T}{(L_{t}-L_{t}^{av})\big{(}G_{MECS,t}-G_{ MECS}^{av}\big{)}}}{\sqrt{\sum\limits_{t=1}^{T}{(L_{t}-L_{t}^{av})^{2}}}\sqrt{\sum \limits_{t=1}^{T}{\big{(}G_{MECS,t}-G_{MECS}^{av}\big{)}^{2}}}} \tag{41}\]where \(L_{t}\) represents the load required to absorb the power output of the MECS at time \(t\), \(L_{t}^{\text{av}}\) represents the average load, \(G_{MECS,t}\) represents the total output of the MECS at time \(t\), and \(G_{MECS,t}^{\text{av}}\) represents the total average output. The load curve may become smoother by optimizing \(G_{MECS,t}\), thus making the output curve trend more consistent with \(L_{t}\). (2) The HS secondary peaking capacity (SPC)  
HSs are characterized by low power generation emissions and high regulation, which allow their joint operation with WPPs and PVs. Except for the HS used for the bundling complementary of WPP and PV, the scheduling plan of the other units should be arranged by considering the HSs' adjustment capability. HSs could be used to perform secondary peaking on the revised load curve, which could promote the load supplied by TPP to be as smooth as possible. This could reduce the start-stop number of TPP and improve the overall operating efficiency. The net load curve for the TPP would be gentler by considering the HSs' adjustability and, thus, improving the operational efficiency. To distribute the residual load in each period as evenly as possible, the peaking mean square deviation is used to describe the HS peaking capacity. It is defined by  
\[\varphi=\frac{1}{T}\left[\sum_{t=1}^{T}(L_{t}-\hat{L}_{t}^{\text{av}})^{2} \right]^{1/2}=\frac{1}{T}\left[\left(L_{t}-g_{HS,t}-\left(g_{IS,t}^{\text{div}}- g_{IS,t}^{\text{sh}}\right)\right)-\frac{1}{T}\sum_{t=1}^{T}\left(L_{t}-g_{HS,t}- \left(g_{IS,t}^{\text{div}}-g_{IS,t}^{\text{sh}}\right)\right)\right]^{2} \right]^{1/2} \tag{42}\]  
where \(\hat{L}_{t}^{2}\) is the surplus load after removing the HS output, which is equal to \((L_{t}-g_{HS,t})\), and \(\hat{L}_{t}^{\text{av}}\) is the average surplus load after removing the HS output. In general, the load demand curve is gentler when \(\varphi\) is smaller, thus reducing the start-shutdown frequency and coal consumption. (3) TPP unit coal consumption  
The MECS can fully utilize the regulation characteristics of the hydropower and thermal power units to promote the grid connection of clean energy sources. The large-scale grid connection of clean energy sources could reduce the coal consumption of TPP; correspondingly, the reasonable arrangement of the left load in TPP could reduce coal consumption, which could reduce pollution emission and power generation costs.