Method for short-term generation scheduling of cascade hydropower plants coupling cluster analysis and decision tree

A method for short-term generation scheduling of cascade hydropower plants coupling cluster analysis and decision tree, wherein comprising the following steps:

• (1) establish matching relationship of energy production between cascade hydropower plants:
• based on historical generation data of cascade hydropower plants, correlation analysis method is adopted to determine the matching relationship of energy production between upstream and downstream hydropower plants, including the following two steps:
• (a) determine impact factors related to energy production of upstream hydropower plant:
• when the upstream hydropower plant has a yearly or higher regulating storage capacity, daily inflow and tailrace water level have a small effect on daily energy production;
• the daily energy production is mainly related to reservoir level and power discharge, so regression analysis method is used to determine a relationship between the daily energy production and reservoir level and power flow discharge as shown in Eq.(1);
• Ei=ƒ(Zupi,qi) (1)
• where Ei is daily energy production of hydropower plant i;
• ƒ represents a functional relationship of daily energy production, reservoir level and power discharge;
• Zupi is reservoir level of hydropower plant i;
• qi is average daily power discharge of hydropower plant i;
• (b) determine the matching relationship of energy production between upstream and downstream hydropower plants:
• for hydraulic-sensitive cascade hydropower plants, local inflow is ignored because upstream and downstream plants are close and local inflow is usually very small;
• reservoir level and outflow of upstream hydropower plant are main factors affecting energy production of downstream hydropower plant, as shown in Eq.(2):
• Ei+1=ƒ(Zupi+1,qi)=ƒ(Zupi+1,Zupi,Ei) (2)
• where Ei+1 is daily energy production of hydropower plant i+1;
• Zupi+1 is reservoir level of hydropower plant i+1;
• (2) cluster typical generation curves of hydropower plants:
• cluster analysis is conducted on historical generation data to determine typical generation curves of each hydropower plant, including the following two steps:
• (a) develop cluster vector:
• load rate in a single period is adopted to form eigenvector R, so as to fully reflect changes of generation within one day, which is represented as Eqs. (3) and (4):
• Rt=Nt/Nmax (3)
• R=(R1,R2, . . . Rn) (4)
• where Rt is eigenvector vector of generation curve in period t;
• Nt is power value of generation curve in period t;
• Nmax is maximum generation of hydropower plant within one day;
• (b) cluster typical generation curve:
• based on cluster vector obtained in step (a), classical k average algorithm is used to cluster the generation curve;
• first, transform historical daily 24-pointgeneration curve using the step (a), and obtain cluster samples;
• second, randomly choose k samples of generation curves and let each sample stand for initial average or center of a cluster;
• rest samples of generation curve are assigned to the most similar cluster according to its distance to each cluster center;
• thus, new center of each cluster can be recalculated;
• an iteration is required until a square error criterion function shown in formula (5) converges;
• V
• =
• ∑
• l
• =
• 1
• k
• 
• ∑
• x
• j
• ∈
• S
• l
• 
• (
• x
• j
• -
• μ
• l
• )
• 2
• (
• 5
• )
• where V is sum of square errors of all generation curve samples in historical data set;
• xj is generation curve sample of a group of cluster vectors;
• μl represents a cluster vector, which is center of cluster Sl;
• (3) make generation scheme based on decision tree:
• based on cluster typical generation curve obtained in step (2), decision tree method is used to train main impact factors of generation scheduling and operation decision to establish a relationship between these factors and generation curves and quickly determine the power generation profile of cascade hydropower plants;
• two parts are included:
• determine impact factors of power generation and establish decision tree of generation scheduling;
• (a) determine impact factors of power generation:
• for an upstream hydropower plant, three main factors are considered, including initial reservoir level, daily energy production and load characteristics during time horizon, as shown in Eq. (6);
• for a downstream hydropower plant, in addition to the above three factors of this plant, the daily energy production and type of generation curves of the upstream hydropower plant should also be considered, as shown in Eq. (7);
• Typei=ƒ(Zupi,Ei,Date) (6)
• Typei+1=ƒ(Zupi+1,Ei+1,Date,Ei,Typei) (7)
• where Typei, Typei+1 are types of generation curve of upstream hydropower plant and downstream hydropower plant, respectively;
• Date is scheduling date;
• (b) establish decision tree of generation scheduling:
• take generation curve number as a category attribute, and make other related factors including energy production, water level and scheduling date as non-category attributes;
• utilize a decision tree algorithm called C4.5 to develop a decision tree of generation scheduling of hydropower plants;
• (4) make local correction for satisfying operation constraints:
• the above step (2) and (3) can determine a generation scheme of cascade hydropower plants;
• however, because of differences in reservoir level, electricity and inflow demand difference, violation of operation constraints may occur in some periods, including generation climb constraint and upper and lower limitation of power generation;
• so it is necessary to slightly adjust generation scheme according to generation climb constraint and upper and lower limitation of power generation while the daily energy production of hydropower plant is controlled;
• thus, feasibility of generation scheme can be ensured.