Multi-reservoir joint operation can alter the temporal and spatial distribution of water resources, which drives the economy-society system development and influ-ences the evolution of ecology and environment system. Corresponding to the four attributes “economic, social, ecological, environmental” of water resources, multi-reservoir joint operation has seven big objectives “flood control, water supply, hydropower generation, navigation, ecology, sediment and environment”.
4.1.1 The Operation Objective for Flood Control
The operation objective for flood control includes minimizing the over stander rate of reservoir downstream flow, minimizing the over stander rate of reservoir down-stream water level, and minimizing the reservoir highest flood level. The operation objective for flood control can be expressed mathematically as the following:
(1) Minimizing the over stander rate of reservoir downstream flow
min floodð 1Þ ¼
Xm
t¼11$ Qt> Qstd,flood
m ð1:11Þ
where Qstd, floodis the reservoir downstream standard flow for the downstream protect objective; Qtis the reservoir downstream flow at the location of protect objective; 1$(Qt> Qstd, flood) means if Qt> Qstd, flood, the count of number is equals to 1; else the count of number is equals to 0.Xm
t¼11$ Qt> Qstd,flood
is the total periods of the reservoir downstream flow at the location of protect
objective over the reservoir downstream standard flow. Flood1 is the over stander rate of reservoir downstream flow.
(2) Minimizing the over stander rate of reservoir downstream water level
min floodð 2Þ ¼
Xm
t¼11$ Zt> Zstd,flood
m ð1:12Þ
where Zstd, flood is the reservoir downstream standard water level for the downstream protect objective; Zt is the reservoir downstream water level at the location of protect objective; 1$(Zt> Zstd, flood) means if Zt> Zstd, flood, the count of number is equals to 1; else the count of number is equals to 0.
Xm
t¼11$ Zð t> Zstd,floodÞ is the total periods of the reservoir downstream water level at the location of protect objective over the reservoir down-stream standard water level. Flood2 is the over stander rate of reservoir downstream water level.
(3) Minimizing the reservoir highest flood level
min floodð 3Þ ¼ max Zð Þt ð1:13Þ where Ztis the reservoir water level at the flood season, Flood3is the reservoir highest flood level.
4.1.2 The Operation Objective for Water Supply
The operation objective for water supply consists of maximizing the water supply amount at the drought season and minimizing the reduction of reservoir outflow into the river after the flood season.
(1) Maximizing the water supply amount at the drought season max WSupð 1Þ ¼ X
t2drought season
Qt∗t ð1:14Þ
where Qt is the water supply amount at the period t in the drought season, WSup1is the total water supply amount at the drought season.
(2) Minimizing the reduction of reservoir outflow into the river after the flood season
min WSupð 2Þ ¼ max Qn Qt ð1:15Þ where Qtis the reservoir outflow into the river after the flood season, Qnis the river natural flow after the flood season, WSup2is the reduction of reservoir outflow into the river after the flood season.
4.1.3 The Operation Objective for Hydropower Generation
The operation objective for hydropower generation mainly consists of maximizing the hydropower generation amount and maximizing the reliability of hydropower generation, which can be expressed mathematically as the following:
(1) Maximizing the hydropower generation amount
max EPowð 1Þ ¼Xm
t¼1
Nt∗t ð1:16Þ
where Ntis the hydropower generated output, EPow1is the total hydropower generation amount at the total operation period.
(2) Maximizing the reliability of hydropower generation
max EPowð 2Þ ¼ Xm
t¼1
1$ Nt> Npro
m ð1:17Þ
where Nprois the hydropower generation guarantee output at the stage t, Ntis the actual hydropower generation at the stage t, 1$(Nt> Nstd, flood) means if Nt> Nstd, flood, the count of number is equals to 1; else the count of number is equals to 0.Xm
t¼11$ Nt> Npro
is the total periods of the actual hydropower generation over he hydropower generation guarantee output, EPow2 is the reliability of hydropower generation.
4.1.4 The Operation Objective for Navigation
The operation objective for navigation includes two main objectives: maximizing the reliability of flow for navigation and maximizing the reliability of water depth for navigation. They can be expressed mathematically as the followings:
(1) Maximizing the reliability of flow for navigation
max Navið 1Þ ¼ Xm
t¼1
1$ Qt> Qpro,navi
m ð1:18Þ
where Qpro, navi is the river flow required for the navigation purpose at the stage t, Qtis the river actual flow at the stage t, 1$(Qt> Qpro, navi) means if Qt> Qpro, navi, the count of number is equals to 1; else the count of number is equals to 0.Xm
t¼11$ Qt> Qpro,navi
is the total periods of the actual river flow
over the river flow required for the navigation purpose, Navi1is the reliability of flow for navigation.
(2) Maximizing the reliability of water depth for navigation
max Navið 2Þ ¼
where Hpro, naviis the river water depth required for the navigation purpose at the stage t, Htis the river actual water depth at the stage t, 1$(Ht> Hpro, navi) means if Ht> Hpro, navi, the count of number is equals to 1; else the count of number is equals to 0.Xm
t¼11$ Ht> Hpro,navi
is the total periods of the actual river water depth over the river water depth required for the navigation purpose, Navi2is the reliability of water depth for navigation.
4.1.5 The Operation Objective for Ecology
The operation objective for ecology is composed of two main objectives: maximiz-ing the reliability of suitable flow for ecology and maximizmaximiz-ing the reliability of minimum flow for ecology. They can be expressed mathematically as the followings:
(1) Maximizing the reliability of suitable flow for ecology
max Ecoð 1Þ ¼
where Qpro, ecois the river flow to satisfy the suitable ecology flow requirement at the stage t, Qtis the river actual flow at the stage t, 1$(Qt> Qpro, eco) means if Qt> Qpro, eco, the count of number is equals to 1; else the count of number is equals to 0.Xm
t¼11$ Qt> Qpro,eco
is the total periods of the actual river flow over the river flow required for suitable ecology, Eco1 is the reliability of suitable flow for ecology.
(2) Maximizing the reliability of minimum flow for ecology
max Ecoð 2Þ ¼
where Qmin, ecois the river flow to satisfy the minimum ecology flow require-ment at the stage t, Qtis the river actual flow at the stage t, 1$(Qt> Qmin, eco) means if Qt> Qmin, eco, the count of number is equals to 1; else the count of
number is equals to 0.Xm
t¼11$ Qt> Qmin,eco
is the total periods of the actual river flow over the minimum ecology flow requirement, Eco2is the reliability of minimum flow for ecology.
4.1.6 The Operation Objective for Sediment
The operation objective for sediment is mainly to satisfy the sediment discharge rate requirement. It can be expressed mathematically as the followings:
max Sedð 1Þ ¼Sedout
Sedin ð1:22Þ
where Sedinis the sediment amount into the reservoir at the stage t, Sedoutis the sediment amount out of the reservoir at the stage t; Sed1 is the sediment discharge rate.
4.1.7 The Operation Objective for Environment
The operation objective for environment is composed of two main objectives:
maximizing the achievement ratio of water quality and minimizing the eutrophia rate, which can be expressed mathematically respectively as the followings:
(1) Maximizing the achievement ratio of water quality
max WQð 1Þ ¼ Xm
t¼1
1$ WQt< WQstd,wq
m ð1:23Þ
where WQstd, wq is water quality standard for some indexes, WQt is water quality index at the stage t, 1$(WQt> WQstd, wq) means if WQt> WQstd, wq, the count of number is equals to 1; else the count of number is equals to 0.
Xm
t¼11$ WQt< WQstd,wq
is the total periods of water quality satisfies the water quality standard, WQ1is the achievement ratio of water quality.
(2) Minimizing the eutrophia rate
max WQð 2Þ ¼ Xm
t¼1
1$ WEutrot> WEutrostd,wq
m ð1:24Þ
where WEutrostd,wqis the eutrophia standard, WEutrotis the eutrophia index at the stage t, 1$(WEutrot> WEutrostd,wq) means if WEutrot> WEutrostd,wq, the
count of number is equals to 1; else the count of number is equals to 0.
Xm
t¼11$ WEutrot> WEutrostd,wq
is the total periods of the water eutrophic level over the eutrophia standard, WQ2is the eutrophia rate.