Hydropower 2016/17. Balance between water availability and water needs

Hydropower 2016/17 Balance between water availability and water needs

Annual flow (dam3) 1918/19 1921/22 1924/25 1927/28 1930/31 1933/34 1936/37 1939/40 1942/43 1945/46 1948/49 1951/52 1954/55 1957/58 1960/61 1963/64 1966/67 1969/70 1972/73 1975/76 1978/79 1981/82 1984/85 Problem Assume that the domestic uses of 40 000 persons are to be satisfied from a given water course with the following flow record of annual values. Is it possible? 1200000 1000000 800000 600000 400000 200000 0 Assuming a net capitation of 150 l/hab/day and an efficiency of 80%, the gross water requirements: Gross capitation = 150/0,8 = 187,5 l/hab/day Daily water needs = 187,5 x 40000 = 7,5 dam 3 Monthly water needs = 7,5 x 30 = 225 dam 3 Annual water needs = 7,5 x 365 = 2738 dam 3 IST: Hydropwer Rodrigo Proença de Oliveira, 2016 2

Annual flow (dam3) 1918/19 1921/22 1924/25 1927/28 1930/31 1933/34 1936/37 1939/40 1942/43 1945/46 1948/49 1951/52 1954/55 1957/58 1960/61 1963/64 1966/67 1969/70 1972/73 1975/76 1978/79 1981/82 1984/85 Annual flow IST: Hydropwer Rodrigo Proença de Oliveira, 2016 3 1000000 900000 800000 700000 600000 500000 400000 300000 200000 100000 2,7 hm3/year0

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Probabability of non exceedance Empirical distribution of annual flow 4 v (1) < v (2) < v (3) <. < v (n) Plotting position: Weibull = i/(n+1) 1918/19, v 1 1919/20, v 2 1920/21, v 3 1921/22, v 4 1922/23, v 5 1923/24, v 6 1924/25, v 7 1925/26, v 8 1926/27, v 9 1927/28, v 10 1928/29, v 11 1984/85, v n 1, v (1), 1/(n+1) 2, v (2), 2/(n+1) 3, v (3), 3/(n+1) 4, v (4), 4/(n+1) 5, v (5), 5/(n+1) 6, v (6), 6/(n+1) 7, v (7), 7/(n+1) 8, v (8), 8/(n+1) 9, v (9), 9/(n+1) 10, v (10), 10/(n+1) 11, v (11), 11/(n+1). n, v (n), n/(n+1) - An empirical estimate of the probability of non-exceedance of a value of order i in a record of n values; If i is small, meaning that the value is one of the smallest in the record, i/(n+1) is close to zero. If i is large, meaning that the value is one of the largest in the8record, i/(n+1) is close to one. 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0 200000 400000 600000 800000 1000000 2,7 hm 3 /year Annual flow volume (dam3)

Monthly flow (dam3) Monthly flow IST: Hydropwer Rodrigo Proença de Oliveira, 2016 5 350000 300000 250000 200000 150000 100000 50000 0 1918 1926 1934 1942 1950 1958 1966 1974 1982

Empirical distribution of annual minimum monthly flow IST: Hydropwer Rodrigo Proença de Oliveira, 2016 6 1918/19, Minimum monthly flow v 1 1919/20, Minimum monthly flow v 2 1920/21, Minimum monthly flow v 3 1921/22, Minimum monthly flow v 4 1922/23, Minimum monthly flow v 5 1923/24, Minimum monthly flow v 6 1924/25, Minimum monthly flow v 7 1925/26, Minimum monthly flow v 8 1926/27, Minimum monthly flow v 9 1927/28, Minimum monthly flow v 10 1928/29, Minimum monthly flow v 11 1984/85, Minimum monthly flow v n 1, v (1), 1/(n+1) 2, v (2), 2/(n+1) 3, v (3), 3/(n+1) 4, v (4), 4/(n+1) 5, v (5), 5/(n+1) 6, v (6), 6/(n+1) 7, v (7), 7/(n+1) 8, v (8), 8/(n+1) 9, v (9), 9/(n+1) 10, v (10), 10/(n+1) 11, v (11), 11/(n+1). n, v (n), n/(n+1) v (1) < v (2) < v (3) <. < v (n) Plotting position: Weibull i/(n+1)

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Empirical distribution of annual minimum monthly flow Probabability of non exceedance 7 1918/19, Minimum monthly flow v 1 1919/20, Minimum monthly flow v 2 1920/21, Minimum monthly flow v 3 1921/22, Minimum monthly flow v 4 1922/23, Minimum monthly flow v 5 1984/85, Esc. Mensal Mínimo v n 1, v (1), 1/(n+1) 2, v (2), 2/(n+1) 3, v (3), 3/(n+1) 4, v (4), 4/(n+1) 5, v (5), 5/(n+1). n, v (n), n/(n+1) 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0 500 1000 1500 2000 225 dam3/monthminimum monthly volume (dam3)

Average daily discharge (m3/s) Average daily discharge IST: Hydropwer Rodrigo Proença de Oliveira, 2016 8 1000 900 800 700 600 500 400 300 200 100 0 1918 1926 1934 1942 1950 1958 1966 1974 1982

Probabability of non exceedance Empirical distribution of annual minimum average daily discharge IST: Hydropwer Rodrigo Proença de Oliveira, 2016 9 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 7500 m 3 /day = 0,1 m 3 /s 0 0,05 0,1 0,15 0,2 0,25 0,3 Minimum daily discharge (m3/s)

Average daily discharge (m3/s) Flow duration curve IST: Hydropwer Rodrigo Proença de Oliveira, 2016 10 1000 900 800 700 600 500 400 300 200 100 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Flow duration or permanence (%)

Average daily discharge (m3/s) Average daily discharge (m3/s) Average daily discharge (m3/s) Flow duration curve IST: Hydropwer Rodrigo Proença de Oliveira, 2016 11 1000 900 800 700 600 500 400 300 200 100 100 90 80 70 60 50 40 30 20 10 0 30 25 20 15 10 5 7500 m 3 /day = 0,1 m 3 /s 0 0 40 80 120 160 200 240 280 320 360 Days 0 40 80 120 160 200 240 280 320 360 Days 0 0 40 80 120 160 200 240 280 320 360 Days

What can be done when the available water resources are not sufficient to satisfy water needs? IST: Hydropwer Rodrigo Proença de Oliveira, 2016 12 Control water demand; Look for new water sources: Superficial sources; Groundwater sources; Water reuse; Dessalinization. To improve regularization capacity, when the problem is a time missmatch between water availability and water demand.

Reservoir sizing

Water storage needs IST: Hydropwer Rodrigo Proença de Oliveira, 2016 14 Inflow Outflow Storage Reservoirs Aquifers Evaporation Recharge Reservoirs and aquifers offer the ability to temporarily store water and to phase water availability with water demand. Albufeiras e aquíferos proporcionam uma capacidade de armazenamento temporário da água o que permite a compatibilização temporal das disponibilidade de água com as necessidades.

Reservoir storage zones IST: Hydropwer Rodrigo Proença de Oliveira, 2016 15 NMC, Nível de Máxima Cheia Maximum flood pool (level) Volume de encaixe de cheias Flood control zone NPA, Nível de Pleno Armazenamento Maximum storage pool (level) Captação de água Water uptake Descarga Spill (through the spillway) Volume útil Active, useful or net storage H, Queda / Head Nme, Nível mínimo de exploração Minimum operating pool (level) Volume morto Dead storage Volume turbinado Turbined volume

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Sizing of flood control zones 16 Inflow NMC NPA Flood storage volume Net volume Discharge Outflow Nme Dead storage Tempo Tempo Flood peak reduction Volume of water temporarily stored in the flood stage pool

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Sizing of the dead storage zone 17 Dead storage / Volume morto: Volume below the lowest uptake level / Volume abaixo do nível da tomada de água de cota mais baixa Dead storage volume depends on / Dimensão do volume morto depende de: Orography of the reservoir location / Orografia do local de implantação da barragem; Reservoir sediment inflow / Caudal sólido afluente à albufeira; Infrastruture lifetime / Expectativa de vida útil da infraestrutura. NMC NPA Sediment deposition Sediment inflow Nme Dead storage volume Bottom discharge

Net storage pool sizing IST: Hydropwer Rodrigo Proença de Oliveira, 2016 18 What is the adequate size to ensure the supply of various uses with a given reliability? Qual deve ser o valor adequado do volume útil de uma albufeira, para satisfazer um conjunto de usos com uma dada garantia de abastecimento? Oversizing / Excesso de volume útil: Higher investment / Maior volume de investimento; Higher operating costs / Maior custo de operação; Larger environment impacts / Impactos mais significativos ; Undersizing /Défice de volume útil: Inadequate reliability /Insuficiente garantia de abastecimento; A large net storage capacity enables an increase flow regulation capacity / Quanto maior o volume maior a capacidade de regularização das afluências; Storage coeficient /Coeficiente de regularização: Storage coef. = Net storage capacity Avg annual inflow Creg << 1 Run-of-river reservoirs Creg < 1 - Creg > 1 Stoage reservoirs

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Mass balance 19 Evaporation Withdrawal NMC Flood control Spill NPA Inflow Nme Net storage Energy H Dead storage Volume turbinado V t+1 = V t + Q t E t R 1 t R 2 t S t Et V t+1 Storage at beginning of month t+1 V t Storage at beginning of month t E t Evaporation (volume) during month t Q t Inflow during month t Qt V R1t R2t St R 1t Volume supplied to use 1 during month t R 2t Volume supplied to use e during month t S t Spilled volume (through the spillway) during month t

Mathematical simulation IST: Hydropwer Rodrigo Proença de Oliveira, 2016 20 Qt Et V R1t R2t St Area-elevation curve Curva de áreas inundadas Water level, H Mass balance: V t+1 = V t + Q t E t R 1 t R 2 t S t Inundated area, A Estimation of evaporation: E t = A t x e t (volume, e.g. dam 3 ) A t - Área of the reservoir lake (e.g. km 2 ) e t Evaporation rate (mm) A = f(v), A = f(h) Area-elevation curve V = f(h), Storage-elevation curve Storage-elevation curve Curva de volumes armazenados Water level, H Stored volume, V

Elevation-volume-area curves - Alqueva IST: Hydropwer Rodrigo Proença de Oliveira, 2016 21

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Release rules 22 Operating rule for a single use / Regra de operação para um único uso R t = f t (V t +Q t, N t ) Standard operating policy Política padrão R t, S t S t N t R t V t - Storage / Volume armazenado Q t -/ Expected inflow / Volume expectável no período N t Water demand / Necessidade de água K t -Storage capacity / Capacidade de armazenamento R t -Supplied volume / Volume atribuído ao uso S t -Spill / Volume descarregado K t V t +Q t

Simulation in MS Excel IST: Hydropwer Rodrigo Proença de Oliveira, 2016 23

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Results 24 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 Out-17 Out-20 Out-23 Out-26 Out-29 Out-32 Out-35 Out-38 Out-41 Out-44 Out-47 Out-50 Out-53 Out-56 Out-59 Out-62 Out-65 Out-68 Out-71 Out-74 Out-77 Out-80 Out-83 Out-86 Out-89 Volume Armazenado (dam3)

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Results 25 50000 K = 45 000 dam 3 N = 8 000 dam 3 /month 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 70000 K = 65 000 dam 3 N = 8 000 dam 3 /month 60000 50000 40000 30000 20000 10000 0 Out-17 Out-20 Out-23 Out-26 Out-29 Out-32 Out-35 Out-38 Out-41 Out-44 Out-47 Out-50 Out-53 Out-56 Out-59 Out-62 Out-65 Out-68 Out-71 Out-74 Out-77 Out-80 Out-83 Out-86 Out-89 Out-17 Out-20 Out-23 Out-26 Out-29 Out-32 Out-35 Out-38 Out-41 Volume Armazenado (dam3) Out-44 Out-47 Out-50 Out-53 Out-56 Out-59 Out-62 Out-65 Out-68 Out-71 Out-74 Out-77 Out-80 Out-83 Out-86 Out-89 Volume Armazenado (dam3)

Performance indicators Expected benefits ( ) / Benefícios expectáveis ( ); Reliability / Garantia ou fiabilidade; Measures the ability to meet water demands / Mede a capacidade do sistema em satisfazer as necessidades; Time : Reliability_T = #years without supply failures/ #anos simulated years Volume: Reliability_V = Supplied volume/ Water needs Vulnerability / Vulnerabilidade: Measures the severity of supply shortages / Mede a gravidade das falhas Average duration of a supply shortage; Duração média das falhas / Supply shortage as a percentage of the demand; % das necessidades não satisfeitas em caso de falha / Robustness (Inverse of vulnerability) / Robustez (Inverso de vulnerabilidade) Resilience / Resiliência: Measures the ability of the system to recover from a supply shortage / Mede a capacidade do sistema em recuperar de uma falha; Number of months the demand is satisfied that follow a month where a suppply shortahe has ocurred over the number of supply shortages (months when demand was not satisfied). Probabilidade de não existir uma falha após uma falha (número de vezes em que uma não-falha sucede a uma falha sobre o número total de falhas) IST: Hydropwer Rodrigo Proença de Oliveira, 2016 26

Yield vs storage vs reliability vs inflow variability Yield vs Storage capacity vs Reliability / Volume fornecido vs volume da albufeira vs garantia; Em Yield Volume fornecido G3 G2 G1 G1 > G2 > G3 Yield vs Storage capacity vs Inflow variability / Volume fornecido vs volume da albufeira para diferentes variabilidades de escoamento afluente; Em Yield, with a given reliability Volume da albufeira, K Volume fornecido com um dado valor de garantia S3 S2 S1 S1 > S2 > S3 Reservoir capacity, K IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Reservoir capacity, K Volume da albufeira, K 27

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Successive peak method 28 Out. 1917, Q1 Nov. 1917, Q2 Dez. 1917, Q3 Jan. 1918, Q4 Fev. 1918, Q5 Mar. 1918, Q6.. Ago. 1990, QM-1 Set. 1990, QM Out. 1917, Q1 Nov. 1917, Q2 Dez. 1917, Q3 Jan. 1918, Q4 Fev. 1918, Q5 Mar. 1918, Q6.. Ago. 1990, QM-1 Set. 1990, QM Out. 1917, Q1, Q1-N Nov. 1917, Q2, Q1+Q2 2N Dez. 1917, Q3, Q1+Q2+Q3 3N Jan. 1918, Q4, Q1+Q2+Q3+Q4 4N Fev. 1918, Q5,. Mar. 1918, Q6,... Ago. 1990, QM-1,. Set. 1990, QM... Out. 1917, Q1... Nov. 1917, Q2... Dez. 1917, Q3... Jan. 1918, Q4... Fev. 1918, Q5... Mar. 1918, Q6..... Ago. 1990, QM-1,... Set. 1990, QM,... Mass curve (Rippl diagram) S Qt - S Nt tempo Period when inflow exceeds demand Period when demand exceeds inflow

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Successive peaks method 29 S Qt - Nt Does not consider evaporation; Assumes demand is satisfied with a 100% reliability. K3 K4 K = Max (K1, K2, Kn) K1 K2 K = max k max k k t=1 Q t N t k Q t N t t=1 time Drought period (water needs exceed water availability) Period with suficient water (water availability exceed water needs)

Reservoir operating policies

Example IST: Hydropwer Rodrigo Proença de Oliveira, 2016 31 Consider a reservoir with 300 hm 3 of net storage capacity and with the following inflow regime, that needs to satisfy the following water needs / Considere uma albufeira com 300 hm 3 de capacidade armazenamento útil e com o seguinte regime de afluências e de necessidades de água que devem ser asseguradas: Fall Winter Spring Summer Average inflow(hm3) 60 150 40 10 Coef. of variation of inflow 0,4 0,4 0,4 0,4 Water needs (hm3) 25 25 100 50 Assumee that the economic losses for not providing water can be estimated by a curve such as the one on the left / Considere ainda que as perdas económicas por falta de abastecimento de água podem ser estimadas por uma curva do seguinte tipo: Perdas económicas (k ) Falha de abastecimento (hm3) If at the end of the Winter the water stored in reservoir is 200 hm 3, how much water should the reservoir supply in the spring? If at the end of the Winter the water stored in reservoir is 100 hm 3, how much water should the reservoir supply in the spring? 500 100

Problem formulation IST: Hydropwer Rodrigo Proença de Oliveira, 2016 32 Produção de electricidade Manutenção de ecossistemas Abastecimento urbano Rega Consider the following system which supplies water for different uses / Considere a seguinte albufeira que tem um conjunto diverso de objetivos; How much water should we allocate to each use and how much water should we save for future use? / Num dado instante, qual deve ser o volume de água a atribuir a cada uso e o volume de água a armazenar para usos futuros? This question arises in two contexts: Management how to get the maximum benefit from na existing system; exploração do máximo benefício de um sistema existente; Planning selection of the best alternative (location and size) of a system stil to be built / seleção da melhor alternativa (definição do local e dimensão) a construir.

Operating policies IST: Hydropwer Rodrigo Proença de Oliveira, 2016 33 What are the factors that condition the allocation of water? Quais são os fatores que devem condicionar a decisão de distribuição dos recursos disponíveis? Available water / Volume de água disponível (i.e. armazenado); Expectations on short term inflows / Expectativas de afluências futuras (dependentes da época do ano); Water demands for each use and/or expected benefits for each use / Necessidades de água para cada uso e/ou função de benefícios expectáveis em função do volume atribuído; How to describe an operating policy? Como explicitar uma política de exploração (i.e. uma regra de operação)?: Rule curves / Curvas guia Release rules (Curvas de alocação) and balancing functions (curvas de balanço) Real-time mathematical models / Modelos matemáticos para gestão em tempo real

Rule curves IST: Hydropwer Rodrigo Proença de Oliveira, 2016 34 Vol armazenado Volume de encaixe de cheias Flood control storage Nivel de pleno armazenamento Satisfação total das necessidades No supply restrictions Restrição parcial das necessidades Curva guia Nível mínimo de exploração Some supply restrictions Out Nov Dez Jan Fev Mar Abr Mai Jun Jul Ago Set Vol armazenado R=10 R=max R=17 R=17 R=20 R=6 R=8 R=12 R=15 R=17 R=20 R=5 R=8 R=8 Curva guia R=4 R=3 R=2 R=1 R=1 R=1 R Volume of water to be supplied as a function of avaliable storage and time-of-the-year. R=0 Out Nov Dez Jan Fev Mar Abr Mai Jun Jul Ago Set

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Release rules 35 Operating rule for a single use / Regra de operação para um único uso R t = f t (V t +Q t, N t ) Standard operating policy Política padrão R t, S t S t N t R t V t - Storage / Volume armazenado Q t -/ Expected inflow / Volume expectável no período N t Water demand / Necessidade de água K t -Storage capacity / Capacidade de armazenamento R t -Supplied volume / Volume atribuído ao uso S t -Spill / Volume descarregado K t V t +Q t

Hedging O conceito de hedging (salvaguarda; cobertura de risco IST: Hydropwer Rodrigo Proença de Oliveira, 2016 36 N t R t, S t Standard operating policy Política padrão N t R t, S t K t K t V t +Q t V t +Q t Some hedging: allows for small supply faillures to safeguard future water demands; the reliability decreases Algum hedging : permite antecipadamente falhas no abastecimento de menor dimensão para salvaguardar o abastecimento no futuro; o nível de garantia (número de falhas em %) é menor. R t, S t N t More hedging: the reliability decreases further Mais hedging ; há mais falhas que são parcialmente evitadas mas o nível de garantia (número de falhas em %) ainda menor. K t V t +Q t N t R t, S t K t V t +Q t Maximizes the reliability: the number of faillures is smaller but when a faillure occurs no water is supplied. Maximiza o nível de garantia: há menos falhas de abastecimento mas quando há são totais.

Single reservoir: one use Release rule Curva A Fornece toda a água que tem, mesmo quando não é possível satisfazer a totalidade das necessidades. Q V R N R+S K Curva A S R V+Q Curva B Só fornece quando consegue satisfazer todas as necessidades. N R+S K Curva B S R V+Q IST: Hydropwer Rodrigo Proença de Oliveira, 2016 37

Single reservoir: 2 uses IST: Hydropwer Rodrigo Proença de Oliveira, 2016 38 Abastecimento urbano R t, S t N t 2 Rega N t 1 Hedging K t V t +Q t

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Reservoir in series 39 Curva de alocação (release rule) R 1 +R 2 +S 1 +S 2 Q 1 V 1 N Q 2 R 1 K 1 +K 2 V 1 +V 2 +Q 1 +Q 2 V 2 R 2 Curvas de distribuição (balancing functions) V 1,V 2 K V 2 2 K 1 V 1 V 1 +V 2

How to use the release rule and the balancing functions Reservoirs in series IST: Hydropwer Rodrigo Proença de Oliveira, 2016 40 We know V 1,t and V 2,t We have and estimation of Q 1,t + Q 2,t V t = V 1,t + V 2,t Release rule: V t + Q 1,t + Q 2,t -> R t and S t V t+1 = V t + Q 1,t + Q 2,t R t - S t V t+1 = V 1,t+1 + V 2,t+1 Balancing functions: V t+1 - > V 1,t+1 V t+1 - > V 2,t+1 R 1,t+1 = V 1,t + Q 1,t S 1,t+1 V 2,t+1 R 2,t+1 = V 2,t + Q 2,t + S 1,t+1 S 2,t+1 V 2,t+1

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Reservoirs in parallel 41 Curva de alocação (release rule) R 1 +R 2 Q 1 Q 2 N V 1 V 2 K1+K2 V1+V2+Q1+Q2 R 1 R 2 Curvas de distribuição V 1,V 2 K1 V Q 1 1 K2 V Q 2 2 K 1 K 2 V 1 V 2 V 1 +V 2

How to apply release rules and balacing curves Reservoirs in parallel IST: Hydropwer Rodrigo Proença de Oliveira, 2016 42 We know V 1,t and V 2,t V t = V 1,t + V 2,t From the release rule: Vt + Q 1,t + Q 2,t -> R t and S t V t+1 = V t + Q 1,t + Q 2,t R t S t V t+1 = V 1,t+1 + V 2,t+1 From the balancing functions: V t+1 - > V 1,t+1 V t+1 - > V 2,t+1 R 1,t+1 = V 1,t + Q 1,t S 1,t V 1,t+1 R 2,t+1 = V 2,t + Q 2,t S 2,t - V 2,t+1

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 Single reservoir for energy production 43 Release rule R+S Q R V E K V+Q When the stored volume is large, a large head is available for power production, which means that the amount of water needed to produce a given amount of energy is small; If the stored volume is small, it is not efficient to waste large amounts of water to produce a small amount of energy.

Energy production IST: Hydropwer Rodrigo Proença de Oliveira, 2016 44 Power / Potência Power demand graph Diagrama de carga Reservoir storage hydroelectric plants Run-of-river hydroelectric plants Thermo power plants 0h Wind, small hydro, photovoltaic 24h Time

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 45

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 One reservoir and one aquifer: one use 46 Depends on: Q Recarga V2 Relative costs of abstraction, pumping, treatment and transport of water from both sources Evaporation rate (losses of water from superficial sources) V1 R1 R2 Ratio between the reservoir capacity and the reservoir inflow (spill risk during the flooding season) N Hydrogeological characteristics of the aquifer, namely its recharge, loss by seepage, storage capacity.

IST: Hydropwer Rodrigo Proença de Oliveira, 2016 And if?? 47 Q1 V2 Q2 V3 Q3 For larger and more complex systems, with a number of water sources and several users, how can we evaluate alternative management policies and select most adequate one? V1 R1 R2 Na1 R3 V4 R4 V5 Q4 E Nr1 Na2 R5 V6

Exercise IST: Hydropwer Rodrigo Proença de Oliveira, 2016 48 A reservoir,with a net storage capacity of 2304 dam 3, stores at the beginning of a given month 1560 dam 3. During that specific month the inflow to the reservoir is 1780 dam 3, the evaporation is 100 dam 3. If 600 000 m 3 are supplied what is the discharge through the spillway.

Exercise IST: Hydropwer Rodrigo Proença de Oliveira, 2016 49 Consider a reservoir, with a net storage capacity of 1.800.000 m 3. At the beginning of a 4-month period the net storage at the reservoir is 900 dam 3 and the expected monthly inflows are 3000 dam 3, 1600 dam 3, 1280 dam 3 and 999 dam 3, after evaporation is deducted. If the monthly water supply target is 1900 dam 3, what is final net storage at the reservoir and what is water supply deficit, if any? How much is discharged through the spillway?