# Comparison of Optimal Hedging Policies for Hydropower Reservoir System Operation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

^{3}).

#### 2.2. Study Area

^{2}and the average flow for power generation is around 16.6 m

^{3}/s. These data were taken from the Tenaga Nasional Berhad, Malaysia.

#### 2.3. Reservoir Operation Policies

#### 2.3.1. One Point Hedging Policy (1PHP)

_{t}) will be less than the available storage (W

_{t}) and release cannot fulfil the target demand (D

_{t}). Sa represents the changing point on the target demand line specified as a decision variable for the 1PHP, which must be simulated or optimized. Moreover, when the amount of available storage touches Sa in 1PHP, the water release could fulfil the target demand until the available storage equals the target demand plus the reservoir capacity. The last stage of hedging policies is the same. If the available storage surpasses the summation of target demand (D

_{t}) and active storage (K), spill (SP

_{t}) will occur [9]. For more information about the formulation of this policy, refer to Table S1 (1PHP).

#### 2.3.2. Two Point Hedging Policy (2PHP)

_{t}+ K and the spill occurs (Figure 4). The rest of the parameters were introduced earlier. For more information about the formulation of this policy, refer to Table S1 (2PHP) [16].

#### 2.3.3. Three-Point Hedging Policy (3PHP)

#### 2.3.4. Discrete Hedging Policies (DHP)

_{t}) is greater than D

_{t}, available storage could fully satisfy target demand. If WA

_{t}is greater than V3 and less than D

_{t}, then the rationing will be happening for the coming time step and only the HF1 of target demand will be provided. If V2 < WA

_{t}< V3, the target demand defines as a fraction of HF2. If WA

_{t}is greater than V1 but less than V2, then the stage-III of rationing will be occurring and the fraction HF3 of target demand will be discharged. In DHP, it is supposed that the minimum trigger-volume always sustain in a reservoir. The trigger-volumes are determined based on flow regime requirement and amount of demand reduction due to water savings [17]. It is worth noting that in order to determine the optimize DPH policy for any reservoir, if the numbers of discrete steps are assumed three steps, six parameters should be optimized including V1, V2, V3 and HF1, HF2, HF3. V1, V2, and V3 are determined as a coefficient of active storage (K), while HF1, HF2, HF3 are defined as a coefficient of target demand (D). The formulations of water release based on discrete hedging policy are described in Table S1 (DHP).

#### 2.3.5. Standard Operating Policy for Hydropower Production (SOPHP)

_{0}), which could produce the target power will be specified based on water availability (S). Therefore, the product of mean head (due to S and zero available storage), S and unit weight of water should produce the target power. The S parameter should be estimated or optimized for a specific reservoir based on the relation between head and storage. The mentioned parameters (head and storage) have a non-linear relationship. It means that when stored in the reservoir is more than S, a head is also more and hence a smaller discharge (R < R

_{0}) is enough to produce the target power (TP). While, with lower storage, a large quantity of water must be discharged to produce the same power. These explanations prove that the water demand is not constant in a case of hydropower reservoir system and vary by water head (or storage availability). Whenever the reservoir reaches the maximum reservoir elevation, the head cannot increase. Hence, if the water availability is more than D + K, the required release to produce TP will be constant [18]. It can be concluded whether available storage is less than S, the release is the same as available storage. Therefore, the system cannot regenerate the target power. When T1 < WA

_{t}< T2, the release is falling due to head increase. If WA

_{t}> T2, the release and head become constant (R

_{f}). The formulations of this policy are described in Table S1 (SOPHP). It is worth noting that this policy allows the managers to produce either TP or less. The definitions of parameters used in this policy are as follows:

_{t}: release at time t, WA

_{t}: Water availability at time t, K: active storage, S: minimum required storage to produce target power, R

_{f}: minimum required release to produce target power at a time of maximum net head.

#### 2.3.6. Binary Standard Operating Policy for Hydropower Production (BSOPHP)

#### 2.3.7. Standard Hedging Policy for Hydropower Production (SHPHP)

_{t}< S1, no turbine is running for operation and output of power is zero. If the available water is between S1 and S2, only one turbine can be employed in generation, which means the power production is 25% of full capacity. Whenever S1 < WA

_{t}< S2, the amount of release to produce (1/4) full capacity will decrease as the head increases. Meanwhile, the release rule has a curve from. A similar strategy is applied for S3 and S4. S3 and S4 are the quantity of available water to produce 75% and 100% of the full capacity respectively. If S2 < WA

_{t}< S3, two turbines utilize, which means the power production is equal to half full capacity. If the S3 < WA

_{t}<S 4, three turbines use for the operation to produce 75% of full capacity. If the WA

_{t}≥ S4, four turbines are operated to produce 100% full capacity. Furthermore, beyond full reservoir capacity (K), the head is constant. Therefore, the release is only a function of available water and the line beyond T5 is a constant line. It is worth noting that the slope of the line which connecting T0, T1, T2, T3, and T4 is 45°. Moreover, the number of decision variables or optimization parameters in this policy depend on the number of turbines. In the above example, the system has four turbines. Therefore, four parameters—including S1, S2, S3, and S4—should be simulated or optimized. The formulations of water release are expanded in Table S1 (SHPHP).

#### 2.4. Objective Function and Constraints

- G
_{t}: energy production in time t (kWh) - η
_{0}: efficiency of the hydropower plant - γ: the specific weight of water (9.81 kN/m
^{3}) - r
_{t}: the discharge in a time interval (m^{3}/s) - H
_{t}: average net head in a time interval - t: shows the duration of release (h)

_{t}, which is used in the formulas such as hedging rules formulation, can be determined R

_{t}= r

_{t}× t. In addition, the objective function must be satisfied with the following constraints during the optimization.

#### 2.4.1. Hydro Plant Discharge Limits

_{t}) must be placed in an allowable range.

_{min}≤ R

_{t}≤ R

_{max}

_{min}is defined as the minimum permissible release and maximum permissible release (R

_{max}) is specified according to full capacity turbines and a capacity of diverting tunnel in a hydropower reservoir system, which is 20.5 m

^{3}/s

#### 2.4.2. Water Balance Equation

_{t}= S

_{t−1}+ I

_{t}− E

_{t}− R

_{t}− SP

_{t}

_{t}: storage at time t, S

_{t−1}: storage at time t − 1, I

_{t}: inflow at time t, E

_{t}: evaporation at time t, R

_{t}: release at time t, SP

_{t}: spill at time t.

#### 2.4.3. Reservoir Storage Volumes

_{min}≤ S

_{t}≤ S

_{max}

_{min}: storage volume at minimum water level (1.6 Mm

^{3}) and S

_{max}: storage at maximum operating level (2.8 Mm

^{3}).

#### 2.4.4. Hydro Plant Power Limits

_{min}≤ G

_{t}≤ G

_{max}

_{min}: minimum values of energy generation (0), G

_{max}: maximum values of power generation (150 MW). The mentioned parameters are determined based on turbine capacity (150 MW).

#### 2.5. Optimization Algorithms

## 3. Results

^{3}. This similarity shows that in a case of optimization, SOPHP is converted to (binary SOPHP). To clarify further, it seems that when the SOPHP model was optimized, the system allows to produce only 0 or target power (TP) and the production below TP is not permitted. So, SOPHP and BSOPHP policies will be the same. According to the characteristics of the SIPS station (which comprises three turbines), the number of decision variables in SHPHP policy is three. These variables are S1, S2, and S3. The constraints of S1 < S2 < S3 is also considered in the process of optimization.

^{3}respectively. It means that when the available storage is less than 2,085,195 m

^{3}, there is no power output. When the available storage is between 2,085,195 and 2,203,957 m

^{3}, only one turbine with the capacity of 50 MW was working. When the available storage is between 2,203,957 and 2,318,751 m

^{3}, two turbines comprised in operation. Finally, if the available storage is more than 2,318,751 m

^{3}, all turbines with total capacity of 150 MW participate in power production.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 12.**Compare monthly mean power generation between constructed models time period (2003–2009) and validation period (2010–2012) in different forms of hedging policies (

**A**–

**G**).

**Figure 13.**Comparison between monthly mean power generation by optimized operational policies and by TNB operation for the period from 2003–2009.

**Figure 14.**Jor reservoir elevation Box plot for different forms of operational policies during construction time.

**Table 1.**Optimization of decision variables during 2003–2009 by using hybrid PSO-GA algorithm for various hedging policies.

Name of Policy | Optimal Points | Storage (m^{3}) |
---|---|---|

SOPHP | S | 2,465,523 |

BSOPHP | S | 2,465,523 |

SHPHP | S1 | 2,085,195 |

S2 | 2,203,957 | |

S3 | 2,318,751 | |

1PHP | Sa | 2,183,452 |

2PHP | Sa | 2,154,853 |

Sb | 2,340,108 | |

3PHP | Sa | 2,038,475 |

Sb | 2,082,471 | |

Sc | 2,324,914 | |

V1 | 1,714,985 | |

V2 | 2,451,289 | |

DHP | V3 | 2,463,421 |

HF1*D | 519,000 | |

HF2*D | 868,000 | |

HF3*D | 961,000 |

^{3}).

Operational Policies Model | Mean Power Generation (kWh) | Total Power Generation (GWh) 2003–2012 |
---|---|---|

BSOPHP | 1,320,942 | 3377.13 |

SOPHP | 1,320,942 | 3377.13 |

SHPHP | 1,325,548 | 3382.43 |

1PHP | 1,320,965 | 3377.45 |

2PHP | 1,320,863 | 3377.71 |

3PHP | 1,321,227 | 3378.13 |

DHP | 1,322,164 | 3378.38 |

TNB | 1,267,158 | 2938.60 |

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**MDPI and ACS Style**

Tayebiyan, A.; Mohammad, T.A.; Al-Ansari, N.; Malakootian, M.
Comparison of Optimal Hedging Policies for Hydropower Reservoir System Operation. *Water* **2019**, *11*, 121.
https://doi.org/10.3390/w11010121

**AMA Style**

Tayebiyan A, Mohammad TA, Al-Ansari N, Malakootian M.
Comparison of Optimal Hedging Policies for Hydropower Reservoir System Operation. *Water*. 2019; 11(1):121.
https://doi.org/10.3390/w11010121

**Chicago/Turabian Style**

Tayebiyan, Aida, Thamer Ahmad Mohammad, Nadhir Al-Ansari, and Mohammad Malakootian.
2019. "Comparison of Optimal Hedging Policies for Hydropower Reservoir System Operation" *Water* 11, no. 1: 121.
https://doi.org/10.3390/w11010121