Optimization and uncertainty analysis of operational policies for multipurpose reservoir system

Abstract

This paper presents optimization and uncertainty analysis of operation policies for Hirakud reservoir system in Orissa state, India. The Hirakud reservoir project serves multiple purposes such as flood control, irrigation and power generation in that order of priority. A 10-daily reservoir operation model is formulated to maximize annual hydropower production subjected to satisfying flood control restrictions, irrigation requirements, and various other physical and technical constraints. The reservoir operational model is solved by using elitist-mutated particle swarm optimization (EMPSO) method, and the uncertainty in release decisions and end-storages are analyzed. On comparing the annual hydropower production obtained by EMPSO method with historical annual hydropower, it is found that there is a greater chance of improving the system performance by optimally operating the reservoir system. The analysis also reveals that the inflow into reservoir is highly uncertain variable, which significantly influences the operational decisions for reservoir system. Hence, in order to account uncertainty in inflow, the reservoir operation model is solved for different exceedance probabilities of inflows. The uncertainty in inflows is represented through probability distributions such as normal, lognormal, exponential and generalized extreme value distributions; and the best fit model is selected to obtain inflows for different exceedance probabilities. Then the reservoir operation model is solved using EMPSO method to arrive at suitable operational policies corresponding to various inflow scenarios. The results show that the amount of annual hydropower generated decreases as the value of inflow exceedance probability increases. The obtained operational polices provides confidence in release decisions, therefore these could be useful for reservoir operation.

Appendix 1

1.1 System performance measures

To assess the reservoir system performance for the operational policies developed for different values of inflow exceedance probabilities, performance measures such as reliability, resilience, and vulnerability (Hashimoto et al. 1982) are evaluated. In a hydropower reservoir system, if hydropower production in a time period is greater than the target power, a satisfactory condition occurs otherwise it is unsatisfactory.

Let Z _t be an index to measure whether the system is in a satisfactory or unsatisfactory state. In a hydropower system, if is the total hydropower production at time step t (E _t ) is greater than or equal to target hydropower (TP _t ) then the system is said to be in satisfactory state and Z _t , is equals to one, otherwise, the system is said to be in unsatisfactory state and the index, Z _t , is equals to zero. Mathematically the index, Z _t , is defined as:

$$ Z_{t} = \,\left\{ \begin{array}{ll} 1 &{\text{if}}\;E_{t} \ge TP_{t} \\ 0 & {\text{else}} \\ \end{array}\right.\quad \forall \;t $$

(20)

To capture the system transition from unsatisfactory state to satisfactory state, an index, W _t , is defined as:

$$W_t = \left\{\begin{array}{ll}1, & \text{if}\;E_{t} < TP_{t} \;\text{and}\;E_{t + 1} \ge TP_{t} \\ 0, & \text{otherwise} \\ \end{array}\right.\quad \forall\;t $$

(21)

Reliability: The reliability can be defined as probability of the system is in satisfactory state. Therefore, this is the indicator of performance of system meeting the target power. Mathematically it can be expressed as (Hashimoto et al. 1982):

$$ \gamma = \frac{{\sum_{t = 1}^{T} {Z_{t} } }}{T}\quad \forall \;t $$

(22)

where γ is the system reliability, whose value ranges within limits of [0, 1] or expressed in terms of percentage; T is the total number of time periods in the operation horizon.

Resiliency: It is an indicator of the speed of recovery from an unsatisfactory condition or failure state. Mathematically it can be expressed as:

$$ \beta = \frac{{\sum_{t = 1}^{T} {W_{t} } }}{{T - \sum_{t = 1}^{T} {Z_{t} } }}\quad \forall \;t $$

(23)

where β is the system resiliency, whose value ranges within limits of 0–1.

Vulnerability: Vulnerability is a statistical measure of the extent or duration of failure, if a failure (or unsatisfactory value) occur. Extent-vulnerability can be defined based on the expected or maximum observed individual or cumulative extent of failure (Loucks 1997). The expected extent-vulnerability ($\varphi_{avg}$) can be defined as:

$$ \varphi_{avg} = \frac{{\sum {D_{t} } }}{{T - \sum\limits_{t = 1}^{T} {Z_{t} } }}\quad \forall \;t $$

(24)

where D _t is the deficit or extent of failure during time period t, which is estimated by $D_{t} = Max(TP_{t} - E_{t}; 0)$