1. **Problem Statement:** We need to optimize the total reliability costs for a distribution system over 15 years, considering device installation costs, operation & maintenance (O&M) costs, and the cost of unreliability measured by EENS (Expected Energy Not Supplied). 2. **Given Data and Parameters:** - Fuse cutout cost: 4500 - Fuse link cost: 100 - Recloser cost: 1,250,000 - Recloser annual O&M: 50,000 - Switch cost: 150,000 - Switch annual O&M: 5,000 - Economic value of EENS: 20 per kWh - Interest rate: 10% (i=0.10) - Equipment life: 15 years - Power factor: 0.9 3. **Formulas and Important Rules:** - Present Worth Factor (PWF) for 15 years at 10% interest: $$\text{PWF} = \frac{1 - (1 + i)^{-n}}{i} = \frac{1 - (1 + 0.10)^{-15}}{0.10}$$ - Total cost for each device at location $j$: $$\text{Total Cost}_j = \text{Installation Cost}_j + (\text{Annual O\&M}_j \times \text{PWF}) + (\text{EENS}_j \times 20)$$ - EENS is calculated from reliability indices and load data; it represents energy not supplied in kWh. - Reliability indices: - SAIFI (System Average Interruption Frequency Index): average number of interruptions per customer. - SAIDI (System Average Interruption Duration Index): average outage duration per customer. - EENS (Expected Energy Not Supplied): energy not supplied due to outages. 4. **Step-by-step process:** 1. Calculate PWF: $$\text{PWF} = \frac{1 - (1 + 0.10)^{-15}}{0.10} = \frac{1 - (1.10)^{-15}}{0.10}$$ 2. For each location, calculate the total cost for each device option (fuse cutout, fuse link, recloser, switch) using the formula above. 3. Determine the reliability indices (SAIFI, SAIDI, EENS) for each device at each location based on failure rates ($\lambda_{qi}$), repair times ($r_{qi}$), number of customers ($N_{qi}$), and load ($L_{qi}$). 4. Calculate EENS for each device at each location: $$\text{EENS}_j = \sum_i \lambda_{qi} \times r_{qi} \times L_{qi} \times \text{pf}$$ 5. Choose the device at each location that minimizes the total cost. 6. Sum the chosen devices' costs and reliability indices to find system-wide SAIFI, SAIDI, and EENS. 7. Calculate Net Present Value (NPV) of the total costs over 15 years using PWF. 5. **Final answers under optimal condition:** - a. Device placement: select device with minimum total cost at each location. - b. Calculate system-level SAIFI, SAIDI, and EENS by aggregating chosen devices' indices. - c. NPV is the sum of installation costs plus O&M costs discounted over 15 years plus cost of unreliability. This formulation allows optimization of reliability costs by balancing installation, maintenance, and unreliability costs over the equipment's lifetime.