Power System Reliability

Loss of Load Probability (LOLP) and Expected Energy Not Served (EENS) in Power System Reliability Evaluation

1. Context

Power system reliability evaluation is broadly divided into adequacy (ability to meet demand) and security (ability to withstand disturbances). LOLP and EENS are the two principal probabilistic adequacy indices used in generation planning — they quantify the risk that installed generating capacity will fail to meet the load demand, taking into account random forced outages of generating units.

2. Loss of Load Probability (LOLP)

Definition: LOLP is the probability (or expected proportion of time) that the system's available generation capacity is less than the load demand.

Computation:

1. Build the Capacity Outage Probability Table (COPT) for all generating units using their Forced Outage Rate (FOR):
   • For a unit of capacity $C_i$ and FOR $q_i$, the two-state model gives: $P(\text{up}) = 1 - q_i, \quad P(\text{down}) = q_i$
   • Convolve all units to obtain the probability $P_k$ of each capacity outage state $O_k$.
2. Arrange the daily peak load duration curve (or hourly load model).
3. For each period $j$ with load $L_j$: $\text{LOLP}_j = \sum_{k:\, O_k > (C_{installed} - L_j)} P_k$
4. Aggregate over the year: $\text{LOLP (annual)} = \frac{1}{N}\sum_{j=1}^{N} \text{LOLP}_j \quad \text{or expressed in days/year}$

Units: Usually expressed as days/year or as a dimensionless probability.

Interpretation: An LOLP of 0.1 day/year means the system is expected to be short of generation on 0.1 day in a year — the standard planning criterion in many utilities (e.g., 1 day in 10 years).

3. Expected Energy Not Served (EENS)

Definition: EENS (also called Expected Unserved Energy, EUE) is the expected amount of energy (MWh) that cannot be supplied to customers over a given period because of generation inadequacy.

Computation: $\text{EENS} = \sum_{j=1}^{N} \sum_{k} P_k \cdot \max\bigl(0,\; L_j - (C_{installed} - O_k)\bigr) \cdot t_j$

where:

• $P_k$ = probability of capacity outage state $O_k$
• $L_j$ = load in period $j$
• $t_j$ = duration of period $j$ (hours)
• The $\max(0,\cdot)$ term captures the magnitude of the shortfall, not just its occurrence.

Units: MWh/year (or GWh/year).

4. Key Differences

5. Role in Reliability Evaluation

1. Generation planning: LOLP is used to decide the reserve margin and the timing/size of new units. A typical NEA-type criterion is LOLP ≤ 0.1 day/year.
2. Economic optimisation: EENS is multiplied by the Value of Lost Load (VOLL) to obtain the Expected Interruption Cost (ECOST): $\text{ECOST} = \text{EENS} \times \text{VOLL}$ This allows comparison of the cost of adding a new plant against the benefit of reduced unserved energy.
3. System expansion studies: Both indices are computed for each candidate expansion plan; the plan that meets the LOLP standard at minimum total cost (investment + ECOST) is selected.
4. Operational use: EENS supports decisions on unit commitment, spinning reserve, and load shedding priorities during peak or outage conditions.
5. Nepal-specific relevance: With a hydro-dominated system, seasonal river-flow variation and dry-season capacity shortage make EENS a particularly meaningful index for NEA's annual load-shedding assessment.

6. Limitations

• Both indices require accurate FOR data and load forecast; errors propagate directly.
• LOLP ignores the depth of the shortage; EENS ignores the frequency.
• Neither captures transmission constraints — these belong to composite/system reliability evaluation.
• They are expected values and do not indicate the worst-case scenario.

7. Conclusion

LOLP and EENS are complementary probabilistic indices for generation adequacy. LOLP serves as the planning standard (risk of shortage), while EENS quantifies the consequence (energy shortfall) and enables economic appraisal through ECOST. Together they provide a rational basis for capacity addition, reserve planning, and reliability-cost trade-off decisions in a power system such as Nepal's.