- Industry: Utilities
- Product(s): @RISK
- Application: Assessing Needs for Equipment Upgrades
Tesla Consultants and Delta Utilities of New Zealand demonstrate how to use probabilistic Monte Carlo simulation in @RISK to assess the need for and the timing of an upgrade of the GXP (the substation that connects a regional area to the transmission grid). Forecast demand data combined with historical failure modes including snow, natural events and equipment failures are considered. The result is a probability density function representing the range of costs to customers for non-supply during contingencies. This is then fed into a Net Present Value (NPV) calculation to determine the maximum amount of capital that could be spent to mitigate these ‘loss of supply’ events.
The most useful thing about @RISK is that it is simpler to demonstrate the model mathematics to colleagues and superiors unfamiliar with the Monte Carlo method. Even if they don’t understand all the background statistics, they can verify much of the model mathematics and input assumptions.Chris O’Halloran, Consulting Engineer with Tesla Consultants
In 2001, Dunedin Electricity had recently purchased the Central Otago Network. DELTA Utilities was an asset management company and contractor providing engineering and construction service for both the Dunedin and Central Otago Electricity Networks. The intention of Dunedin Electricity was to be a ‘Good Corporate Citizen’ on behalf of the Frankton area electricity consumers and to determine a robust economic rationale before committing the Dunedin Electricity and New Zealand’s government-owned Transmission Lines Company, Transpower, to upgrading the Cromwell to Frankton transmission network.
Distribution companies face a balancing act of delivering an electrical connection to customers that both optimizes reliability and cost. Part of that challenge is determining when to reinforce supply circuits (often by duplication) to enhance reliability on behalf of a varied aggregation of customers. “During periods of high growth, premature augmentation of the network is financially trivial since the increased demand quickly brings increased revenue,” says Chris O’Halloran, Consulting Engineer with Tesla Consultants. “But what about low growth scenarios, how far can the conventional ‘n-1’ deterministic criteria be pushed? What if the peak load is seasonal?”
For some years prior, Dunedin Electricity's Asset Management Plan had stated that in financial decision making, it valued the cost of unserved energy to the community as:
- $5.52 per unserved kWh for residential customers
- $55.20 per unserved kWh for commercial and industrial customers
“Given that the CEO of DELTA remained supportive, in our analysis, we assumed that even if feeders [high voltage overhead lines] comprising of residential circuits were targeted for load shedding, [disconnecting customers intentionally to reduce overloading on the network], some commercial and industrial customers would still be affected,” says O’Halloran. “Knowing this, we valued lost load at $10.49 per unserved kWh 4.”
Up-rating of the transmission network would naturally incur increased line charges from Transpower. To relieve the 38MVA constraint, Transpower had indicated an ongoing increase in line (or connection) charges that translated to a Present Value (PV) of $674,000 in today’s dollars.
“From Dunedin Electricity’s perspective, if the PV of the ‘cost of unserved energy’ exceeded the PV of the ‘increased Transpower line charges,’ the right decision was to proceed with the transmission or GXP upgrade,” says O’Halloran. “The issue is then, how do we quantify our confidence in that decision, and at what point?”
To make some assessment of the likely impact of exceeding the ‘n-1’ threshold, DELTA engineers suggested using a Monte Carlo approach using @RISK. With the loading information well in hand, DELTA sought information from Transpower into the reliability of the circuits and network supplying the Frankton GXP. The intention was to determine how often and for how long load might need to be shed in order not to overload either of the two 110/33kV transformers at Frankton.
Transpower supplied records of the history of the previous 11 years outage on these circuits. In New Zealand, the sub-alpine environment gets quite a bit of snow in winter. The sub-alpine environment is also quite mountainous making access by repair crews difficult in winter—thus, it was important to have confidence in the repair duration. “Given the sub-alpine environment in which these 220kV and 110kV circuits operate, this gave us some confidence by which to model the likely outage durations,” says O’Halloran. “From there, our approach was to synthesize a history of failures and repairs throughout the yearly profile to determine the amount of load that would need to be shed or curtailed on a yearly basis and how often this might occur.”
O’Halloran and his team assumed that an 11kV feeder (or two) somewhere in the Frankton network would be disconnected if normal ripple-based load control (i.e., SmartGrid power management) was unable to limit demand on the GXP to 38MVA. “Additionally, we included in the model a 35MVA limit for the first two hours of any circuit outage; just to be pessimistic about how precise a system operator might be able to limit demand,” O’Halloran adds.
The @RISK model in Microsoft Excel sampled the annual 2002 half-hour data with a uniform distribution throughout the year, except for snow failures which occur only in the winter months. “We applied a Poisson distribution for the number of each kind of failures, and then applied the constraint to see how much load would be unserved and accumulated this for an annual figure,” O’Halloran explains. “This process was repeated 50,000 times and for each Growth scenario (5%, 7.5%,10%, 15%, and 20%)”
The other statistic of interest is how many load shedding decisions will need to be made in a given year for each growth scenario and their likelihood. Figure 4, below, shows the range of outcomes to the different growth scenarios:
“The reader will note that as we consider higher growth scenarios, we can have less confidence that no load shedding will be required due to insufficient transformer capacity at Frankton, and that in the extreme case, the maximum number of possible load shedding events increases,” says O’Halloran. “If delaying up-rating or replacing the FKN transformer and allowing the increasing load to exceed ‘n-1’ criteria is the agreed course of action, the network operators would need to have plans in place to shed load since it is likely this facility would be required every 2 years by the time the loading reaches the +7.5% Growth scenario mark. It is likely the first stage response would be automated.”
Present Value Analysis
By using the total unserved energy distribution as the cost of unserved energy for each of the future years (up to 20 years in this case), O’Halloran was able to derive a probability density function of the Present Value of the future costs of non-supply. When a series of probability density function is summed in this way, the mean (or average) stays similar, and the standard deviation reduces, effectively smoothing the extremes. The result is often a LogNormal looking distribution as shown in the following figures:
O’Halloran and his team also used @RISK to determine the sensitivity of the unserved energy and the number of annual load-sheds for the ‘+20% Growth’ scenario. Perhaps unsurprisingly, transformers outage feature strongly given the three-month outage time, whereas snow is considered the most likely cause for a load shed event. “This type of analysis can be useful for refining what input data is important to have the most confidence in the conclusion,” says O’Halloran.
O’Halloran and his team made a recommendation to defer a transformer up-rating when the load is forecast to increase by 5% to 10% above the 2002 profile. “It’s a little daring, but not wildly outside the realms of conventional planning, especially given the seasonal nature of the load as it was,” he says. “The most useful thing about @RISK is that it is simpler to demonstrate the model mathematics to colleagues and superiors unfamiliar with the Monte Carlo method,” O’Halloran continues. “Even if they don’t understand all the background statistics, they can verify much of the model mathematics and input assumptions. When using the manual calculation methods, the visual feedback of seeing each iteration provides confidence in the modeling method and therefore the value of process.”