DK Hydrotech - Hydrotechnical Engineering and Data Analysis

>The planning of pumped-storage hydropower (PSH) raises an interesting question about electricity price volatility and supply risk, and I jumped at an opportunity to look into the problem through a graduate course in Risk and Decision Analysis in Civil Engineering Systems.  The writeup that follows is an informal summary of the study I undertook for the course.

## Abstract

The viability of pumped-storage hydropower (PSH) is primarily a function of demand volatility, or the sub-daily variability of electricity pricing in regional wholesale markets.  Often overlooked however is the risk in capital expenditure [1].  This study approached the viability of PSH using Monte Carlo simulation, where development and operating costs were modelled as random variables based on historical information about storage hydropower projects (n = 112).  Revenue was simulated as a random variable based on historical electricity spot market data.  The simulation results suggest the optimal pumped storage plant size balances the expectation (risk) of electricity wholesale price volatility and the risk associated with wholesale price forecasting and project capital costs.

## Data and Assumptions

Based on a constant storage reservoir volume and assuming a **daily cycle**, a perfect demand (price) forecast would allow a plant to generate energy when the price (revenue) is highest during peak demand hours of the day, and to consume energy when the price (cost) is lowest, late at night.  The hourly price data used for the study shows multiple dominant frequencies, namely seasonal and day of week variability, however the diurnal pattern is dominant.

![Variability in electricity spot market pricing.](/media/editor/daily_price_2_20200113213050846996.png "Variability in electricity spot market pricing.")

Based on historical sub-daily electricity wholesale price variability, a larger plant capacity would generate the greatest revenue given perfect forecasting.  Processing the full plant storage volume during the highest-priced, single hour, each day, represents the upper bound revenue estimate, and a benchmark for forecast performance.  For an equal volume reservoir, a smaller plant capacity then increases the plant cycle duration, conceding a lower average daily price differential (assuming perfect price forecasting).  **For some reservoir volume, the longer cycle duration of a smaller plant effectively hedges against imperfect forecast performance.**  In addition, the longer plant cycle duration is associated with a smaller plant capacity and lower risk associated with capital costs.

Despite the abundance of agencies and companies warehousing data relevant to this topic, only one of my requests for information received a response (thanks to the nice folks at the Idaho National Engineering and Environmental Lab).  As a result, I had to resort to using cost and electricity pricing from different regions, **making the comparison completely invalid** for drawing conclusions about pumped storage in BC, but still demonstrates an interesting analytical approach that raises interesting questions about structure in electricity spot market prices.  The input data are as follows:

| Parameter | Description | Source |
|---|---|---|
| Development Cost | Estimated unit development costs for 112 storage facilities | [Idaho National Engineering and Environmental Laboratory](https://www1.eere.energy.gov/water/pdfs/doewater-00662.pdf)|
| Fixed Operating Cost | Estimated unit *fixed* operation costs for 112 storage facilities | [Idaho National Engineering and Environmental Laboratory](https://www1.eere.energy.gov/water/pdfs/doewater-00662.pdf)|
| Variable Operating Cost | Estimated unit *variable* operation costs for 112 storage facilities | [Idaho National Engineering and Environmental Laboratory](https://www1.eere.energy.gov/water/pdfs/doewater-00662.pdf)|
| Electricity Price (PH) | Wholesale electricity spot market price for the Luzon region in the Philippines. (hourly, 2006-2019) | Retrieved from [Philippine Wholesale Electricity Spot Market.](http://www.wesm.ph/) |
| Electricity Price (ON) | Wholesale electricity spot market price for Ontario, Canada (hourly, 2002-2019) | Retrieved from [HOEP.](http://www.ieso.ca/en/Power-Data/Price-Overview/Hourly-Ontario-Energy-Price) |
| Currency Exchange | Historical daily currency data (PH to USD, CAD to USD) | [Pacific Exchange Rate Service](http://fx.sauder.ubc.ca/) (with thanks to Dr. Antweiler at UBC) |

Several probability distributions were assessed for fitting the cost variables.  Importantly, the results were not highly sensitive to the distribution, but the probability distribution was selected to be conservative in model results.

![Probability distributions of project costs.](/media/editor/cost_distributions2_20200113200448037594.png "Probability distributions of project costs.")

Hourly electricity market price data were hard to come by.  The open-source electricity market data from the Philippines and Ontario, Canada were used to derive a series representing the daily price differentials, the distribution of which is approximated well by the exponential function.

Project performance was simulated over a 40 year planning horizon, and a 5% discount rate was assumed.  The results shown (in the title image for IRR and below for NPV) suggests that the cost penalty of building and operating a larger plant favours smaller plants with longer cycle durations.  In addition, the smaller plant and longer cycle duration **limits the value at risk substantially**, and to a smaller extent the value at gain.

![Simulation results showing the reduced risk associated with smaller plant capacity and longer plant cycle duration.](/media/editor/npv_sim_20200113213828978945.png "Simulation results showing the reduced risk associated with smaller plant capacity and longer plant cycle duration.")

Results are presented in the table below for the range of facility capacity scenarios based on Philippine wholesale electricity spot price data.   The Ontario data (not shown) exhibited the same general trends, despite having unique daily price distributions and seasonality.

| Capacity [MW] | Cycle Duration [hours] | Expected NPV [$M] | **Mean** Deterministic NPV [$M] | **Median** Deterministic NPV [$M] |
|---|---|---|---|---|
| 250 | 2 | -58 | 28 | -171 |
| 125 | 4 |  124 | 200 | 28 |
| 83 | 6 | 151 | 220 | 68 |
| 63 | 8 | 143 | 212 | 77 |
| 50 | 10 | 123 | 187 | 72 |

This basic exercise in asking what makes pumped storage hydropower viable raises interesting questions like:

1. What is the impact of adding storage to the grid?  i.e., if enough energy is readily offered to satisfy peak demand, the spot price should be driven downward.  i.e. the larger the plant, the harder it pulls the rug from under its own feet.  What then is the marginal effect of adding storage?   
2. The most difficult assumption to address is that of stationarity of the distribution of daily prices.  Two approaches come to mind: what supply and demand conditions could arise to reduce the variability in sub-daily spot price differential the point where pumped storage is no longer viable, and  
3. What storage project characteristics afford the most resiliency against reduction in sub-daily spot pricing variability?

## References

1. Pineau PO. Fragmented markets: Canadian electricity sectors’ underperformance. InEvolution of Global Electricity Markets 2013 Jan 1 (pp. 363-392). Academic Press.

Pumped Storage Hydropower

Posted: Jan. 13, 2020