Systemic Simulation of Smart Grids : First Results

The month of August provides me with the opportunity to get back to my computer and to resume my programming projects. I have been able to complete the first step of S3G (Systemic Simulation of Smart Grids) which I started last year. I had the opportunity to attend the EU-US Frontiers of Engineering Symposium, where I have presented my project and received encouraging and interesting feedback.

The objective of S3G is to simulate the production and consumption of electricity throughout a long period of time (15 years). The S3G model, which is illustrated by the following figure, may be summarized with five parts:

• Energy demand: for each city, energy demand is generated from an hour-by-hour and day-by-day template, adding some random variation (the extent of which is a model parameter) together with a city-specific variation. This number is then reduced by the amount of “negaWatts”, computed from the total amount invested by the city. The model uses a ratio obtained from a concave-increasing function of the investment.
• Dynamic Pricing: both suppliers and operators use a simple affine pricing model, with a constant price when the demand is less than a “base power”, and a linear formula when the demand is higher.
• Production: suppliers use nuclear power according to planned schedule and adjust to resulting demand with fossil plants. Operators always use their green power (store it in the “buffer” or resell it when there is too much of it). They adjust to the city demand with their own fossil plant and wholesale electricity from suppliers, at the lowest marginal cost.
•  Consumption: The actual electricity consumption for each city is the demand, minus “shaving”, which is obtained by applying an S-curve to the sale price.
• Market-share: for each city, the market balance between the national supplier and the local operator is determined yearly using another S-curve.

This S3G model is both simple and complex. It is simple because it is based on a handful of equations, resulting in a simulation code that is 500 lines long. On the other hand, it is a complex model for two reasons. On the one hand, there are multiple feedback and interaction loops that make it difficult to analyze how the system will react to perturbations. On the other hand, there are many unknown parameters in this model (such as market sensitivity, demand-response behavior, negaWatt capabilities, etc.). 

The following figure shows, on the right part, a rough summary of the simulation loop that is run for each time period (3 hours, hence 8 times per day). On the left part, it shows the three main GTES generic procedures.

I have already spent some time on computational experiments that will be presented at CSDM in December. A GTES simulation run returns the average and standard deviation of a few key business parameters, as well as some indication of the Nash convergence. Giving averages and a few deviations is a poor restitution of the rich data gathered during the computational experiment, but the goal is simply to “get a feeling for what is happening”, as opposed to producing a forecast. The current set of experiments is designed to understand the main issues that were exposed in the previous post. I have defined a fictional country somehow similar to France decomposed into 10 regions/cities. I have run 8 experiments that may be defined as follows:

1. The “default” is a reference point, from which “what-if” sensitivity analysis is made. The economic parameters are set in such a way that alternate operators start with a 20% market-share and should be able to increase it if they demonstrate a better management of variability.
2. The second experience raises the variability of energy consumption (globally), while the third experience raises the local variability (each city is more different from each other).
3. The fourth experiment doubles the fossil energy price (gas and coal). In the default scenario, it is randomly drawn between 20€ and 40€/MWh.
4. The fifth experiment imposes a 5% reduction of the nuclear assets for the supplier during the first 5 years.
5. The sixth experiment sets a carbon tax at 100€/t, the proceeds of which is used by the “regulator” to subsidize green energy investment.
6. The seventh experiment explores the impact of overall demand variation in the next 15 years. The model assumes a constant growth/decline of electricity demand which is expressed as a percentage. This experiment plays with different values to see if demand impacts the profitability of smart grids.
7. The last experiment is a small variation of the first one, where wholesale prices are more rigidly constrained. During this set of experiment, I considered that the constraints that regulate wholesale prices for the supplier are fixed. An interesting next step will be to make them a strategic parameter for the regulator (which is a better representation of reality and makes for a more interesting game).

I still need to do some additional tuning before presenting my results at CSDM. I will then make my slides available on this blog. For once, I need to run longer simulations (with larger samples) to ensure that the Monte-Carlo sampling is stable. I also want to introduce better local optimization meta-heuristics, such as Tabu search. One of the key issues for smart grid is the pricing model, both for the operator and the supplier. The more complex the pricing model, the better the actor may play with the demand-response concept. However, a more complex princing model requires better optimization techniques to ensure that the automatic computation from GTES (where each actor “learns” its “best response”) is relevant.

This being said, here are a few findings that may be drawn from the hundreds of runs made with the S3G model, and that are worth sharing:

•  There is a systemic benefit of distribution and autonomy to cope with variation. This is shown in our second and third line. It is a “subtle” variation (small effects), which means that the economy of the local operator is dominated by its capacity to operate at much lower customer management costs than the supplier.
• CO2 tax increases play a very small role, and one that is difficult to anticipate since it both favors the local operator (support green subsidies) and the supplier (raises the difference between fossil and nuclear).
• “De-nuclearization” is a favorable scenario for smart grid operators, as are most regulations that are adverse to the supplier. The obvious limitation is the resulting price increase that reduces the total economy output (and the country’s competitiveness).
• The “community advantage” (that is, the ability for a local operator to better manage the demand-response loop because it is “closer” to its end customer) is marginal, and it is quite unclear if the payback from demand-response management is enough to sustain the operator’s business model.
• Investing in local storage is never an interesting option (at current prices). We needed to slash the price by over an order of magnitude to see a viable payback in less than 10 years.
• There is a clear competition between local operators and suppliers. The learning component of GTES makes for “agile” players who react closely to each other signals. The pricing structure plays an important role (we have only explored a simple variable pricing scheme). A logical consequence is the importance of regulation.
• The results are sensitive to the strategies of the player. A next step for S3G is to build a “strategy matrix”, which is a tabular “what-if” sensitivity analysis where we see what happens if the goals of the players are changed.