Object function

We have a TIMES-model that is able to run in two ”modes”,

1)     The TIMES-model recieves exogenous electricity prices from an external power market model. This TIMES-model does not include any power generating technologies.

2)     The TIMES-model has endogenous electricity price. In this model, power generating technologies are included.

My question is how will this affect the optimal solution on the demand side?

In the first case the model will "see” future electricity prices for all future years towards 2020 and optimize investments in demand technologies such as electric heaters, pellets boilers or district heating. (NB! Norway uses a lot of electricity for heating, therefore this is of great importanceSmile).

However in the latter case, I claim that the model will not "see” future electricity price towards 2020 in the same way, as this price is computed in an equilibrium with the supply side in each time step. Is this true?

My question is actually on how the objective function in the TIMES-model is build. In the Documentation for the TIMES Model PART I it says on page 37 that "the investments and dismantling costs are transformed into streams of annual payments, computed for each year of the horizon, along the lines suggested above”. Further that "annual costs, are added to the annualized capital cost payments, minus salvage value, to form the ANNCOST quantity”. And in the end "TIMES computes for each region a total net present value of the stream of annual costs, discounted to a user selected reference year.”

When looking at the equation on top of page 38, I still cannot figure out how the NPV for each year is calculated.

I assume that NPV for year one, let's say this is 2006, is calculated first. In year 1 there will be made some new investments based on the available energy prices and technology costs in the same year. But, will future energy prices affect these investment decisions? Will a high rise in electricity price in 2015 affect the investment decision in 2006 in the choice of heating system? If so, the optimal solution would be different in mode 1) than in mode 2) as the TIMES-model does not know the future electricity prices in 2020 in mode 2).

Any comment on this issue would be most helpful.

Dear Karen,

I think the answer depends on the way you run the TIMES model. For some discussion of the different modes of running TIMES, see Part I of the Documentation, page 30.

The standard way of running TIMES models is with perfect foresight, but TIMES can also be run in a time-stepped fashion, where the model has foresight only over a limited portion of the horizon, say one period. Another way to introduce limited foresight is the Stochastic Programming option of TIMES, where the model may only assume probabilities for the future states of the world. (Contrary to what the documentation says, both of these alternative modes are currently available in TIMES.)

In the perfect foresight mode, I think it is correct to say that the model will see all the future prices, irrespective of them being exogenous or endogenous.

Best wishes,

Dear Antti,

Thank you for your answer.

You say that "the model will see all future prices irrespective of them being exogenous or endogenous."

I still do not agree with you in the case of endogenous electricity prices.

When making an investment decition in 2006, let's say in an heat pump, the consumer considers future electricity price (in 2010, 2015, 2020) and finds the NPV of this technology and compares it with a pellets burner considering future pellets price, finding NPV.

When electricity prices are endogenous they are dependent on capital investments on both the production and consumption side. So how can the consumer in 2006 consider the electricity price in 2010, when this price depends on the investement choice (investing in a heat pump will give higher el-price, than investing in a pellets burner) of the same consumer today (2006)? My question is, what comes first? Or is the consumption and production iterated several times? In that case, how many times?

Thanks for the follow-up, Karen.

As mentioned in the TIMES documentation, in the perfect foresight mode the TIMES model has "complete knowledge of the market's parameters, present and future. Hence, the equilibrium is computed by maximizing total surplus in one pass for the entire set of periods."

When solving the model by optimizing with perfect foresight, the model does not iterate over the periods considered, but all model periods are optimized simultaneously. This type of model solution is also called inter-temporal optimization.  And it has the mathematical property that all the prices in all of the model periods are known when optimizing the decision variables in any period (e.g. investments in 2006).

For another reference, you could, for example, see what the International Handbook on the Economics of Energy (2009) says about perfect foresight models:


Quote from page 62: "A major criticism of most models of optimal extraction of a depletable resource is that they are 'perfect foresight' in nature. In particular, the dynamic optimization framework used in such models allows all future prices to influence the current outcome, meaning we typically solve for optimal paths."

Quote from page 261: "Perhaps one of the most limiting is the assumption of perfect foresight over the forecast horizon. This assumption results in 'optimistic' solutions based on the underlying assumption of perfect knowledge by firms and consumers of not only current but future energy prices as well as technology and technological change."

I am not sure whether these explanations can convince you.  But as far as I understand, the inter-temporal optimization mode of TIMES can, indeed, take into account the inter-dependencies between e.g. the investment decisions in 2006 and the endogenous prices in 2020, simultaneously.

Anyway, in TIMES you are by no means limited to the perfect foresight assumption, but can choose between various alternative ways of running the model.

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