The patterns in the market don't seem all that sophisticated. The traders react 'here and now' on information. 
So I wish to model the bid/ask side where I - perhaps based on historical estimations - can find variables and their corresponding parameter values which tell me how traders react when, say, a huge amount of wind hits the market. Or when they don't react to this information at all. The 'sensitivity' towards information is different from day to day.

Are there  historical , geographical data about wind or other non financial information that you are going to attach to pricing data?

Are there  historical , geographical data about wind or other non financial information that you are going to attach to pricing data?

Initially, I only wish to add one variable: the value of up/down regulation in the market (i.e. if there is less/more electricity in the market than firstly anticipated by the TSO's =  transmission system operator )

This up/down regulation is a value of the function which underlying are outside temperature, wind, etc. The values of the up/down should be assigned to factors that you wish to take into account in your model. I afraid the there is no historical data for wind though outside temperature data set is available to use as a variable which affect on demand of electricity which is a component of the electricity price. On the other hand in such setting it might be a single bid-ask median price will be quite sufficient for modeling. 

Okay... What if we assume the following
a) The bid-ask price is given
b) I only wish to calculate the impact that the (up/down)regulation has on the price
How would you then calculate future bid-ask price?

And...
1) Let us hold wind, solar and all other parameters outside for now. 
2) I can afterwards generate a separate model which includes these factors and use them to generate a price. 

Yes, you have to start with something simple. And build up bit by bit.

Step1: What are your dependent variables? Bid and ask. Done!

Step 2: What are your independent variables? Time. What else?  Maybe nothing. You could just have a simple stochastic process. 

Type of model:

1. Deterministic.
2. Stochastic
3. Statistical (explanatory variables?)
4. From first principles. How should the market behave?

Do you have any data?

P

Okay... What if we assume the following
a) The bid-ask price is given
b) I only wish to calculate the impact that the (up/down)regulation has on the price
How would you then calculate future bid-ask price?

And...
1) Let us hold wind, solar and all other parameters outside for now. 
2) I can afterwards generate a separate model which includes these factors and use them to generate a price. 

Instead to model bid-ask prices which should be stochastic I would recommend to use median price S ( t , [$]\omega[$] ) as it usually used and  the h ( t , [$]\omega[$] ) = 0.5 [ ask ( t ) - bid ( t ) ] spread that actually can be modeled by the same type as S GBM for example. If you wish to get the trading liquidity effect for the next order approximation of the pricing model one can incorporate S and h in the right hand side of the ( S , h ) stochastic system. If we are interesting in more explicit temperature effect it makes sense to use small disturbed periodic coefficients. Presenting a model of underlying you can start with a simple derivatives contract such as forwards. To study formally options contracts in a bid-ask format could be not straightforward because I am not sure whether or not there exists a BS hedged portfolio, as far as the same asset in long and in short position follows the same equation. It should be used to eliminate risky term in the portfolio. 

Yes, you have to start with something simple. And build up bit by bit.

Step1: What are your dependent variables? Bid and ask. Done!

Step 2: What are your independent variables? Time. What else?  Maybe nothing. You could just have a simple stochastic process. 

Type of model:

1. Deterministic.
2. Stochastic
3. Statistical (explanatory variables?)
4. From first principles. How should the market behave?

Do you have any data?

P

I have all data on electricity prices for each trade at each time. I consider hour-contracts from hour1 until hour24. Obviously, the hours close to each other have a high(er) correlation and their behaviour could be modelled using VECM (which I plan to do)
My goal is then to be able to predict how the bid-ask is going to develop, once the TSO's make their information available to the market. Thus the answer is (3) and (4). 
But again - how to model (3) and (4)??

Thus what is the "best" way of modeling a response in price based on a specific parameter, when you want to consider the bid and ask side?

Are you looking at spot prices or futures?  Asking about Bid and Ask pricing is very confusing in this context.  Do you actually mean Supply and Demand pricing?

In terms of spot price
Renewable (Wind/Hydro/Solar/Nuclear) tend to bid at 0
Thermal (Coal, Gas, Bio) bid at their marginal cost, sometimes below.  
Market price = the bid price of the supplier that can satisfy demand if supply is added in the order of cheapest first (+ network and other costs).  

The game then becomes, how much electricity will be generated on a given day vs how much is demanded by the market.  
There is a large literature on modelling electricity prices e.g.
http://repository.cmu.edu/cgi/viewconte ... statistics

In terms of futures, bids and asks are set by the market makers, as with any other commodity market.  

Yes, that is completely correct. Yet I wish to model the price both from the buyer as well as seller (which I believe is easily done by subtracting/adding risk once having the price)

There are only bid & ask historical data is available. Their difference represents trading liquidity. One can interpret ask price as a max price for which a hypothetical buyer agrees to buy an asset and buy price is a min price for which hypothetical seller agrees to sell the asset. There are only three variables bid , ask , and the spread ask-bid and only two are independent. Hence you can take for example one price bid or ask and spread or middle price 0. 5 [ ask+ bid] and spread for modelling or other which you think has a more clearly representation.

I guess we’re talking spot electricity.
The bid-ask spread itself is mean reverting/stationary, so this could be modeled as an AR process. and would be dynamic.
Intra-day prices have seasonality, so a a fast Fourier regression can capture the cycles.
Spot electricity is local – a function of weather, fuel price, demand schedules, outages and so on.
A spot electricity price can be represented as a GBM model with a mean reverting drift with an additional poisson process that represents price spikes. The risk is in the short end - power prices have a volatility term structure that attenuates as T-t gets large.

Thus what is the "best" way of modeling a response in price based on a specific parameter, when you want to consider the bid and ask side?

I have a couple of background question.
Which geographical region are you looking at?
And, is this power data coming from a spot auction market? Or is this from continually traded front contracts.
Obviously, if you are looking at simple auction out-turn prices then you are less interested in used the machinery of stochastic processes,
and you get much more bang for your intellectual buck if you look at simple regression analyses with the explanatory variables in question
(maybe regressed to price spreads to de-trend the influence of fuels etc). 
However, since you talk about bid/ask, I wonder what precisely it is you are after.  
In my view it is important to differentiate when you are modelling information impacting prices for power for delivery of a 
fixed maturity vs. a rolling contract with rolling explanatory data. 
e.g. do you want to look at the dynamics of for instance, the price of peak power for Sept2 as quoted over the period aug15 to sep1 as prompt wind forecasts
are published over this period, or are you more interested in the summary statistics of all hourly spot over a period vs. wind forecasts and looking to see if the dayahead market prices a systematic wind risk premium?