Optimized control of an energy supplying system or an energy consuming system

The present invention relates to systems and method for control of an energy supplying system or an energy consuming system, in particular of a such a system having a buffer in which energy can be stored so that energy can be supplied to the network or energy taken from the network. The invention is particularly, but not exclusively, applicable to energy generating systems in which a CHP (Combined Heat and Power) installation is involved which can simultaneously supply heat and electrical power.

STATE OF THE ART

Technical solutions have been proposed in order to overcome the drawbacks of increasing energy prices and the environmental consequences of energy generation and energy conversion. One solution, which is applied more and more, is the use of CHP (Combined Heat and Power) installations which make it possible to recuperate energy losses - the heat lost during the production of electricity- as a useful source of heat. A typical example of the application of CHP's can be found in the horticultural industry with greenhouses for the production of vegetables, plants, flowers, etc. In such applications, the "waste" heat is used for heating the greenhouses while the generated electricity is sold to the electrical market.

However, the time heat is needed is not coinciding with the time electricity can be sold and the situation could happen that the owner has a big need for heating the greenhouses at a moment where the need for electrical power is very low and the price, the owner can get for the electricity is also very low, e.g. over night. As a consequence, the efficiency of the whole installation could be dropping and could even be negative. One way of meeting this possible lack in efficiency of the installation is to provide a buffer in which heat energy can be stored so that the CHP can be run at moments of high electricity need but the "lost" heat energy can be used at moments of low electricity need.

In order to get a reasonable safety, a classic heating unit is always foreseen in such installations. Indeed, it cannot be excluded that at certain moments, when there is there no possibility to deliver electrical power to the market, there exists a demand for heat while the buffer is nearly empty. To cope with such situations, a conventional heating unit (CHU) is provided. Managing such a rather complex installation- a CHP unit, a buffer, a CHU unit and a user of heat power, the installation being further connected with the electrical power network- is not easy and at regular moments a decision is to be taken which unit should be working and with which capacity so that the buffer is not overfilled and not empty either while at the same time the demand of heat must be satisfied. To make things worse, it often happens during cold winter days that a full buffer is consumed during one night. The glasshouse will only remain warm if such situations are foreseen, so that the buffer is full at dawn and both installations are ready to supply additional heat.

The system is even more complicated by the fluctuating prices on the electricity market. An electrical energy producer wanting to sell the power he is generating is confronted with a fluctuating demand of electricity and with market prices, which by consequence are also fluctuating over time. Special auction processes are organized to bring together buyers and sellers. Due to these fluctuations, the overall efficiency gain of the installation may be decreased by the lower results at the selling market. Different solutions have been proposed for solving the problems of producers having a plurality of pure electricity generation units and operating on one or more markets.

The article by Javad Sadeh e.a.:" A risk-based approach for bidding strategy in an electricity pay-as-bid auction" in "European Transactions on electrical power", 2009, pages 39-55, describes an optimization process to be used by a Generation Company having multiple production units and operating on a single market. The optimization process uses a probability density function (pdf) for estimating the price at each hour.

The article by Chefi Treki e.a.:" Optimal capacity allocation in multiauction electricity markets under uncertainty" in "Computers & Operations Research", Vol. 32, 2005, pages 201-217 describes a method, to be used by a seller having a plurality of production units and operating on different markets. The method solves the problem of deciding which production unit to commit for a given time period and which quantity of electrical energy to offer on the different markets.

The article by H. Lund e.a. "Management of fluctuations in wind power and CHP comparing two possible Danish strategies" in "Energy", 2002, volume 27. no 5, pages 471-483 describes the problems linked with the integration of CHP and wind energy. According to this article, a solution could be found by investments in heat storages and proposes to add heat pumps to the CHP units.

In none of these articles the problem of optimization of a CHP installation, comprising a CHP unit and delivering energy to a local customer and electricity to different markets is discussed.

In the case of the greenhouses, which is given here as an example, the problem of optimization is even more complicated by the fact that in most of these installations, a classic heating unit is also provided in order to further stabilize the whole system against fluctuations of the need of thermal energy, fluctuations of the market prices, etc.

In such a case, reaching an optimized efficiency is difficult to achieve because the installation is delivering two different kinds of energy: heat and electricity and two separate generators are used: one producing only thermal energy and another producing thermal energy and electrical energy. The heat demand develops independently from the demand of electrical energy. The heat demand and the demand for electrical energy are also fluctuating over the day and over the year. Certain installations need more heat over night than during the day, because night temperatures are normally lower than temperatures over day while electricity consumption is normally dropping during the night. This difficulty is also complicated by the existence of different markets for electrical energy: producers of electricity deliver normally electrical energy on the basis of contracts of quite different duration: there are contracts covering months, other cover a day and even a single hour.

Another example can be found in cooling installations. Considering a certain amount of "overcooling" as a buffer (say that normally a cooling is foreseen up to -20° C, when cooling to -25° C there is a buffer between -20° C and -25° C). In this example, it may be more efficient to overcool up to - 25° C when electricity prices are low and use the "stored cooling capacity" for times when electricity is expensive. Of course, the cooling devices will work less efficient if cooling to -25°C has to be reached. So again, careful considerations have to be taken to decide when this strategy is used.

In all the given examples, it is important for the producers and the consumers to run the production or consumption facilities with optimized efficiency in order to maximize their profits or to minimize their losses.

SUMMAR OF THE INVENTION.

It is an object of the present invention to provide a fuel control system for a local energy supplying and/or energy consuming system, in particular such a system having a buffer for storing energy, so that the demand for energy by the consuming system is always satisfied while the level of stored energy in the buffer remains between a given maximum and a given minimum.

It is further an object of this invention to provide an optimized control of an energy supplying system or an energy consuming system, in particular of a such a system having a buffer in which energy can be stored so that energy can be supplied to the network or energy taken from the network in a way that the system is operating in an optimized way.

This object is achieved by a fuel control system for a local energy supplying and/or an energy consuming system, wherein the local energy system comprises a first controllable electrical unit outputting electrical power and generating a first heat flux within a series of time periods and/or a second controllable electrical unit receiving electrical power and absorbing a second heat flux within the series of time periods, both first and second electrical networks being connected to an electrical network. The electrical power received or generated within any time period is at least partially stochastically variable within a first probability distribution function and the demand for electrical power being controlled by a hybrid open loop/closed loop regulatory mechanism, there being some electrical energy received or output within any time period. The local energy system further comprises a controllable fuel powered heating unit for outputting a third heat flux within the series of time periods and a controllable heat buffer for storing any or all of the first to third heat fluxes and outputting a fourth heat flux within the series of time periods. The fuel powered heating unit is coupled to the heat buffer. The local energy system further comprises a heat flux user thermally coupled to the heat buffer. The demand for heat power by the heat flux user within the series of time periods is stochastically variable within a second probability distribution. A controller is coupled to the first and/or second electrical unit, the fuel powered heating unit and the heat flux user for exchanging control variables therewith and for controlling fuel supply to the fuel powered heating unit so that

1. a) the demand for heat power by the heat flux user is satisfied in any of the time periods and
2. b) the heat buffer is not overfull or empty in any of the time periods. According to the present invention, the first controllable electrical unit may be a CHP-unit, and each time period may be divided into successive sub-periods. The local energy system and in particular the hybrid open loop/closed loop regulatory mechanism may further comprise means for determining for each sub-period on a historical basis a statistical price of the electrical energy in at least one market served by the electrical network, means for determining for each sub-period on a historical basis a statistical value of the demand of heat flux by the user and means for deriving, for each sub-period, from said statistical price and said statistical value the quantity of fuel needed by the CHP-unit so that the working of the local energy supplying and/or energy consuming system is optimized. According to the present invention, the local energy system may further comprise means for deriving, for each sub-period, from said statistical price and said statistical value the quantity of fuel needed by the heating unit or a cooling unit so that the working of the local energy supplying and/or energy consuming system is optimized.

According to the present invention, the determining the statistical price may be done by on the basis of a temporal probability density function. According to the present invention, the determining the statistical value of the heat demand may be done by on the basis of a temporal probability density function.

According to the invention, the electrical network may be serving at least two different markets in which electrical energy is handled at different prices, and the means for determining the statistical price, may determine the price on each of these markets.

According to the present invention, the deriving of the quantity of fuel needed by the CHP-unit and the quantity of fuel needed by the heating unit may be performed at two levels: a first level deriving the fuel needed by the CHP-unit for covering the electricity production, demanded by the one of the markets and a second level deriving the fuel needed by the CHP-unit for covering the electricity production, demanded by the other of the two markets and deriving the fuel needed by the heating unit.

It is also an object of the present invention to provide a computer program product comprising program code means stored on a computer readable medium and adapted for performing the deriving the quantity of fuel needed by the CHP-unit and the quantity of fuel needed by the heating unit or the cooling unit as described above, when said program is run on a computer.

It is a further object of the present invention to provide a local energy supplying and/or an energy consuming system which comprises a first controllable electrical unit outputting electrical power and generating a first heat flux within a series of time periods and/or a second controllable electrical unit receiving electrical power and absorbing a second heat flux within the series of time periods, both first and second electrical networks being connected to an electrical network. The electrical power received or generated within any time period is at least partially stochastically variable within a first probability distribution function and the demand for electrical power is controlled by a hybrid open loop/closed loop regulatory mechanism. Some electrical energy is received or output within any time period. The local energy supplying and/or an energy consuming system comprises further a controllable fuel powered heating unit for outputting a third heat flux within the series of time periods, a controllable heat buffer for storing any or all of the first to third heat fluxes and outputting a fourth heat flux within the series of time periods. The fuel powered heating unit is coupled to the heat buffer. The local energy supplying and/or an energy consuming system comprises also a heat flux user thermally coupled to the heat buffer, the demand for heat power by the heat flux user within the series of time periods being stochastically variable within a second probability distribution. The local energy supplying and/or an energy consuming system comprises further a fuel control system as described above.

It is a still further object of the present invention to provide a method for optimizing control of a CHP installation. The installation comprises a CHP-unit and a buffer and the installation is delivering energy to a consumer and electrical energy to an electrical network. The method is adapted to control the CHP installation over a given period of time, the given period of time being divided into successive sub-periods. The method comprises the steps of determining for each sub-period on a historical basis a statistical price of the electrical energy in at least one market served by the electrical network, determining for each sub-period on a historical basis a statistical value of the demand of energy by the consumer and deriving, for each sub-period, from said statistical price and said statistical value the quantity of fuel needed by the CHP-unit.

According to the present invention, the installation may deliver heating energy to a consumer and the installation may further comprise a conventional heating unit. The method may further comprise the step of deriving, for each sub-period, from said statistical price and said statistical value the quantity of fuel needed by the conventional heating apparatus. According to the present invention, the determining the statistical price may be done by on the basis of a temporal probability density function. According to the present invention, the determining the statistical value of the heat demand may be done by on the basis of a temporal probability density function.

According to the present invention, the electrical network may be serving different markets in which electrical energy is handled at different prices (during the same sub-period), and the method may comprise the step of determining of a statistical price on each of these markets.

According to the present invention, the deriving of the quantity of fuel needed by the CHP-unit and the quantity of fuel needed by the conventional heating apparatus may be performed at two levels: a first level deriving the fuel needed by the CHP-unit for covering the electricity production, demanded by the day ahead market and a second level deriving the fuel needed by the CHP-unit for covering the electricity production, demanded by the continuous intraday market (CIM).

BRIEF DESCRIPTION OF THE DRAWINGS

• Fig. 1 illustrates a typical CPH installation, used fur greenhouse heating.
• Fig. 2 illustrates the timeline of Day ahead bidding and the timeline of CIM-bidding.
• Fig. 3 gives the probability of getting on the Day ahead market a given price as function of time.
• Fig. 4 gives the probability of getting on the CIM-market a given price as function of time.
• Fig. 5 gives development of the heat demand over 24 hours.
• Fig. 6 shows a computing system schematically such as for use with the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention will be described in detail with respect to some particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting.

Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

It is to be noticed that the term "comprising", used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.

In the present application, by "optimizing the working of a system" is meant the control of the system so that efficiency is optimized and that profits are maximized or costs minimized.

The terms "control over a period of time" and "sub-periods" are also used in the description and claims. By "period of time" or "time period" is meant a certain period, starting at a given time e.g. 0 hrs and ending at another time e.g. 24 hrs later. In the example given the period of time covers thus a normal day. The period of time can be subdivided in a number of sub-periods: e.g. the period of time may comprise 24 successive sub-periods of one hour. Variables used in the control method, of the present invention, may vary within the period of time and may remain stable during each sub-period. Still according to the example given below, the 24 hrs period of time is subdivided in 24 successive sub-periods, each sub-period having a duration of one hour.

By "buffer" is meant in the present description and in the appending claims a device wherein a certain amount of energy can be stored. This may be a separate device e.g. a boiler wherein thermal energy is stored but it can also be a consuming device itself e.g. a building can represent an energy storing buffer when it is allowed to heat that building in excess of the normal temperature by a certain amount of degrees.

The invention will be explained in more detail on the basis of a CHP installation used for the heating of greenhouses and selling electrical energy on a double market. As illustrated in figure 1, the complete installation comprises a CHP unit (1), a conventional heating unit (2), a buffer (3) and one or more greenhouses (4). In the example, the CHP uses gas as fuel, but other kinds of fuel are also possible like solid or liquid fuel, waste material or garbage e.g. wood, straw, etc. The electrical energy (P_el), generated by the CHP is proportional to the quantity of fuel, fed to the CHP (q). The heat energy (P_th ), delivered by the CHP, is also proportional to the quantity of fuel, fed to the CHP (a).

The heat (P_H ) delivered by the conventional heating installation is proportional to the quantity of fuel feeding it (q).

The heat, produced by the CHP unit and by the conventional heating unit is stored in buffer (3); the amount of heat stored in the buffer at the beginning of a certain sub-period k is represented by x_k. The amount of heat, needed by the greenhouses during a certain sub-period k is represented by W_k.

In the example, the installation is delivering electrical energy to two submarkets: the Day ahead market and the CIM-market or the Continuous Intraday Market. Such markets are modeled as a hybrid open loop/closed loop regulatory mechanism.

Normally, the electricity market may include different sub-markets, e.g.:

• a market based on long-term contracts, where electrical energy may be sold months ahead;
• the day ahead market where the electrical energy is traded one day before delivery;
• the continuous-intraday-market (CIM) where electrical energy may be traded the day itself until 10 minutes before delivery.

There exist also other sub-markets for the delivery of electrical energy (e.g. the adjustment market, the balancing market, etc). Each market has its own price and trading rules, valid for a certain sub-period. In the given example, only two sub-markets are involved: the day ahead and the CIM market, although the principles of the invention may also be applied to other submarkets.

The invention can also be used to control energy fluxes if no markets are (temporarily) available or if only one market is used.

In the case of a CHP, a long-term contract market is not always the most interesting choice; indeed, in this market prices are always lower although they guarantee a certain security.

On the short time however, there exist generally rather precise forecasts regarding temperature, speed and direction of wind, etc. so that the need of heat can be predicted with a relative precision. Even the evolution of need of heat over a 24 hour period of a day is very well predictable, taking into account historical data. Figure 5 shows the statistical evolution of the demand of heat by a greenhouse for a particular day (24 hrs) of the year.

A typical example of the selling process of electrical power on the two markets of the example, the day ahead market and the CIM-market, is illustrated in figure 2. On the day ahead market, electrical energy can be offered until 6 a.m. of the day before (D-1) and the electricity is to be delivered on day D. The offer is limited to a particular hour (sub-period) of day D, i.e. there is an offer of a certain quantity of electrical energy, to be delivered during a certain hour at a certain price. For a popular day-ahead market in Belgium, i.e. the Belpex market, these biddings must be received by the market before 6 am of D-1. The market matches demand and supply by calculating an equilibrium price and provides allocations to all players at 11 a.m. of day D-1. This market is modeled as an open loop regulatory mechanism as the amount of energy to be delivered is set in advance.

On the continuous intraday market (CIM) in Belgium an offer for delivery of electricity during a particular hour can go out from 24 hours before the hour until 10 minutes before that particular hour. Here power is traded if a "match" is found.

Regarding the electricity production on day D, the selling process is developing as follows:

• from 0 a.m of D-1, an offer can be made on the CIM-market for electricity to be delivered on 0 a.m. of day D; such an offer can be accepted which has consequences for future offers and prices relating to day D;
• each following hour of D-1, a new CIM-offer can go out for day D and this can include energy and prices for the next hour of day D;
• until 6 a.m. of D-1, a day ahead offer can be issued for each hour of day D; at this hour the day-ahead market closes;
• on 11 a.m. of D-1, the day ahead market closes;
• from 0 a.m. of day D, the quantities of electrical energy, agreed on the day-ahead market and on the CIM-market, are to be delivered.

The CIM market is modeled as a closed loop regulatory mechanism as the demand is updated at regular times and these feedback from the market in real time.

Accordingly, the combination of a first market like the CIM market and a second market like the day ahead market is modeled as a hybrid open loop/closed loop regulatory mechanism.

Figure 3 shows an example of the 24 hours evolution of the probability to get a certain price on the day-ahead market. As can be expected, the lowest prices are situated around 4 a.m. and the highest prices around 10 a.m. Typically, the spread (which corresponds to the uncertainty) is higher over day than during night. The black vertical line represents the points of break-even: there is no gain of loss by the system.

Figure 4 shows an example of the 24 hours evolution of the probability to get a certain price on the CIM- market. In the shown example, there is a big chance that there are no buyers, which explains the high probability to get a price of 0 €/MWh. The black vertical line represents again the points of break-even: there is no gain of loss by the system.

Figure 5 illustrates a typical evolution over 24 hours of the probable heat demand. In this example, there is a high demand over night. The spread however is relatively stable.

From the above, it can be deduced that the quantity of electrical energy, to be generated by the CHP, can change every hour and that price, paid for the generated electrical energy, can also change every hour. This is valid on both markets: the day ahead market and the CIM-market. As stated above, in the example, the period of time is 24 hours (staring at 0 hrs) and this period of time is subdivided in 24 sub-periods. Any optimization has to take this into account: when optimizing over a 24 hr day (the period of time), this must be done in discrete steps, one step per hour.

An algorithm has been developed to optimize the control of the installation by determining the quantity of fuel needed to feed the installation when profit is to be maximized. The novelty of this algorithm is that it can guarantee to find an optimal solution, i.e. no better solution exist, and that it is able to combine markets, which act on different time scales, like day-ahead market (days) and CIM (hours). The control of the local energy supplying and/or an energy consuming system, taking into account the day ahead market conditions, can be considered an open loop regulatory mechanism with no feedback of the real situation of the system, contrary to the control of the local energy supplying and/or an energy consuming system, taking into account the CIM-conditions which is a closed loop regulatory mechanism in which the real time variables of the system are also taken into account.

An optimized control of the installation depends on the following variables:

• general variables:

  • t time; in the calculation the time is represented by subscript "k", indicating the k-th sub-period; k= 0, 1, 2,...., N.
  • x _k state-of-charge of buffer at the beginning of the k-th sub-period;

• stochastic variables:

  • p _k day ahead price during the k-th sub-period;
  • r _k CIM price during the k-th sub-period;
  • w _k heat demand by greenhouses during the k-th sub-period;

• control variables:

  • u_k quantity of fuel used for generating the electrical energy to the day ahead market during the k-th sub-period;
  • v _k quantity of fuel used for generating the electrical energy to the CIM market during the k-th sub-period;
  • q _k quantity of fuel fed to the CHU (classic heating unit) during the k-th sub-period;

According to the invention, optimized control of the installation can be reached by determining for which values of these control variables (i.e. the quantity of fuel necessary to feed the CHP and the quantity for feeding the CHU) profit is maximized. Obviously, such values are dependent on the other variables.

Taking the global system into account, the following problem has to be solved: $${\left[u_1{v}_1{q}_1\dots u_k{v}_k{q}_k\dots u_N{v}_N{q}_N\right]}^{*}=\arg \underset{u_1,v_1,q_1,\dots ,u_k,v_k,q_k,\dots ,u_N,v_N,q_N}{\min }\left({\displaystyle \sum _{k=1}^{N-1}}\mathrm{E}\left\{C_k^{\$}\left(u_k{v}_k{q}_k{p}_k{r}_k\right)\right\}+\underset{x}{\mathrm{E}}\left[C_N\left(x\right)\right]\right)$$

subject to $$u_k+q_k+v_k\le 1.5\mathit{MW},$$ $$0\le x_k\le 12\mathit{MWh},$$ $$.37\le q_k\le 1.5\mathit{MW}\mathrm{\vee }{q}_k=0,$$ $$.84\le u_k\le 1.2\mathit{MW}\mathrm{\vee }{u}_k=0,$$ $$.84\le v_k\le 1.2\mathit{MW}\mathrm{\vee }{v}_k=0,$$ $$x_1-x_{\mathit{initial}}=0$$ $${\mathrm{P}}_{k+1}\left(x\right)-{\mathrm{P}}_{k+1}\left(x\left(x_k{u}_k{v}_k{q}_k{w}_k\right)\right)=0$$

with $$u_k=u_k\left(p_k\right),$$ $$v_k=v_k\left(x_k{u}_k{p}_k{r}_k{w}_k\right)$$ $$q_k=q_k\left(x_k{u}_k{p}_k{r}_k{w}_k\right)\mathrm{.}$$ $$x_{k+1}\left(x_k{u}_k{v}_k{q}_k{w}_k\right)=x_k+{\eta }_{\mathit{th}}\left(u_k+v_k\right)+{\eta }_{\mathit{HI}}{q}_k-w_k$$ $$\begin{array}{l}{C}_k^{\$}\left(u_k{v}_k{q}_k{p}_k{r}_k\right)=p_{\mathit{gas}}\left(u_k+v_k+q_k\right)+M\left(u_k\ne 0\mathrm{\vee }{v}_k\ne 0\right)-{\eta }_{\mathit{el}}\left(u_k{p}_k+v_k{r}_k\right)\\ C_N\left(x\right)=0\end{array}$$

wherein:

• (B1) is the general equation to be optimized. The control variables (u, v, q) ,can be found at the left-hand side: the quantity of fuel corresponding to the electrical energy delivered at the day ahead market, the quantity of fuel corresponding to the electrical energy delivered to the CIM- market and the quantity of fuel used by the CHU respectively. By the index k is indicated that these three variables can change for each sub-period. The optimum values of these control variables are found by maximizing the right-hand side of the equation, taking into account the constraints given under (B2) to (B8). Symbol E represents the expected value of the function within brackets and arg min represents the algorithm that find those (u, v, q) for which the function (in the present example the sum of two expected values) becomes a minimum.

• (B2): indicates that the total energy of the complete installation (CHP and CHU) is limited.
• (B3): indicates that the buffer has a minimum and maximum 'state-of-charge'.
• (B4): indicates that the energy of the CHU, expressed as a quantity of used fuel, can vary between a minimum of 0.37 MW and a maximum of 1.2MW. The values of 0.37 MW and 1.2 MW are only given here as an example and they may differ from one installation to another.
• (B5-B6): are equations, analogue to equation (B4), but for the CHP.
• (B7): says that the initial situation of the system is known.
• (B8): is a guarantee of continuity: the probability that the system during sub-period k is evolving into a situation x should be equal to the probability that that the system is in a situation x at the beginning of sub-period k+1.
• (B9): the quantity of fuel corresponding to the electrical energy delivered at the day ahead market is only depending on the price on the day ahead market.
• (B10-B11): the quantity of fuel corresponding to the electrical energy delivered at the CIM- market and the quantity of fuel used by the CHU are both depending on (x_k,u_k,v_k,q_k,w_k). So depending on the intraday evolution of the system, the outcome of these variables may change.

Equations (B 12-B 14) represent specific characteristics of the system. In the case of a CHP is:

• (B12): the evolution equation (determining the state of the buffer at the beginning of sub-period (k+1) in function of its state at the beginning of sub-period (k).
• (B13): the profit, made during the sub-period k.
• (B14): the terminal profit function (a supposition).

All values given in the equations (B2) to (B6) are given as an example and are depending on the actual installation.

Equation (B1) can be minimized using dynamic programming. This method is well-known per se and can be found in the specialized literature, e.g. the original article by Bellman: "Dynamic Programming" or the book: "Dynamic Programming and Optimal Control" by D.P. Bertsekas.

As a result of this minimization, values are found for the control variables (u, v, q) at each sub-period and the corresponding amount of fuel for feeding the CHP-unit and the CHU-unit are determined.

Another example of the present invention can be found in industrial cooling installations. Because in such installations storing of cooling energy in a particular buffer may be problematic, it is proposed to use the cooling unit itself as a buffer by allowing the temperature to vary between two values. E.g., allowing a spread of temperature between - 20°C and -25°C, the buffer reaches its maximum state of charge when the temperature of the cooling unit is -25°C and its minimum state of charge when the temperature of the cooling unit is -20°C.

In this example the equations become: $$x_{k+1}\left(x_k{u}_k{v}_k{w}_k\right)=x_k-\eta \left(u_k+v_k\right)/c+w_k/c$$ $$C_k^{\$}\left(u_k{v}_k{q}_k{p}_k{r}_k\right)=\eta \left(u_k{p}_k+v_k{r}_k\right)$$ $$C_N\left(x\right)=0$$

whereby η is the efficiency of the cooling unit and c the heat capacity. As an example, the constraints could be: $$-25\le x_k\le -20\mathit{°}C,$$ $$m_1\le u_k\le M_2\mathrm{\vee }{u}_k=0,$$ $$m_1\le v_k\le M_2\mathrm{\vee }{v}_k=0,$$ $$x_1-x_{\mathit{initial}}=0$$ $${\mathrm{P}}_{k+1}\left(x\right)-{\mathrm{P}}_{k+1}\left(x\left(x_k{u}_k{v}_k{w}_k\right)\right)=0$$

whereby m₁ represents the minimum energy of the cooling unit and M₂ the maximum energy.

Here again, a general equation like (B1) can be written and this equation minimalized for certain values of u and v (no variable q because there is no independent cooling unit).

The above-described method embodiments of the present invention may be implemented in a processing system 200 such as shown in figure 8. Figure 8 shows one configuration of processing system 200 that can be implemented on a mobile phone, a PDA, a laptop, a personal computer etc. It includes at least one programmable processor 203 coupled to a memory subsystem 205 that includes at least one form of memory, e.g., RAM, ROM, and so forth. It is to be noted that the processor 203 or processors may be a general purpose, or a special purpose processor, and may be for inclusion in a device, e.g., a chip that has other components that perform other functions. The processor may also be an FPGA or other programmable logic device. Thus, one or more aspects of the present invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The processing system may include a storage subsystem 207 that has at least one disk drive and/or CD-ROM drive and/or DVD drive. In some implementations, a display system, a keyboard, and a pointing device may be included as part of a user interface subsystem 209 to provide for a user to manually input information. Ports for inputting and outputting data also may be included, especially interfaces for capturing physical values relevant to energy consumption or generation, e.g. an interface to a CHP unit, and/or a classic heating unit, and/or a buffer and/or one or more users of energy such as a greenhouse. Interfaces may also be provided for control of fuel use by a CHP, e.g. gas as fuel, or solid or liquid fuel, waste material or garbage e.g. wood, straw, etc. More elements such as network connections, interfaces to various devices, and so forth, may be included, either by wire line or wireless connections, but are not illustrated in figure 8. The various elements of the processing system 200 may be coupled in various ways, including via a bus subsystem 213 shown in figure 8 for simplicity as a single bus, but will be understood to those in the art to include a system of at least one bus. The memory of the memory subsystem 205 may at some time hold part or all (in either case shown as 201) of a set of instructions that when executed on the processing system 200 implement the steps of the method embodiments described herein. Thus, while a processing system 200 such as shown in figure 8 is prior art, a system that includes the instructions to implement aspects of the methods for control of a CHP according to the present invention is not, and therefore figure 8 is not labelled as prior art.

The present invention also includes a computer program product, which provides the functionality of any of the methods according to the present invention when executed on a computing device. Such computer program product can be tangibly embodied in a carrier medium carrying machinereadable code for execution by a programmable processor. The present invention thus relates to a carrier medium carrying a computer program product that, when executed on computing means, provides instructions for executing any of the methods as described above. The term "carrier medium" refers to any medium that participates in providing instructions to a processor for execution. Such a medium may take many forms, including but not limited to, non-volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as a storage device which is part of mass storage. Common forms of computer readable media include, a CD-ROM, a DVD, a flexible disk or floppy disk, a tape, a memory chip or cartridge or any other medium from which a computer can read. Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution. The computer program product can also be transmitted via a carrier wave in a network, such as a LAN, a WAN or the Internet. Transmission media can take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications. Transmission media include coaxial cables, copper wire and fibre optics, including the wires that comprise a bus within a computer. The present invention is not limited to the examples given above but other embodiments of the invention are possible. The buffer of heating installations including a CHP may be constituted by the thermal inertia of a building which is to be heated. In such an embodiment, the temperature of the building may vary between two temperatures and heat energy may be stored by increasing the temperature of the building beyond the lowest of these two temperatures.