**3. Optimization procedure**

180 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

**Figure 7.** Turbine (Left) and Pump (Right) characteristic curves and operating conditions.

tariff from Madeira Electricity Company (www.eem.pt), as presented in Figure 8.

**Figure 8.** Electricity tariff used in the model (Source: www.eem.pt).

The electricity tariff used in this study, for Socorridos system, is based on the 2006 electricity

volume of water in the system is in Socorridos reservoir.

This pumping station was designed to pump 40000 m3 of water stored in Socorridos reservoir during 6 h, for the electricity low peak hours (from 0 to 6 am). In the remaining hours of the day, the water is discharged from Covão reservoir to Socorridos hydropower station, in reverse flow direction, in order to produce energy. By the end of the day, the total

> Costs associated with the operation of pumping systems represent a significant amount of expenses of a water supply system (Ramos and Covas, 1999). For this reason, it is desirable to optimize the operation of pumps such that all demands are met and, simultaneously, the total pumping cost is minimized.

Typically, pump operation in water supply systems is controlled by water levels at the downstream storage tanks: upper and lower operating water levels are set up in storage tanks such that when these levels are reached, pumps start-up or stop.

Pumped-Storage and Hybrid Energy Solutions

Towards the Improvement of Energy Efficiency in Water Systems 183

• Maximum water level rise/decrease for each time step - *NQmax*

programming (LP) and the other using a non linear programming (NLP).

<sup>6</sup> <sup>24</sup> ,

*B h*

hour; *ηB,T* are the pump and turbine efficiency; and *h* is the hour of the day.

*c*

1 7

= = η

*f dN c dN*

where *cB* represents the electricity tariff for each hour; *dN* is the water level raise or decrease in Covão reservoir, for each hour; *cT* is the produced hydroelectricity selling price for each

The above function represents the sum of the water level variation in Covão multiplied by the electricity costs/selling price, throughout one day. Meaning that if there is a raise in Covão reservoir water level (*dN*>0), the pump station is operating and has a cost *cB* associated for each hour. If, on the other hand, there is a decrease in Covão reservoir water level (*dN*<0), the system is discharging water from Covão to Socorridos and consequently, producing energy that can be sold at a price *cT*. With this function it is possible to provide the electricity costs for the pumping hours and the selling price for the electricity production

= ⋅ + ⋅⋅

*h h B*

The hourly limits relatively to the pipe flow restrictions are presented in Table 2.

**Hours Lower Upper** *0 to 6* 0 *NQmax 6 to 24 -NQmax* 0

From 0 to 6 am it is only possible to pump water since the lower bound is zero. From 6 am

For the non linear programming case (NLP) there is no need to impose pumping and power hours because the program will choose which solution is the best in order to obtain the

For this situation, two optimization programs were developed: one using linear

For the linear programming case (LP), it is assumed that the water pumping occurs during the first six hours of the day (from 0 to 6 am) and in the remaining hours the system can only produce energy by hydropower. This is to simulate the normal operation mode. The

( )

(1)

η

,

*h Th T h*

• Reservoirs diameter (m) - *D*

• Wind turbine power curve.

objective function to minimize is the following:

**3.1. Pump-storage/hydro** 

• Wind speed curve;

hours.

**Table 2.** Hourly restrictions LP.

forward only turbine operation is allowed.

major benefits. Then the objective function to minimize is:

The problem consists of defining the hourly operations for the pumps and turbines in the previous presented system, for a period of one day. The goal is to establish a sequence of decisions, for a determined time period, in order to obtain the most economical solution and, at the same time, the better social and environmental solution in terms of guarantee of water supply to populations. The intention is to obtain the pumps and turbines operation time for each hour, so that the maximum benefit from hydropower production and the minimum costs from the pumping station energy consumption are attained.

The problem was solved in terms of water level variation in Covão reservoir. The rules from the optimization model are directly implemented in EPANET model. This procedure is possible since the water level variations are directly proportional to the amount of energy produced or consumed, when the flow and head are considered constants along the simulation time. The time period considered is one day with an hourly time step.

The complexity of the problem is related to:


An integrated software tool has been developed together with EPANET model (Rossman, 2000) to evaluate the results of the optimization model, in order to verify if the behaviour of the hydraulic components of the system (reservoir levels, flow) is maintained between the desired maximum and minimum limits. To solve the problem several variables are identified, as well as the objective function, which represents the quantity that should be minimized or maximized, the problem constraints associated to the physical capacities of the hydraulic system, and the water demands.

Hence the variables of the optimization process are the following ones:


tanks such that when these levels are reached, pumps start-up or stop.

minimum costs from the pumping station energy consumption are attained.

simulation time. The time period considered is one day with an hourly time step.

The complexity of the problem is related to:

the hydraulic system, and the water demands.

• Hourly water inlet in Covão (m) - *NIN* • Maximum flow in the penstock (m3s-1) - *Q*

• Electricity tariff (€) - *c*

• Hourly water consumption in Covão (m) - *NCC*

• Initial water level in Covão reservoir (m) - *NIC* • Initial water level in Socorridos reservoir (m) - *NIS* • Maximum water level in Covão reservoir (m) - *NMAXC* • Maximum water level in Socorridos reservoir (m) - *NMAXS* • Minimum water level in Covão reservoir (m) - *NMINC* • Minimum water level in Socorridos reservoir (m) - *NMINS*

Hence the variables of the optimization process are the following ones:

the next hours;

completely fulfilled.

Typically, pump operation in water supply systems is controlled by water levels at the downstream storage tanks: upper and lower operating water levels are set up in storage

The problem consists of defining the hourly operations for the pumps and turbines in the previous presented system, for a period of one day. The goal is to establish a sequence of decisions, for a determined time period, in order to obtain the most economical solution and, at the same time, the better social and environmental solution in terms of guarantee of water supply to populations. The intention is to obtain the pumps and turbines operation time for each hour, so that the maximum benefit from hydropower production and the

The problem was solved in terms of water level variation in Covão reservoir. The rules from the optimization model are directly implemented in EPANET model. This procedure is possible since the water level variations are directly proportional to the amount of energy produced or consumed, when the flow and head are considered constants along the

• the effects of time propagation when an operation is carried, because this will influence

• the hydraulic restrictions of the system, like the maximum flow in the pipes, the water level in the reservoirs and the water consumption by the population, have to be

An integrated software tool has been developed together with EPANET model (Rossman, 2000) to evaluate the results of the optimization model, in order to verify if the behaviour of the hydraulic components of the system (reservoir levels, flow) is maintained between the desired maximum and minimum limits. To solve the problem several variables are identified, as well as the objective function, which represents the quantity that should be minimized or maximized, the problem constraints associated to the physical capacities of • Wind turbine power curve.

#### **3.1. Pump-storage/hydro**

For this situation, two optimization programs were developed: one using linear programming (LP) and the other using a non linear programming (NLP).

For the linear programming case (LP), it is assumed that the water pumping occurs during the first six hours of the day (from 0 to 6 am) and in the remaining hours the system can only produce energy by hydropower. This is to simulate the normal operation mode. The objective function to minimize is the following:

$$f = \sum\_{h=1}^{6} \left( \frac{c\_{B,h}}{\eta\_B} \cdot dN\_h \right) + \sum\_{h=7}^{24} \left( c\_{T,h} \cdot \eta\_T \cdot dN\_h \right) \tag{1}$$

where *cB* represents the electricity tariff for each hour; *dN* is the water level raise or decrease in Covão reservoir, for each hour; *cT* is the produced hydroelectricity selling price for each hour; *ηB,T* are the pump and turbine efficiency; and *h* is the hour of the day.

The above function represents the sum of the water level variation in Covão multiplied by the electricity costs/selling price, throughout one day. Meaning that if there is a raise in Covão reservoir water level (*dN*>0), the pump station is operating and has a cost *cB* associated for each hour. If, on the other hand, there is a decrease in Covão reservoir water level (*dN*<0), the system is discharging water from Covão to Socorridos and consequently, producing energy that can be sold at a price *cT*. With this function it is possible to provide the electricity costs for the pumping hours and the selling price for the electricity production hours.

The hourly limits relatively to the pipe flow restrictions are presented in Table 2.


**Table 2.** Hourly restrictions LP.

From 0 to 6 am it is only possible to pump water since the lower bound is zero. From 6 am forward only turbine operation is allowed.

For the non linear programming case (NLP) there is no need to impose pumping and power hours because the program will choose which solution is the best in order to obtain the major benefits. Then the objective function to minimize is:

$$f = \sum\_{h=1}^{24} \left[ \frac{c\_{B,h}}{\eta\_B} \cdot \left( \frac{dN\_h + \left|dN\_h\right|}{2} \right) + c\_{Th} \cdot \eta\_T \cdot \left( \frac{dN\_h - \left|dN\_h\right|}{2} \right) \right] \tag{2}$$

Pumped-Storage and Hybrid Energy Solutions

Towards the Improvement of Energy Efficiency in Water Systems 185

**Figure 10.** Wind speed average values for typical winter and summer conditions, 100 m above the

The constraints for all of the cases presented, linear and non linear programming, are the

1. The guaranty of water supply to the Câmara de Lobos population must be provided,

3. The maximum water flow, in each time step, depends on the systems characteristics

An integrated software tool has been developed for determining the optimum pump and turbine schedules and reservoirs water levels, that minimize pumping costs (i.e., maximize

maintaining a minimum water level in both reservoirs; 2. The water in the reservoirs can not exceed the maximum level;

and the electromechanical equipment.

**Figure 11.** Typical FL2500 power curve.

**4. Hydraulic model implementation** 

ground.

following:

Hence, if the water level variation in Covão reservoir is positive (pumping situation), the term related to the turbine operation is zero. The opposite is also verified. The hourly limits relatively to the pipe flow restrictions are presented in Table 3.


**Table 3.** Hourly restrictions NLP.

This means that, for this case, the only restriction is that the water level variation for each time step cannot be greater than *NQmax*.

#### **3.2. Pump-storage/hydro with wind power**

For this case the non linear programming (NLP Winter and NLP Summer) was used since the objective function is also non-linear:

$$f = \sum\_{h=1}^{24} \left\{ \left| \frac{\left| \frac{N\upsilon\_h}{dN\_h} - 1 \right| - \left( \frac{N\upsilon\_h}{dN\_h} - 1 \right)}{2} \right| \cdot \frac{c\_{B,h}}{\eta\_B} \cdot \left( \frac{dN\_h + \left| dN\_h \right|}{2} \right) + c\_{T,h} \cdot \eta\_T \cdot \left( \frac{dN\_h - \left| dN\_h \right|}{2} \right) \right| \right\} \tag{3}$$

where *Nv* is the water level rising to Covão reservoir due to wind power for each hour.

With the former function, the electricity cost for each hour is not the same as the tariff, but it varies according to the contribution of wind available energy. The wind energy is assumed to have a null cost since no energy from the grid is necessary for its generation. Therefore, for each hour, if all of the energy for pumping water is provided by the wind turbines, it has a null cost; if one part of the energy comes from the electrical grid and the other from the wind turbines, the cost is a fraction of the tariff. For example, if one third of the energy for pumping is provided by the wind turbines for one time step, the cost of energy to pump water in this time step is two thirds of the original tariff.

The hourly limits related to the pipe flow restrictions of the system are the same as the previous case (NLP) where the wind component was not considered.

The wind data used for this case is presented in Figure 10. The curves represent typical winter and summer situations for a weather station in Portugal.

The wind turbine chosen was a *Fuhrländer FL2500* (www.friendly-energy.de) with a power curve presented in Figure 11. It was assumed that the system has five of these turbines, so that the maximum power demand by the water pumps in one hour could be provided.

**Figure 10.** Wind speed average values for typical winter and summer conditions, 100 m above the ground.

The constraints for all of the cases presented, linear and non linear programming, are the following:


**Figure 11.** Typical FL2500 power curve.

184 Energy Efficiency – The Innovative Ways for Smart Energy, the Future Towards Modern Utilities

*f c*

<sup>1</sup> 2 2

Hence, if the water level variation in Covão reservoir is positive (pumping situation), the term related to the turbine operation is zero. The opposite is also verified. The hourly limits

> **Hours Lower Upper** *0 to 24 - NQmax NQmax*

This means that, for this case, the only restriction is that the water level variation for each

For this case the non linear programming (NLP Winter and NLP Summer) was used since

222

(3)

*h h Bh h h h h*

*dN dN c dN dN dN dN*

 

−− − + − <sup>=</sup> ⋅ ⋅ + ⋅⋅

*Bh h h h h Th T*

 + − = ⋅ + ⋅⋅

η

(2)

,

*Th T*

η

*c dN dN dN dN*

<sup>24</sup> ,

*h B*

relatively to the pipe flow restrictions are presented in Table 3.

= η

**Table 3.** Hourly restrictions NLP.

1

=

time step cannot be greater than *NQmax*.

the objective function is also non-linear:

**3.2. Pump-storage/hydro with wind power** 

<sup>24</sup> ,

*h B*

water in this time step is two thirds of the original tariff.

previous case (NLP) where the wind component was not considered.

winter and summer situations for a weather station in Portugal.

*h h*

*Nv Nv*

1 1

*f c*

η

where *Nv* is the water level rising to Covão reservoir due to wind power for each hour.

With the former function, the electricity cost for each hour is not the same as the tariff, but it varies according to the contribution of wind available energy. The wind energy is assumed to have a null cost since no energy from the grid is necessary for its generation. Therefore, for each hour, if all of the energy for pumping water is provided by the wind turbines, it has a null cost; if one part of the energy comes from the electrical grid and the other from the wind turbines, the cost is a fraction of the tariff. For example, if one third of the energy for pumping is provided by the wind turbines for one time step, the cost of energy to pump

The hourly limits related to the pipe flow restrictions of the system are the same as the

The wind data used for this case is presented in Figure 10. The curves represent typical

The wind turbine chosen was a *Fuhrländer FL2500* (www.friendly-energy.de) with a power curve presented in Figure 11. It was assumed that the system has five of these turbines, so that the maximum power demand by the water pumps in one hour could be provided.

### **4. Hydraulic model implementation**

An integrated software tool has been developed for determining the optimum pump and turbine schedules and reservoirs water levels, that minimize pumping costs (i.e., maximize

off-peak electrical energy consumption) and maximize energy production. This tool incorporates a 'hydraulic simulator' that describes the hydraulic behaviour of the system during 24 hour simulation (EPANET), and an 'optimization solver' based on Linear and Non-linear programming to determine the optimal solution without violating system constraints (e.g., minimum and maximum allowable water levels in the storage reservoirs) and ensuring that downstream demands are satisfied. In Figure 12 the model scheme of Socorridos-Covão system is presented.

Pumped-Storage and Hybrid Energy Solutions

Towards the Improvement of Energy Efficiency in Water Systems 187

For the NLP modes, with and without wind turbines, the behaviour of pump and turbine operation is quite different from each other. The results vary due to the non linearity of the

objective function and also according to the wind availability for each hour.

**Figure 13.** Water level variation in Covão and Socorridos reservoirs.

As for Covão as for Socorridos the storage reservoirs are tunnels made in rocks. However during modelling implementation these tunnels are approximated by regular cylindrical reservoirs of variable levels with the same volume of the real case. For modelling purposes a discharge control valve, with 2 m3/s as the control parameter, was implemented in order to simulate the hydropower installed at topographic level 89 m. The pump station is installed at 85 m.

**Figure 12.** Model scheme of hydraulic system used in the optimization process.
