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Optimal schedule with precipitation
The optimal schedules for the valve and pump obtained assuming about 1-mm of precipitation event between midnight and 1 AM are shown in figures 4.5(c) and 4.5(d). Since the rain is assumed to fall both on the rooftop and the lawn, both the valve and pump optimal schedules switch for less duration than when there is no precipitation taking place. The solenoid valve switches on at 01:00 hours but since there is precipitation taking place, it switches off in the next sampling interval. The harvesting of rain water and opening of the valve cause the height of the water in the tank to rise to 0.57 m. This precipitation event also causes the water level in the soil to rise to 29.31 cm. Thereafter the water level remains constant in both the tank and soil until 03:00 for the tank when the solenoid next switches on and 03:15 when the pump switches on. The pump switches off at 03:30 for 15 minutes enabling the water height in the tank to reach a peak of 0.93 m. Thereafter the pump switches on, while the solenoid valve is still filling the tank, until 05.15, where they both switch off. During this duration, the water height in the tank drops to 0.23 m while the water level in the soil rises to 29.89 cm. Thereafter, both the solenoid valve and the pump remain off for the rest of the control horizon. Therefore, the water height in the tank remain constant at 0.23 m while the water level in the soil drops due to evapotranspiration losses to 28.73 cm. About 5.9 mm of water is pumped for irrigation in this scenario.
With the 1-mm precipitation event, about 120 l of rain water is harvested from the rooftop and stored in the tank. Even though the same 1-mm rain is assumed to have fallen on the lawn, it is not sufficient to maintain the soil water content as required during the control horizon leading to about 5.9 mm of irrigation water being applied, which is less than 6.7 mm applied when no precipitation takes place.
This leads to about 0.4 mm more water content being left in the soil at the end of the control horizon as seen in Figure 4.7. Part of this 5.9 mm of irrigation water is met by harvested water stored in the tank effectively leading to conservation of 120 l of municipal water during this day. Over a long time, with more precipitation events, more water would be harvested leading to even higher water conservation.
SYNOPSIS
Optimal irrigation scheduling in urban lawns can have direct and indirect benefits. This chapter shows the potential direct benefits including significant savings in the cost water by about 14.7% and 17.4% relative to the Acclima TDT scheduling and regular irrigation, respectively, when optimally scheduling using municipal water directly. Optimal scheduling with RWH lowers this cost even further by 20.5% and 23.4% relative to the Acclima TDT scheduling and regular irrigation respectively. Following implementation of water conservation measures, the consequent potential savings in energy cost in the RWH system are 14.3% and 73.8% relative to the Acclima TDT and regular irrigation respectively.
These savings result from the load shifting to off-peak times as well as just the necessary amount of water is pumped to the lawn. Furthermore, the Pretoria method maximizes the pump life by minimizing the maintenance cost resulting from switching frequency better.
The optimal control systems can potentially lead to improved economic efficiency through cost savings of both water and energy. In addition, the optimal controller with RWH best suits application in developing nations where water demand far surpasses the supply requiring water storage. It not only leads to water conservation but also reduces the demand of potable water from municipal sources as well as shifting and reducing the load on the power utility.
Closed-loop algorithm
Closed-loop MPC obtains the current control action by solving, in each sampling time, a finite horizon open-loop optimal control problem using the current state of the plant as the initial state. The optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. This process is repeated throughout the entire control period [20]. Using the principle of
the receding horizon control in closed-loop MPC, only the first element in the control vector Xmpc is implemented after each iteration, ignoring the rest of the elements [158]. The state of the plant (water level in the tanks) is measured. During the next iteration, k + 1, the objective function and the
constraints are updated while taking the previous state of the tanks (water level at sampling time k ) as the initial state. The process of optimization is carried out in real time over the new control horizon (Nc = N ?k+1) to give the receding horizon control law. Similar to the open-loop control algorithm, the control vector, Xmpc, contains the control variables such that,
CHAPTER 1 INTRODUCTION
1.1 DEMAND SIDE MANAGEMENT
1.2 OPTIMAL CONTROL STRATEGIES
1.2.1 Implementation
1.3 CONTRIBUTION AND RESEARCH OBJECTIVES
1.4 THESIS LAYOUT
CHAPTER 2 ENERGY-WATER DEMAND SIDE MANAGEMENT: LITERATURE REVIEW
2.1 INTRODUCTION
2.2 ENERGY DEMAND MANAGEMENT
2.3 WATER DEMAND MANAGEMENT
2.4 ENERGY-WATER NEXUS DEMAND MANAGEMENT
2.5 CONTROL METHODS FOR ENERGY-WATER SYSTEMS
CHAPTER 3 OPTIMAL ENERGY-WATER MANAGEMENT IN HOUSEHOLDS WITH PUMP-STORAGE SCHEME
3.1 INTRODUCTION
3.2 LAYOUT AND FORMULATION
3.2.1 Schematic layout .
3.2.2 Open-loop optimal control system
3.2.3 Algorithm for solving the open-loop optimization problem
3.2.4 Closed-loop MPC system
3.3 GENERAL DATA
3.3.1 Case study
3.3.2 Time-of-use electricity tariff
3.4 SIMULATION RESULTS AND DISCUSSION .
3.4.1 Control systems without disturbance
3.4.2 Control systems with disturbance
3.4.3 Discussion
3.5 SYNOPSIS
CHAPTER 4 ENERGY-WATER OPTIMIZATION OF ROOFTOP WATER HARVESTING FOR LAWN IRRIGATION
4.1 INTRODUCTION .
4.2 LAYOUT AND FORMULATION
4.2.1 Schematic layout
4.2.2 Optimal scheduling without rooftop water harvesting
4.2.3 Optimal scheduling with rooftop water harvesting .
4.2.4 The Pretoria method to reduce pump maintenance cost
4.3 GENERAL DATA .
4.4 SIMULATION RESULTS AND DISCUSSION
4.5 SYNOPSIS
CHAPTER 5 OPTIMAL ENERGY-WATER MANAGEMENT IN URBAN RESIDENTIAL BUILDINGS THROUGH GREY WATER RECYCLING
5.1 INTRODUCTION
5.2 CONTROLLER DEVELOPMENT
5.3 GENERAL DATA
5.4 SIMULATION RESULTS AND DISCUSSION
5.5 SYNOPSIS
CHAPTER 6 OPTIMAL MANAGEMENT OF A GREY & RAIN WATER RECYCLING SYSTEM FOR RESIDENTIAL HOUSES
CHAPTER 7 OPTIMAL CONTROL OF HEAT PUMP WATER HEATER – INSTANTANEOUS SHOWER USING INTEGRATED RENEWABLE – GRID ENERGY SYSTEMS
CHAPTER 8 MODEL PREDICTIVE CONTROL OF HEAT PUMP WATER HEATER INSTANTANEOUS SHOWER POWERED WITH INTEGRATED RENEWABLE – GRID ENERGY SYSTEMS .
CHAPTER 9 COMPARISON OF LIFE CYCLE COST ANALYSIS
CHAPTER 10 CONCLUSIONS
REFERENCES
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OPTIMAL ENERGY-WATER NEXUS MANAGEMENT IN RESIDENTIAL BUILDINGS INCORPORATING RENEWABLE ENERGY, EFFICIENT DEVICES AND WATER RECYCLING
