Predictive control of chillers has been used to reduce operating costs and, less frequently, energy consumption primarily by limiting peak cooling demand and shifting thermal loads. In some cases, inverse models of building cooling loads have been used simply to calculate the power consumption for an HVAC system with an assumed demand limiting, energy savings or cost reduction control strategy. In these cases, simple zone temperature setpoint schedules or other control schedules are proposed (not determined by an optimization algorithm) which will reduce energy consumption or operating costs [Braun et al 2001, Braun and Lee 2006, Lee and Braun 2008].
A more rigorous approach, though one that requires significantly more information, model complexity, and computational resources is to identify control schedules using an optimization algorithm. [Braun 1990] takes an approach similar to that developed in this research. An optimization algorithm is presented that includes: a temperature-CRTF model of zone temperature response similar to that described in chapter 4; a cooling plant power model as a function of chilled water loop load, the outdoor wet-bulb temperature, and supply air temperature difference; and an air handler power consumption model. An optimization is
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performed to minimize the following objective function with respect to zone temperature set points Tz: (19)
∑
= × = K 1 k z *(T (k),f(k)) P ) k ( RJ v v subject to constraint Tz,min(k)≤Tz(k)≤Tz,max(k)
In equation (19), R(k) is an electricity rate at time k and P* is the optimal cooling plant consumption at time k. The sum is over time k=1 through K where k can be 24 hours into the uure. P*depends not only on current conditions at time k, but also on zone temperature setpoints and exogenous variables other times. As a consequence, P* is a function of a vector of zone temperature setpoints Tz(k)
v
and a vector of exogenous variablesfv(k). fv(k) includes solar loads, internal loads and outdoor climate conditions at times k. An optimization over the vector of temperature setpoints Tz(k)
v
is performed to minimize electricity cost (or energy consumption with R(k) = 1 for all k). The power consumption for HVAC equipment at each time k is calculated based on cooling loads, computed from a CRTF model, with fixed indoor temperature setpoints Tz(k)
v
.
The cooling loads at a given time k depend on current and past temperature setpoints. Consequently, calculation of cooling loads, power consumption, and costs at future time steps requires iteration of the CRTF using zone temperature set point history at each time step. For a given set point, the power consumption is a non-linear function depending on the operating state of the HVAC equipment and loads. Furthermore, the power consumption can be discontinuous as a result of changing operating states in HVAC equipment, such as when a chiller, pump or fan is on or off. [Braun 1990] applied a direct search method to optimize equation (19), solving for zone temperature set points that minimize electric costs due to HVAC power consumption over a 24 hour period.
[Henze et al 1997] develops an optimal pre-cooling control algorithm for ice-storage active TES under time-of-use (TOU) electricity pricing with a simplified chiller that has only two operating states. These two chiller operating states are modeled using one electric input ratio (EIR or 1/COP) while the chiller is chilling water and one, separate, lower EIR while the chiller is generating ice. An optimization is performed to minimize cooling costs by adjusting the time and duration over which the chiller produces ice for later use, or produces chilled water for immediate use to meet cooling loads not supplied by discharging the ice-storage. Dynamic programming is employed for optimization, which can be applied to problems where states are uniquely defined and do not depend on the path taken to reach a given state, such as the amount of ice stored in an ice storage system.
In [Henze et al 2004], an optimal chiller control algorithm is developed to minimize cooling costs for passive and active TES combined under a dynamic utility rate structure. However, the problem is greatly simplified by assuming, again, a constant chiller COP or EIR for chilled water and ice-making operation, independent of outdoor temperature and supply air or zone air temperature. The problem is thus split into two separate optimizations: one in which zone air
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temperature set points are optimized to minimize cooling load (where power consumption is assumed to be directly proportional to cooling load); and another in which an optimal charging and discharging schedule for active TES is determined to meet a total daily cooling calculated from the passive storage optimization. By separating the passive and active TES optimization problems and treating chiller performance as a constant, the passive TES optimization remains a linear problem in which zone temperatures are adjusted to minimize cooling load under an assumed active TES charging and discharging schedule. This allows for the application of a quasi-Newton optimization method to the passive TES problem, coupled with a dynamic programming optimization for the active TES problem.
[Snyder and Newell 1990] use a 2R1C building model to find optimal control strategies for cooling cost minimization through load shifting and demand limiting. However, the problem is reduced to three variables: the pre-cooling start time; the duration of time the zone is allowed to float until it reaches maximum allowed temperature; and the thermal mass temperature at the start of the occupied period.
[Chen 2001, Chen 2002] develop a predictive control algorithm to minimize cost or energy consumption of a radiant floor heating system. Similar to [Henze et al 2003], the efficiency of the heating plant is not weather dependent or dependent on past heating rates. As a result, the optimization problem remains linear in thermal loads and temperature response.
[Wang and Ma 2008] provides an overview of supervisory and optimal control methods for HVAC systems. It includes a review of optimization methods employed for supervisory or predictive HVAC control such as direct search, sequential quadratic, conjugate gradient, simulated annealing, genetic algorithm, and others.
Drawing from this past research, a framework for a pre-cooling control optimization will be developed that determines on optimal chiller control schedule for each hour, 24 hours-ahead, that pre-cools a concrete-core radiant floor/TES system to maintain thermal comfort later in the day.