Rolling Horizon Control of a Photovoltaic Shading Louver Considering Thermal State Inheritance and Occupancy Requirements

Abstract

Hourly angle optimization for photovoltaic (PV) shading is conducted by selecting values from independent fixed-angle simulations, although the selected hours do not share a consistent building thermal history. This study develops a database-based constant-action rolling horizon look-ahead heuristic that minimizes net electricity for a PV louver in a Beijing office while correcting thermal-history inconsistency. Nineteen angles from 0° to 90° were simulated to construct hourly thermal and PV maps. Schedules were generated for horizons of 1–48 h under a 10° h⁻¹ movement limit and evaluated by continuous EnergyPlus replay. The independently optimized sequence predicted −310.90 kWh of annual net energy, whereas continuous replay yielded −101.61 kWh, revealing a 209.29 kWh state-inheritance error dominated by HVAC electricity. The 12 h horizon minimized net energy at −119.11 kWh. A 24 h horizon incurred a 5.89 kWh penalty while reducing angle changes and total rotation by approximately 65%, indicating a favorable energy–movement compromise. Requiring an angle of at least 15° during occupancy eliminated full closure at a net-energy cost of 35.79 kWh. Continuous replay and operating constraints are therefore necessary when translating fixed-angle databases into implementable façade controls.

1. Introduction

The buildings and construction sector remains central to the global energy and climate challenge, accounting for approximately 32% of global energy use and 34% of energy- and process-related carbon dioxide emissions [1]. Evidence synthesized across building types and climates indicates that net- or nearly zero operational outcomes are technically achievable, but their broad deployment depends on deep demand reduction before residual loads are matched with renewable generation [2]. Reviews of worldwide building energy use similarly identify envelope improvement, efficient building services, and on-site renewable production as complementary pathways rather than interchangeable measures [3]. This need is intensified by urbanization, greater reliance on space conditioning, and rising expectations for indoor environmental quality. The façade is especially influential because it mediates conduction, solar heat gain, daylight, and the connection between indoor conditions and a highly variable outdoor environment. In highly glazed buildings, transparent areas may reduce lighting demand and provide useful winter solar gains, but they can also increase cooling loads, perimeter discomfort, and heat loss. A fixed envelope cannot be simultaneously optimized for these time-dependent demands.

Adaptive façades address this mismatch by changing their optical, thermal, or geometric characteristics in response to operating conditions. Early work documented advances in responsive materials, movable assemblies, performance evaluation, and control of climate-adaptive building shells [4]. Nevertheless, performance assessment remains a barrier to reliable design, operation, maintenance, and market adoption [5]. Reviews of multifunctional adaptive façades and dynamic shading further show that energy generation, insulation, ventilation, daylight, geometry, sensing, and actuation must be evaluated as one controlled system [6,7]. The literature on dynamic daylighting and simulation-based façade control likewise reports substantial energy and comfort potential while identifying limited operational validation and the difficulty of balancing daylight, glare, view, and thermal objectives as persistent gaps [8,9]. To manage the dynamic trade-offs between solar energy harvest, shading, and operational constraints, advanced decision-support frameworks and multi-criteria simulation workflows have proven essential across photovoltaic-integrated configurations [10].

Within this field, a photovoltaic-integrated shading device (PVSD) is attractive because one façade component can regulate solar gains and daylight while generating electricity. Previous studies have demonstrated this potential across several geometries and climates. Zou et al. coordinated HVAC, lighting, and electricity generation for a dynamic vertical PV envelope [11], while Jayathissa et al. coupled radiation, PV, daylight, and building energy calculations to optimize dynamic BIPV shading [12]. Tracking strategy and climate were shown to influence smart PV-blind performance [13], and rotating, sliding, and combined PV overhangs produced configuration- and climate-dependent benefits in residential applications [14,15,16]. Office studies extended the objective to joint energy and daylight performance [17], and later work examined hot-climate applications [18] and orientation- and latitude-dependent control [19]. Related design studies found that multi-objective optimization explicitly balanced PV exposure, daylight, and view for flexible PV shading [20]. Collectively, this evidence supports dynamic PV shading, but it also demonstrates that the preferred angle depends on what is optimized and how coupled effects are evaluated.

The remaining difficulty is temporal consistency. Many parametric workflows select a preferred angle at each hour from separate annual fixed-angle simulations. In such a database, the thermal state associated with an hour and angle has developed under that angle during all preceding hours. Stitching preferred records therefore combines mutually incompatible indoor-air and fabric temperatures, so the lookup value may differ from the performance of the same schedule when applied continuously. Model predictive control (MPC) provides a general framework for propagating building dynamics, forecasts, and constraints through sequential decisions [21]. However, full MPC requires a control-oriented model and disturbance forecasts, and prediction-horizon selection must balance the time scale of building thermal response against model and computational burden [22]. The issue also bears on energy flexibility: a façade-related change in demand or on-site generation is useful only when the underlying response is dynamically realizable, and its baseline and performance boundary are explicit [23].

This study builds on the PV-integrated louver configuration proposed by Zou et al. [11] but addresses a different question: how should an hourly angle schedule derived from fixed-angle simulations be converted into an implementable annual trajectory? The primary purpose is to minimize net electrical energy, defined as room electricity demand minus PV generation; PV production, thermal shading response, and daylight-responsive lighting are coupled contributors rather than separate objectives. A computationally light, database-based constant-action rolling horizon look-ahead heuristic is developed and assessed through continuous EnergyPlus replay. The objectives are to (1) quantify the error caused by stitching independent fixed-angle states; (2) compare horizons of 1, 3, 6, 12, 24, and 48 h under a 10° h⁻¹ movement limit; (3) distinguish the energy-optimal horizon from a lower-movement engineering compromise; and (4) quantify the energy and actuation effects of preventing full closure during occupied periods. The contribution is therefore not another component-level comparison of PV shading geometries, but a reproducible evaluation of thermal-state inheritance, horizon selection, and operational constraints in a low-complexity control workflow.

2. Materials and Methods

2.1. Description of the Case Study and PV Louver System

The case study represents a perimeter office room in Beijing, China (39.80° N, 116.47° E). The annual simulation used the Chinese Standard Weather Data file and comprised 8760 h. The room is 5.0 m wide, 5.0 m deep, and 3.0 m high, giving a floor area of 25 m² and a volume of 75 m³. A 4.8 m × 2.184 m window occupies 69.9% of the south wall. The south wall is exposed to the outdoors, while the remaining walls, floor, and ceiling are adiabatic; the model should therefore be interpreted as a controlled perimeter-zone case rather than a whole-building representation.

The external device consists of 24 horizontally stacked PV louver slats mounted across the full window width (Figure 1). Each slat is 4.8 m long and 0.091 m wide, with a 0.091 m spacing and a 0.05 m separation from the glazing. The slat-angle convention defines 0° as fully closed and 90° as fully open. The feasible angle set contains 19 positions at 5° intervals. The same convention and geometry were used in the thermal and PV models so that hourly outputs could be matched without interpolation between angles. For each fixed angle, EnergyPlus calculated solar position and geometric beam and diffuse shading at every timestep; shading therefore varied with louver angle, solar altitude, and solar azimuth rather than being imposed as a constant factor.

Figure 1. Case study and PV louver configuration: (a) single-zone office with a south-facing external PV louver; (b) enlarged slat and PV-module arrangement adjacent to the glazing; and (c) side-view angle convention for 0° (fully closed), 45°, and 90° (fully open). Colors distinguish the functional blocks and have no quantitative meaning. In the lower panel, the orange dashed curves represent hourly results stitched from independent fixed-angle simulations, whereas the green solid curve represents a continuously inherited thermal-state trajectory.

Thermal and daylight calculations were performed in EnergyPlus 25.2 [24] using six timesteps per hour, the Conduction Transfer Function heat-balance algorithm, and the SplitFlux daylighting method. The double glazing has a center-of-glass U-value of 1.8 W·(m²·K)⁻¹, a solar heat-gain coefficient of 0.40, and a visible transmittance of 0.80. Occupancy was scheduled on weekdays from 08:00 to 18:00 at 0.16 person·m⁻². Lighting and equipment power densities were 6 and 12 W·m⁻², respectively. Continuous daylight dimming automatically adjusted electric-lighting power at every timestep, including when louver closure reduced daylight, to maintain a 300 lx setpoint at the reference point. Infiltration was 0.3 air changes per hour.

A packaged terminal heat pump served the zone. Its rated cooling and heating coefficients of performance were 3.0 and 2.5, respectively. Occupied heating and cooling setpoints were 20 and 26 °C; during unoccupied periods, they were relaxed to 15 and 30 °C. The model calculates transient envelope conduction, short- and long-wave exchange, convection, internal gains, daylight-responsive lighting, and HVAC response. No moisture-buffering, vapor-transport, contaminant, or indoor-air-quality model was activated. Accordingly, the term thermal state refers here to sensible energy stored in the zone air and construction layers, rather than coupled heat-and-moisture storage.

PV generation was calculated for 24 crystalline–silicon modules using the EnergyPlus equivalent one-diode model in decoupled heat-transfer mode. The total active area was 10.335 m², and the nominal array capacity was approximately 2.39 kW. The one-diode model represents irradiance- and cell-temperature-dependent DC output. The analysis uses this DC electricity as its accounting boundary; downstream inverter and balance-of-system losses are not subtracted. The principal geometric, operating, and simulation inputs are summarized in Table 1.

Table 1. Case-study building, system, and simulation inputs.

Category	Parameter	Value
Location	Weather and site	Beijing CSWD; 39.80° N, 116.47° E
Geometry	Room dimensions	5.0 m × 5.0 m × 3.0 m; 25 m2; 75 m3
Geometry	South window	4.8 m × 2.184 m; WWR 69.9%
Boundary	Exposure	South wall outdoors; other surfaces adiabatic
Glazing	Thermal/optical properties	U = 1.8 W·(m2·K)−1; SHGC = 0.40; VT = 0.80
PV louver	Slat geometry	24 slats; 4.8 m × 0.091 m; 0.091 m spacing
PV louver	Mounting and angles	0.05 m from glass; 0–90° at 5° intervals
Internal gains	People/lighting/equipment	0.16 person·m−2; 6 W·m−2; 12 W·m−2
Schedule	Main occupancy	Weekdays, 08:00–18:00; 2922 h·year−1
Daylighting	Lighting control	Continuous dimming; 300 lx reference setpoint
Air exchange	Infiltration	0.3 h−1
HVAC	PTHP and setpoints	COP 2.5 heating/3.0 cooling; occupied 20/26 °C
PV	Array and model	24 crystalline modules; 10.335 m2; ≈2.39 kW; DC output
Simulation	Engine and resolution	EnergyPlus 25.2; 6 timesteps·h−1; 8760 h

2.2. Development of the Performance Database

For each angle α ∈ A = {0°, 5°, …, 90°}, one annual building simulation and one corresponding annual PV simulation were completed. The resulting performance database contains 8760 hourly records for each of the 19 angles. Each building record includes packaged-terminal-heat-pump (PTHP), lighting, and equipment electricity, together with zone conditions and setpoint-unmet time. Each PV record contains angle-specific hourly electricity. No angular interpolation was used. For hour t and angle α, the net electrical energy E_net (kWh) was defined as Equation (1).

$$E_{\mathrm{net}}\left(t,\alpha \right)=E_{\mathrm{HVAC}}\left(t,\alpha \right)+E_{\mathrm{light}}\left(t,\alpha \right)+E_{\mathrm{equip}}\left(t,\alpha \right)-E_{\mathrm{PV}}\left(t,\alpha \right)$$

(1)

where E_HVAC is the electrical energy consumed by the packaged terminal heat pump, kWh; E_light is the lighting electricity consumption, kWh; E_equip is the equipment electricity consumption, kWh; E_PV is the PV electricity generation, kWh; t is the hourly time index; and α is the louver angle. Annual values are obtained by summing Equation (1) over the 8760 h. Equation (1) treats PTHP, lighting, and equipment electricity as positive demand and subtracts PV generation. Negative annual net energy denotes that simulated annual PV generation exceeds room electricity demand within this boundary; it does not imply negative physical energy consumption or account for export restrictions. Equipment electricity is included in the room balance but is independent of the louver angle.

The database serves two purposes. First, it provides the direct hourly estimate used by the static and rolling-horizon schedulers. Second, it supplies angle-matched PV output after an angle sequence has been dynamically replayed. The thermal and lighting columns are not used as final results for a changing-angle schedule because doing so would retain the incompatible fixed-angle states that this study seeks to quantify (Figure 2).

Figure 2. Workflow for database-based angle scheduling, continuous dynamic replay, and net-energy evaluation. Colors distinguish the functional blocks and have no quantitative meaning. In the lower panel, the orange dashed curves represent hourly results stitched from independent fixed-angle simulations, whereas the green solid curve represents a continuously inherited thermal-state tra-jectory.

2.3. Static Hourly Optimization and Thermal State Inconsistency

The conventional static hour-wise sequence is obtained as

$${\alpha }_{\mathrm{static}}\left(t\right)=\underset{\alpha \in A}{\arg \min }{E}_{\mathrm{net},\mathrm{lookup}}\left(t,\alpha \right)$$

(2)

where α_static(t) is the statically optimized louver angle at hour t; A is the discrete set of 19 candidate angles from 0° to 90° at 5° intervals; E_net,lookup is the hourly net energy obtained directly from the fixed-angle performance database, kWh. Equation (2) selects the lowest net-energy record independently at every hour. Its annual lookup estimate is the sum of these selected records. This sequence is mathematically feasible in terms of the 5° angle set but is not constrained by actuator speed; its largest hourly step is 90°. More importantly, the selected records do not form a continuous thermal trajectory because every fixed-angle simulation carries a different preceding history.

To isolate this effect, the identical αstatic schedule was imposed through an EnergyPlus Schedule:File object in one continuous annual simulation. The commanded value was held over each hour while EnergyPlus advanced at 10 min timesteps. HVAC and lighting electricity were thereby recalculated from the thermal state produced by the actual preceding angles. The annual state-inheritance error ΔE_state (kWh) was defined as

$$\Delta E_{\mathrm{state}}={\displaystyle \sum _t{E}_{\mathrm{net},\mathrm{dynamic}}\left(t|{\alpha }_{static}\right)}-{\displaystyle \sum _t{E}_{\mathrm{net},\mathrm{lookup}}\left(t,{\alpha }_{static}\left(t\right)\right)}$$

(3)

where E_net,dynamic is the hourly net energy obtained by continuously replaying the static optimal angle schedule in EnergyPlus, kWh. A positive ΔE_state means that the stitched lookup underestimates the net electricity of the dynamically realizable sequence and therefore overstates its benefit. Because the lookup and replay use the same hourly angles and PV values, their difference isolates the building-side consequence of replacing fixed-angle histories with one continuous history.

2.4. Constant-Action Rolling Horizon Angle Selection

A computationally light constant-action rolling horizon look-ahead heuristic was constructed from the fixed-angle database. At hour t, feasible candidates were limited by the command implemented in the preceding hour so that the movement rate did not exceed 10° h⁻¹, as shown in Equation (4):

$$A_{\mathrm{t}}=\left\{\alpha \in A:\left|\alpha -{\alpha }_{\mathrm{t}-1}\right|\le 10°\right\}$$

(4)

where A_t is the set of feasible louver angles at hour t; α_t−1 is the angle implemented during the preceding hour; and 10° is the maximum allowable angular change between two consecutive hourly commands. For each feasible candidate, the controller accumulated lookup net energy over a future window of H hours, as shown in Equations (5) and (6). To keep the online problem small, the candidate under evaluation was assumed to remain constant throughout that window.

$$J_{\mathrm{t}}\left(\alpha ;H\right)={\displaystyle \sum _{k=t}^{\min \left(t+H-1,T\right)}{E}_{\mathrm{net},\mathrm{lookup}}\left(k,\alpha \right)}$$

(5)

$${\alpha }_{\mathrm{t},*}=\underset{\alpha \in A_{\mathrm{t}}}{\arg \min }{J}_{\mathrm{t}}\left(\alpha ;H\right)$$

(6)

where J_t(α;H) is the cumulative lookup net energy associated with candidate angle α at decision hour t over a horizon of H hours, kWh; H is the rolling-horizon length, h; k is the hourly index within the prediction horizon; T is the final hour of the annual simulation; E_net,lookup(k,α) is the database-based net energy at hour k for candidate angle α; and min(t + H − 1,T) prevents the prediction window from extending beyond the end of the annual simulation; α_t,* is the optimal louver angle selected at hour t.

Only the first selected angle was implemented. The horizon then advanced by 1 h and the calculation was repeated using the newly implemented angle as the movement reference. The initial angle was 90°. Numerically equal objective values were resolved by first choosing the angle nearest to the previous command and then, if a tie remained, the larger angle. Prediction horizons of 1, 3, 6, 12, 24, and 48 h were tested. The complete scheduling procedure, including the tie-breaking rule, occupancy constraint, and continuous dynamic evaluation, is summarized in Algorithm S1. A reference implementation of database construction, rolling-horizon scheduling, EnergyPlus case generation, and result reconciliation is provided as Supplementary Code S1. Full MPC normally propagates a control-oriented state model and optimizes a future input trajectory subject to dynamic constraints [25,26]. The present formulation instead evaluates one constant candidate over each horizon. This reduces the online decision space and permits direct use of the fixed-angle database, but it may also limit the benefit obtained from long forecasts.

2.5. Continuous Dynamic Replay and PV Generation Matching

Every generated sequence was subjected to one continuous annual EnergyPlus replay. The scheduled slat angle affected solar transmission, daylight-responsive lighting, zone heat balance, and HVAC operation while retaining one evolving thermal state. Hourly PV generation was then selected from the 19-angle PV database according to the implemented command. This hybrid treatment assumes that, under the decoupled PV model, hourly PV output depends on contemporaneous weather and angle but has no relevant building thermal memory. The reported dynamic net energy is therefore the sum of replayed HVAC and lighting electricity, angle-independent equipment electricity, and angle-matched PV generation. The variables included in the machine-readable hourly output are defined in Table S1.

This distinction is important throughout the paper. A value labeled lookup is calculated entirely from fixed-angle database records, whereas a value labeled dynamic or replay uses the continuous EnergyPlus result for building electricity. All conclusions and baseline comparisons use the dynamic value unless explicitly stated otherwise.

2.6. Minimum Opening Constraint During Occupancy

The unconstrained energy-optimal strategy frequently selected 0°, corresponding to complete visual closure. Reviews of occupancy-responsive control and adaptive behavior show that blind operation is influenced by solar conditions, glare, view, privacy, access to controls, and the preceding blind state, rather than occupancy alone [27,28,29]. A practical sensitivity case was therefore generated for the 12 h horizon. Main occupied hours were those for which the EnergyPlus occupancy-schedule fraction was at least 0.5. During these hours, the angle was required to be at least 15°; 0° remained feasible outside occupancy. This is intentionally only an operational usability proxy: it prevents complete closure but is not a daylight, glare, view, or occupant-response model and does not claim visual comfort.

The 10° h⁻¹ movement limit also required the controller to anticipate the beginning of occupancy. If dt denotes the number of hours until the next main occupied hour, the following pre-opening bound was applied, as shown in Equation (7):

α_t ≥ max(0°, 15° − 10° d_t)

(7)

where d_t is the number of hours remaining until the next main occupied hour, and the maximum function ensures that the pre-opening lower bound does not fall below 0°.

Thus, the required lower bound rises as occupancy approaches. For example, a fully closed device can move from 0° to 5° 1 h before occupancy and to 15° at the occupied hour without violating the movement limit.

2.7. Simulation Cases and Performance Indicators

The energy indicators were annual PTHP, lighting, equipment, gross, PV, and net electricity. Gross electricity is the sum of PTHP, lighting, and equipment electricity. Operational indicators were heating and cooling setpoint-unmet hours, the annual number of angle changes, total absolute angular rotation, the maximum hourly step, and occupied-period angle distributions. Total rotation δ was calculated as Equation (8):

$$\delta ={\displaystyle \sum _t\left|{\alpha }_{\mathrm{t}}-{\alpha }_{\mathrm{t}-1}\right|}$$

(8)

Three practical references were emphasized: fixed 45°, fixed 90°, and a room without the PV blind. The no-blind case isolates the combined consequence of adding both shading and PV generation; it is not a pure control comparison. Fixed 45° and 90° retain the same device and are therefore the more informative references for angle control. Fixed 0° was retained only as a theoretical fully closed bound because it blocks the opening throughout the year. To avoid mathematical instability, percentage improvements in net energy were not reported when the baseline net balance was close to zero or negative. Where normalization was useful, the absolute net-energy difference was divided by the gross electricity of the relevant baseline.

2.8. Model Verification and Data Consistency

All annual cases contained 8760 hourly records and completed without severe or fatal EnergyPlus errors. For the dynamic cases, the simulated blind-angle output agreed with the intended command at every hour; the maximum numerical mismatch was below 8 × 10–15°. The controlled replays reported one or two non-fatal warning groups. The no-blind reference was completed successfully but repeated a packaged-terminal heat-pump coil diagnostic 722 times under extreme psychrometric conditions. This was a psychrometric rather than a capacity-undersizing warning, and the warning count does not represent unmet-load hours. The case recorded 4.00 h of occupied heating setpoint-unmet time and 117.83 h of occupied cooling setpoint-unmet time. Although the results indicate unmet cooling demand under peak unshaded conditions, its contribution cannot be attributed specifically to the diagnostic. The no-blind case is therefore retained as a qualified reference, while the main control conclusions rely on cases with the same PV louver.

Energy totals were independently reconstructed from the hourly output columns. Equipment electricity was 783.00 kWh in every case, as required by the common schedule. PV totals for a dynamic sequence were also recalculated by matching every hourly command to the corresponding database column. These checks verified record alignment, angle convention, unit conversion, and the separation between lookup and replay accounting. The principal model, data-alignment, and controller checks are summarized in Table S2.

3. Results

3.1. Difference Between Lookup Estimates and Dynamic Replay

The hour-wise static lookup produced an annual net-energy estimate of −310.90 kWh, whereas continuous replay of the identical angle sequence yielded −101.61 kWh (Figure 3). The 209.29 kWh difference is equivalent to 11.0% of the lookup gross electricity demand and changes the apparent surplus by approximately two thirds. The stitched calculation is therefore not a small numerical approximation; it gives a materially different assessment of annual performance.

Figure 3. Comparison of the annual net energy obtained from database lookup and continuous dynamic replay: (a) annual net energy of each control strategy and (b) the difference between the two evaluation methods. Positive differences indicate that the lookup estimate overstates the achievable performance.

PV generation was identical in the two calculations because the same hourly angles were used. The discrepancy arose almost entirely on the building side: PTHP electricity increased from 819.06 to 1019.19 kWh (+200.12 kWh), while lighting electricity increased from 292.67 to 301.83 kWh (+9.16 kWh). PTHP demand accounted for 95.6% of the total state-inheritance error. This allocation indicates that the dominant cause was the altered sensible thermal trajectory, with a smaller contribution from the interaction between changing shade position and continuous daylight simulation.

Rolling-horizon schedules also exhibited lookup-to-replay differences of 107.72, 121.60, 115.45, 110.44, 86.34, and 51.34 kWh for H = 1, 3, 6, 12, 24, and 48 h, respectively (Table 2). Longer horizons tended to reduce the mismatch because they generated smoother schedules, but the reduction was not monotonic up to 12 h, and no tested rolling case eliminated it. Consequently, a rate constraint and a look-ahead objective improve implementability but cannot substitute for continuous replay.

Table 2. Lookup and dynamic-replay net energy and state-inheritance error.

Strategy	Lookup Net (kWh)	Dynamic Replay (kWh)	State Error (kWh)
Static hourly optimum	−310.90	−101.61	209.29
RH1	−211.74	−104.02	107.72
RH3	−232.08	−110.49	121.60
RH6	−227.84	−112.39	115.45
RH12	−229.55	−119.11	110.44
RH24	−199.57	−113.22	86.34
RH48	−164.06	−112.73	51.34

The static sequence also illustrates why it should not be interpreted as a deployable optimum. It contained 1365 angle changes, accumulated 66,910° of rotation, and included a 90° 1-h step. In comparison, the rolling schedules respected the 10° h⁻¹ limit and accumulated 2910–11,725° of rotation. The static lookup is useful as an optimistic reference for the database, whereas the replayed and rate-constrained sequences are the appropriate basis for control conclusions.

3.2. Comparison with Fixed Angle and Unshaded Cases

Figure 4 compares the continuous annual energy balance of the principal references and selected controllers. Fixed 45° and fixed 90° produced net-energy values of −15.70 and 247.63 kWh, respectively, while the no-PV-shading room consumed 1648.83 kWh. RH12 achieved −119.11 kWh and was therefore 103.41 kWh better than fixed 45° and 366.74 kWh better than fixed 90°. Because the fixed 45° net balance is close to zero, dividing by its net value would produce an unstable and misleading percentage. Normalized by each fixed case’s gross electricity demand, the RH12 advantages were 4.83% and 21.34%, respectively.

Figure 4. Annual electricity balance of the baseline and selected control cases: (a) PV generation and building electricity components; (b) resulting net energy. The vertical zero lines distinguish generation or surplus from consumption: PV generation is plotted on the negative side in panel (a), while negative net energy in panel (b) indicates that annual PV generation exceeds building electricity demand.

The component balance explains these differences. Relative to fixed 45°, RH12 reduced gross building electricity by 27.57 kWh and increased PV generation by 75.83 kWh; both effects improved the net result. Relative to fixed 90°, however, RH12 used 396.54 kWh more gross electricity because the more closed schedule increased lighting and PTHP demand. This penalty was more than offset by 763.28 kWh of additional PV generation. Dynamic control therefore did not minimize every component independently; it found a better annual balance between demand and generation.

The no-PV-shading case had the lowest lighting electricity (61.39 kWh) and lower PTHP electricity than the louvered cases (804.45 kWh), but it had no on-site generation. Its 1767.94 kWh difference from RH12 therefore combines the introduction of the PV array, the thermal and daylight effects of external shading, and the angle-control strategy. This result supports the overall PV-shading concept but should not be reported as a control-only saving. The fixed-angle comparisons provide cleaner evidence that dynamic operation adds value after the device is installed.

3.3. Influence of the Prediction Horizon

The dynamically evaluated net energy improved from −104.02 kWh at H = 1 h to −110.49 kWh at 3 h, −112.39 kWh at 6 h, and −119.11 kWh at 12 h (Figure 5a). The adjacent gains of 6.47, 1.90, and 6.72 kWh did not form a strictly diminishing series. More importantly, increasing H beyond 12 h reversed the trend: net energy rose to −113.22 kWh at 24 h and −112.73 kWh at 48 h. RH12 was therefore the finite energy optimum among the horizons tested, rather than an arbitrary upper limit on the analysis.

Figure 5. Influence of prediction horizon on annual control performance: (a) annual net energy for the evaluated horizons; (b) relationship between net energy, total louver rotation, and the number of angle changes. The vertical dotted line in panel (a) marks the minimum-net-energy horizon of 12 h. The line in panel (b) denotes the Pareto frontier, and the arrow indicates the preferred direction toward lower net energy and reduced actuator movement. Marker size indicates annual angle changes.

The deterioration at longer horizons came from the demand–generation balance. Compared with RH12, RH24 generated 9.91 kWh more PV electricity but consumed 15.79 kWh more gross building electricity, giving a 5.89 kWh net penalty. RH48 generated 28.48 kWh more PV than RH12, but gross electricity increased by 34.86 kWh, resulting in a 6.38 kWh penalty. Thus, longer horizons favored angles with greater PV output but did not sufficiently account for the accompanying HVAC and lighting consequence when those angles were replayed dynamically. To test the downstream conversion boundary without rerunning the controller, a post-hoc 95% DC-to-AC conversion was applied to the unchanged RH12, RH24, and RH48 schedules, which bracket the reported energy optimum. Their annual AC-adjusted net balances were −7.40, −1.02, and 0.41 kWh, respectively; RH12 therefore remained the best of these principal horizon candidates. This is a uniform conversion sensitivity, not an inverter part-load curve or a re-optimization of the schedules.

The nonmonotonic response is consistent with the constant-action look-ahead formulation. As H increases, one candidate angle is required to perform well over a wider range of future solar and load conditions while being assumed constant throughout the window. The optimizer can consequently favor a persistent, PV-oriented angle and become less responsive to near-term building demand. Because the final building response is obtained from a continuous replay rather than the same lookup states used in the objective, increasing H also does not guarantee a monotonic reduction in dynamic net energy. The observed 12 h optimum is therefore specific to the present building, climate, database, and controller structure.

3.4. Balance Between Energy Performance and Actuator Movement

Energy performance is only one criterion for a movable façade. RH12 changed angle 1272 times and accumulated 11,260° of annual rotation. RH24 was 5.89 kWh worse in net energy, but it reduced changes to 451 and rotation to 3940°, as well as decreases of 64.5% and 65.0%, respectively (Figure 5b). The energy penalty was only 0.28% of RH12 gross electricity. RH48 further reduced changes to 354 and rotation to 2910°, but its net energy was 0.50 kWh worse than RH24; the additional 24 h of look-ahead therefore yielded movement savings without an energy benefit.

These results define two legitimate selections. RH12 is preferred when annual net energy is the sole objective. RH24 lies near the knee of the energy–movement relationship and is a plausible product-oriented setting when actuator wear, acoustic disturbance, and maintenance are important. RH48 may be relevant where movement must be minimized, but the present analysis contains no actuator life cycle or monetary model that would justify selecting it. The movement indicators should therefore be interpreted as transparent engineering proxies, not as measured durability.

3.5. Influence of the Minimum Opening Constraint

The occupied-period angle distribution revealed a practical weakness that was not visible in the annual energy total. Unconstrained RH12 selected 0° during 1957 of the 2922 main occupied hours (66.97%). The occupied minimum of 15° eliminated all fully closed and below-15° hours (Figure 6a). The constrained schedule was exactly 15° for 1839 h (62.94%) and above 15° for 1083 h (37.06%), with a mean occupied angle of 33.76°.

Figure 6. Effects of the occupied-period minimum-opening constraint: (a) cumulative distributions of louver angle during the 2922 main occupied hours; (b) decomposition of the annual net-energy penalty; and (c) additional actuator movement relative to unconstrained RH12 control. The vertical dashed line and shaded region in panel (a) indicate the 15° minimum angle and the range excluded during occupancy, respectively. The dotted connectors in panel (b) show the cumulative changes in the net-energy decomposition.

The constraint reduced lighting electricity by 13.02 kWh and PTHP electricity by 0.68 kWh, so gross demand fell from 2115.18 to 2101.48 kWh. The more open positions, however, reduced PV generation by 49.49 kWh. The resulting annual net energy increased from −119.11 to −83.32 kWh, a penalty of 35.79 kWh or 1.69% of unconstrained RH12 gross demand (Figure 6b). Heating setpoint-unmet time increased slightly from 17.17 to 17.83 h, while cooling unmet time remained 1.00 h. The energy penalty was therefore driven by lost generation rather than an increase in HVAC or lighting demand.

Despite the penalty, RH12-Occ15 remained 67.61 kWh better than fixed 45° and 330.95 kWh better than fixed 90°. The constraint thus retained the principal benefit of dynamic control while removing its most restrictive occupied state. It did not, however, reduce actuator activity: angle changes rose from 1272 to 2231 (+75.4%) and rotation from 11,260° to 18,770° (+66.7%) because the controller repeatedly reopened for occupancy and recovered energy-oriented positions afterward (Figure 6c). A minimum-opening rule should consequently be paired with a switching penalty or deadband if movement is a design priority. The complete energy and control impacts of the minimum-opening constraint are summarized in Table 3.

Table 3. Energy and control impact of the occupied-period minimum-angle constraint.

Metric	RH12	RH12-Occ15	Change
PTHP electricity (kWh)	1011.19	1010.51	−0.68
Lighting electricity (kWh)	320.99	307.97	−13.02
Gross electricity (kWh)	2115.18	2101.48	−13.70
PV generation (kWh)	2234.29	2184.79	−49.49
Net energy (kWh)	−119.11	−83.32	+35.79
Occupied 0° hours (h)	1957	0	−1957
Annual angle changes	1272	2231	+959
Total rotation (°)	11,260	18,770	+7510

The 15° case is best understood as an operational usability proxy rather than visual-comfort control. It prevents complete closure but does not establish daylight glare probability (DGP), spatial daylight autonomy (sDA), work-plane illuminance, illuminance uniformity, or view quality, all of which vary with sky condition, solar position, interior layout, and view direction. Its value is methodological: a readily interpretable operational condition is imposed in the same sequential framework, and its effects on energy and movement are quantified rather than assumed.

4. Discussion

4.1. Physical Explanation for the Difference Between Lookup and Dynamic Results

The 209.29 kWh difference between the static lookup and its continuous replay confirms that thermal-state inheritance is a first-order methodological issue. A record selected from the fixed 0° simulation, for example, carries wall and zone temperatures produced by prolonged closure, whereas a record selected from the fixed 90° simulation carries a different preceding solar and HVAC history. Alternating those records preserves neither state. The replay replaces these incompatible snapshots with one causal trajectory, so the current HVAC operation responds to heat stored or released under the angles actually used in previous hours.

The error decomposition supports this interpretation. More than 95% of the static discrepancy was attributable to PTHP electricity, while PV generation was held identical and the lighting contribution was small. The result therefore cannot be explained by PV bookkeeping; it reflects sensible heat storage and delayed HVAC response. Studies of short-term flexibility in building thermal mass show that the magnitude and duration of a usable response depend on insulation, emission system, season, and the building time constant [30]. Although the present study does not deliberately charge or discharge the room as thermal storage, the same state dependence explains why a louver action can affect later loads. The remaining 51–122 kWh errors in the rolling cases further show that smoother movement alone does not make a stitched database thermally consistent. A fixed-angle performance map can support screening and scheduling, but a continuous simulation—or an online model that propagates state—is needed before an annual saving is claimed.

4.2. Selection of an Appropriate Prediction Horizon

The horizon analysis produced separate energy and engineering recommendations. RH12 minimized annual net energy, whereas RH24 retained nearly the same performance with approximately 65% less movement. This distinction is consistent with the MPC literature, which treats horizon selection as a balance among building dynamics, forecast usefulness, constraints, and solution effort [21,25,26]. Laguna et al. likewise showed that an appropriate horizon depends on the building thermal response and need not increase indefinitely [22]. The present study adds a façade-specific observation: even with perfect database knowledge, a longer horizon can worsen realized performance when the simplified prediction objective and continuously replayed building dynamics are not identical.

Evidence from occupied buildings also cautions against judging predictive control only by idealized optimization results. A 2-month heating experiment reported weather-informed MPC savings of 15–28%, while emphasizing their dependence on the building, HVAC system, and implementation effort [31]. Seven months of MPC operation in a Swiss office demonstrated reliable integrated control of thermal systems, ventilation, and blinds; EnergyPlus-based comparison indicated approximately 17% savings, but the associated modeling and engineering costs remained a barrier [32]. A recent plus-energy housing study similarly found that forecast quality and commercial-system controllability reduced the benefits observed under idealized predictive control [33]. These percentages are not directly comparable with the present net-energy balance, yet they reinforce the rationale for a transparent, database-based method and for separating predicted from dynamically realized performance.

The nonmonotonic result should not be presented as evidence that 12 h is universally optimal. The building has one exposed façade, adiabatic internal boundaries, and a particular Beijing weather sequence; other thermal masses, orientations, HVAC schedules, or climates can shift the useful time scale. Moreover, the controller evaluates a constant candidate rather than an angle trajectory. A trajectory-based optimizer could exploit a 24–48 h forecast by planning different future positions, whereas the current controller asks one angle to represent the whole window. That simplification makes the method suitable for precomputed maps and embedded implementation, but it is also the likely reason that additional look-ahead ceased to improve annual energy. With identical forecasts, constraints, and a state model, a trajectory optimizer has a larger feasible decision space and should not perform worse in its internal objective than the constant-action approximation; however, the realized improvement at 24 or 48 h cannot be quantified without implementing and replaying that optimizer.

Adiabatic internal boundaries suppress heat exchange with adjacent zones and core spaces. In a multi-zone building, partitions and floor slabs can add effective thermal storage, while inter-zone heat flow and different schedules can either damp or reinforce perimeter loads; these effects alter the thermal time constant and may shift the preferred horizon. Cooling-dominated climates would generally increase the value of solar rejection, whereas heating-dominated climates can place greater value on useful solar gains. The direction and magnitude of the horizon shift therefore cannot be inferred universally without multi-climate, whole-building simulation.

4.3. Practical Implications of the Minimum Opening Constraint

The occupied minimum illustrates why a façade controller should be evaluated against operating requirements, not only an annual energy objective. Energy-only RH12 closed the louver for approximately two thirds of main occupied hours. Preventing this state cost 35.79 kWh·year⁻¹ yet slightly reduced gross building demand because increased daylight outweighed the small HVAC change. The loss arose from PV generation, making the trade-off physically transparent: the user-oriented rule moved the device away from generation-favorable closed positions during occupied periods.

Occupancy-based control studies emphasize that predicted benefits depend on how presence and user requirements are represented [27,28]. Field observations of motorized shades and dimmable lighting further show that occupants prefer individualized control and that easier access to controls can increase daylight use [34]. More explicit automated strategies have optimized venetian-blind position for daylight and glare using real-time simulation [35]; a self-commissioning glare-based controller maintained its prescribed visual-comfort region for 96% of working hours while moving the shade an average of 2.54 times per day [36]. The current 15° rule is deliberately more modest: it prevents complete closure and is easy to implement, but it does not establish visual comfort or a healthy indoor environment. A subsequent controller should replace the angular proxy with work-plane illuminance, daylight glare probability, view openness, and user override while adding a switching penalty, minimum dwell time, or hysteresis to limit the movement increase observed here.

4.4. Comparison with Previous Studies

The present findings complement, rather than replace, earlier evidence on the energy potential of dynamic PV façades. Dynamic BIPV and PV-blind studies have shown that attainable performance varies with climate, geometry, orientation, PV efficiency, and control logic [11,12,13,14,15,16,17,18,19]. Design-oriented research has likewise demonstrated that the optimum inclination of shading-type BIPV cladding changes with orientation and energy-accounting boundary [37], while multi-objective optimization of flexible PV shading exposes explicit trade-offs among incident solar energy, daylight, and outward visibility [20]. These studies establish the component and multi-domain foundation for the controller evaluated here.

Closely related non-PV shading research provides an additional benchmark for interpretation. Coupled thermal and lighting simulations showed that shading control must be coordinated with electric-lighting control because improvements in one end use can be offset by another [38]. Integrated office simulations found that automated dynamic shading can reduce total demand and improve daylight relative to fixed shading, while component-level heating, cooling, and lighting responses may move in conflicting directions [39]. Multi-climate louver analysis also showed that fixed shading can save cooling energy in solar-dominated locations yet increase annual demand where reduced winter gains are more consequential [40]. These results support the coupled accounting used here, but they do not address whether hourly records taken from independent fixed-angle histories remain valid after being assembled into one changing schedule. That state-consistency test is the specific methodological extension provided by the present study.

Direct comparison of reported percentage savings is nevertheless inappropriate because the studies differ in climate, façade area, building type, reference case, adjustment frequency, PV efficiency, and whether electricity is reported before or after inverter losses. In the present room, the 1767.94 kWh difference between RH12 and no shading is dominated by the addition of PV capacity and cannot be interpreted as the isolated benefit of rolling-horizon control. The cleaner control comparison is with the same device at fixed 45° and 90°, for which RH12 improved the annual net balance by 103.41 and 366.74 kWh. Reporting absolute component balances alongside these differences avoids the inflated percentages that arise when a fixed case already has a near-zero or negative net balance.

The methodological contribution is the explicit test of whether a database-derived schedule remains advantageous after it inherits one continuous thermal state. Earlier PV-shading studies established that dynamic angles can be beneficial [11,12,13,14,15,16,17,18,19,20,37]; the present results show that the method used to assemble and evaluate those angles can alter the estimated annual net balance by more than the advantage of RH12 over fixed 45°. At the same time, this controller should not be described as full MPC. It uses perfect future database values, a constant-action horizon, and offline annual replay, whereas MPC normally propagates a control-oriented state model and optimizes a future input trajectory [21,25,26]. Its intended position is between independent hourly selection and full MPC: a low-complexity scheduler with explicit movement and occupancy constraints, followed by state-consistent verification.

From an energy-flexibility perspective, the movable louver can reshape both demand and on-site generation, but the study does not yet quantify response to tariffs, carbon intensity, or grid requests. Reynders et al. showed that flexibility conclusions depend strongly on the definition, baseline, and metric adopted [23], while IEA EBC Annex 67 positioned building thermal mass, HVAC operation, electric vehicles, and plug loads as potential services to future energy systems [41]. The present façade is another controllable resource, but the term operational flexibility is used here only for its ability to alter façade-related demand and generation. Demonstrating grid-interactive flexibility would require time-varying signals, a defined reference trajectory, and metrics such as shifted energy, peak reduction, rebound, response duration, and recovery.

4.5. Limitations and Directions for Future Research

Several limitations define the scope of the conclusions. First, the model represents one south-facing perimeter room in Beijing, with adiabatic boundaries on five surfaces; whole-building interactions, alternative orientations, and other climates were not tested. Second, the controller uses perfect future values from annual fixed-angle simulations. Weather, occupancy, and load forecast errors were therefore absent. Third, candidates were assumed constant over each look-ahead window, and the fixed-angle lookup did not propagate a thermal state. The continuous EnergyPlus run verified each completed schedule but did not feed the replayed state back into the scheduling objective. Fourth, PV electricity was selected from a decoupled fixed-angle database and reported on a DC basis, excluding inverter, wiring, curtailment, storage, and export constraints. While site-level operational electricity is the primary focus of envelope control, comprehensive evaluation of solar-integrated systems requires extending accounting boundaries to encompass multi-criteria techno-economic and environmental metrics [42]. No irradiance-triggered fully open rule was imposed: during zero- or low-PV periods, the heuristic continued to minimize net room electricity, so 90° was selected only when it minimized the stated objective.

Fifth, the model treats sensible heat transfer but not moisture storage, vapor transport, ventilation-driven contaminant transfer, or indoor air quality. It therefore contributes to the thermal-control aspect of the target research area but does not claim coupled heat-and-mass-transfer results. Sixth, the 15° threshold is an openness proxy rather than evidence of visual comfort, view quality, or occupant acceptance; observed blind behavior and field interaction studies indicate that these responses are heterogeneous and affected by the control interface [28,29,34]. Seventh, movement count and rotation are proxies for actuator burden; drive electricity, torque, wind safety, mechanical wear, noise, and maintenance cost were not simulated. Finally, the repeated non-fatal coil diagnostic in the no-blind reference introduces uncertainty into that benchmark, although it did not affect completion, and the control conclusions rely primarily on the fixed-louver cases.

Future work should use a reduced-order thermal model or co-simulation interface that propagates temperature—and, where relevant, humidity—inside the optimizer. Weather and occupancy uncertainty should be represented explicitly, and a trajectory optimizer with switching penalties, deadbands, minimum dwell times, and actuator energy would allow longer horizons to be assessed on the same basis as full predictive control [25,26]. Illuminance and glare metrics should replace the minimum-angle proxy, supported by user-override logic and commissioning procedures similar to those developed for advanced blind controllers [35,36]. Finally, multi-climate and whole-building studies should include inverter and grid interactions so that energy flexibility, peak demand, carbon emissions, and economic value can be evaluated on a common boundary. Field validation should begin with an instrumented perimeter office and then expand to multiple rooms and a whole building to test forecasting, commissioning, user overrides, actuator reliability, and inter-zone coupling under real operation. Furthermore, evaluating the operational energy savings of dynamic PV facades must eventually be integrated with life-cycle assessment (LCA) methodologies to account for the embodied impacts of actuators, PV modules, and framing hardware over the system’s lifespan [43].

5. Conclusions

This study developed and evaluated a database-based constant-action rolling horizon look-ahead heuristic for a PV-integrated external louver. Nineteen fixed-angle simulations were used to generate candidate schedules, and continuous EnergyPlus replay was used to assess the consequences of thermal-state inheritance. Four conclusions can be drawn:

(1)

Independent hourly selection materially overestimated achievable performance. The static lookup predicted −310.90 kWh of annual net energy, while replay of the same schedule yielded −101.61 kWh. The 209.29 kWh error was 95.6% attributable to additional PTHP electricity, confirming that causal thermal history must be retained when a changing façade schedule is evaluated.

(2)

RH12 achieved the lowest dynamic net energy (−119.11 kWh) among horizons of 1–48 h and improved the annual net balance by 103.41 kWh relative to fixed 45° and 366.74 kWh relative to fixed 90°. Longer look-ahead was not automatically beneficial: the extra PV generation at 24 and 48 h was outweighed by higher dynamically replayed building electricity.

(3)

The energy optimum and the lower-movement design point were different. Relative to RH12, RH24 incurred a 5.89 kWh penalty—0.28% of RH12 gross demand—while reducing angle changes and total rotation by approximately 65%. RH12 is therefore the energy-oriented selection for this case, whereas RH24 provides a defensible engineering compromise when actuator activity matters.

(4)

An occupied minimum angle of 15° eliminated 1957 h of full closure at an annual net-energy cost of 35.79 kWh. The constrained strategy remained better than fixed 45° and 90° but increased actuator movement. Operational constraints can therefore be incorporated without losing the principal control benefit, although future implementations should combine explicit daylight and view criteria with movement penalties.

Overall, fixed-angle databases are useful for low-complexity control development, but their predicted schedules require continuous, state-consistent verification. The numerical optimum reported here is case-specific; the transferable result is the evaluation framework that separates database prediction, dynamic realization, and practical operating requirements.