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318 Dan Simhas, Claudiu Popovici r r ⋅ i l i (13) x i x = 0 i ⋅l (14) where: l i – the length of the cable segment between lamps Using (13) and (14), (11) becomes: ΔU pk ⎛ ⎜ P − = ⎝ k−1 ∑ i= 1 P Li − k ⋅ ΔP psegment U spl ⎞ ⎟ ⋅ ⎠ l k ⋅ ( r + x ⋅ tgϕ) 0 0 + ΔU p( k−1) (15) and replacing (2) and (15) in (10), results in (16), representing the actual power consumed by each lamp: P Lk ⋅ ( K 1 + K ⋅ = PN 2 ⎛ ⎜ P − ⋅ ⎝ k −1 ∑ i= 1 P Li − k ⋅ ΔP psegment ⎞ ⎟ ⋅lk ⋅ ⎠ U ( r + x ⋅ tgϕ) 2 spl 0 0 + ΔU p( k −1) As active power consumed by each lamp is different, the metered power is the summation of power consumption of each lamp: ⋅U spl ) (16) P = = 0 ∑ n j P Lj (17) In the case of Pitesti Street Lighting Project, phase active energy is recorded by meter, with 15 minutes integration period (configurable from 1 – 60 minutes). Thus, using (1) it is considered that one or more lamps are burned when the difference between mean active power – resulted from measured active energy (12) – and the total computed active power per phase is higher the rated active power of a lamp (11). n fN −∑ PLj PN (18) j P
A smart grid application – street lighting management system 319 From the active energy provided by the meter, per phase, mean active power is calculated: P fN 60[min] [ kW ] = Ea[ kWh] ⋅ (19) p[min] where p=1,3,5,10,15,30,45,60 – is the configured integration period. Similarly, from metering data, the average power factor per integration period is computed, using active and reactive power: P cosϕ = (20) 2 2 P + Q Using a general variation law for high pressure sodium vapors lamp [17], it can be written: ⎛ ⎜ P − ⋅ ⎝ k−1 ∑ i= 1 P Li P Lk = .1⋅ P ⋅ (2.5 + 1. 5 ⋅ − k ⋅ ΔP 1 N psegment ⎞ ⎟⋅ ⎠ l k U ⋅ ( r + x ⋅tgϕ) 2 spl 0 0 + ΔU p( k−1) ⋅U spl ) (21) Using (21), actual consumption of the lamps is computed, from metering data and rated constants. To prove the validity of the theoretical model, the voltage and active power variation, as resulted from metering values, is analyzed, in a monitored area of the street lighting system – no lamps were burned during the monitored period. The monitored area had 24 lamps with a rated power of 250 W for each lamp. Same interval of similar days was used for the analysis. In the Figs. 3.4 (a) and (b), measured voltage and active power values are displayed. In Fig. 3.5 active power values calculated based on (21) are shown.
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