The document proposes a two-stage power management algorithm for a network of energy harvesting sensors (EHS). The first stage involves optimizing the duty cycle and gain threshold for each node based on the total power allocation. The second stage optimizes the total power allocation based on the harvested power to maximize throughput while maintaining energy neutrality across all nodes. Simulation results show the normalized throughput increases with the average harvested power.

1. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Duty Cycling and Power Management with
a Network of Energy Harvesting Sensors
Srinivas Reddy and Chandra R. Murthy
{srinivaskrn,cmurthy1}@gmail.com
Dept. of ECE, Indian Institute Science, Bangalore, India
Apr. 5th, 2012
Power Management Algorithms for a Network of EHS

2. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Outline
1 System Model
2 First Stage: Duty Cycling
3 Second Stage: Power Allocation
4 Conclusions
Power Management Algorithms for a Network of EHS

3. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
System Model
Single hop EHS network with K nodes transmitting data to
powered destination
Single MCS transmission by each node
Transmission based on channel measurement
Leads to truncated channel inversion (TCI)
Duty-cycling across nodes to prevent collisions
Goal
Find the optimum power allocation and duty-cycle to maximize
the sum throughput subject to energy neutrality at each
individual node.
Power Management Algorithms for a Network of EHS

4. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Block Diagram of Each EHS Node
Energy Harvester Transceiver
Inefficient
Super Capacitor
Battery
Figure: Power flow diagram: Harvest-use-store model
The remaining circuitry (sensor) is assumed to consume a
fixed power and hence not shown
Power Management Algorithms for a Network of EHS

5. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Timing Diagram
Constant Power (CP) slots
Harvested Power
Channel Power Gain
(Independent)
Constant Channel (CC) slots
0 Tc 2Tc 3Tc Tp 2Tp
Figure: Constant channel and constant power slots
Power Management Algorithms for a Network of EHS

6. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Role of Supercapacitor
Supplied/Taken by
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transmit power
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Figure: Supercapacitor supplies power variations around the mean
allotted power within a CP slot
Battery storage efficiency: η
Supercapacitor assumed perfectly efficient
Battery sees a constant load
Power Management Algorithms for a Network of EHS

7. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Proposed Solution
First Stage: choose duty cycle Di and gain threshold γm,i
at each node as functions of Pa
Requires knowledge of sum power allotted at the nodes
Assumes identical channel statistics
Goal: max. channel statistics-averaged sum throughput
Second Stage: choose power allocation vector Pa as a
function of the harvested power vector Ph
Requires knowledge of harvested power at each node
Goal: max. sum throughput over harvested power statistics
Power Management Algorithms for a Network of EHS

8. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
First Stage Problem Setup
To choose: duty cycle Di and gain threshold γm,i at each
node as functions of Pa
Average data rate of the i-th node
Ri (Pa ) = Ron Di 1 − Fγ (γm,i )
Optimization problem
K
max Ri (Pa )
Di ≥0,γm,i ≥0, i Di =1
i=1
Subject to the power constraint
∞
P0
Di γ fγ (γ)dγ = Pa,i , i = 1, . . . , K
γm,i
Assumes identical channel statistics fγ (γ) from each node to destination
Power Management Algorithms for a Network of EHS

9. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
First Stage Solution
K
Using Lagrange mult. λ with i=1 Di = 1, can show
Pa,i
Diopt = K
i=1 Pa,i
Channel gain threshold γm,i = γm at all nodes!
The optimum γm satisfies
∞ K
fγ (γ) i=1 Pa,i
γ dγ = P0
γm
And the optimized sum throughput
L
RΣ (Pa ) Riopt (Pa ) = Ron [1 − Fγ (γm )]
i=1
Power Management Algorithms for a Network of EHS

10. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Second Stage Problem Setup
Now lets optimize Pa
Optimization problem
max E {RΣ (Pa )}
Pa (Ph )≥0
The expectation is over the joint distribution of Ph
Subject to energy neutrality at node i, 1 ≤ i ≤ K :
∞
Pa,i −πh
Ai Pa,i + (1 − Ai ) πh + η fPh,i (πh )dπh = E Ph,i
0
where Ai = 1 if Pa,i < πh and 0 otherwise.
In the above, the variable of integration πh is the power harvested at the i-th node
Power Management Algorithms for a Network of EHS

11. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Simplification of Second Stage
Recall: RΣ (Pa ) depends only on K Pa,i (through γm )
i=1
Now, when Ph,i > Pa,i , some nodes can deposit
energy into battery
When Ph,i < Pa,i , some nodes must draw energy
from battery
Energy efficient design: sum power energy neutrality ∗∗
∞
Pa,Σ −πh
A Pa,Σ + (1 − A) πh + η fPh,Σ (πh )dπh = E Ph,Σ
0
where A = 1 if Pa,Σ < πh and 0 otherwise.
K
Note: πh = i=1 Ph,i is the sum power harvested and fP (·) is its PDF
h,Σ
Tries to minimize wasteful cycling of energy through battery
Power Management Algorithms for a Network of EHS

12. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Second Stage Solution
New optimization problem
max RΣ (Pa ) Ron [1 − Fγ (γm )]
Pa,Σ (Ph,Σ )
subject to ∗∗
Same as the “outer stage optimization” in our past work!
[RM TWC ’11, Accepted]
Working with a fictitious EHS which harvests the sum
power, and under a sum-power energy neutrality constraint
Optimal solution:

 P1 if Ph,Σ ≥ P1 ;
opt
Pa,Σ = P2 if Ph,Σ ≤ P2 ;
Ph,Σ if P2 < Ph,Σ < P1 .

Power Management Algorithms for a Network of EHS

13. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Second Stage Solution (Cont’d)
For optimality, P1 and P2 should satisfy
dRΣ dRΣ
=η
dPa,Σ Pa,Σ =P1 dPa,Σ Pa,Σ =P2
For energy neutrality, P1 and P2 should satisfy
P2 ∞
[P2 − πh ]fPh,Σ (πh )dπh = η [πh − P1 ]fPh,Σ (πh )dπh
0 P1
Power Management Algorithms for a Network of EHS

14. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Power Allocation for Each Node (1/2)
opt
Given Pa,Σ , to find Pa,i that satisfy EN at each node
Recall sum power allocation rule:

 P1 if Ph,Σ ≥ P1 ;
opt
Pa,Σ = P2 if Ph,Σ ≤ P2 ;
Ph,Σ if P2 < Ph,Σ < P1 .

Many ways of allotting Pa,i s.t. Pa,i = Pa,Σ
Individual energy neutrality conditions
∞
Pa,i −πh
Ai Pa,i + (1 − Ai ) πh + η fPh,i (πh )dπh = E Ph,i
0
where Ai = 1 if Pa,i < πh and 0 otherwise.
Power Management Algorithms for a Network of EHS

15. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Power Allocation for Each Node (2/2)
Proposed allotment scheme:
+

 P − Ph,Σ −P1 − P if Ph,Σ ≥ P1 ;

 h,i K e,i
Pa,i = P2 −Ph,Σ
if Ph,Σ ≤ P2 ;
 Ph,i + ηK

Ph,i if P2 < Ph,Σ < P1 .

(j)
Let Pe,i denote the Pe,i in CP slot j
Update equation for Pe,i is as follows:
 +
 −Ph,i + Ph,Σ −P1 + P (j) if Ph,Σ ≥ P1 ;

 K e,i
(j+1) (j)
Pe,i = if Ph,Σ ≤ P2 ;
 Pe,i
 (j)
Pe,i if P2 < Ph,Σ < P1 .

Note: in the above, Ph,i , Ph,Σ are the harvested powers in the j-th CP slot.
Power Management Algorithms for a Network of EHS

16. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Simulation Result
Figure: Normalized throughput Vs. E {Ph }, for η = 0.8, K = 10.
Harvested power uniformly distributed between [0, 2E {Ph }]
Power Management Algorithms for a Network of EHS

17. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
Conclusions
Solved duty cycling and power allocation problems in an
EHS network with K nodes
Two-stage approach:
Inner stage: duty cycle = fraction of allotted power
Outer stage: total allotted power = clipped version of total
harvested power (suboptimal solution)
Solution of simple form ⇒ easy implementation
Future work: accounting for channel estimation errors,
battery energy leakage, data arrival process,
retransmissions, etc
Power Management Algorithms for a Network of EHS

18. System Model
First Stage: Duty Cycling
Second Stage: Power Allocation
Conclusions
The End
Thank you very much!
Questions?
Chandra Murthy
cmurthy@ece.iisc.ernet.in
(This work was supported in part by a research grant from the
Aerospace Network Research Consortium.)
Power Management Algorithms for a Network of EHS