A Model for Multi-Energy Demand Response with Its Application in Optimal TOU Price
Abstract
:1. Introduction
2. Modeling for Multi-Energy User’s Response in TOU Price
2.1. Energy Flows of Multi-Energy DR in TOU Price
2.2. Modeling of the Response Characteristics of Multi-Energy DR in TOU Price
2.3. Analysis on Saturation Point
2.3.1. CHP Capacity
2.3.2. Electricity Load
3. Optimal TOU Pricing
Optimization Problem of TOU Pricing
4. Case Study
4.1. Analysis of Multi-Energy User’s Response Characteristics
4.2. Optimal TOU
5. Conclusions
- The electricity response amount in peak (or valley) hours varies linearly by the increment of electric prices in peak (valley) hours and flat hours; whereas gas response in peak (valley) hours is proportional to the increment of the square of peak (valley) price and flat price.
- The peak–peak elasticity of electricity response is determined by k1, which depends on the electric efficiency of IES; whereas peak–flat elasticity is determined by k0, which depends on both electric and heat efficiency.
- A smaller HER of CHP brings about a larger potential of electric response.
- The TOU price scheme is better to smooth electric load curve and, meanwhile, saves more in the overall system’s cost and energy purchase cost than the flat price scheme.
- The decision of TOU electric price should not only compare the marginal cost of electricity supply with wholesale price c0 of gas, but also ensure an appropriate electricity-to-gas price ratio.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Acronyms | |
IES | Integrated energy system |
DR | Demand response |
TOU | Time-of-use |
CCHP | Combined cooling, heat and power |
CHP | Combined heat and power |
EB | Electric boiler |
TF | Transformer |
HS | Heat storage |
HER | Heat-to-electricity ratio |
Symbols | |
X, Y | Electricity, gas, respectively |
x, y | The purchased amount of electricity and gas |
Le, Lh | Electricity, heat load |
xe, xh | The purchase of electricity to satisfy electricity, heat load separately |
ηex, ηhx | Electric and heat efficiency of electric equipment (TF, EB here) |
ηey, ηhy | Electric and heat efficiency of CHP |
φ(y) | Output function of CHP |
m, n | Coefficients of CHP’s output function |
t | Time interval of one day |
zt | Conversion variable of yt |
at, bt | Electricity, gas price at time slot t |
xe,max, xh,max | Corresponding to maximum of input of TF, EB, separately |
ymax | Maximum of input of CHP |
p, f, v | Peak, flat, valley |
Tp, Tf, Tv | Peak, flat, valley hours separately |
q | Vector of decision variables |
μ1,t, μ2,t | Dual variables |
λ* | Lagrangian multiplier corresponding to optimal solution |
f | Objective function |
h | Equality constraints |
g | Inequality constraints; |
, | First partial derivatives of f, g |
, | Electricity and gas response at t in sth TOU scheme |
ap, av, af | electricity prices in peak, valley, flat hours |
k1, k2, k0 | Coefficients of response model |
a | Electric price vector |
I, J | Number of bus and electric supplier |
, | Vector of electric and gas demands, electricity productions |
Gas demand at bus i at time slot t | |
Py,t | Gas wholesale at time slot t |
Electricity production cost at t for supplier j | |
c1,j | Unit production cost for electric supplier j |
c0 | Wholesale price of gas |
Lx,t, Zt | A set of equality, inequality constraints of the electrical system operation |
amin, amax | Lower and upper limits of electric price |
, | Lower and upper limit of electric generation |
, | Lower and upper limit of gas wholesale |
,, | Column vector of dual variables |
, | Dual variables |
Peak-flat elasticity |
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Overall System’s Cost ($) | Energy Purchase Cost ($) | |
---|---|---|
Flat price | 220,541 | 125,599 |
TOU | 171,272 | 107,785 |
Wholesale Price c0 of Gas ($/1000 m3) | Bus | TOU Electric Price | ||
---|---|---|---|---|
Peak | Flat | Valley | ||
20 | C | 64 | 40 | 30 |
D | 64 | 40 | 30 | |
33 | C | 64 | 40 | 30 |
D | 44.08 | 40 | 30 | |
40 | C | 52.69 | 33.83 | 22.20 |
D | 40 | 30 | 14 | |
50 | C | 40 | 34.45 | 23.85 |
D | 40 | 30 | 14 | |
80 | C | 40 | 30 | 14 |
D | 40 | 30 | 14 |
Retail Price b0 of Gas ($/1000 m3) | Bus | TOU Electric Price | ||
---|---|---|---|---|
Peak | Flat | Valley | ||
50 | C | 40 | 30 | 14 |
D | 40 | 30 | 14 | |
60 | C | 40 | 30 | 30 |
D | 40 | 30 | 16.27 | |
75 | C | 41.26 | 33.21 | 14 |
D | 40 | 30 | 14 | |
90 | C | 52.69 | 22.2 | 33.83 |
D | 40 | 30 | 14 | |
100 | C | 60 | 40 | 30 |
D | 40 | 35.28 | 15.18 | |
115 | C | 64 | 40 | 30 |
D | 48 | 40 | 30 | |
135 | C | 64 | 40 | 30 |
D | 64 | 40 | 30 |
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Zhao, N.; Wang, B.; Wang, M. A Model for Multi-Energy Demand Response with Its Application in Optimal TOU Price. Energies 2019, 12, 994. https://doi.org/10.3390/en12060994
Zhao N, Wang B, Wang M. A Model for Multi-Energy Demand Response with Its Application in Optimal TOU Price. Energies. 2019; 12(6):994. https://doi.org/10.3390/en12060994
Chicago/Turabian StyleZhao, Nan, Beibei Wang, and Mingshen Wang. 2019. "A Model for Multi-Energy Demand Response with Its Application in Optimal TOU Price" Energies 12, no. 6: 994. https://doi.org/10.3390/en12060994