# Operational Planning and Bidding for District Heating Systems with Uncertain Renewable Energy Production

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## Abstract

**:**

## 1. Introduction

#### 1.1. Description of Electricity Markets

#### 1.2. Related Work

- The above-mentioned gap is addressed by extending the VPP bidding method of [8], which only considers power production, to a DH setting. Furthermore, we add a second model to optimize the trading on the balancing market after the day-ahead market is cleared. The underlying stochastic programs for modeling the operation of the DH system are formulated in a general manner to be applicable to arbitrary sets of production units in DH systems.
- In contrast to previous work, the method explicitly accounts for the uncertainty coming from RES production in both heat and power and enables us to perform an analysis of the impact of the different uncertainty sources.
- The method is analyzed using a real case study based on the Hvide Sande DH system in Denmark that allows us to draw conclusions on: (a) the behavior of the system under uncertain RES production; (b) the impact of including balancing market trading in the planning method; (c) the benefits of including renewable power production in the portfolio; and (d) the annual system costs compared to traditional bidding methods based on forecasts.
- An additional contribution is a new approach to generate scenarios for balancing market price scenarios needed for the stochastic programming, addressing the balancing market-related operation.

## 2. Operational Planning Model

#### 2.1. Optimization for the Day-Ahead Market

#### 2.2. Optimization for the Balancing Market

## 3. Modeling Uncertainty

#### 3.1. Wind Power Production Forecast

#### 3.2. Solar Thermal Forecast

#### 3.3. Day-Ahead Electricity Price Forecast

#### 3.4. Scenario Generation for RES Production and Day-Ahead Market Prices

#### 3.5. Scenario Generation for Balancing Prices

Algorithm 1 Generate balancing price scenarios. |

1: for each $\omega \in \Omega $ do |

2: $t\leftarrow 1$ |

3: while $t\le \left|\mathcal{T}\right|$ do |

4: ${\tau}_{\omega}^{\mathrm{T}(+/-)}=-{\tau}^{\mathrm{T}(+/-)}\xb7ln\left({u}_{1}\right)$ where ${u}_{1}\sim \mathcal{U}(0,1)$ is random |

5: ${\tau}_{\omega}^{\mathrm{D}(+/-)}=-{\tau}^{\mathrm{D}(+/-)}\xb7ln\left({u}_{2}\right)$ where ${u}_{2}\sim \mathcal{U}(0,1)$ is random |

6: ${t}^{\mathrm{Start}}\leftarrow \mathrm{min}\{\left|\mathcal{T}\right|,round(t+{\tau}_{\omega}^{\mathrm{T}(+/-)})\}$ |

7: ${t}^{\mathrm{End}}\leftarrow \mathrm{min}\{\left|\mathcal{T}\right|,round(t+{\tau}_{\omega}^{\mathrm{T}(+/-)}+{\tau}_{\omega}^{\mathrm{D}(+/-)})\}$ |

8: for ${t}^{\prime}=t$ to ${t}^{\mathrm{Start}}$ do |

9: $\Delta {\lambda}_{{t}^{\prime},\omega}^{(\mathrm{UP}/\mathrm{DOWN})}$ = 0 |

10: end for |

11: for ${t}^{\prime}={t}^{\mathrm{Start}}+1$ to ${t}^{\mathrm{End}}$ do |

12: $\Delta {\lambda}_{{t}^{\prime},\omega}^{(\mathrm{UP}/\mathrm{DOWN})}$ = ${f}^{(+/-)}\left({\tau}^{\mathrm{D}(+/-)}\right)+{\epsilon}_{{t}^{\prime}}^{(+/-)}$ where ${\epsilon}_{{t}^{\prime}}^{(+/-)}\sim \mathcal{N}(\mu ,{\sigma}^{2})$ is random |

13: end for |

14: $t\leftarrow {t}^{\mathrm{End}}+1$ |

15: end while |

16: end for |

17: Return $\Delta {\lambda}_{t,\omega}^{(+/-)}$ |

## 4. Operational Scheduling and Bidding Method

## 5. Case Study

## 6. Analysis of the Experimental Results

- After day-ahead market closure for day d (day $d-1$): Evaluate the day-ahead market bids with the now known electricity prices and save production amounts of won bids.
- Each hour on day d:
- (a)
- (b)
- Evaluate the balancing-market bids with the now known balancing electricity prices; fix the committed production amounts; and resolve the model to get actual costs and thermal storage levels.

- Move to the next day

#### 6.1. Influence of Uncertainty and Number of Bidding Curve Steps on the Day-Ahead Market Results

#### 6.2. Impact of Special Tariff for the Electric Boiler

#### 6.3. Analysis of Yearly Production

#### 6.4. Value of Including Balancing Market Trading

#### 6.5. Behavior of the System in the Case of Upward and Downward Regulation

#### 6.5.1. Upward Regulation

#### 6.5.2. Downward Regulation

## 7. Summary and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Wind power prediction process. (

**a**) Wind power curve using real data for one year of power production and wind speed in Nord Pool DK1; (

**b**) wind power predictions for a one-day receding horizon and the normalized wind speed.

**Figure 2.**Distributions of elapsed time between and duration of upward regulation, as well as average regulating prices for year 2017 in the Nord Pool bidding area DK1. (

**a**) Time elapsed between upward regulation periods; (

**b**) duration of upward regulation and price deviation.

**Figure 3.**Scenarios for balancing prices. (

**a**) Ten scenarios generated by Algorithm 1; (

**b**) Ten scenarios generated by the method proposed in [31].

**Figure 5.**Comparison of different uncertainty setups and number of steps in the bidding curves in the day-ahead market optimization. The values shown are total annual system cost.

**Figure 6.**Power from the wind turbines used for the electric boiler as a special tariff ${C}^{\mathrm{T}}$ or traded on the day-ahead market as well as total annual system cost. The values are given for varying the special tariff operation cost of the electric boiler.

**Figure 7.**Annual system behavior on a monthly time-scale. (

**a**) Legend; (

**b**) power sold on the markets and system cost (top), as well as power production by the different units (bottom); (

**c**) heat production by the different units (top) and average electricity prices (bottom).

**Figure 9.**Upward regulation provided on 9 March 2017. (

**a**) Bidding curves and won bids (marked with ×); (

**b**) system operation: upward regulation amount including day-ahead and balancing prices (top), power production (middle), and heat production (bottom).

**Figure 10.**Upward regulation provided on 27 March 2017. (

**a**) Bidding curves and won bids (marked with ×); (

**b**) system operation: upward regulation amount including day-ahead and balancing prices (top), power production (middle), and heat production (bottom).

**Figure 11.**Downward regulation provided on 6 February 2017. (

**a**) Bidding curves and won bids (marked with ×); (

**b**) system operation: day-ahead committed amount, downward regulation amount, as well as day-ahead and balancing prices (top), power production (middle), and heat production (bottom).

**Figure 12.**Downward regulation provided on 10 September 2017. (

**a**) Bidding curves and won bids (marked with ×); (

**b**) system operation: day-ahead committed amount, downward regulation amount, as well as day-ahead and balancing prices (top), power production (middle), and heat production (bottom).

Sets | |

$\mathcal{T}=\{1,\dots ,|\mathcal{T}\left|\right\}$ | Set of time periods t |

$\mathcal{U}$ | Set of heat production units u |

${\mathcal{U}}^{\mathrm{CHP}}\subset \mathcal{U}$ | Subset of CHP production units |

${\mathcal{U}}^{\mathrm{H}}\subset \mathcal{U}$ | Subset of heat-only production units |

${\mathcal{U}}^{\mathrm{EL}}\subset \mathcal{U}$ | Subset of power to heat production units |

${\mathcal{U}}^{\mathrm{RES}}\subset \mathcal{U}$ | Subset of stochastic heat production units |

$\mathcal{G}$ | Set of intermittent renewable power-only producers g |

$\mathcal{S}$ | Set of heat storage tanks s |

$\Omega $ | Set of scenarios $\omega $ |

Parameters | |

${C}_{u}^{\mathrm{H}}$ | Cost for producing heat with unit $u\in \mathcal{U}$ (DKK/MWh-heat) |

${C}_{g,u}^{\mathrm{T}}$ | Tariff cost for producing power with unit $g\in \mathcal{G}$ and using it to produce heat in unit $u\in {\mathcal{U}}^{\mathrm{EL}}$ (DKK/MWh-el) |

${\overline{Q}}_{u}/{\underline{Q}}_{u}$ | Maximum/minimum heat production for unit $u\in \mathcal{U}$ (MWh-heat) |

${A}_{u}^{\mathrm{DH}}$ | Binary parameter: 1, if unit $u\in \mathcal{U}$ is connected to the DH system, 0 otherwise |

${A}_{u,s}^{\mathrm{S}}$ | Binary parameter: 1, if unit $u\in \mathcal{U}$ is connected to the thermal storage s, 0 otherwise |

${\phi}_{u}$ | Heat-to-power ratio for unit $u\in {\mathcal{U}}^{\mathrm{CHP}}$ ($\mathrm{MWh}-\mathrm{heat}/\mathrm{MWh}-\mathrm{el}$) |

${S}_{s}^{0}$ | Initial level in storage s (MWh-heat) |

$\overline{{S}_{s}}/\underline{{S}_{s}}$ | Maximum/minimum heat level in storage s (MWh-heat) |

${\lambda}_{t}$ | Electricity price for time period $t\in \mathcal{T}$ (DKK/MWh-el) |

${\lambda}_{t}^{+}$/${\lambda}_{t}^{-}$ | Penalty for positive/negative imbalance in time period $t\in \mathcal{T}$ (DKK/MWh-el) |

${\lambda}_{t}^{\mathrm{UP}}$/${\lambda}_{t}^{\mathrm{DOWN}}$ | Upward/downward regulating price for time period $t\in \mathcal{T}$ (DKK/MWh-el) |

${Q}_{t}^{\mathrm{D}}$ | Heat demand for time period $t\in \mathcal{T}$ (MWh-heat) |

${P}_{g,t,\omega}^{\mathrm{RES}}$ | Stochastic power production of power-only unit $g\in {\mathcal{G}}^{\mathrm{RES}}$ |

${Q}_{u,t,\omega}^{\mathrm{RES}}$ | Stochastic heat production from heat production unit $u\in {\mathcal{U}}^{\mathrm{RES}}$ |

${\pi}_{\omega}$ | Probability of scenario $\omega \in \Omega $ |

$\beta $ | Parameter that determines the deviation of the penalty for the positive and negative imbalance |

Variables | |

${p}_{t,\omega}^{\mathrm{BID}}\in {\mathbb{R}}_{0}$ | Power bid to the day-ahead market unit in period $t\in \mathcal{T}$ (MWh-el) |

${q}_{u,t,\omega}\in {\mathbb{R}}_{0}^{+}$ | Heat production of heat unit $u\in \mathcal{U}$ in period $t\in \mathcal{T}$ (MWh-heat) |

${q}_{u,t,\omega}^{\mathrm{DH}}\in {\mathbb{R}}_{0}^{+}$ | Heat production of unit $u\in \mathcal{U}$ inserted into the grid in period $t\in \mathcal{T}$ (MWh-heat) |

${q}_{u,s,t,\omega}^{\mathrm{S}}\in {\mathbb{R}}_{0}^{+}$ | Heat production of unit $u\in \mathcal{U}$ inserted into storage s in period $t\in \mathcal{T}$ (MWh-heat) |

${p}_{u,t,\omega}^{\mathrm{CHP}}\in {\mathbb{R}}_{0}^{+}$ | Power production of unit $u\in {\mathcal{U}}^{\mathrm{CHP}}$ in period $t\in \mathcal{T}$ (MWh-el) |

${p}_{u,t,\omega}^{\mathrm{GRID}}\in {\mathbb{R}}_{0}$ | Power obtained from the grid to produce heat with unit $u\in {\mathcal{U}}^{\mathrm{EL}}$ in period $t\in \mathcal{T}$ (MWh-el) |

${p}_{g,u,t,\omega}^{\mathrm{HEAT}}\in {\mathbb{R}}_{0}^{+}$ | Power production of unit $g\in \mathcal{G}$ that serves the heat production of unit $u\in {\mathcal{U}}^{\mathrm{EL}}$ in period $t\in \mathcal{T}$ (MWh-el) |

${p}_{g,t,\omega}^{\mathrm{GEN}}\in {\mathbb{R}}_{0}^{+}$ | Power generation from unit $g\in \mathcal{G}$ in period $t\in \mathcal{T}$ (MWh-el) |

${p}_{t,\omega}^{+/-}\in {\mathbb{R}}_{0}^{+}$ | Positive/negative power imbalance purchased/sold in period $t\in \mathcal{T}$ and scenario $\omega $ (MWh-el) |

${p}_{t,\omega}^{\mathrm{UP}/\mathrm{DOWN}}\in {\mathbb{R}}_{0}^{+}$ | Upward/downward regulating power purchased/sold in period $t\in \mathcal{T}$ and scenario $\omega $ (MWh-el) |

${\sigma}_{s,t,\omega}\in {\mathbb{R}}_{0}^{+}$ | Level in storage s at time period $t\in \mathcal{T}$ (MWh-heat) |

${\sigma}_{s,t,\omega}^{\mathrm{OUT}}\in {\mathbb{R}}_{0}^{+}$ | Heat flowing from the storage s to the DH in period $t\in \mathcal{T}$ (MWh-heat) |

${\tau}^{T+}$ | Mean time to activate upward regulation (hours) |

${\tau}^{\mathrm{T}-}$ | Mean time to activate downward regulation (hours) |

${\tau}^{\mathrm{D}+}$ | Mean duration for upward regulation (hours) |

${\tau}^{\mathrm{D}-}$ | Mean duration for downward regulation (hours) |

${f}^{+}\left({\tau}^{\mathrm{D}+}\right)$ | Function for the upward regulation value given an upward time duration length |

${f}^{-}\left({\tau}^{\mathrm{D}-}\right)$ | Function for the downward regulation value given a downward time duration length |

$\Delta {\lambda}_{t,\omega}^{\mathrm{UP}}$ | Matrix of values for the upward regulation (%) |

$\Delta {\lambda}_{t,\omega}^{\mathrm{DOWN}}$ | Matrix of values for the downward regulation (%) |

$|\Omega |$ | Number of considered scenarios |

$\left|\mathcal{T}\right|$ | Forecast horizon |

${u}_{1},{u}_{2}$ | Random variables uniformly distributed between 0 and 1 |

${\epsilon}_{t}^{+},{\epsilon}_{t}^{-}$ | Normally-distributed random noise added to the function ${f}^{+}\left({\tau}^{\mathrm{D}+}\right)$/${f}^{-}\left({\tau}^{\mathrm{D}-}\right)$ |

Unit | Set | ${\mathit{C}}_{\mathit{u}}^{\mathit{H}}$ | ${\mathit{C}}_{\mathit{u}}^{\mathit{T}}$ | ${\overline{\mathit{Q}}}_{\mathit{u}}$ | ${\overline{\mathit{P}}}_{\mathit{u}}$ | ${\mathit{\phi}}_{\mathit{u}}$ | ${\mathit{A}}_{\mathit{u}}^{\mathrm{DH}}$ | ${\mathit{A}}_{\mathit{u},\mathit{s}}^{\mathit{S}}$ | |
---|---|---|---|---|---|---|---|---|---|

ST1 | ST2 | ||||||||

CHP1 | ${\mathcal{U}}^{\mathrm{CHP}}$ | 689.01 | - | 4.63 | 3.62 | 1.28 | 0 | 1 | 0 |

CHP2 | ${\mathcal{U}}^{\mathrm{CHP}}$ | 689.01 | - | 4.63 | 3.62 | 1.28 | 0 | 1 | 0 |

GB1 | ${\mathcal{U}}^{\mathrm{H}}$ | 401.30 | - | 10.37 | 0.00 | - | 0 | 1 | 0 |

GB2 | ${\mathcal{U}}^{\mathrm{H}}$ | 416.29 | - | 3.77 | 0.00 | - | 0 | 1 | 0 |

EB | ${\mathcal{U}}^{EL}$ | 359.98 | 49.52 | 6.00 | 0.00 | 1.00 | 0 | 1 | 0 |

SC | ${\mathcal{U}}^{\mathrm{RES}}$ | 0.00 | - | 100.00 | 0.00 | - | 0 | 0 | 1 |

WF | $\mathcal{G}$ | 0.00 | - | 0.00 | 0.00 | - | - | - | - |

$\overline{S}$ | $\underline{S}$ | ${\sigma}_{0}$ | |||||||

ST1 | $\mathcal{S}$ | 115.88 | 0.00 | 57.94 | |||||

ST2 | $\mathcal{S}$ | 48.67 | 0.00 | 24.34 |

Setting | Total System Cost (DKK) | $\Delta $ |
---|---|---|

Perfect information incl.balancing market | 2,499,205 | - |

Perfect information excl.balancing market | 3,414,310 | +37% |

Stochastic incl. balancing market | 3,655,798 | +7% |

Stochastic excl. balancing market | 3,956,530 | +8% |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Blanco, I.; Guericke, D.; Andersen, A.N.; Madsen, H.
Operational Planning and Bidding for District Heating Systems with Uncertain Renewable Energy Production. *Energies* **2018**, *11*, 3310.
https://doi.org/10.3390/en11123310

**AMA Style**

Blanco I, Guericke D, Andersen AN, Madsen H.
Operational Planning and Bidding for District Heating Systems with Uncertain Renewable Energy Production. *Energies*. 2018; 11(12):3310.
https://doi.org/10.3390/en11123310

**Chicago/Turabian Style**

Blanco, Ignacio, Daniela Guericke, Anders N. Andersen, and Henrik Madsen.
2018. "Operational Planning and Bidding for District Heating Systems with Uncertain Renewable Energy Production" *Energies* 11, no. 12: 3310.
https://doi.org/10.3390/en11123310