# An Integration Mechanism between Demand and Supply Side Management of Electricity Markets

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## Abstract

**:**

## 1. Introduction

- Different from the existing market mechanism where the ISO only declares a single demand in the wholesale market, in our mechanism, the ISO declares a demand interval to the wholesale market for each hour. The demand interval is easy to estimate and more robust than a single demand and enables the ISO to handle unpredictable demand under the DR programs in our mechanism.
- The proposed mechanism also enables the ISO to realize the goals of dynamic pricing and demand response by utilizing smart meters such as effectively reducing CO
_{2}emission, minimizing bills for customers and maximizing the profit for both retailers and generators. The related smart pricing methods for the retailer are also proposed in the context of this new market integration mechanism. - An efficient algorithm is proposed to find the match equilibrium between the demand and supply side for the proposed new integration mechanism. Moreover, a formal proof process is also provided in this paper, which shows that the proposed algorithm and mechanism are effective and valid for the real market.

## 2. Problem Description

- Step 1. ISO declares the demand interval of each hour of the next day to all the generators:

- Step 2. Each generator decides its hourly bid curve, based on the declared demand interval from ISO:

- Step 3. After receiving the bid curve from each generator, the ISO calculates the aggregated bids curve (step function) for each hour.

- Step 4. Based on hourly MCP functions, the retailers decide their optimal prices for their customers. Then the total customers’ demand function, which is a function of the MCP, can be obtained by the retailer and sent back respectively to the ISO.

- Step 5. After receiving the customers’ demand function from each retailer, the ISO aggregates these functions to a demand function which is dependent on the MCP. Based on the obtained MCP functions and demand function, the next step of the proposed mechanism consists of the ISO finding the balance points between the demand and supply. The balance points in each hour of the next day are the proposed result of this mechanism.

## 3. Generation Side

Algorithm 1 Calculate the MCP function of hour h | |

Input: Each generator’s bid curve of hour h: generator i’s bid curve can be represented as a set of bid segments (${p}_{i,{m}_{i},h\text{}},(\underset{\_}{{q}_{i,{m}_{i},h\text{}}},\text{}\overline{{q}_{i,{m}_{i},h\text{}}}],\text{}{m}_{i}\text{}=1,2,\dots ,{m}_{i}$) sorted by the bid price in the increasing order; | |

Output:MCP function of hour h; | |

1: | For each generator $i$, get the unit price ${p}_{i,{m}_{i},h\text{}}$ and the corresponding quantity bids ${q}_{i,{m}_{i},h\text{}}$ (${q}_{i,{m}_{i},h\text{}}=\overline{{q}_{i,{m}_{i},h\text{}}}-\underset{\_}{{q}_{i,{m}_{i},h\text{}}}$) of each segment in the generator i’s bidding curve of hour h. |

2: | Let ${p}_{1}\le {p}_{2}\le \dots \le {p}_{{S}_{h}}$ be the ordered unit prices ${p}_{i,{m}_{i},h\text{}}$ of all segments in generators’ bidding curves and ${q}_{1},{q}_{2},\dots ,{q}_{{S}_{h}}$ be the corresponding quantity bids $\text{}{q}_{i,{m}_{i},h\text{}}$, where ${s}_{h}$ is the number of total segments in all generators’ bidding curves. |

3: | Assigns the value of ${p}_{1}$ and ${q}_{1}\text{}$ to $\text{}MC{P}_{h,1}\text{}$ and $\text{}{S}_{h,1}$ respectively, assigns $0$ and ${q}_{1}$ to the lower and upper bound of ${s}_{h,1}$ respectively. |

4: | Fork = 2 to ${S}_{h}$ do |

5: | Assigns the value of ${p}_{k}$ and ${q}_{k}\text{}$ to $\text{}MC{P}_{h,k}\text{}$ and $\text{}{S}_{h,k}$ respectively; assign $\text{}\underset{\_}{{S}_{h,k-1}}+{q}_{k}$ to the upper bound of $\text{}{s}_{h,k}$ and assign the value of upper bound of $\underset{\_}{{S}_{h,k-1}}$ to the lower bound of ${s}_{h,k}$. |

6: | End for |

7: | A new set of segments ($MC{P}_{h,k},(\underset{\_}{{S}_{h,k}},\text{}\overline{{S}_{h,k}}],\text{}k=1,2,\dots ,{s}_{h}$) is obtained, which can be plotted as a step function in the coordinate system. This new step function is the MCP function in hour h (Equation (1)). |

## 4. Retailer’s Pricing Optimization

## 5. Balancing the Demand Side and Supply Side

#### 5.1. Match Equilibrium

**Definition**

**1.**

^{11}. It is unrealistic, or impossible, for each retailer to solve the problem in Equation (5) so many times.

#### 5.2. Proposed Algorithm

Algorithm 2 Analytical optimization method | |

Input:MCP function of each hour (Table 1); A random MCP vector generating from Table 1. | |

Output: A MCP vector (which reaches the match equilibriums); | |

1: | Retailers calculate problem (5) by using the input MCP vector; |

2: | The ISO calculates $E{r}_{h}$ for each hour and gets a vector: Er = $(E{r}_{1},E{r}_{2},\dots ,E{r}_{H})$; |

3: | While$\forall h\in (1,\dots ,H),$ exists $E{r}_{h}\ne 0$; |

4: | Find hour h in the set of $(1,\dots ,H)$, where $h=argmax\left\{\left|E{r}_{h}\right|\right\}$; |

5: | If $E{r}_{h}\text{}0$ & $MC{P}_{h}\ne MC{P}_{h}^{1}$; |

6: | Decreases $MC{P}_{h}$ to the value of previous segment in Table 1; |

7: | If $E{r}_{h}\text{}0\text{}\text{}MC{P}_{h}\ne MC{P}_{h}^{{S}_{h}}$; |

8: | Increases $MC{P}_{h}$ to the value of next segment in Table 1; |

9: | Retailers calculate problem (5) under the modified new MCP vector and get new $E{r}_{h}$ for each hour; |

10: | End while; |

11: | Output the final MCP vector and each retailer’s estimated demand. |

**Definition**

**2.**

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Theorem**

**3.**

**Proof.**

#### 5.3. Cases of Renewable Energy Integration

## 6. Numerical Results

#### Analysis of the Results

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Parameter | Description |

h | h-th hour |

$i$ | $i$-th generator |

j | j-th retailer |

${m}_{i}$ | The number of segments in this generator i’s bid curve |

${p}_{i,{m}_{i}\text{}}$ | Bid price of ${m}_{i}$-th segment in generator i’s bid curve |

$\underset{\_}{{q}_{i,{m}_{i}\text{}}}$ | Lower bound of ${m}_{i}$-th segment in generator i’s bid curve |

$\overline{{q}_{i,{m}_{i}\text{}}}$ | Upper bound of ${m}_{i}$-th segment in generator i’s bid curve |

$MC{P}_{h}$ | Market clear price in hour h |

${s}_{h}$ | The number of total segments in all generators’ bidding curves (MCP function) of hour h, where ${s}_{h}={\displaystyle \sum}_{i}{m}_{i}\text{}$ |

${S}_{h,k}$ | The k-th segment of the proposed step function (aggregated bidding curve) in hour h |

${D}_{h}$ | the demand from the retail market in hour h |

$MC{P}_{h}^{k}$ | The corresponding unit price of ${S}_{h,k}$ |

${\beta}_{h,c}$ | The cross-price elasticity |

${\beta}_{h,h}$ | The self-elasticity |

${p}_{h}^{max}$ | The maximum price that the retailer can offer to its customers |

${p}_{h}^{min}$ | The minimum price that the retailer can offer to its customers |

${C}_{N}^{j}$ | The total bill constraint of retailer j’s customers |

${p}_{h}^{j}$ | The retailer j’s optimal retail price in hour h |

${p}_{h}^{j}$ | The total demand of retailer j’s customers in hour h |

$E{r}_{h}$ | Fitness value of a MCP vector in hour h (Analytical optimization Method) |

Er | Fitness value of a MCP vector (Analytical optimization Method) |

$MC{P}_{v}$ | The MCP vector which makes the electricity market reaches the match equilibrium |

$MC{P}_{h}^{{s}_{h}}$ | Market clearing price for ${s}_{h}$-th segment in hour h under the MCP table (Table 1) |

$-h$ | All hours in (1, … H) except for hour h |

${D}_{h}^{r,j}$ | Retailer j’s demand in hour h. |

$P{R}_{j}$ | Retailer j’s profit in period (1, … H). |

P | Peak hour |

o | Off-peak hour |

$\underset{\_}{{S}_{h,{s}_{h}}}$ | Lower bound of $MC{P}_{h}$’s corresponding supply in Table 1 |

$\overline{{S}_{h,{s}_{h}}}$ | Upper bound of $MC{P}_{h}$’s corresponding supply in Table 1 |

${P}_{peak}$ | The value of peak point in x axis for quadratic function. |

${S}_{max}$ | The biggest number in the vector (${s}_{1},{s}_{2}\dots {s}_{h}\dots {s}_{H}$) |

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**Figure 3.**Example of generators’ bid curve and the aggregated bidding curve. (

**a**) Generator 1’s bid curve; (

**b**) Generator 2’s bid curve; (

**c**) The aggregated bidding curve.

**Figure 6.**The solution space of three scenarios for problem in Equation (13). (

**a**) Scenario 3; (

**b**) Scenario 1(1); (

**c**) Scenario 1(2); (

**d**) Scenario 2(1); (

**e**) Scenario 2(2).

$\mathit{H}\mathit{o}\mathit{u}\mathit{r}\text{}1$ | … | $\mathit{H}\mathit{o}\mathit{u}\mathit{r}\text{}\mathit{h}$ | … | ||

MCP | Supply Segments | MCP | Supply Segments | ||

$MC{P}_{1}^{1}$ | $(\underset{\_}{{S}_{1,1}},\overline{{S}_{1,1}}]$ | … | $MC{P}_{h}^{1}$ | $(\underset{\_}{{S}_{h,1}},\overline{{S}_{h,1}}]$ | … |

$MC{P}_{1}^{2}$ | $(\underset{\_}{{S}_{1,2}},\overline{{S}_{1,2}}]$ | … | $MC{P}_{h}^{2}$ | $(\underset{\_}{{S}_{h,2}},\overline{{S}_{h,2}}]$ | … |

… | … | … | … | … | … |

$MC{P}_{1}^{{s}_{1}}$ | $(\underset{\_}{{S}_{1,{s}_{1}}},\overline{{S}_{1,{s}_{1}}}]$ | … | … | … | … |

$MC{P}_{h}^{{s}_{h}}$ | $(\underset{\_}{{S}_{h,{s}_{h}}},\overline{{S}_{h,{s}_{h}}}]$ | … | |||

… |

$\mathit{M}\mathit{C}{\mathit{P}}_{\mathit{h}}$ | Segment Scale | $\underset{\xaf}{{\mathit{S}}_{\mathit{h}}}(\mathit{M}\mathit{C}{\mathit{P}}_{\mathit{h}})$ | $\overline{{\mathit{S}}_{\mathit{h}}}(\mathit{M}\mathit{C}{\mathit{P}}_{\mathit{h}})$ | Segment Number |
---|---|---|---|---|

25.5510 | 7100 | 20,200 | 27,300 | 1 |

26.6490 | 12,500 | 27,300 | 39,800 | 2 |

27.5010 | 8300 | 39,800 | 48,100 | 3 |

28.3853 | 8400 | 48,100 | 56,500 | 4 |

30.0894 | 7500 | 56,500 | 64,000 | 5 |

32.2739 | 9000 | 64,000 | 73,000 | 6 |

35.2795 | 7100 | 73,000 | 87,000 | 7 |

37.8002 | 12,500 | 87,000 | 91,500 | 8 |

42.3322 | 8300 | 91,500 | 98,900 | 9 |

Hour | ${\mathit{z}}_{\mathit{h}}$ | Hour | ${\mathit{z}}_{\mathit{h}}$ | Hour | ${\mathit{z}}_{\mathit{h}}$ |
---|---|---|---|---|---|

1 | 920.28 | 9 | 4958.7 | 17 | 0 |

2 | 0 | 10 | 463.02 | 18 | 0 |

3 | 0 | 11 | 0 | 19 | 0 |

4 | 0 | 12 | 0 | 20 | 0 |

5 | 0 | 13 | 0 | 21 | 123.434 |

6 | 0 | 14 | 0 | 22 | 176.395 |

7 | 0 | 15 | 0 | 23 | 0 |

8 | 0 | 16 | 0 | 24 | 0 |

Hour | $\mathit{E}{\mathit{r}}_{\mathit{h}}$ | Hour | $\mathit{E}{\mathit{r}}_{\mathit{h}}$ | Hour | $\mathit{E}{\mathit{r}}_{\mathit{h}}$ |
---|---|---|---|---|---|

1 | 0 | 9 | 0 | 17 | 0 |

2 | 0 | 10 | 0 | 18 | 0 |

3 | 0 | 11 | 0 | 19 | 0 |

4 | 0 | 12 | 0 | 20 | 0 |

5 | 0 | 13 | 0 | 21 | 0 |

6 | 0 | 14 | 0 | 22 | 0 |

7 | 0 | 15 | 0 | 23 | 0 |

8 | 0 | 16 | 0 | 24 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Z.; Zeng, X.; Meng, F. An Integration Mechanism between Demand and Supply Side Management of Electricity Markets. *Energies* **2018**, *11*, 3314.
https://doi.org/10.3390/en11123314

**AMA Style**

Liu Z, Zeng X, Meng F. An Integration Mechanism between Demand and Supply Side Management of Electricity Markets. *Energies*. 2018; 11(12):3314.
https://doi.org/10.3390/en11123314

**Chicago/Turabian Style**

Liu, Zixu, Xiaojun Zeng, and Fanlin Meng. 2018. "An Integration Mechanism between Demand and Supply Side Management of Electricity Markets" *Energies* 11, no. 12: 3314.
https://doi.org/10.3390/en11123314