# Investment Incentives in Competitive Electricity Markets
## 6 Mathematical Formulation
### Six-Bus Power Transmission Network
#### 7.1.4 Smart Hybrid Market  
In the hybrid market, construction of new units are increased by 3300 MW in the peak technology compared to the EO design. The average market price is decreased by 0.31% and 5.46% compared to FC and CP policies, respectively, because of different kinds of investment. However, the market price is increased by 1.19% compared to EO policy. In addition, the social welfare is increased by 8.09%, 31.22% and 0.21%, compared to EO, CP and FC markets, respectively. On the other hand, the total profit of investors is increased by 93.07% and 58.86% compared to FC and CP policies, respectively. The total profits is comprised by five terms that are the expected profit obtained by selling energy of existing units in the spot market, the expected profits of the strategic investor obtained by selling a pre-determined part of production in a firm contractual market, the expected profits obtained by the capacity payments for new units, the expected profits obtained by the capacity payments of the existing units and the cost of operation of new units. The total profit in the hybrid market is more than others so that the total profit of strategic producer in the hybrid market is 9, 1.59 and 1.93 times higher than those of EO, CP and FC markets, respectively. As a result, it can be concluded that the hybrid policy makes a strategic producer better off in the investment.  
Figure 8 shows the total energy produced by units for different market design. Energy produced by the new strategic unit in CP, FC and H policies is decreased by 28.64%, 7.16% and 3.36% compared to EO designs, respectively. In addition, the energy produced by the new strategic units in FC and H markets are increased compared to the CP market. There is more interest in investing in peak technologies to benefit from investment incentives in all market designs, while the possibility of investment in base technology is very low. Energy produced by the existing strategic units is increased by 18.03% in CP policy compared to EO design. However, those of FC and H policies are decreased by 3.94% and 3.24% compared to EO policy, respectively. Energy produced by the non-strategic strategic units in CP, FC and H policies are increased by 22.26%, 7.08% and 5.43% compared to EO design, respectively.  
The net surplus of non-strategic producers in the CP market are 16%, 14% and 15% more than those of EO, FC and H markets, respectively. As a result, it can be concluded that CP policy makes non-strategic better off in the long term. The net surplus of Consumers is of the effect of various designs of the market on consumer welfare. The net surplus of Consumers is 55.3 ME, 44.69 ME, 51.6 ME, and 52.4 ME in the EO, CP, FC, and H designs, respectively. In terms of levelized value (present worth of consumer surplus divided by present worth of consumption), these equalled 5.09 \(\in\)/MWh, 4.12 \(\in\)/MWh, 4.73 \(\in\)/MWh, and 4.82 \(\in\)/MWh, respectively. As a result, EO policy makes consumers better off in the long term.  
Figure 8: Total energy produced by units in different market designs.  
Table 1 shows the reliability indices of various markets. Network reliability depends on the number of invested units, their capacity and the energy consumption so that it is observed that investment incentives improve the reliability indices.