Power system planning considering demand side response

The large-scale integration of wind power into the grid requires the redesign and expansion of the transmission network. The volatility of wind power and the limited application of energy storage have prompted the inclusion of demand-side response in transmission planning to improve the resilience of the grid. In this paper, a power system planning model that incorporates demand-side response is developed and the model is solved by using a greedy stochastic adaptive search process. Based on the results of the Garver 6-node test, the old and new models are compared to validate the effectiveness of the power system planning model considering demand side response.


Introduction
Wind power generation is recognized as a clean and sustainable energy source driven by concerns over energy scarcity, environmental pollution, and climate change associated with traditional fossil fuels [1][2].However, integrating wind power, particularly in regions with wind resources distant from load centers like China [3], poses challenges.Wind power's intermittent nature, limited energy storage [4], and the existing grid's inadequacies necessitate grid reconfiguration and strengthening.Additionally, the development of demand response mechanisms allows users to adjust electricity consumption in real time, enhancing grid flexibility and cost-effectiveness [5].Therefore, successful grid planning requires balancing safety and economic efficiency while accommodating power system diversification [6].
In [7], a novel transmission grid expansion planning method is introduced.It minimizes investment costs and wind curtailment while addressing load and wind power uncertainty.This approach uses fuzzy clustering for load and wind condition determination, followed by an optimal integer genetic algorithm based on DC power flow equations to identify new transmission line locations.In [8], a framework for integrating renewable energy sources (RESs) into Iran's National Power Grid (INPG) by minimizing total costs and enhancing system reliability is introduced.It employs mixed-integer programming and an augmented epsilon-constraint method for problem-solving.The model considers linear constraints and reveals trade-offs between cost and reliability.In [9] and [10], a probabilistic approach is adopted.In [9], the impact of intermittent wind-based RES on transmission network planning is assessed, optimizing reinforcements to avoid curtailment.In [10], simulations with Latin Hypercube Sampling and Two Point Estimation Method are used to consider power flow variability from renewables and international exchange while reducing computation time.This paper's core focus is the integration of demand response strategies with wind power to enhance the economic viability and security of the grid.It introduces a transmission grid planning model that relies on demand-side response, using the IEEE GARVER 6-node system as a practical example, which illustrates the model's superior economic efficiency.

Model theory
Traditional transmission grid planning aims to minimize the overall cost, which includes investment costs and operational costs while ensuring safety.The model characterizes the system from the perspective of direct current (DC) power flow and the constraints include that under normal operating conditions, the current on each branch does not exceed the limit and satisfies Kirchhoff's equations among others.
The conventional transmission planning model is expressed as follows.The first is the objective c is the investment cost per unit length of the system line, ij k is the number of line returns between nodes, ij l is the length of the line.00 mc is the maintenance cost, 0 m is the operating cost coefficients, 0 c is the operating cost of the system.
Next, there are Kirchhoff's equation constraints.Followed by the Kirchhoff equation constraints, () Finally, there are safety constraints to ensure that the limits are not exceeded.
In order to cope with the volatility of wind power, the objective function is modified by considering the demand side response mechanism in the planning.
In terms of constraints, it is necessary to add constraint (7), which ensures that the power cuts are  This paper employs the Greedy Randomized Adaptive Search Procedure (GRASP) to solve the model.The procedure is as follows: 1) The data including the power grid structure, load levels, and actual wind power output are input into the model, creating an electricity system planning model that considers demand response.
2) The total cost Z is set to a large value and defines the maximum number of iterations in the program as N.
3) A feasible plan is constructed that maximizes wind power utilization while satisfying all constraints.
4) A local search is conducted on the constructed feasible plan to obtain a local optimum solution.The total cost obtained after the search is denoted as V.
5) The iteration count k is increased by 1 and Z is compared to H.If Z is greater than H, Z is updated; Otherwise, Z is unchanged.If k is greater than N is checked.If it is, the program is terminated; Otherwise, step 3 is returned to continue.

Verification
The Garver 6 node system is used to examine the power system planning considering demand side response.The network structure of the system is shown in Figure .Nodes 1 and 3 are conventional power sources and 6 is wind power.It is required to connect 6 to the grid.Assuming a maximum of four circuits can be installed between nodes, the system's line parameters are detailed in Table 1 with a cost of $200,000 per kilometer of line.Node load demands are presented in Table 2.For annual load analysis, load levels are categorized into six classes based on their proportions, as outlined in Table 3.It is assumed that users of the same load class offer the same compensation rates for reducing their electricity consumption, as shown in Table 4. Node 1 has an output of 130 MW, node 3 generates 90 MW and the output at node 6 comes from an actual wind farm in Shanghai.Wind power is assumed to be fully integrated.Operating costs, being significantly smaller than construction costs, are similar between the two models and are therefore negligible in calculations.The results of the transmission grid planning are shown in Figure 2. As observed from Figure 2, the expansion demands have decreased between nodes 2-4, 3-6 and 4-6, leading to reduced investment costs.Conversely, there is an increased expansion demand between nodes 2-3, primarily due to the demand response mechanism mitigating capacity constraints.Overall, when considering demand response, the total cost of demand response and some line expansions remains lower than the cost of planning without considering demand response.Specifically, the investment cost for transmission lines with the demand response mechanism is $38.8 million and the cost of implementing the demand response mechanism is $1.684 million.In contrast, traditional transmission planning incurs an investment cost of $46.94 million, resulting in savings of $6.556 million.Therefore, introducing the demand response mechanism in transmission planning not only addresses the intermittency and volatility of wind power output but also enhances the overall economic and societal benefits of transmission planning.

Conclusions 1)
With the rapid growth of wind power, the power system faces significant uncertainty in electricity generation.Demand response enhances the elasticity of users' electricity consumption, enabling them to adapt to situations with lower wind power output, thereby increasing the flexibility and security of the grid.
2) After considering demand response in the model, both line investment costs and demand-side costs can be jointly considered, further enhancing the economic efficiency of the grid while ensuring safety.
3) Recognizing that the integration of wind power has become a challenge, the assumptions made in this paper (complete wind power integration) tend to be idealized.It is possible to further incorporate the wind power integration rate into the objective function to achieve a balance between integration rate and economic efficiency.

iNG
is the ith node generating unit, i N L is the number of transmission lines at the ith node.G P δ is the generation output of the εth generator, L P δ is the εth transmission line tidal current.N B is the number of nodes in the transmission system.Di P is the load power at the ith node.i π and j π are the phase angles at the ends of the branch.B δ is the transmission line conductance matrix.
Gδare the maximum/minimum output of the generator and max P Lδ is the line capacity.

NH
is the number of load classes divided into different periods of electricity consumption.p T is the duration of the pth load class.that users are willing to cut per unit of time in the pth load class at the ith node and i p r is the compensation fee for the reduction of electricity that is acceptable to power users in the pth load class at the ith node.

within a reasonable range and to extend Equation ( 2
obtain a diagram illustrating the relationships between the concepts of this model, as shown below.

Figure 3 .
Figure 3. Transmission planning result before/after considering the demand response mechanism.

Table 1 .
Parameters of transmission lines.

Table 2 .
The original load in Garver's 6-bus system.

Table 3 .
The load and duration at each load level.

Table 4 .
Bids for load curtailment at each load level.