Objectives: - Identify the key factors in the electricity market. - Describe the different types of markets in the power sector. - Compare and contrast the current practices in European and U.S. electricity markets. - Formulate the market-clearing procedure as a linear optimization problem, excluding the transmission network. # Outline - Various market actors - Various types of electricity market - European vs U.S.electricity markets - Market-clearing as a linear optimisation problem ## 1. Market actors - Also referred to as “market players” or “market participants” - ! Which market actors have we identified so far? ### Power demands: - Large consumers, e.g., industrial plants - Retailers: Buy and resell electricity to smaller consumers. A retailer is an intermediate market actor (or trader) who purchases electricity in bulk from electricity markets and sells it to a large number of small-scale consumers, e.g., households. Examples in Denmark:![[Pasted image 20260814131639.png]] ### Market operator A non-profit entity that receives all offers from producers and bids from consumers - clears the market by maximizing social welfare, and ultimately distributes the market-clearing outcomes, including prices and quantities. ![[Pasted image 20260814131811.png]] ### System operator - Transmission System Operator (TSO): Responsible for the safe operation of the underlying power grid at the high-voltage transmission level (typically a meshed grid), ensuring supply security, real-time power supply and demand balance, and system stability. - Example in Denmark: - ![[Pasted image 20260814132009.png]] - In Europe: **ENTSO-E (European Network of Transmission System Operators for Electricity)** coordinates all European TSOs to run the high-voltage grid, set common rules, and coordinate cross-border electricity markets.![[Pasted image 20260814132023.png]] - Distribution System Operator (DSO): Responsible for the safe operation of the underlying power grid at the medium- and low-voltage distribution level (typically a radial grid). - A **radial grid** is a **tree-like distribution network** where electricity flows in **one direction** from the substation to consumers, with **no loops**. - TSO transmission grids are **meshed** (many loops), whereas distribution grids are **radial** (one path). - ![[Pasted image 20260814132420.png]] - Market Regulator: Responsible for monitoring market performance in both the short and long run, as well as designing appropriate market regulations and policies. - ![[Pasted image 20260814132541.png]] - Other market actors: - Traders (both physical and purely financial), - Balancing Responsible Parties (BRPs), - Flexibility Aggregators, - and other relevant market actors will be introduced throughout the course as needed. ## 2. Various types of electricity market Three main markets with different products are: - Capacity markets - Energy markets - Ancillary service markets ### 2.1 Capacity markets - Designed to ensure that **sufficient** generation capacity (measured in MW) is available to maintain supply security and support reliable system operation. - Any producer submitting an offer to the electricity market—regardless of whether it is accepted or rejected—is eligible for compensation based on their availability (measured in EUR/MW). - Capacity payments serve as an incentive for power producers to invest in new generation assets over the long term. - Who pays the bill: The final consumer. However, this course will not cover capacity markets. ### 2.2 Energy market A central marketplace for exchanging energy (in MWh): - **1) Futures markets**: - Long-term financial contracts (with a time span of up to 6 years) - Purpose: Price hedging and risk management for buyers and sellers - Example: NASDAQ Commodities in Scandinavian countries - Note: This topic will not be covered in this course. - **2) Day-ahead market**: - Also known as the "spot market" - Timing: Cleared 12–36 hours before the actual delivery time - Example: Nord Pool Elspot, which is cleared at noon on day D-1 for energy exchange during each hour of day D (from midnight to midnight), resulting in different market prices and quantities for each hour. - **3) Intra-day market**: - This market provides an opportunity to "modify" day-ahead schedules in case of updated forecasts, asset failures, or trading purposes. It operates as a continuous and/or discrete auction-based trading platform between the day-ahead market and real-time. - Previously it was just a continuous market: A **continuous market** is a trading system where **orders are matched instantly and continuously** whenever a buy and sell order meet—with **no fixed auction time**, trading 24/7, no gate closure, or market clearing. - Example: It starts at 3 PM on D-1 and ends 1 hour before real-time. Three discrete auction-based sessions (ID-A) and a continuous platform (ID-C) are available. The current time resolution is 1 hour, but it will shift to 15 minutes soon. - **4) Balancing market**: - Also known as the "imbalance" market or the "real-time" market. - This market operates close to real-time system operations. - Purpose: To ensure power supply-demand balance and the safe operation of the system.![[Pasted image 20260814134855.png]] ### 2.3 Ancillary service markets These markets allow the system operator to procure services necessary for the secure and reliable operation of the system. E.g.: - Primary reserves - Secondary reserves - Tertiary reserves - Black-start capability - Reactive and voltage-control reserves - And more.![[Pasted image 20260814135029.png]] >⚡ FCR, aFRR, mFRR - **FCR – Frequency Containment Reserve** _Instant, automatic response_ to stabilize frequency after a disturbance (first seconds). - **aFRR – Automatic Frequency Restoration Reserve** _Automatic ramping_ to restore frequency and relieve FCR (seconds → minutes). - **mFRR – Manual Frequency Restoration Reserve** _Manually activated_ reserve (TSO triggers) to restore balance and replace aFRR (minutes → 15 min). ![[Pasted image 20260814135814.png]] # 3. European vs U.S.electricity markets ![[Pasted image 20260814140150.png]] Europe: 6 nodes (for example) -> split 2 zones In terms of market and system operation: - In Europe: Market operators and system operators are separate entities (e.g., Nord Pool as the market operator and Energinet as the TSO). - In the U.S.: An Independent System Operator (ISO) is responsible for both clearing the market and operating the system (e.g., CAISO and PJM). In terms of network modeling for market clearing: - In Europe: The transmission network is modeled in a simplified manner (using zonal representation) within the day-ahead and intraday market-clearing process. There is no detailed network modeling within each bidding zone. - In the U.S.: The transmission network is fully modeled using a nodal representation and a linearized power flow model in all market-clearing problems. In terms of energy and reserve markets: - In Europe: The reserve markets are cleared separately by the TSOs (e.g., Energinet) before the day-ahead energy market is cleared by the market operator. - In the U.S.: A joint energy and reserve market exists in the day-ahead time stage, cleared by the ISO, resulting in an energy and reserve dispatch co-optimization problem. European vs U.S. electricity markets Regarding complex offers versus complex market clearing: - **In Europe:** Market actors, such as power producers, are responsible for ensuring their offers/bids adhere to their technical constraints (e.g., ramp limits, minimum production limits, and minimum up/down time limits for conventional generators). Market actors internalize their technical limits within their own offers/bids: They offer/bid for their entire portfolio within a bidding zone (not per asset). This results in complex orders (bids and offers), while the market-clearing process remains relatively simple. ## 3. Market-clearing as a linear optimization problem An illustrative problem ![[Pasted image 20260814192638.png]] Inelastic demand: Consumers buy the same amount no matter the price. -> the price does NOT affect demand - demand is fixed The market‑clearing price is determined **only by generator offers**, because demand does **not change** when price changes. **Example:** Demand = 40 MW (inelastic) Even if price is €10, €20, or €100 → demand stays **40 MW**. Primal variables: $$ p_{W1},\; p_{G1},\; p_{G2} $$ $$ \min\; C = 0 \cdot p_{W1} + 20 \cdot p_{G1} + 30 \cdot p_{G2} $$ $$ 0 \le p_{W1} \le 20 $$ $$ 0 \le p_{G1} \le 50 $$ $$ 0 \le p_{G2} \le 100 $$ Power balance (inelastic demand): $$ p_{W1} + p_{G1} + p_{G2} = D $$ Dual variables: $$ \lambda = \text{market-clearing price} $$ Numerical example ($D = 40$ MW): $$ p_{W1} = 20,\quad p_{G1} = 20,\quad p_{G2} = 0 $$ Market-clearing price: $$ \lambda = 20\ \text{€/MWh} $$ A **dual variable** is the **shadow price** of a constraint — it tells you **how much the objective would improve if you relax that constraint by 1 unit**. In electricity markets: - The **dual variable of the power-balance constraint** = **market-clearing price** - It represents the **value of one extra MW of demand** - If demand increases by 1 MW, the objective cost increases by $\lambda$ (the dual) Example constraint: $$ p_{W1} + p_{G1} + p_{G2} = D $$ Dual variable: $$ \lambda = 20\ \text{€/MWh} $$ Meaning: If demand increases by **1 MW**, total system cost increases by **€20** → that’s the **market price**. $\mu$: The dual variable for an inequality constraint. It measures the **shadow price** of relaxing that constraint by **1 unit**. **$\mu$ is the dual variable for an inequality constraint.** It tells you whether a limit is **active (binding)**. - If the limit **binds** → $\mu > 0$ - If the limit **does NOT bind** → $\mu = 0$ Example constraint: $$ p_{G1} \le 50 $$ - If $p_{G1} = 50$ → limit is active → $\mu > 0$ - If $p_{G1} < 50$ → limit is not active → $\mu = 0$ In your numerical example, G1 produces **20**, so the limit is not binding: $$ \mu = 0 $$ The **Lagrange equation** (Lagrangian) is what you get when you combine: - the **objective function**, and - all the **constraints**, - multiplied by their **dual variables** ($\lambda, \mu$). **Goal:** To combine the **objective** and **all constraints** into **one single function** so we can apply the **KKT conditions** and find the **optimal solution + optimal prices (dual variables)**. KKT: Karush-Kuhn-Tucker conditions ![[Pasted image 20260814194952.png]] Objective: $$ \min C = 0p_{W1} + 20p_{G1} + 30p_{G2} $$ Constraints: $$ p_{W1} + p_{G1} + p_{G2} = D \quad (\lambda) $$ $$ 0 \le p_i \le \overline{p}_i \quad (\mu_i^{low},\; \mu_i^{up}) $$ ### **Lagrangian Function** $$ L = 0p_{W1} + 20p_{G1} + 30p_{G2} + \lambda(D - p_{W1} - p_{G1} - p_{G2}) + \mu_{W1}^{up}(p_{W1} - 20) + \mu_{G1}^{up}(p_{G1} - 50) + \mu_{G2}^{up}(p_{G2} - 100) $$ *(Note: Usually, bounds are written as $p_i - p_i^{up} \le 0$, so we add $\mu_i^{up}(p_i - p_i^{up})$).* That’s the **Lagrange equation**: **objective + duals × constraints**. ![[Pasted image 20260814194531.png]] ![[Pasted image 20260814194909.png|327]] > $\bar{\mu}$ **$\bar{\mu}$ is the dual variable for the** _**upper bound**_ **of an inequality constraint.** - Every variable has **two limits**: - **lower limit** → $\mu^{low}$ (or $\underline{\mu}$) - **upper limit** → $\mu^{up}$ (or $\overline{\mu}$) So: - If the **upper limit is binding** → $\overline{\mu} > 0$ - If the **upper limit is NOT binding** → $\overline{\mu} = 0$ ![[Pasted image 20260814195033.png]]![[Pasted image 20260814195118.png]] KKT Conditions of the market-clearing optimization problem: ![[Pasted image 20260814195316.png]] KTT Conditions of the market-clearing optimisation ![[Pasted image 20260814195629.png]] How to verify the market-clearing price by the KKT conditions ![[Pasted image 20260814200043.png]] Example with different demand First, if the demand is 0 ![[Pasted image 20260814200132.png]] What is the price in here, if the demand quantity is around 80 MW ![[Pasted image 20260814200223.png]] What is the price in here, if the demand is 70 The right and left hand side if we decrease and increase the demand a bit -> the price will vary -> therefore, it will be in the range of [20,30] ![[Pasted image 20260814200239.png]] ## An Illustrative example: Price-elastic demand Now the demand will be affected by the price ![[Pasted image 20260814200512.png]] ## Market clearing with price-elastic demand ![[Pasted image 20260815112928.png]] ## Market clearing as a linear optimisation problem ![[Pasted image 20260815112959.png]] SW: Social welfare ## Electricity price in DK ![[Pasted image 20260815113452.png]] ## Kahoot - Q1: A retailer: Buys power from the market in bulk and sells it to small consumers. - Q2: Which of following choices include only market operators? - Nord Pool, EPEX, EEX (a leading international commodity exchange based in Leipizig, Germany) - EPEX: European Power Exchange (a major pan-European marketplace where short-term electricity contracts are brought and sold). - Q3: A transmission system operator (TSO): operates the high-voltage transmisison grid. - Q4: The Nordic TSOs are Energinet, Svenska Krafnat, Stattnet, Fingrid - Q5: Nord Pool clears Day a head, intraday - It doesn't reserve, and balancing markets - In Denmark: - **Energinet** clears: - FCR (primary reserves) - aFRR (secondary reserves) - mFRR (manual reserves) - Balancing market (real‑time) In Finland: - **Fingrid** clears the same types of reserve and balancing markets. - Q6: Which entities coordinate national TSOs and regulators, respectively, at the European Level? - ENTSO-e and ACER - Q7: A residental customer at a certain addres can choose her [...] among various options - Retailer: A residential customer **can choose her electricity retailer** because retailers are **competitive companies**. They offer different: - prices (fixed/variable) - contract types - green energy options Retailers buy electricity from markets (day‑ahead, intraday) and sell it to households. So customers are free to switch between them - **2. TSO/DSO = no choice** A customer **cannot choose** the **TSO** or **DSO** because: - They are **natural monopolies** tied to the physical grid. - The **TSO** runs the national transmission grid (e.g., Energinet, Fingrid). - The **DSO** runs the local distribution grid (e.g., Radius, Cerius). - They are **regulated**, not competitive. - They **do not sell electricity** — they only transport it and ensure reliability. - Q8: Which choice correctly represents the chronological order of market clearing? - Future, day-ahead, intraday, balancing - Q9: How many zone exists in the following countries, respectively: Denmark, Norway, Sweden, Finland, Germany and France? - 2, 5, 4, 1,1,1 - Q10: Which of the following is correct about European electricity markets? - The network is simplistically represented in a zone setup. - Q11: Which of the following is NOT correct about US electricity market? - ISO clears the reserve market after the energy market - Correct: - **1. ISO = both market operator AND system operator** U.S. ISOs/RTOs (e.g., CAISO, PJM) **clear the market AND operate the grid**. This is different from Europe, where Nord Pool ≠ Energinet. - **2. Network is fully modeled (nodal)** - U.S. markets use **nodal pricing** with a **linearized power‑flow model** in all clearing problems. - **3. Joint energy + reserve co‑optimization** In the U.S., **day‑ahead energy and reserve markets are cleared together** by the ISO. - **4. Simple bids, complex clearing**: - Producers submit **technical constraints** (ramp limits, min up/down times, etc.). This makes the clearing problem a **unit commitment** with binary variables. - NOT Correct: In the **U.S. ISO/RTO markets**, the **day‑ahead energy market and reserve market are cleared** _**together**_ in **one single co‑optimization**. From here - **Nodal model** - **Joint clearing of energy + reserves** - **Unit commitment with binary variables** - Q12: Which of the following is the correct formulation of the Lagrangian function? - ![[Pasted image 20260815120157.png]] - Q13: Which does this complementary slackness condition entail? - ![[Pasted image 20260815120259.png]] Q14: What is the objective function for the market-clearing optimisation problem? ![[Pasted image 20260815120355.png]] Correct answer: D - Elastic Demand -M maximise the objective function Q15: What is the market-clearing price (in euros/MWh) ![[Pasted image 20260815120445.png]] Any price between 30 and 40 Q16: Which of the following statements about the KKT conditions are correct (there maybe multiple correct answers)![[Pasted image 20260815120559.png]] - **1. The dual variable of an equality constraint can take any real value** ✅ Correct - Equality constraints h(x)=0 have **no sign restriction** on their dual variable λ. - It can be **positive, negative, or zero**, depending on whether relaxing the constraint increases or decreases the objective. - In contrast, inequality constraints g(x)≤0 have **non‑negative** duals μ≥0. - **2. The KKT conditions can be used to verify the market‑clearing price* ✅ Correct - In electricity markets, the **dual variable of the power‑balance constraint** equals the **market‑clearing price**. - Solving the KKT system gives both **optimal dispatch (primal)** and **prices (dual)**. - Hence, checking the KKT conditions confirms that the computed price satisfies optimality. - **3. The KKT conditions can be solved as a system of equations** ✅ Correct - The KKT conditions combine - **Stationarity** (gradient equations), - **Primal feasibility** (constraints), - **Dual feasibility** (sign restrictions), - **Complementary slackness** (products = 0). - Together, they form a **system of equations and inequalities** that can be solved numerically. **4. Complementary condition includes the product of a primal and a dual variable** ✅ Correct - For each inequality constraint gi(x)≤0, the KKT condition requires: $$μi⋅gi(x)=0$$ - This means either the constraint is **active** (gi(x)=0,μi>0) or **inactive** (gi(x)<0,μi=0). - That product term is the **complementary slackness condition**. - Q17: What is the common range of electricity prices typial residental consumers in Denmark (in Euro/KWh, including Tax)? - 0.2 - 0.5